Monday, July 15, 2019

Possibility and Necessity: Kierkegaard Meets Nietzsche

Filed under: General — Tags: — m759 @ 7:29 AM

The previous post’s search for Turing + Dyson yielded a
quotation from Kierkegaard on possibility and necessity.
Further details —

See also . . .

Nietzsche, 'law in becoming' and 'play in necessity'

Nietzsche on Heraclitus— 'play in necessity' and 'law in becoming'— illustrated.

Tuesday, April 17, 2018

A Necessary Possibility*

Filed under: General,Geometry — m759 @ 10:00 AM

"Without the possibility that an origin can be lost, forgotten, or
alienated into what springs forth from it, an origin could not be
an origin. The possibility of inscription is thus a necessary possibility,
one that must always be possible."

— Rodolphe Gasché, The Tain of the Mirror ,
     Harvard University Press, 1986

IMAGE- Harvard University Press, 1986 - A page on Derrida's 'inscription'

An inscription from 2010 —

An inscription from 1984 —

American Mathematical Monthly, June-July 1984, p. 382


Triangles are square

"Every triangle consists of  n congruent copies of itself"
is true if and only if  n is a square. (The proof is trivial.) 
— Steven H. Cullinane

* See also other Log24 posts mentioning this phrase.

Thursday, January 31, 2013

Necessary Possibility

Filed under: General — Tags: — m759 @ 9:05 PM

The inscription  link in the previous post suggests
a review of the rather paradoxical concept of 
"necessary possibility."

See a deconstructionist view , a scholarly view,
and a graphic view.

Wednesday, January 30, 2013

Abstract Possibility

Filed under: General — m759 @ 1:01 PM

Today's NY Times  "Stone Links" to philosophy include
a link to a review of a collection of Hilary Putnam's papers.

Related material, from Putnam's "What is Mathematical
" (Historia Mathematica  2 (1975): 529-543)—

"In this paper I argue that mathematics should be interpreted realistically – that is, that mathematics makes assertions that are objectively true or false, independently of the human mind, and that something answers to such mathematical notions as ‘set’ and ‘function’. This is not to say that reality is somehow bifurcated – that there is one reality of material things, and then, over and above it, a second reality of ‘mathematical things’. A set of objects, for example, depends for its existence on those objects: if they are destroyed, then there is no longer such a set. (Of course, we may say that the set exists ‘tenselessly’, but we may also say the objects exist ‘tenselessly’: this is just to say that in pure mathematics we can sometimes ignore the important difference between ‘exists now’ and ‘did exist, exists now, or will exist’.) Not only are the ‘objects’ of pure mathematics conditional upon material objects; they are, in a sense, merely abstract possibilities. Studying how mathematical objects behave might better be described as studying what structures are abstractly possible and what structures are not abstractly possible."

See also Wittgenstein's Diamond and Plato's Diamond.

Thursday, November 12, 2020


Filed under: General — m759 @ 11:16 AM

Related material for comedians

Thursday, August 21, 2014


Filed under: Uncategorized — m759 @ 1:00 AM

( A sequel to  Lux )

“By groping toward the light we are made to realize
how deep the darkness is around us.”

— Arthur Koestler, The Call Girls: A Tragi-Comedy ,
Random House, 1973, page 118

Robin Williams and the Stages of Math

i)   shock & denial
ii)  anger
iii) bargaining
iv) depression
v)  acceptance

A related description of the process —

“You know how sometimes someone tells you a theorem,
and it’s obviously false, and you reach for one of the many
easy counterexamples only to realize that it’s not a
counterexample after all, then you reach for another one
and another one and find that they fail too, and you begin
to concede the possibility that the theorem might not
actually be false after all, and you feel your world start to
shift on its axis, and you think to yourself: ‘Why did no one
tell me this before?’ “

— Tom Leinster yesterday at The n-Category Café

See as well . . .

Damonizing Your Opponent

Tuesday, July 21, 2020


Filed under: General — m759 @ 5:13 AM
From “Nabokov’s Crosswords of Composition,” by
Rebecca Freeh-Maciorowski, a paper presented at NEMLA, dated 15 October 2014 —

“In a way, Nabokov’s entire oeuvre might be built upon one all-encompassing ‘crossword,’ a possibility raised by W.W. Rowe when he writes ‘Words and phrases seem faintly but undeniably to catch many others in the prism of their associations and connotations, almost as if Nabokov’s entire oeuvre were planned from the very start’ (viii). Turning to Pale Fire , the work of Simon Rowberry provides evidence of a whole network of ‘themed entries’ within this novel, what Rowberry refers to as ‘the novel’s promiscuous intertextuality.’ Alternately, the points and coordinates that Nabokov refers to constitute the composition’s ‘checked cells.’ The checked cells are the basic mechanism of the crossword puzzle; essentially, they are the guiding force of the entire puzzle, controlling both the construction and solution. These are the cells within the crossword puzzle in which two words intersect. In Nabokov’s compositional crossword, the ‘checked cells’ are those points which combine disparate entities, places of intersection, where objects and themes converge.”

Rowe, W.W., Nabokov’s Deceptive World , New York University Press, 1971.

Rowberry, Simon, “Pale Fire  as a Hypertextual Network.” 22nd ACM Hypertext Conf., Eindhoven, Netherlands. 6-9 June 2011. Web.

The Rowberry date appears to be, specifically, 8  June 2011:

A Kinbote note — See also this  journal on 8 June 2011.

Update of 3:03 PM ET the same day —

In keeping with Kinbote’s character as an unreliable narrator . . .
Rowberry’s Eindhoven slides  indicate he spoke on 9  June 2011.

See as well the Log24 post  “Historical Fiction” from June 2011.

Wednesday, April 15, 2020

“Causal Invariance” According to Wolfram

Filed under: General — Tags: — m759 @ 12:40 AM

Stephen Wolfram yesterday —

“Causal invariance may at first seem like a rather obscure property.
But in the context of our models, we will see in what follows that
it may in fact be the key to a remarkable range of fundamental features
of physics, including relativistic invariance, general covariance, and
local gauge invariance, as well as the possibility of objective reality in
quantum mechanics.”

From . . .

Sunday, April 12, 2020

Blackboard Jungle Continues.

Filed under: General — m759 @ 10:00 PM

From a post this morning  by Peter J. Cameron
in memory of John Horton Conway —

” This happened at a conference somewhere in North America. I was chairing the session at which he was to speak. When I got up to introduce him, his title had not yet been announced, and the stage had a blackboard on an easel. I said something like ‘The next speaker is John Conway, and no doubt he is going to tell us what he will talk about.’ John came onto the stage, went over to the easel, picked up the blackboard, and turned it over. On the other side were revealed five titles of talks. He said, ‘I am going to give one of these talks. I will count down to zero; you are to shout as loudly as you can the number of the talk you want to hear, and the chairman will judge which number is most popular.’ “
From Log24 on August 21, 2014
Thursday, August 21, 2014


Filed under: Uncategorized — m759 @ 1:00 AM

( A sequel to  Lux )

“By groping toward the light we are made to realize
how deep the darkness is around us.”

— Arthur Koestler, The Call Girls: A Tragi-Comedy ,
Random House, 1973, page 118

Robin Williams and the Stages of Math

i)   shock & denial
ii)  anger
iii) bargaining
iv) depression
v)  acceptance

A related description of the process —

“You know how sometimes someone tells you a theorem,
and it’s obviously false, and you reach for one of the many
easy counterexamples only to realize that it’s not a
counterexample after all, then you reach for another one
and another one and find that they fail too, and you begin
to concede the possibility that the theorem might not
actually be false after all, and you feel your world start to
shift on its axis, and you think to yourself: ‘Why did no one
tell me this before?’ “

— Tom Leinster yesterday at The n-Category Café

Sunday, March 24, 2019

Espacement: Geometry of the Interstice in Literary Theory

Filed under: General — Tags: , , , , — m759 @ 3:28 AM

"You said something about the significance of spaces between
elements being repeated. Not only the element itself being repeated,
but the space between. I'm very interested in the space between.
That is where we come together." — Peter Eisenman, 1982


Parrhesia  No. 3 • 2007 • 22–32

(Up) Against the (In) Between: Interstitial Spatiality
in Genet and Derrida

by Clare Blackburne

Blackburne — www.parrhesiajournal.org 24 —

"The excessive notion of espacement  as the resurgent spatiality of that which is supposedly ‘without space’ (most notably, writing), alerts us to the highly dynamic nature of the interstice – a movement whose discontinuous and ‘aberrant’ nature requires further analysis."

Blackburne — www.parrhesiajournal.org 25 —

"Espacement  also evokes the ambiguous figure of the interstice, and is related to the equally complex derridean notions of chora , différance , the trace and the supplement. Derrida’s reading of the Platonic chora  in Chora L Works  (a series of discussions with the architect Peter Eisenman) as something which defies the logics of non-contradiction and binarity, implies the internal heterogeneity and instability of all structures, neither ‘sensible’ nor ‘intelligible’ but a third genus which escapes conceptual capture.25 Crucially, chora , spacing, dissemination and différance  are highly dynamic concepts, involving hybridity, an ongoing ‘corruption’ of categories, and a ‘bastard reasoning.’26 Derrida identification of différance  in Margins of  Philosophy , as an ‘unappropriable excess’ that operates through spacing as ‘the becoming-space of time or the becoming-time of space,’27 chimes with his description of chora  as an ‘unidentifiable excess’ that is ‘the spacing which is the condition for everything to take place,’ opening up the interval as the plurivocity of writing in defiance of ‘origin’ and ‘essence.’28  In this unfolding of différance , spacing  ‘insinuates  into  presence an  interval,’29 again alerting us to the crucial role of the interstice in deconstruction, and, as Derrida observes  in Positions ,  its  impact  as  ‘a movement,  a  displacement  that  indicates  an  irreducible alterity’: ‘Spacing is the impossibility for an identity to be closed on itself, on the inside of its proper interiority, or on its coincidence with itself. The irreducibility of spacing is the irreducibility of the other.’30"

25. Quoted in Jeffrey Kipnis and Thomas Leeser, eds., 
Chora L Works. Jacques Derrida and Peter Eisenman  
(New York: The Monacelli Press, 1997), 15.

26. Ibid, 25.

27. Derrida, Margins of Philosophy.
(Brighton: The Harvester Press, 1982), 6 and 13.

28. Derrida, Chora L Works , 19 and 10.

29. Ibid, 203.

30. Derrida, Positions , 94.

Friday, June 8, 2018

For Anthony Bourdain

Filed under: General — m759 @ 2:00 PM

Flashback —

Thursday, August 21, 2014


Filed under: Uncategorized — m759 @ 1:00 AM 

( A sequel to  Lux )

“By groping toward the light we are made to realize
how deep the darkness is around us.”

— Arthur Koestler, The Call Girls: A Tragi-Comedy ,
Random House, 1973, page 118

Robin Williams and the Stages of Math

i)   shock & denial
ii)  anger
iii) bargaining
iv) depression
v)  acceptance

A related description of the process —

“You know how sometimes someone tells you a theorem,
and it’s obviously false, and you reach for one of the many
easy counterexamples only to realize that it’s not a
counterexample after all, then you reach for another one
and another one and find that they fail too, and you begin
to concede the possibility that the theorem might not
actually be false after all, and you feel your world start to
shift on its axis, and you think to yourself: ‘Why did no one
tell me this before?’ “

— Tom Leinster yesterday at The n-Category Café

Tuesday, July 11, 2017

Dialogue from Plato’s Cave

Filed under: General — Tags: — m759 @ 10:15 AM

At  scifi.stackexchange.com

Why was the Cosmic Cube named the Tesseract 
in the Marvel movie series? Is there any specific reason 
for the name change? According to me, Cosmic Cube
seems a nice and cooler name.

— Asked March 14, 2013, by Dhwaneet Bhatt
At least it wasn't called 'The AllSpark.' 
It's not out of the realm of possibility

— Solemnity, March 14, 2013

Tuesday, September 27, 2016

Chomsky and Lévi-Strauss in China

Filed under: General,Geometry — Tags: — m759 @ 7:31 AM

Or:  Philosophy for Jews

From a New Yorker  weblog post dated Dec. 6, 2012 —

Happy Birthday, Noam Chomsky” by Gary Marcus—

“… two titans facing off, with Chomsky, as ever,
defining the contest”

“Chomsky sees himself, correctly, as continuing
a conversation that goes back to Plato, especially
the Meno dialogue, in which a slave boy is
revealed by Socrates to know truths about
geometry that he hadn’t realized he knew.”

Socrates and the slave boy discussed a rather elementary “truth
about geometry” — A diamond inscribed in a square has area 2
(and side the square root of 2) if the square itself has area 4
(and side 2).

Consider that not-particularly-deep structure from the Meno dialogue
in the light of the following…

The following analysis of the Meno diagram from yesterday’s
post “The Embedding” contradicts the Lévi-Strauss dictum on
the impossibility of going beyond a simple binary opposition.
(The Chinese word taiji  denotes the fundamental concept in
Chinese philosophy that such a going-beyond is both useful
and possible.)

The matrix at left below represents the feminine yin  principle
and the diamond at right represents the masculine yang .

      From a post of Sept. 22,
Binary Opposition Illustrated” —

A symbol of the unity of yin and yang —

Related material:

A much more sophisticated approach to the “deep structure” of the
Meno diagram —

The larger cases —

The diamond theorem

Tuesday, May 24, 2016

Rosenhain and Göpel Revisited

The authors Taormina and Wendland in the previous post
discussed some mathematics they apparently did not know was
related to a classic 1905 book by R. W. H. T. Hudson, Kummer's
Quartic Surface

"This famous book is a prototype for the possibility
of explaining and exploring a many-faceted topic of
research, without focussing on general definitions,
formal techniques, or even fancy machinery. In this
regard, the book still stands as a highly recommendable,
unparalleled introduction to Kummer surfaces, as a
permanent source of inspiration and, last but not least, 
as an everlasting symbol of mathematical culture."

— Werner Kleinert, Mathematical Reviews ,
     as quoted at Amazon.com

Some 4×4 diagrams from that book are highly relevant to the
discussion by Taormina and Wendland of the 4×4 squares within
the 1974 Miracle Octad Generator of R. T. Curtis that were later,
in 1987, described by Curtis as pictures of the vector 4-space over
the two-element Galois field GF(2).

Hudson did not think of his 4×4 diagrams as illustrating a vector space,
but he did use them to picture certain subsets of the 16 cells in each
diagram that he called Rosenhain and Göpel tetrads .

Some related work of my own (click images for related posts)—

Rosenhain tetrads as 20 of the 35 projective lines in PG(3,2)

IMAGE- Desargues's theorem in light of Galois geometry

Göpel tetrads as 15 of the 35 projective lines in PG(3,2)

Anticommuting Dirac matrices as spreads of projective lines

Related terminology describing the Göpel tetrads above

Ron Shaw on symplectic geometry and a linear complex in PG(3,2)

Thursday, March 31, 2016

Devil’s Gate Revisited

Filed under: General — Tags: — m759 @ 10:27 AM

The revisiting, below, of an image shown here in part
on Spy Wednesday, 2016, was suggested in part by
a New York Times  obituary today for a Nobel-prize
winning Hungarian novelist. 

Note the references on the map to 
"Devil's Gate" and "Pathfinder."

See also the following from a review of The Pathseeker , a novel 
by the Nobel laureate (Imre Kertész), who reportedly died today —

The commissioner is in fact not in search of a path, but rather of traces of the past (more literally the Hungarian title means ‘trace seeker’). His first shock comes at his realization that the site of his sufferings has been converted into a museum, complete with tourists “diligently carrying off the significance of things, crumb by crumb, wearing away a bit of the unspoken importance” (59). He meets not only tourists, however. He also comes across paradoxically “unknown acquaintances who were just as much haunted by a compulsion to revisit,” including a veiled woman who slowly repeats to him the inventory of those she lost: “my father, my younger brother, my fiancé” (79). The commissioner informs her that he has come “to try to redress that injustice” (80). When she asks how, he suddenly finds the words he had sought, “as if he could see them written down: ‘So that I should bear witness to everything I have seen’” (80).

The act of bearing witness, however, proves elusive. In the museum he is compelled to wonder, “What could this collection of junk, so cleverly, indeed all too cleverly disguised as dusty museum material, prove to him, or to anyone else for that matter,” and adds the chilling observation, “Its objects could be brought to life only by being utilized” (71). As he touches the rust-eaten barbed wire fence he thinks, “A person might almost feel in the mood to stop and dutifully muse on this image of decay – were he not aware, of course, that this was precisely the goal; that the play of ephemerality was merely a bait for things” (66). It is this play of ephemerality, the possibility that the past will be consigned to the past, against which the commissioner struggles, yet his struggle is frustrated precisely by the lack of resistance, the indifference of the objects he has come to confront. “What should he cling on to for proof?” he wonders. “What was he to fight with, if they were depriving him of every object of the struggle? Against what was he to try and resist, if nothing was resisting?” (68) He had come with the purpose of “advertis[ing] his superiority, celebrat[ing] the triumph of his existence in front of these mute and powerless things. His groundless disappointment was fed merely by the fact that this festive invitation had received no response. The objects were holding their peace” (109). 

In point of fact The Pathseeker  makes no specific mention either of the Holocaust or of the concentration camps, yet the admittedly cryptic references to places leave no doubt that this is its subject. Above the gate at the camp the commissioner’s wife reads the phrase, “Jedem das Seine,” to each his due, and one recalls the sign above the entrance to the camp at Buchenwald. Further references to Goethe as well as the Brabag factory, where Kertész himself worked as a prisoner, confirm this. Why this subterfuge on the part of the author? Why a third-person narrative with an unnamed protagonist when so many biographical links tie the author to the story? One cannot help but wonder if Kertész sought specifically to avoid binding his story to particulars in order to maintain the ultimately metaphysical nature of the quest. Like many of Kertész’s works,The Pathseeker  is not about the trauma of the Holocaust itself so much as the trauma of survival. The self may survive but the triumph of that survival is chimerical.

Translator Tim Wilkinson made the bold decision, in translating the title of the work, not to resort to the obvious. Rather than simply translate Nyomkereső , an allusion to the Hungarian translation of James Fenimore Cooper’s The Pathfinder , back into English, he preserves an element of the unfamiliar in his title. This tendency marks many of the passages of the English translation, in which Wilkinson has opted to preserve the winding and often frustratingly serpentine nature of many of the sentences of the original instead of rewriting them in sleek, familiar English.  . . .

— Thomas Cooper

"Sleek, familiar English" —

"Those were the good old days!" — Applegate in "Damn Yankees"
(See previous post.)

Saturday, March 28, 2015

Against Dryness

Filed under: General — Tags: — m759 @ 3:24 PM


"July 5, 2012, begins normally enough —
Ben Affleck’s character goes for a drink
at the bar he co-owns with his hilariously
sarcastic twin sister Margo …."

Margo Dunne: Well, the Irish prince graces us
with his presence. [she flicks water in his face]
Nick Dunne: His majesty prefers not to be moistened.

Margo and Nick go on to discuss what Nick should get
his wife as a fifth ("wood") anniversary present.

One possibility, from the German website EinsteinSpiele.de —

(Suggested by the word Legespiel  in yesterday's link Tribute.)

See also the above date — July 5, 2012 — in this journal.

Friday, January 2, 2015

Coincidentia Oppositorum

Filed under: General — m759 @ 2:00 PM

A sequel to New Year's Greeting from Franz Kafka:


From "Kafka and the Coincidence of Opposites," by
Dennis McCort, Syracuse University —

… my aim in the following pages is to identify and examine the particular dynamics of Kafka's mysticism through an analysis of this principle of the coincidence of opposites, first as a recurrent motif in his intellectual life, and then as a thematic and structural force in several key works of short fiction. Since the coincidentia, as the "abstract essence" of dialectical logic, may be said to subsume all experiential content, it becomes intrinsically more interesting as form than as content, and we will thus be examining a variety of Kafka's coincidentia-generated binaries (e.g., conscious/unconscious, freedom/bondage, wisdom/ignorance), first in a series of short parables and finally in two of the longer short fictions, "Die Verwandlung" [“The Metamorphosis”] and “Vor dem Gesetz” [“Before the Law”]. Moreover, since the coincidentia, understood in the German and other mystical traditions familiar to Kafka as the original Oneness of the pairs of opposites, is precisely what the human mind obscures as it conceptually bifurcates things in order to "get at them," we will be focusing especially on those relatively rare instances in Kafka's fiction in which the mind of the character or persona goes beyond its own intrinsic limits. This is in support of the case for Kafka's mystical insight as a mainspring of his literary creativity and, more generally, for Kafka as essentially a spiritual writer, convinced in the end of the human being's capacity to transcend, however remote the possibility, the suffering of separation built into his or her own dualistic consciousness.

Friday, September 26, 2014


Filed under: General — Tags: — m759 @ 11:30 AM

For T. S. Eliot’s birthday:

“Time present and time past
Are both perhaps present in time future,
And time future contained in time past.
If all time is eternally present
All time is unredeemable.
What might have been is an abstraction
Remaining a perpetual possibility
Only in a world of speculation.
What might have been and what has been
Point to one end, which is always present.”

— Opening passage of  Four Quartets

See also the previous post.

Saturday, September 20, 2014

The Metaphysics of Entities

Filed under: General — Tags: — m759 @ 11:00 AM

Anthony Lane in The New Yorker , issue dated Sept. 22, 2014:

"The hero of 'The Zero Theorem' is a computer genius called Qohen Leth
(Christoph Waltz)…. He is the sole resident of a derelict church, where,
on a crucifix in front of the altar, the head of Christ has been replaced by
a security camera. No prayers are ever said, and none are answered.

In short, the place is deconsecrated, but to claim that it lacks any spark of
sacred yearning would be wrong, because Qohen devotes his days to seeking
the Zero Theorem, which—whatever it may be—lies at the fuzzy limit of
human powers. We crunch entities,” he says, as if that explained anything.
His employer is Mancom, a large corporation that, in Orwellian fashion,
oversees ordinary lives, although it betrays more frantic desperation than
glowering threat."

One approach to the metaphysics of entities was indicated in the previous
post, 'Metaphysics for Gilliam." A different approach:

"Categories, Sets, and the Nature of Mathematical Entities,"
by Jean-Pierre Marquis, Ch. 13, pp. 181-192, in the 2006 book
The Age of Alternative Logics , ed. by van Benthem et al.
(Springer, Netherlands).

From pages 182-183 —

13.2 The nature of mathematical entities

Let us start with the nature of mathematical entities in general and with a
rough and classical distinction that will simply set the stage for the picture we
want to develop. We essentially follow Lowe 1998* for the basic distinctions. We
need to distinguish between abstract and concrete entities, on the one hand, and
universals and particulars on the other hand. For our purpose, it is not necessary
to specify a criterion of demarcation between abstract and concrete entities. We
simply assume that such a distinction can be made, e.g. concrete entities can
change whereas abstract entities cannot. We assume that a universal is an entity
that can be instantiated by entities which themselves are not instantiable, the
latter being of course particulars. Given these distinctions, an entity can be a
concrete particular, a concrete universal, an abstract particular or an abstract

Our focus here is between the last two possibilities. For we claim that the
current conception of sets makes them abstract particulars whereas for objects
defined within categories, mathematical entities are abstract universals. This,
we claim, is true of category theory as it is.

* Lowe, E.J., 1998, The Possibility of Metaphysics , Oxford: Clarendon Press.

Thursday, August 21, 2014


Filed under: General,Geometry — m759 @ 1:00 AM

( A sequel to Lux )

“By groping toward the light we are made to realize
how deep the darkness is around us.”

— Arthur Koestler, The Call Girls: A Tragi-Comedy ,
Random House, 1973, page 118

Robin Williams and the Stages of Math

i)   shock & denial
ii)  anger
iii) bargaining
iv) depression
v)  acceptance

A related description of the process —

You know how sometimes someone tells you a theorem,
and it’s obviously false, and you reach for one of the many
easy counterexamples only to realize that it’s not a
counterexample after all, then you reach for another one
and another one and find that they fail too, and you begin
to concede the possibility that the theorem might not
actually be false after all, and you feel your world start to
shift on its axis, and you think to yourself: ‘Why did no one
tell me this before?’ “

— Tom Leinster yesterday at The n-Category Café

Friday, February 21, 2014

Night’s Hymn of the Rock

Filed under: General,Geometry — Tags: , , — m759 @ 3:33 AM

One way of interpreting the symbol  IMAGE- Modal Diamond in a square 
at the end of yesterday's post is via
the phrase "necessary possibility."

See that phrase in (for instance) a post
of July 24, 2013, The Broken Tablet .

The Tablet  post may be viewed in light
of a Tom Wolfe passage quoted here on
the preceding day, July 23, 2013—

IMAGE- Tom Wolfe in 'The Painted Word' on conceptual art

On that  day (July 23) another weblog had
a post titled

Wallace Stevens: Night's Hymn of the Rock.

Some related narrative —

IMAGE- The 2001 film 'The Discovery of Heaven'

I prefer the following narrative —

Part I:  Stevens's verse from "The Rock" (1954) —
"That in which space itself is contained"

Part II:  Mystery Box III: Inside, Outside (2014)

Thursday, February 20, 2014

Relativity Blues

Filed under: General,Geometry — Tags: , — m759 @ 9:00 AM


A review of this date in 2005 —

Modal Theology

“We symbolize logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes)).”

— Keith Allen Korcz

And what do we  
   symbolize by   The image “http://www.log24.com/theory/images/Modal-diamondbox.gif” cannot be displayed, because it contains errors. ?

Sunday, October 6, 2013

Sunday Dinner (continued)

Filed under: General — Tags: , — m759 @ 2:00 PM

Judith Shulevitz in The New York Times
on Sunday, July 18, 2010
(quoted here Aug. 15, 2010) —

“What would an organic Christian Sabbath look like today?”

One possibility —

See also The Pride of Lowell  (Oct. 3, 2012)
and, a year later, The Hunt for Green October .

Tuesday, September 3, 2013

“The Stone” Today Suggests…

Filed under: General,Geometry — m759 @ 12:31 PM

A girl's best friend?

The Philosopher's Gaze , by David Michael Levin,
U. of California Press, 1999, in III.5, "The Field of Vision," pp. 174-175—

The post-metaphysical question—question for a post-metaphysical phenomenology—is therefore: Can the perceptual field, the ground of perception, be released  from our historical compulsion to represent it in a way that accommodates our will to power and its need to totalize and reify the presencing of being? In other words: Can the ground be experienced as  ground? Can its hermeneutical way of presencing, i.e., as a dynamic interplay of concealment and unconcealment, be given appropriate  respect in the receptivity of a perception that lets itself  be appropriated by  the ground and accordingly lets  the phenomenon of the ground be  what and how it is? Can the coming-to-pass of the ontological difference that is constitutive of all the local figure-ground differences taking place in our perceptual field be made visible hermeneutically, and thus without violence to its withdrawal into concealment? But the question concerning the constellation of figure and ground cannot be separated from the question concerning the structure of subject and object. Hence the possibility of a movement beyond metaphysics must also think the historical possibility of breaking out of this structure into the spacing of the ontological difference: différance , the primordial, sensuous, ekstatic écart . As Heidegger states it in his Parmenides lectures, it is a question of "the way historical man belongs within the bestowal of being (Zufügung des Seins ), i.e., the way this order entitles him to acknowledge being and to be the only being among all beings to see  the open" (PE* 150, PG** 223. Italics added). We might also say that it is a question of our response-ability, our capacity as beings gifted with vision, to measure up to the responsibility for perceptual responsiveness laid down for us in the "primordial de-cision" (Entscheid ) of the ontological difference (ibid.). To recognize the operation of the ontological difference taking place in the figure-ground difference of the perceptual Gestalt  is to recognize the ontological difference as the primordial Riß , the primordial Ur-teil  underlying all our perceptual syntheses and judgments—and recognize, moreover, that this rift, this  division, decision, and scission, an ekstatic écart  underlying and gathering all our so-called acts of perception, is also the only "norm" (ἀρχή ) by which our condition, our essential deciding and becoming as the ones who are gifted with sight, can ultimately be judged.

* PE: Parmenides  of Heidegger in English— Bloomington: Indiana University Press, 1992

** PG: Parmenides  of Heidegger in German— Gesamtausgabe , vol. 54— Frankfurt am Main: Vittorio Klostermann, 1992

Examples of "the primordial Riß " as ἀρχή  —

For an explanation in terms of mathematics rather than philosophy,
see the diamond theorem. For more on the Riß  as ἀρχή , see
Function Decomposition Over a Finite Field.

Thursday, August 8, 2013

Heaven’s Gate

Filed under: General — Tags: — m759 @ 3:01 PM

Yesterday's post Devil's Gate provided a dark view of life and culture.

A more cheerful view is provided by the late Gail Levin,
a maker of PBS "American Masters" documentaries
that included, notably, Jeff Bridges and Marilyn Monroe.

Levin reportedly died at 67 on July 31, 2013.*

An image from an interview with Levin —

The date in the image, July 19th, 2006, is the broadcast
date of the PBS "American Masters" program on Monroe.
A check for synchronicity shows there was no Log24 post
on that date.

See, however, posts for the day before— "Sacred Order"—
and the day after— "Bead Game."

A related quote from an article linked to in the latter—

"First world culture, which is 'pagan and in the majority
everywhere,' has as its defining characteristic
a 'primacy of possibility,' or pop— a broadly inclusive
concept that covers everything from the Aboriginal
dreamtime to Plato’s Forms."

Review by Jess Castle of Philip Rieff’s 
Sacred Order/Social Order, Vol. 1: My Life among the
Deathworks: Illustrations of the Aesthetics of Authority
University of Virginia Press, 2006. 256 pages, $34.95.

This quote may serve as the missing July 19, 2006, post.

Related material:  Dreamtime,  Possibility,  and Plato's Forms.

* See that date in this journal for two less famous American
  masters, artist Edward Valigursky and writer Robert Silverberg.

Wednesday, July 24, 2013

The Broken Tablet

Filed under: General,Geometry — Tags: — m759 @ 3:33 AM

This post was suggested by a search for the
Derridean phrase "necessary possibility"* that
led to web pages on a conference at Harvard
on Friday and Saturday, March 26**-27, 2010,
on Derrida and Religion .

The conference featured a talk titled
"The Poetics of the Broken Tablet."

I prefer the poetics of projective geometry.

An illustration— The restoration of the full
15-point "large" Desargues configuration in
place of the diminished 10-point Desargues
configuration that is usually discussed.

IMAGE- The proof of the converse of Desargues' theorem involves a third triangle.

Click on the image for further details.

* See a discussion of this phrase in
  the context of Brazilian religion.

** See also my own philosophical reflections
   on Friday, March 26, 2010:
   "You Can't Make This Stuff Up." 

Friday, February 1, 2013

Get Quotes

Filed under: General — Tags: , — m759 @ 4:01 PM

For Tony Kushner fans:

For logic fans:

IMAGE- NY Times market quotes, American Express Gold Card ad, Kevin Spacey in 'House of Cards' ad

John Searle on Derrida:

On necessity, possibility, and 'necessary possibility'

In the box-diamond notation, the axiom Searle quotes is


"The euclidean property guarantees the truth of this." — Wikipedia

Linking to Euclid

Clicking on "euclidean" above yields another Wikipedia article

"In mathematics, Euclidean relations are a class of binary relations that satisfy a weakened form of transitivity that formalizes Euclid's 'Common Notion 1' in The Elements : things which equal the same thing also equal one another."

Verification: See, for instance, slides on modal logic at Carnegie Mellon University and modal logic at plato.stanford.edu.

Monday, October 8, 2012

This Poet You’ve Snatched

Filed under: General — Tags: — m759 @ 10:09 PM

IMAGE- Oct. 7, 2012 post by Margaret Soltan with passages by Salinger on education and DeLillo on hat measurements

Some background from today's New York Times

IMAGE- Oct. 8, 2012, NY Times obituary for Vietnamese imprisoned poet

From DeLillo's novel Mao II  in  the paragraph immediately preceding
the Ritz-hat passage quoted by Soltan—

"He could have told George he was writing about the hostage to bring him back, to return a meaning that had been lost to the world when they locked him in that room. Maybe that was it. When you inflict punishment on someone who is not guilty, when you fill rooms with innocent victims, you begin to empty the world of meaning and erect a separate mental state, the mind consuming what's outside itself, replacing real things with plots and fictions. One fiction taking the world narrowly into itself, the other fiction pushing out toward the social order, trying to unfold into it. He could have told George a writer creates a character as a way to reveal consciousness, increase the flow of meaning. This is how we reply to power and beat back our fear. By extending the pitch of consciousness and human possibility. This poet you've snatched. His detention drains the world of one more thimble of meaning."

For related ways of draining the world of meaning, see the politically loaded leftist vocabulary of International Art English

IAE has a distinctive lexicon: aporia , radically , space , proposition , biopolitical , tension , transversal , autonomy . An artist’s work inevitably interrogates, questions, encodes, transforms, subverts, imbricates, displaces—though often it doesn’t do these things so much as it serves to, functions to, or seems to (or might seem to) do these things.  [Alix Rule and David Levine, July 30, 2012]

See also this evening's post Issue 16.

Thursday, May 24, 2012

Dark, Dark, Dark

Filed under: General — Tags: — m759 @ 12:00 PM

Damnation Morning

From her left arm hung a black handbag that closed with a drawstring and from which protruded the tip of a silvery object about which I found myself apprehensively curious.

Her right arm was raised and bent, the elbow touching the door frame, the hand brushing back the very dark bangs from her forehead to show me the sigil, as if that had a bearing on her question.

The sigil was an eight-limbed asterisk made of fine dark lines and about as big as a silver dollar. An X superimposed on a plus sign. It looked permanent.

IMAGE- 'Eight-limbed asterisk' of Fritz Leiber (square version)

Except for the bangs she wore her hair pinned up. Her ears were flat, thin-edged, and nicely shaped, with the long lobes that in Chinese art mark the philosopher. Small square silver flats with rounded corners ornamented them.

Her face might have been painted by Toulouse-Lautrec or Degas. The skin was webbed with very fine lines; the eyes were darkly shadowed and there was a touch of green on the lids (Egyptian?—I asked myself); her mouth was wide, tolerant, but realistic. Yes, beyond all else, she seemed realistic.

Mary Karr

You’re not afraid to show yourself at your lowest ebb. In Lit, you stop breast-feeding because you’ve started drinking again. You describe yourself hiding in a closet with a bottle of whiskey, a bottle of Listerine, and a spit bowl.

It’s not a proud moment. The temptation in Lit was to either make myself seedy or show some glamour. But there wasn’t any. It was just dark, dark, dark for days. Ugly.

Were you surprised by how deeply people related to this dark stuff?

If I’m doing my job then I’m able to make the strange seem familiar. Bad memoirs try to make the strange stranger, to provide something for people to gawk at. I try to create an experience where no matter how bizarre something is, it seems normal. I don’t want readers to balk, I want them to be in the experience. My goal isn’t for people to go, “Oh, poor little Mary Karr,” but rather to have the reader go, “I can be an asshole too,” or just to have enthusiasm for the possibility for change.

Tuesday, May 22, 2012

Included Middle

Filed under: General,Geometry — m759 @ 2:01 PM


"In logic, the law of excluded middle (or the principle of excluded middle) is the third of the so-called three classic laws of thought. It states that for any proposition, either that proposition is true, or its negation is.

The law is also known as the law (or principleof the excluded third (or of the excluded middle), or, in Latinprincipium tertii exclusi. Yet another Latin designation for this law is tertium non datur: 'no third (possibility) is given.'"

"Clowns to the left of me, jokers to the right"

 — Songwriter who died on January 4, 2011.

Online NY Times  on the date of the songwriter's death—

"A version of this review appeared in print
on January 4, 2011, on page C6 of the New York edition." 


"The philosopher Hubert Dreyfus and his former student
Sean Dorrance Kelly have a story to tell, and it is not
a pretty tale for us moderns. Ours is an age of nihilism,
they say, meaning not so much that we have nothing
in which to believe, but that we don’t know how to choose
among the various things to which we might commit
ourselves. Looking down from their perches at Berkeley
and Harvard, they see the 'human indecision that
plagues us all.'"

For an application of the excluded-middle law, see
Non-Euclidean Blocks and Deep Play.

Violators of the law may have trouble* distinguishing
between "Euclidean" and "non-Euclidean" phenomena
because their definition of the latter is too narrow,
based only on examples that are historically well known.

See the Non-Euclidean Blocks  footnote.

* Followers  of the excluded-middle law will avoid such
trouble by noting that "non-Euclidean" should mean
simply "not  Euclidean in some  way "— not  necessarily
in a way contradicting Euclid's parallel postulate.

But see Wikipedia's defense of the standard, illogical,
usage of the phrase "non-Euclidean."


Tertium Datur

Froebel's Third Gift

"Here I am, stuck in the middle with you."

Monday, May 21, 2012

Child’s Play (continued*)

Filed under: General — Tags: — m759 @ 7:59 PM

You and I …

we are just like a couple of tots…



Born 1973 in Bergen. Lives and works in Oslo.


2000 – 2004 National Academy of Fine Arts, Oslo
1998 – 2000 Strykejernet Art School, Oslo, NO
1995 – 1998 Philosophy, University of Bergen

University of Bergen—

 It might therefore seem that the idea of digital and analogical systems as rival fundaments to human experience is a new suggestion and, like digital technology, very modern. In fact, however, the idea is as old as philosophy itself (and may be much older). In his Sophist, Plato sets out the following ‘battle’ over the question of ‘true reality’:

What we shall see is something like a battle of gods and giants going on between them over their quarrel about reality [γιγαντομαχία περì της ουσίας] ….One party is trying to drag everything down to earth out of heaven and the unseen, literally grasping rocks and trees in their hands, for they lay hold upon every stock and stone and strenuously affirm that real existence belongs only to that which can be handled and offers resistance to the touch. They define reality as the same thing as body, and as soon as one of the opposite party asserts that anything without a body is real, they are utterly contemptuous and will not listen to another word. (…) Their adversaries are very wary in defending their position somewhere in the heights of the unseen, maintaining with all their force that true reality [την αληθινήν ουσίαν] consists in certain intelligible and bodiless forms. In the clash of argument they shatter and pulverize those bodies which their opponents wield, and what those others allege to be true reality they call, not real being, but a sort of moving process of becoming. On this issue an interminable battle is always going on between the two camps [εν μέσω δε περι ταυτα απλετος αμφοτέρων μάχη τις (…) αει συνέστηκεν]. (…) It seems that only one course is open to the philosopher who values knowledge and truth above all else. He must refuse to accept from the champions of the forms the doctrine that all reality is changeless [and exclusively immaterial], and he must turn a deaf ear to the other party who represent reality as everywhere changing [and as only material]. Like a child begging for 'both', he must declare that reality or the sum of things is both at once [το όν τε και το παν συναμφότερα] (Sophist 246a-249d).

The gods and the giants in Plato’s battle present two varieties of the analog position. Each believes that ‘true reality’ is singular, that "real existence belongs only to" one side or other of competing possibilities. For them, difference and complexity are secondary and, as secondary, deficient in respect to truth, reality and being (την αληθινήν ουσίαν, το όν τε και το παν). Difference and complexity are therefore matters of "interminable battle" whose intended end for each is, and must be (given their shared analogical logic), only to eradicate the other. The philosophical child, by contrast, holds to ‘both’ and therefore represents the digital position where the differentiated two yet belong originally together. Here difference, complexity and systematicity are primary and exemplary.

It is an unfailing mark of the greatest thinkers of the tradition, like Plato, that they recognize the digital possibility and therefore recognize the principal difference of it from analog possibilities.

— Cameron McEwen, "The Digital Wittgenstein,"
    The Wittgenstein Archives at the University of Bergen

* See that phrase in this journal.

Sunday, July 10, 2011

Wittgenstein’s Diamond

Filed under: General,Geometry — Tags: , — m759 @ 9:29 AM

Philosophical Investigations  (1953)

97. Thought is surrounded by a halo.
—Its essence, logic, presents an order,
in fact the a priori order of the world:
that is, the order of possibilities * ,
which must be common to both world and thought.
But this order, it seems, must be
utterly simple . It is prior  to all experience,
must run through all experience;
no empirical cloudiness or uncertainty can be allowed to affect it
——It must rather be of the purest crystal.
But this crystal does not appear as an abstraction;
but as something concrete, indeed, as the most concrete,
as it were the hardest  thing there is
(Tractatus Logico-Philosophicus  No. 5.5563).

— Translation by G.E.M. Anscombe


All propositions of our colloquial language
are actually, just as they are, logically completely in order.
That simple thing which we ought to give here is not
a model of the truth but the complete truth itself.

(Our problems are not abstract but perhaps
the most concrete that there are.)

97. Das Denken ist mit einem Nimbus umgeben.
—Sein Wesen, die Logik, stellt eine Ordnung dar,
und zwar die Ordnung a priori der Welt,
d.i. die Ordnung der Möglichkeiten ,
die Welt und Denken gemeinsam sein muß.
Diese Ordnung aber, scheint es, muß
höchst einfach  sein. Sie ist vor  aller Erfahrung;
muß sich durch die ganze Erfahrung hindurchziehen;
ihr selbst darf keine erfahrungsmäßige Trübe oder Unsicherheit anhaften.
——Sie muß vielmehr vom reinsten Kristall sein.
Dieser Kristall aber erscheint nicht als eine Abstraktion;
sondern als etwas Konkretes, ja als das Konkreteste,
gleichsam Härteste . (Log. Phil. Abh.  No. 5.5563.)

See also

Related language in Łukasiewicz (1937)—


* Updates of 9:29 PM ET July 10, 2011—

A  mnemonic  from a course titled “Galois Connections and Modal Logics“—

“Traditionally, there are two modalities, namely, possibility and necessity.
The basic modal operators are usually written box (square) for necessarily
and diamond (diamond) for possibly. Then, for example, diamondP  can be read as
‘it is possibly the case that P .'”

See also Intensional Semantics , lecture notes by Kai von Fintel and Irene Heim, MIT, Spring 2007 edition—

“The diamond symbol for possibility is due to C.I. Lewis, first introduced in Lewis & Langford (1932), but he made no use of a symbol for the dual combination ¬¬. The dual symbol was later devised by F.B. Fitch and first appeared in print in 1946 in a paper by his doctoral student Barcan (1946). See footnote 425 of Hughes & Cresswell (1968). Another notation one finds is L for necessity and M for possibility, the latter from the German möglich  ‘possible.’”

Barcan, Ruth C.: 1946. “A Functional Calculus of First Order Based on Strict Implication.” Journal of Symbolic Logic, 11(1): 1–16. URL http://www.jstor.org/pss/2269159.

Hughes, G.E. & Cresswell, M.J.: 1968. An Introduction to Modal Logic. London: Methuen.

Lewis, Clarence Irving & Langford, Cooper Harold: 1932. Symbolic Logic. New York: Century.

Sunday, May 1, 2011

Quarantine Story

Filed under: General — Tags: , — m759 @ 11:02 PM

A link in the previous post to Delos in this journal mentions physicist John Cramer.

His daughter Kathryn's weblog mentions the following story—

Graffiti in the Library of Babel  • David Langford

—from her forthcoming anthology Year's Best SF 16 .

From the Langford story—

"'I suppose we have a sort of duty…' Out of the corner of her eye Ceri saw her notes window change. She hadn't touched the keyboard or mouse. Just before the flatscreen went black and flickered into a reboot sequence, she saw the coloured tags where no tags had been before. In her own notes. Surrounding the copied words 'quarantine regulations.'"

Related material from this journal last Jan. 9

"Show me all  the blueprints."
 – Leonardo DiCaprio in "The Aviator" (2004)


DiCaprio in "Inception"

In the "blueprints" link above, DiCaprio's spelling of "Q-U-A-R-A-N-T-I-N-E" is of particular interest.

See also a search for Inception in this journal.

A post on a spelling bee at the end of that search quotes an essay on Walter Benjamin—

This blissful state between the world and its creator as expressed in Adamic language has its end, of course, in the Fall.  The “ignorance” introduced into the world that ultimately drives our melancholic state of acedia has its inception with the Fall away from the edenic union that joins God’s plan to the immediacy of the material world.  What ensues, says Benjamin, is an overabundance of conventional languages, a prattle of meanings now localized hence arbitrary.  A former connection to a defining origin has been lost; and an overdetermined, plethoric state of melancholia forms.  Over-determination stems from over-naming.  “Things have no proper names except in God.  . . . In the language of men, however, they are overnamed.”  Overnaming becomes “the linguistic being of melancholy.”7

7 Walter Benjamin, “On Language as Such and On the Languages of Man,” Edmund Jephcott, tr., Walter Benjamin , Selected Writings , Volume I:  1913-1926 , Marcus Bullock and Michael W. Jennings, eds., Cambridge, MA, Harvard University Press, 1997, p. 73.

Compare and contrast with a remark by a translator mentioned here previously

I fancy, myself, that this self-consciousness about translation dates approximately from the same time as man's self-consciousness about language itself. Genesis tells us that Adam named all the animals (just as in Indian tradition the monkey-god Hanuman invented grammar by naming all the plants in the Garden of Illo Tempore). No doubts, no self-consciousness: "Whatever Adam called every living creature, that was the name thereof." (Genesis II, 19). But after the expulsion from Paradise I see Adam doubting  the moment the possibility occurs that another name might  be possible. And isn't that what all translators are? Proposers, in another language, of another name ?

— Helen Lane in Translation Review , Vol. 5, 1980

Saturday, March 19, 2011

Knecht Moves

Filed under: General — m759 @ 2:45 AM

In memory of David Rumelhart, who "explored the possibility of formulating a formal grammar to capture the structure of stories." (Wikipedia)

Rumelhart died on Sunday, March 13, 2011.*

So set 'em up, Joe

I've got a little schema you oughta know….

So make it one for my baby and one more for the road.

* From that date: The Counter and Twenty-Four.

Saturday, March 5, 2011

Personal Link

Filed under: General,Geometry — m759 @ 9:00 PM

A search for some background on Dmitri Tymoczko, the subject of yesterday's evening entry on music theory, shows that his name and mine once both appeared in the same web page— "This Week's Finds in Mathematical Physics (Week 234)," by John Baez, June 12, 2006 (linked to by the Wikipedia article on transformational music theory).

In that page, Baez speculates on the possibility of a connection between music theory and Mathieu groups and says—

"For a pretty explanation of M24, also try this:

Steven H. Cullinane, Geometry of the 4 × 4 square, http://finitegeometry.org/sc/16/geometry.html."

I know of no connection* between the groups I discussed there and music theory. For some background on Tymoczko's work, see the helpful survey "Exploring Musical Space," by Julian Hook (Science  magazine, 7 July 2006).

* Apart, that is, from the tesseract (see Geometry of the 4 × 4 Square) shown by Tymoczko in a 2010 lecture


This is perhaps "Chopin's tesseract" from section 8.5 of Tymoczko's new book
A Geometry of Music  (Oxford University Press, 2011).

Tuesday, December 14, 2010

Types of Ambiguity —

Filed under: General,Geometry — m759 @ 9:48 PM

Galois Meets Doctor Faustus

Galois's theory of mathematical  ambiguity (see June 14) —

  My principal meditations for some time have been directed towards
  the application of the theory of ambiguity to transcendental
  analysis.  It was a question of seeing a priori in a relation
  between quantities or transcendent functions, what exchanges one
  could make, which quantities one could substitute for the given
  quantities without the original relation ceasing to hold.  That
  immediately made clear the impossibility of finding many expressions
  that one could look for.  But I do not have time and my ideas are
  not yet well developed on this ground which is immense.

 — Evariste Galois, testamentary letter, translated by James Dolan

Thomas Mann on musical  ambiguity in his novel Doctor Faustus


Related material — Some context for the above and some remarks on the German original.

Sunday, August 15, 2010

The Game

Filed under: General — Tags: , , — m759 @ 11:07 PM
'Magister Ludi,' or 'The Glass Bead Game,' by Hermann Hesse

We shall now give a brief summary of the beginnings of the Glass Bead Game. It appears to have arisen simultaneously in Germany and in England. In both countries, moreover, it was originally a kind of exercise employed by those small groups of musicologists and musicians who worked and studied in the new seminaries of musical theory. If we compare the original state of the Game with its subsequent developments and its present form, it is much like comparing a musical score of the period before 1500, with its primitive notes and absence of bar lines, with an eighteenth-century score, let alone with one from the nineteenth with its confusing excess of symbols for dynamics, tempi, phrasing, and so on, which often made the printing of such scores a complex technical problem.

The Game was at first nothing more than a witty method for developing memory and ingenuity among students and musicians. And as we have said, it was played both in England and Germany before it was ‘invented’ here in the Musical Academy of Cologne, and was given the name it bears to this day, after so many generations, although it has long ceased to have anything to do with glass beads.

The inventor, Bastian Perrot of Calw, a rather eccentric but clever, sociable, and humane musicologist, used glass beads instead of letters, numerals, notes, or other graphic symbols. Perrot, who incidentally has also bequeathed to us a treatise on the Apogee and Decline of Counterpoint, found that the pupils at the Cologne Seminary had a rather elaborate game they used to play. One would call out, in the standardized abbreviations of their science, motifs or initial bars of classical compositions, whereupon the other had to respond with the continuation of the piece, or better still with a higher or lower voice, a contrasting theme, and so forth. It was an exercise in memory and improvisation quite similar to the sort of thing probably in vogue among ardent pupils of counterpoint in the days of Schütz, Pachelbel, and Bach — although it would then not have been done in theoretical formulas, but in practice on the cembalo, lute, or flute, or with the voice.

Bastian Perrot in all probability was a member of the Journeyers to the East. He was partial to handicrafts and had himself built several pianos and clavichords in the ancient style. Legend has it that he was adept at playing the violin in the old way, forgotten since 1800, with a high-arched bow and hand-regulated tension of the bow hairs. Given these interests, it was perhaps only natural that he should have constructed a frame, modeled on a child’s abacus, a frame with several dozen wires on which could be strung glass beads of various sizes, shapes, and colors. The wires corresponded to the lines of the musical staff, the beads to the time-values of the notes, and so on. In this way he could represent with beads musical quotations or invented themes, could alter, transpose, and develop them, change them and set them in counterpoint to one another. In technical terms this was a mere plaything, but the pupils liked it; it was imitated and became fashionable in England too. For a time the game of musical exercises was played in this charmingly primitive manner. And as is so often the case, an enduring and significant institution received its name from a passing and incidental circumstance. For what later evolved out of that students’ sport and Perrot’s bead-strung wires bears to this day the name by which it became popularly known, the Glass Bead Game.

Hermann Hesse

“For although in a certain sense and for light-minded persons non-existent things can be more easily and irresponsibly represented in words than existing things, for the serious and conscientious historian it is just the reverse. Nothing is harder, yet nothing is more necessary, than to speak of certain things whose existence is neither demonstrable nor probable. The very fact that serious and conscientious men treat them as existing things brings them a step closer to existence and to the possibility of being born.”

— “Albertus Secundus,” epigraph to The Glass Bead Game

From DownloadThat.com

(Click to enlarge.)


Sunday, August 8, 2010


Filed under: General — m759 @ 3:48 AM

From the preface to the inaugural issue of Tympanum: A Journal of Comparative Literary Studies

Regarding the choice of name for this journal, tympan or tympanum is a word that designates several objects at once. Tympan is perhaps first of all a typographical term: as a printer's term in early book production, a tympan designated "the iron frame covered with parchment on which the paper was placed." Taken as an anatomical term, the word tympanum is another term for the eardrum, the oblique stretching of tissue between the auditory canal and the middle ear that allows one to hear: to hear others, to hear music, or even to hear oneself speak. The tympanum is a partition of the ear that separates inside from outside, translating various tones and punctuations, a liminal membrane traversed by hearing others speak. In this instance, the tympanum is a tissue, a weave or web  that mediates hearing. It is by extension the term for the diaphragm of a tele-phone, that technological figure of the spatialization of the voice. As an architectural term tympanum names the pediment that sits atop the cornice or frieze of a building. And to this heterogeneous list one might add that in ancient Greece a tympanum, like the stoa or colonnades, was a gathering space for the discussion of philosophy. All these meanings could be enlisted to indicate the interests of this new journal.

By its very nature, a world wide web site would be a site of a mediation of or meditation on the problematic of space and place (in short: of "site" itself), and of their dislocation. In this way the web opens the possibility for a journal concerned with the problem of a mediated or textualized hearing.

Several of the articles contained in this first issue of Tympanum  share a thematic of location and of reading and hearing….

Deborah Levitt's essay on Heidegger and theatre, in its exploration of the problem of space and place, implicitly touches on the very medium of the web: the perpetual dislocation of place from space. Levitt couples several of Heidegger's writings together with Artaud's on her Freiburg-Paris Express. Levitt's meditation on theory and theatre is at once incisive and innovative, and locates its opening problematic in the substitution of a metaphysics of sight by site, a move which she says opens a spatiality. In a recent issue of Assemblage,  Sam Weber makes some remarks on the metaphysics of site that could indeed be used as a succinct introduction to the problems that Levitt's essay, Heidegger and the Theatre of Truth, engages:

If what we call "space" is, like the Platonic chora, on the one hand always already caught up in the process of making room  for that determinate other  of space that can be called place  or site,  and if, on the other hand, this process of making room  remains distinct from the particular places and sites it makes way for, then the emergence of the latter from the former will inevitably appear as a more or less violent event.  Violent, because the staking out of territory and the assignment of positions and posts can never simply legitimate itself in terms of preexisting borders. It cannot do this, since there is no original order to which such a process of partition might appeal without equivocation. In place  of such an origin, there is chora: the process of partition and repartition as such,  except that "as such" here is impossible to distinguish from: "as other." Such partition and repartition constitute the law,  the nomos,  of chora…3

3 Samuel Weber, "The Parallax View: Place and Space in Plato and Benjamin," Assemblage  20, MIT Press: 1993: 88.

The Tympanum  preface (1998) is by Peter Woodruff.

Wallace Stevens—

"The pediment
Lifts up its heavy scowl before them."

Scowl courtesy of Samuel Weber—


  • Author of "The Parallax View"
  • Assemblage, No. 20, Violence, Space
    (Apr., 1993), pp. 88-89
    (article consists of 2 pages)
  • Published by: The MIT Press

Saturday, July 10, 2010

A Manifold Showing

Filed under: General — m759 @ 7:11 AM

"Heidegger suggests that we experience the saying of language as a shining forth:

'It lets what is coming to presence shine forth, lets what is withdrawing into absence vanish.  The saying is by no means the supplemental linguistic expression of what shines forth; rather, all shining and fading depend on the saying that shows.' (pp. 413-414).

But what is the basis and origin of this possibility of saying?  The happening of saying in the clearing, its allowing things to shine forth, can also be called an 'owning.' Owning is the event of a thing’s coming into its own, of its showing itself as itself. Heidegger also calls it 'propriating,' 'en-owning,' or Ereignis:

'Propriation gathers the rift-design of the saying and unfolds it in such a way that it becomes the well-joined structure of a manifold showing. (p. 415)'"

— "Heidegger: On the Way to Language," by Paul Livingston

Page references are apparently to Heidegger's Basic Writings, edited by David Farrell Krell, HarperCollins paperback, 1993.

See also Shining Forth.

Wednesday, July 7, 2010

07 Book

Filed under: General — m759 @ 6:29 AM


A Talent for Writing, and Falling Into Things


The above headline from this morning's New York Times  is a rather strong reminder of a post linked to here last night—  a post from April 10, 2004 (Holy Saturday), titled "Harrowing."

The book under review is a biography of William Golding, also quoted here in "Harrowing."

From that post—

“There is a suggestion of Christ descending into the abyss for the harrowing of Hell.  But it is the Consul whom we think of here, rather than of Christ.  The Consul is hurled into this abyss at the end of the novel.”

– Stephen Spender, introduction to Malcolm Lowry's Under the Volcano

Related material:

Theater of Truth

 rift-design— Definition by Deborah Levitt

"Rift.  The stroke or rending by which a world worlds, opening both the 'old' world and the self-concealing earth to the possibility of a new world. As well as being this stroke, the rift is the site— the furrow or crack— created by the stroke. As the 'rift design' it is the particular characteristics or traits of this furrow."

– "Heidegger and the Theater of Truth," in Tympanum: A Journal of Comparative Literary Studies, Vol. 1, 1998

See also "harrow up" + Hamlet  in this journal.

Tuesday, July 6, 2010

What “As” Is

Filed under: General,Geometry — Tags: , , , , — m759 @ 8:00 PM

or:  Combinatorics (Rota) as Philosophy (Heidegger) as Geometry (Me)

“Dasein’s full existential structure is constituted by
the ‘as-structure’ or ‘well-joined structure’ of the rift-design*…”

— Gary Williams, post of January 22, 2010


Gian-Carlo Rota on Heidegger…

“… The universal as  is given various names in Heidegger’s writings….

The discovery of the universal as  is Heidegger’s contribution to philosophy….

The universal ‘as‘ is the surgence of sense in Man, the shepherd of Being.

The disclosure of the primordial as  is the end of a search that began with Plato….
This search comes to its conclusion with Heidegger.”

— “Three Senses of ‘A is B’ in Heideggger,” Ch. 17 in Indiscrete Thoughts

… and projective points as separating rifts

Image-- The Three-Point Line: A Finite Projective Space

    Click image for details.

* rift-design— Definition by Deborah Levitt

Rift.  The stroke or rending by which a world worlds, opening both the ‘old’ world and the self-concealing earth to the possibility of a new world. As well as being this stroke, the rift is the site— the furrow or crack— created by the stroke. As the ‘rift design‘ it is the particular characteristics or traits of this furrow.”

— “Heidegger and the Theater of Truth,” in Tympanum: A Journal of Comparative Literary Studies, Vol. 1, 1998

Wednesday, June 23, 2010

Group Theory and Philosophy

Filed under: General,Geometry — Tags: — m759 @ 5:01 PM

Excerpts from "The Concept of Group and the Theory of Perception,"
by Ernst Cassirer, Philosophy and Phenomenological Research,
Volume V, Number 1, September, 1944.
(Published in French in the Journal de Psychologie, 1938, pp. 368-414.)

The group-theoretical interpretation of the fundaments of geometry is,
from the standpoint of pure logic, of great importance, since it enables us to
state the problem of the "universality" of mathematical concepts in simple
and precise form and thus to disentangle it from the difficulties and ambigui-
ties with which it is beset in its usual formulation. Since the times of the
great controversies about the status of universals in the Middle Ages, logic
and psychology have always been troubled with these ambiguities….

Our foregoing reflections on the concept of group  permit us to define more
precisely what is involved in, and meant by, that "rule" which renders both
geometrical and perceptual concepts universal. The rule may, in simple
and exact terms, be defined as that group of transformations  with regard to
which the variation of the particular image is considered. We have seen
above that this conception operates as the constitutive principle in the con-
struction of the universe of mathematical concepts….

                                                              …Within Euclidean geometry,
a "triangle" is conceived of as a pure geometrical "essence," and this
essence is regarded as invariant with respect to that "principal group" of
spatial transformations to which Euclidean geometry refers, viz., displace-
ments, transformations by similarity. But it must always be possible to
exhibit any particular figure, chosen from this infinite class, as a concrete
and intuitively representable object. Greek mathematics could not
dispense with this requirement which is rooted in a fundamental principle
of Greek philosophy, the principle of the correlatedness of "logos" and
"eidos." It is, however, characteristic of the modern development of
mathematics, that this bond between "logos" and "eidos," which was indis-
soluble for Greek thought, has been loosened more and more, to be, in the
end, completely broken….

                                                            …This process has come to its logical
conclusion and systematic completion in the development of modern group-
theory. Geometrical figures  are no longer regarded as fundamental, as
date of perception or immediate intuition. The "nature" or "essence" of a
figure is defined in terms of the operations  which may be said to
generate the figure.
The operations in question are, in turn, subject to
certain group conditions….

                                                                                                    …What we
find in both cases are invariances with respect to variations undergone by
the primitive elements out of which a form is constructed. The peculiar
kind of "identity" that is attributed to apparently altogether heterogen-
eous figures in virtue of their being transformable into one another by means
of certain operations defining a group, is thus seen to exist also in the
domain of perception. This identity permits us not only to single out ele-
ments but also to grasp "structures" in perception. To the mathematical
concept of "transformability" there corresponds, in the domain of per-
ception, the concept of "transposability." The theory  of the latter con-
cept has been worked out step by step and its development has gone through
various stages….
                                                                                 …By the acceptance of
"form" as a primitive concept, psychological theory has freed it from the
character of contingency  which it possessed for its first founders. The inter-
pretation of perception as a mere mosaic of sensations, a "bundle" of simple
sense-impressions has proved untenable…. 

                             …In the domain of mathematics this state of affairs mani-
fests itself in the impossibility of searching for invariant properties of a
figure except with reference to a group. As long as there existed but one
form of geometry, i.e., as long as Euclidean geometry was considered as the
geometry kat' exochen  this fact was somehow concealed. It was possible
to assume implicitly  the principal group of spatial transformations that lies
at the basis of Euclidean geometry. With the advent of non-Euclidean
geometries, however, it became indispensable to have a complete and sys-
tematic survey of the different "geometries," i.e., the different theories of
invariancy that result from the choice of certain groups of transformation.
This is the task which F. Klein set to himself and which he brought to a
certain logical fulfillment in his Vergleichende Untersuchungen ueber neuere
geometrische Forschungen

                                                          …Without discrimination between the
accidental and the substantial, the transitory and the permanent, there
would be no constitution of an objective reality.

This process, unceasingly operative in perception and, so to speak, ex-
pressing the inner dynamics of the latter, seems to have come to final per-
fection, when we go beyond perception to enter into the domain of pure
thought. For the logical advantage and peculiar privilege of the pure con –
cept seems to consist in the replacement of fluctuating perception by some-
thing precise and exactly determined. The pure concept does not lose
itself in the flux of appearances; it tends from "becoming" toward "being,"
from dynamics toward statics. In this achievement philosophers have
ever seen the genuine meaning and value of geometry. When Plato re-
gards geometry as the prerequisite to philosophical knowledge, it is because
geometry alone renders accessible the realm of things eternal; tou gar aei
ontos he geometrike gnosis estin
. Can there be degrees or levels of objec-
tive knowledge in this realm of eternal being, or does not rather knowledge
attain here an absolute maximum? Ancient geometry cannot but answer
in the affirmative to this question. For ancient geometry, in the classical
form it received from Euclid, there was such a maximum, a non plus ultra.
But modern group theory thinking has brought about a remarkable change
In this matter. Group theory is far from challenging the truth of Euclidean
metrical geometry, but it does challenge its claim to definitiveness. Each
geometry is considered as a theory of invariants of a certain group; the
groups themselves may be classified in the order of increasing generality.
The "principal group" of transformations which underlies Euclidean geome-
try permits us to establish a number of properties that are invariant with
respect to the transformations in question. But when we pass from this
"principal group" to another, by including, for example, affinitive and pro-
jective transformations, all that we had established thus far and which,
from the point of view of Euclidean geometry, looked like a definitive result
and a consolidated achievement, becomes fluctuating again. With every
extension of the principal group, some of the properties that we had taken
for invariant are lost. We come to other properties that may be hierar-
chically arranged. Many differences that are considered as essential
within ordinary metrical geometry, may now prove "accidental." With
reference to the new group-principle they appear as "unessential" modifica-

                 … From the point of view of modern geometrical systematization,
geometrical judgments, however "true" in themselves, are nevertheless not
all of them equally "essential" and necessary. Modern geometry
endeavors to attain progressively to more and more fundamental strata of
spatial determination. The depth of these strata depends upon the com-
prehensiveness of the concept of group; it is proportional to the strictness of
the conditions that must be satisfied by the invariance that is a universal
postulate with respect to geometrical entities. Thus the objective truth
and structure of space cannot be apprehended at a single glance, but have to
be progressively  discovered and established. If geometrical thought is to
achieve this discovery, the conceptual means that it employs must become
more and more universal….

Monday, June 14, 2010

Theory of Ambiguity

Filed under: General,Geometry — m759 @ 5:01 PM

Théorie de l'Ambiguité

According to a 2008 paper by Yves André of the École Normale Supérieure  of Paris—

"Ambiguity theory was the name which Galois used
 when he referred to his own theory and its future developments."

The phrase "the theory of ambiguity" occurs in the testamentary letter Galois wrote to a friend, Auguste Chevalier, on the night before Galois was shot in a duel.

Hermann Weyl in Symmetry, Princeton University Press, 1952—

"This letter, if judged by the novelty and profundity of ideas it contains, is perhaps
  the most substantial piece of writing in the whole literature of mankind."

Conclusion of the Galois testamentary letter, according to
the 1897 Paris edition of Galois's collected works—

Image-- Galois on his theory of ambiguity, from Collected Works, Paris, 1897

The original—

Image-- Concluding paragraphs, Galois's 'last testament' letter to Chevalier, May 29, 1832

A transcription—

Évariste GALOIS, Lettre-testament, adressée à Auguste Chevalier—

Tu sais mon cher Auguste, que ces sujets ne sont pas les seuls que j'aie
explorés. Mes principales méditations, depuis quelques temps,
étaient dirigées sur l'application à l'analyse transcendante de la théorie de
l'ambiguité. Il s'agissait de voir a priori, dans une relation entre des quantités
ou fonctions transcendantes, quels échanges on pouvait faire, quelles
quantités on pouvait substituer aux quantités données, sans que la relation
put cesser d'avoir lieu. Cela fait reconnaitre de suite l'impossibilité de beaucoup
d'expressions que l'on pourrait chercher. Mais je n'ai pas le temps, et mes idées
ne sont pas encore bien développées sur ce terrain, qui est

Tu feras imprimer cette lettre dans la Revue encyclopédique.

Je me suis souvent hasardé dans ma vie à avancer des propositions dont je n'étais
pas sûr. Mais tout ce que j'ai écrit là est depuis bientôt un an dans ma
tête, et il est trop de mon intérêt de ne pas me tromper pour qu'on
me soupconne d'avoir énoncé des théorèmes dont je n'aurais pas la démonstration

Tu prieras publiquement Jacobi et Gauss de donner leur avis,
non sur la vérité, mais sur l'importance des théorèmes.

Après cela, il y aura, j'espère, des gens qui trouveront leur profit
à déchiffrer tout ce gachis.

Je t'embrasse avec effusion.

                                               E. Galois   Le 29 Mai 1832

A translation by Dr. Louis Weisner, Hunter College of the City of New York, from A Source Book in Mathematics, by David Eugene Smith, Dover Publications, 1959–

You know, my dear Auguste, that these subjects are not the only ones I have explored. My reflections, for some time, have been directed principally to the application of the theory of ambiguity to transcendental analysis. It is desired see a priori  in a relation among quantities or transcendental functions, what transformations one may make, what quantities one may substitute for the given quantities, without the relation ceasing to be valid. This enables us to recognize at once the impossibility of many expressions which we might seek. But I have no time, and my ideas are not developed in this field, which is immense.

Print this letter in the Revue Encyclopédique.

I have often in my life ventured to advance propositions of which I was uncertain; but all that I have written here has been in my head nearly a year, and it is too much to my interest not to deceive myself that I have been suspected of announcing theorems of which I had not the complete demonstration.

Ask Jacobi or Gauss publicly to give their opinion, not as to the truth, but as to the importance of the theorems.

Subsequently there will be, I hope, some people who will find it to their profit to decipher all this mess.

J t'embrasse avec effusion.
                                                     E. Galois.   May 29, 1832.

Translation, in part, in The Unravelers: Mathematical Snapshots, by Jean Francois Dars, Annick Lesne, and Anne Papillaut (A.K. Peters, 2008)–

"You know, dear Auguste, that these subjects are not the only ones I have explored. For some time my main meditations have been directed on the application to transcendental analysis of the theory of ambiguity. The aim was to see in a relation between quantities or transcendental functions, what exchanges we could make, what quantities could be substituted to the given quantities without the relation ceasing to take place. In that way we see immediately that many expressions that we might look for are impossible. But I don't have the time and my ideas are not yet developed enough in this vast field."

Another translation, by James Dolan at the n-Category Café

"My principal meditations for some time have been directed towards the application of the theory of ambiguity to transcendental analysis. It was a question of seeing a priori in a relation between quantities or transcendent functions, what exchanges one could make, which quantities one could substitute for the given quantities without the original relation ceasing to hold. That immediately made clear the impossibility of finding many expressions that one could look for. But I do not have time and my ideas are not yet well developed on this ground which is immense."

Related material

"Renormalisation et Ambiguité Galoisienne," by Alain Connes, 2004

"La Théorie de l’Ambiguïté : De Galois aux Systèmes Dynamiques," by Jean-Pierre Ramis, 2006

"Ambiguity Theory, Old and New," preprint by Yves André, May 16, 2008,

"Ambiguity Theory," post by David Corfield at the n-Category Café, May 19, 2008

"Measuring Ambiguity," inaugural lecture at Utrecht University by Gunther Cornelissen, Jan. 16, 2009

Saturday, May 8, 2010

A Better Story —

Filed under: General — Tags: — m759 @ 1:00 PM

Or, “Get me rewrite!”

Today’s New York Times online–

Rebecca Newberger Goldstein imagines a story about academics discussing literary theory—

“Rumors had reached us of a doctrine called Theory emanating from distant corners of the university. We in the Department of Philosophy understood it immediately as a grand hoax. I will not dwell on my particular amusement, in which I was so tragically at odds with my collaborator, Theo Rhee….

… It was at this moment that Hans Furth appeared and ambled over….”

And thanks to Google Books, here he is—

“…I can imagine the decisive evolutionary beginnings of humans and societies… not in an adult version, but in the playful mentality of children…. An unlikely story? Perhaps. I am looking out for a better story.”

Hans G. Furth, Desire for Society: Children’s Knowledge as Social Imagination, published by Springer, 1996, p. 181

As am I. (See previous post.) One possibility, from 1943— “Mimsy Were the Borogoves.”

Another possibility, from 1953—  not Theo Rhee, but rather “Loo Ree.”

Friday, April 16, 2010

The Craft, continued

Filed under: General — m759 @ 2:22 PM

Image--Movie poster for 'The Craft'

"Honesty's the best policy."
— Miguel de Cervantes   

"Liars prosper."
— Anonymous   

— Epigraphs to On Writing:
A Memoir of the Craft
by Stephen King

Lavender Blue,
Dilly, Dilly,
Lavender Green…
Image-- Spacek as Carrie

The cruelest month continues…

"…as Newton conceived it, the distinction between
the individualities of two particles is so marked that
it is impossible for them ever to coincide or for
either of them to alter the being of the other…."

"Waves interfere with each other because they are
interchangeable and thus not distinguishable;
two processes can coincide in space and time
but two substances cannot. Thus the wave
reveals a whole new possibility of identity…."

"The concept of a field is elusive."

— Peter Pesic, Seeing Double: Shared Identities
in Physics, Philosophy, and Literature
Chapter 6, "The Fields of Light"

Sunday, April 4, 2010

Virgil Vigil

Filed under: General — m759 @ 1:00 AM

Two definitions–

"In Dante's Inferno  the Harrowing of Hell is mentioned in Canto IV by the pilgrim's guide Virgil." —Wikipedia

"The Easter Vigil…. is held in the hours of darkness between sunset on Holy Saturday and sunrise on Easter Day." —Wikipedia

Two more, of acronyms coined by Philip Rieff

"Rieff is critical of the present 'pop' culture that glories in the 'primacies of possibility' and prefers 'both/and' to 'either/or.' … the 'via'— the 'vertical in authority'—… teaches us our place as we assent to and ascend on via’s ladder." —Philip Manning

Related material:


The infinity symbol, as sketched in a touching
attempt at scholarship by the late
"both/and" novelist David Foster Wallace


The Cartesian cross


The lemniscate


Lemniscate with Cartesian cross

A more traditional symbol
that has been described as
  the cross of St. Boniface
See also The Eight, a novel
by Katherine Neville related
to today's date, 4/4–

Saturday, February 13, 2010

Entertainment continued

Filed under: General,Geometry — m759 @ 9:28 AM

Logic is all about the entertaining of possibilities.”

– Colin McGinn, Mindsight: Image, Dream, Meaning,
   Harvard University Press, 2004

Geometry of Language,
continued from St. George's Day, 2009

Professor Arielle Saiber with chess set

Excerpt from Jasper Hopkins's 'Concise Introduction to the Philosophy of Nicholas of Cusa

Related material:

Prima Materia,
The Galois Quaternion,
and The Wake of Imagination.

See also the following from a physicist
(not of the most orthodox sort, but his remarks
  here on Heisenberg seem quite respectable)–

Ian J. Thompson, 7 Dec. 2009

Quantum mechanics describes the probabilities of actual outcomes in terms of a wave function, or at least of a quantum state of amplitudes that varies with time. The public always asks what the wave function is, or what the amplitudes are amplitudes of. Usually, we reply that the amplitudes are ‘probability amplitudes’, or that the wave function is a ‘probability wave function’, but neither answer is ontologically satisfying since probabilities are numbers, not stuff. We have already rehearsed the objections to the natural world being made out of numbers, as these are pure forms. In fact, ‘waves’, ‘amplitudes’ and ‘probabilities’ are all forms, and none of them can be substances. So, what are quantum objects made of: what stuff?

According to Heisenberg [6], the quantum probability waves are “a quantitative formulation of the concept of ‘dynamis’, possibility, or in the later Latin version, ‘potentia’, in Aristotle’s philosophy. The concept of events not determined in a peremptory manner, but that the possibility or ‘tendency’ for an event to take place has a kind of reality—a certain intermediate layer of reality, halfway between the massive reality of matter and the intellectual reality of the idea or the image—this concept plays a decisive role in Aristotle’s philosophy. In modern quantum theory this concept takes on a new form; it is formulated quantitatively as probability and subjected to mathematically expressible laws of nature.” Unfortunately Heisenberg does not develop this interpretation much beyond the sort of generality of the above statements, and the concept of ‘potentiality’ remains awkwardly isolated from much of his other thought on this subject [7]. It is unclear even what he means by ‘potentia’.


Heisenberg, W. 1961 On Modern Physics, London: Orion Press.


[6] W. Heisenberg, ‘Planck’s discovery and the philosophical problems of atomic physics’, pp. 3-20 in Heisenberg (1961).

[7] Heisenberg, for example, brings into his thought on quantum physics the Kantian phenomena/noumena distinction, as well as some of Bohr’s ideas on ‘complementarity’ in experimental arrangements.

Friday, December 25, 2009

Brightness at Noon

Filed under: General,Geometry — m759 @ 12:00 PM

New York Times online front page
Christmas morning:

“Arthur Koestler, Man of Darkness”–

NY Times front page, Christmas morning 2009

The photo is of Koestler in 1931 on a zeppelin expedition to the North Pole.

The Act of Creation is, I believe, a more truly creative work than any of Koestler’s novels….  According to him, the creative faculty in whatever form is owing to a circumstance which he calls ‘bisociation.’ And we recognize this intuitively whenever we laugh at a joke, are dazzled by a fine metaphor, are astonished and excited by a unification of styles, or ’see,’ for the first time, the possibility of a significant theoretical breakthrough in a scientific inquiry. In short, one touch of genius—or bisociation—makes the whole world kin. Or so Koestler believes.”

– Henry David Aiken, The Metaphysics of Arthur Koestler, New York Review of Books, Dec. 17, 1964

From Opus Postumum by Immanuel Kant, Eckart Förster, Cambridge U. Press, 1995, p. 260:

“In January 1697, Leibniz accompanied his New Year Congratulations to Rudolf August with the design of a medal with the duke’s likeness on one side, and the ‘image of Creation’ in terms of the binary number system on the other. Concerning the inscription on this side, Leibniz writes: ‘I have thought for a while about the Motto dell’impresa and finally have found it good to write this line: omnibus ex nihilo ducendis SUFFICIT UNUM [To make all things from nothing, UNITY SUFFICES], because it clearly indicates what is meant by the symbol, and why it is imago creationis’ (G. F. Leibniz, Zwei Briefe über das binäre Zahlensystem und die chinesische Philosophie, ed. Renate Loosen and Franz Vonessen, Chr. Belser Verlag: Stuttgart 1968, p. 21).”

Leibniz, design for medallion showing binary numbers as an 'imago creationis'

Figure from Rudolf  Nolte’s
Gottfried Wilhelms Baron von Leibniz
Mathematischer Beweis der Erschaffung und
Ordnung der Welt in einem Medallion…
(Leipzig: J. C. Langenheim, 1734).

Leibniz, letter of 1697:

“And so that I won’t come entirely empty-handed this time, I enclose a design of that which I had the pleasure of discussing with you recently. It is in the form of a memorial coin or medallion; and though the design is mediocre and can be improved in accordance with your judgment, the thing is such, that it would be worth showing in silver now and unto future generations, if it were struck at your Highness’s command. Because one of the main points of the Christian Faith, and among those points that have penetrated least into the minds of the worldly-wise and that are difficult to make with the heathen is the creation of all things out of nothing through God’s omnipotence, it might be said that nothing is a better analogy to, or even demonstration of such creation than the origin of numbers as here represented, using only unity and zero or nothing. And it would be difficult to find a better illustration of this secret in nature or philosophy; hence I have set on the medallion design IMAGO CREATIONIS [in the image of creation]. It is no less remarkable that there appears therefrom, not only that God made everything from nothing, but also that everything that He made was good; as we can see here, with our own eyes, in this image of creation. Because instead of there appearing no particular order or pattern, as in the common representation of numbers, there appears here in contrast a wonderful order and harmony which cannot be improved upon….

Such harmonious order and beauty can be seen in the small table on the medallion up to 16 or 17; since for a larger table, say to 32, there is not enough room. One can further see that the disorder, which one imagines in the work of God, is but apparent; that if one looks at the matter with the proper perspective, there appears symmetry, which encourages one more and more to love and praise the wisdom, goodness, and beauty of the highest good, from which all goodness and beauty has flowed.”

See also Parable.

Wednesday, December 2, 2009

I thought I heard them say, “Welcome to…”

Filed under: General — m759 @ 11:30 AM


The William James Hotel

Charles A.  Hobbs,

paper at William James Studies

"There are at least two well known examples that James employs to illustrate what is meant by this formulation of pragmatism. Returning here to pragmatic method, the second of these, drawn from the Italian thinker Giovanni Papini, is meant to illustrate how this method is compatible with a number of varying results, that is, how this method is one of pluralism.26 With a remarkable illustration of the meaning of pragmatism, we are asked to understand James's pragmatic method as being like a hotel corridor, one whose doors lead to numerous rooms in which there are thinkers involved with numerous types of projects and pursuits. There could, for example, be a metaphysical idealist in one room and a committed anti-metaphysical thinker in another, both in the same hotel. In any case, James holds that his pragmatic method remains neutral with regard to the various types of thought taking place within the rooms.27

The hotel represents a great deal of the world of thinking.28 The various rooms represent individual philosophies. Of course, the corridor represents pragmatism, which is the connection between these, the philosophical method of choice and action. We might also say that pragmatism affords us our one chance at escaping the isolation of the individual rooms. This corridor method allows one to move from one concept or theory to another concept or theory. It does so insofar as it offers a concrete manner in which to comprehend, enter, or 'penetrate' a given theory, and in which to step outside of the theory so to test and contrast it with other theories. That is, to enter or leave their various rooms, the varying occupants must employ the pragmatic method.

Accordingly, we see that, for James, pragmatism is not a set doctrine. Again, it is a method, one that allows for a great many differing views to co-exist under the same umbrella, for pragmatism '…has no dogmas, and no doctrines save its method.'"29

26 The Writings of William James: A Comprehensive Edition, ed. John J. McDermott (Chicago: The University of Chicago Press, 1977), p. 380.

27 Following Papini, James says that pragmatic method "Lies in the midst of our theories, like a corridor in a hotel. Innumerable chambers open out of it. In one you may find a man writing an atheistic volume; in the next some one on his knees praying for faith and strength; in a third a chemist investigating a body's properties. In a fourth a system of idealistic metaphysics is being excogitated; in a fifth the impossibility of metaphysics is being shown. But they all own the corridor, and all must pass through it if they want a practicable way of getting into or out of their respective rooms." Ibid.

28 Not included would be dogmatists such as dictators and/or theocrats, for they are fundamentally closed to inquiry.

29 The Writings of William James, p. 380.

Tuesday, August 18, 2009

Tuesday August 18, 2009

Filed under: General,Geometry — Tags: — m759 @ 12:00 PM

Prima Materia

(Background: Art Humor: Sein Feld (March 11, 2009) and Ides of March Sermon, 2009)

From Cardinal Manning’s review of Kirkman’s Philosophy Without Assumptions

“And here I must confess… that between something and nothing I can find no intermediate except potentia, which does not mean force but possibility.”

— Contemporary Review, Vol. 28 (June-November, 1876), page 1017


Cardinal Manning, Contemporary Review, Vol. 28, pages 1026-1027:

The following will be, I believe, a correct statement of the Scholastic teaching:–

1. By strict process of reason we demonstrate a First Existence, a First Cause, a First Mover; and that this Existence, Cause, and Mover is Intelligence and Power.

2. This Power is eternal, and from all eternity has been in its fullest amplitude; nothing in it is latent, dormant, or in germ: but its whole existence is in actu, that is, in actual perfection, and in complete expansion or actuality. In other words God is Actus Purus, in whose being nothing is potential, in potentia, but in Him all things potentially exist.

3. In the power of God, therefore, exists the original matter (prima materia) of all things; but that prima materia is pura potentia, a nihilo distincta, a mere potentiality or possibility; nevertheless, it is not a nothing, but a possible existence. When it is said that the prima materia of all things exists in the power of God, it does not mean that it is of the existence of God, which would involve Pantheism, but that its actual existence is possible.

4. Of things possible by the power of God, some come into actual existence, and their existence is determined by the impression of a form upon this materia prima. The form is the first act which determines the existence and the species of each, and this act is wrought by the will and power of God. By this union of form with the materia prima, the materia secunda or the materia signata is constituted.

5. This form is called forma substantialis because it determines the being of each existence, and is the root of all its properties and the cause of all its operations.

6. And yet the materia prima has no actual existence before the form is impressed. They come into existence simultaneously;

[p. 1027 begins]

as the voice and articulation, to use St. Augustine’s illustration, are simultaneous in speech.

7. In all existing things there are, therefore, two principles; the one active, which is the form– the other passive, which is the matter; but when united, they have a unity which determines the existence of the species. The form is that by which each is what it is.

8. It is the form that gives to each its unity of cohesion, its law, and its specific nature.*

When, therefore, we are asked whether matter exists or no, we answer, It is as certain that matter exists as that form exists; but all the phenomena which fall under sense prove the existence of the unity, cohesion, species, that is, of the form of each, and this is a proof that what was once in mere possibility is now in actual existence. It is, and that is both form and matter.

When we are further asked what is matter, we answer readily, It is not God, nor the substance of God; nor the presence of God arrayed in phenomena; nor the uncreated will of God veiled in a world of illusions, deluding us with shadows into the belief of substance: much less is it catter [pejorative term in the book under review], and still less is it nothing. It is a reality, the physical kind or nature of which is as unknown in its quiddity or quality as its existence is certainly known to the reason of man.

* “… its specific nature”
        (Click to enlarge) —

Footnote by Cardinal Manning on Aquinas
The Catholic physics expounded by Cardinal Manning above is the physics of Aristotle.

For a more modern treatment of these topics, see Werner Heisenberg’s Physics and Philosophy. For instance:

“The probability wave of Bohr, Kramers, Slater, however, meant… a tendency for something. It was a quantitative version of the old concept of ‘potentia’ in Aristotelian philosophy. It introduced something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and reality.”

Compare to Cardinal Manning’s statement above:

“… between something and nothing I can find no intermediate except potentia…”

To the mathematician, the cardinal’s statement suggests the set of real numbers between 1 and 0, inclusive, by which probabilities are measured. Mappings of purely physical events to this set of numbers are perhaps better described by applied mathematicians and physicists than by philosophers, theologians, or storytellers. (Cf. Voltaire’s mockery of possible-worlds philosophy and, more recently, The Onion‘s mockery of the fictional storyteller Fournier’s quantum flux. See also Mathematics and Narrative.)

Regarding events that are not purely physical– those that have meaning for mankind, and perhaps for God– events affecting conception, birth, life, and death– the remarks of applied mathematicians and physicists are often ignorant and obnoxious, and very often do more harm than good. For such meaningful events, the philosophers, theologians, and storytellers are better guides. See, for instance, the works of Jung and those of his school. Meaningful events sometimes (perhaps, to God, always) exhibit striking correspondences. For the study of such correspondences, the compact topological space [0, 1] discussed above is perhaps less helpful than the finite Galois field GF(64)– in its guise as the I Ching. Those who insist on dragging God into the picture may consult St. Augustine’s Day, 2006, and Hitler’s Still Point.

Friday, March 20, 2009

Friday March 20, 2009

Filed under: General — Tags: — m759 @ 11:07 AM
Happy Birthday,
Holly Hunter

Epigraph to The Glass Bead Game:

Non entia enim licet quodammodo levibusque hominibus facilius atque incuriosius verbis reddere quam entia, veruntamen pio diligentique rerum scriptori plane aliter res se habet: nihil tantum repugnat ne verbis illustretur, at nihil adeo necesse est ante hominum oculos proponere ut certas quasdam res, quas esse neque demonstrari neque probari potest, quae contra eo ipso, quod pii diligentesque viri illas quasi ut entia tractant, enti nascendique facultati paululum appropinquant.
           tract. de cristall. spirit.
           ed. Clangor et Collof. lib. I, cap. 28.

In Joseph Knecht’s holograph translation:.

For although in a certain sense and for light-minded persons non-existent things can be more easily and irresponsibly represented in words than existing things, for the serious and conscientious historian it is just the reverse. Nothing is harder, yet nothing is more necessary, than to speak of certain things whose existence is neither demonstrable nor probable. The very fact that serious and conscientious men treat them as existing things brings them a step closer to existence and to the possibility of being born.

Video -- 'The  Piano,' Part 11

Saturday, March 7, 2009

Saturday March 7, 2009

Filed under: General,Geometry — Tags: , , — m759 @ 12:00 PM

One or Two Ideas
Today's birthday: Piet Mondrian
From James Joyce's A Portrait of the Artist as a Young Man:

he hearth and began to stroke his chin.

–When may we expect to have something from you on the esthetic question? he asked.

–From me! said Stephen in astonishment. I stumble on an idea once a fortnight if I am lucky.

–These questions are very profound, Mr Dedalus, said the dean. It is like looking down from the cliffs of Moher into the depths. Many go down into the depths and never come up. Only the trained diver can go down into those depths and explore them and come to the surface again.

–If you mean speculation, sir, said Stephen, I also am sure that there is no such thing as free thinking inasmuch as all thinking must be bound by its own laws.


–For my purpose I can work on at present by the light of one or two ideas of Aristotle and Aquinas.

–I see. I quite see your point.

Besides being Mondrian's birthday, today is also the dies natalis (in the birth-into-heaven sense) of St. Thomas Aquinas and, for those who believe worthy pre-Christians also enter heaven, possibly of Aristotle.

Pope Benedict XVI explained the dies natalis concept on Dec. 26, 2006:

"For believers the day of death, and even more the day of martyrdom, is not the end of all; rather, it is the 'transit' towards immortal life. It is the day of definitive birth, in Latin, dies natalis."

The Pope's remarks on that date
were in St. Peter's Square.
From this journal on that date,
a different square —
The Seventh Symbol:

Box symbol

Pictorial version
of Hexagram 20,
Contemplation (View)

The square may be regarded as
symbolizing art itself.
(See Nov.30 – Dec.1, 2008.)

In honor of
Aristotle and Aquinas,
here is a new web site,
with versions of the diamond shape
made famous by Mondrian

Cover of  Mondrian: The Diamond Compositions

— a shape symbolizing
possibility within modal logic
 as well as the potentiality of
 Aristotle's prima materia.

Thursday, January 15, 2009

Thursday January 15, 2009

Filed under: General — Tags: — m759 @ 6:00 PM
Harvard, Magic,
and The New York Times

The New York Times Magazine for next Sunday:

The Edge of the Mystery, by Matt Bai–

“Weeks before the election of 1960, Norman Mailer, already an accomplished novelist, sat down to write his first major work of political journalism, an essay for Esquire in which he argued that only John F. Kennedy could save America… the only kind of leader who could rescue it, who could sweep in an era of what Mailer called ‘existential’ politics, was a ‘hipster’ hero– someone who welcomed risk and adventure, someone who sought out new experience, both for himself and for the country….

… Mailer essentially created a new genre for a generation of would-be literary philosophers covering politics….  By 1963, Mailer and other idealists were crushed to discover that Kennedy was in fact a fairly conventional and pragmatic politician, more Harvard Yard than Fortress of Solitude.”

The New York Times today:

Magic and Realism, by Roger Cohen–

“… what I want from the Obama administration is something more than Harvard-to-the-Beltway smarts. I want magical realism.”

Mailer and Cohen, taken together, suggest I should review two authors– Picard and Hesse– I encountered as a Harvard freshman in 1960.

Max Picard:

“In the ‘Prologue in Heaven’ in Goethe’s Faust a powerful silence is produced by the powerful word after each verse. There is an active, audible silence after every verse. The things that were moved into position by the word stand motionless in the silence, as if they were waiting to be called back into the silence and to disappear therein. The word not only brings the things out of silence; it also produces the silence in which they can disappear again.”


Kennst du den Faust?

Den Doktor?

Meinen Knecht!

Online Etymology Dictionary:

O.E. cniht “boy, youth, servant,” common W.Gmc. (cf. O.Fris. kniucht, Du. knecht, kneht “boy, youth, lad,” Ger. Knecht “servant, bondsman, vassal”), of unknown origin. Meaning “military follower of a king or other superior” is from c.1100. Began to be used in a specific military sense in Hundred Years War, and gradually rose in importance through M.E. period until it became a rank in the nobility 16c. The verb meaning “to make a knight of (someone)” is from c.1300. Knighthood is O.E. cnihthad M.H.G. “the period between childhood and manhood;” sense of “rank or dignity of a knight” is from c.1300. The chess piece so called from c.1440.

Further background on the word “Knecht”–

'Magister Ludi,' or 'The Glass Bead Game,' by Hermann Hesse

Epigraph to Magister Ludi
(Joseph Knecht’s translation):

“… For although in a certain sense and for light-minded persons non-existent things can be more easily and irresponsibly represented in words than existing things, for the serious and conscientious historian it is just the reverse. Nothing is harder, yet nothing is more necessary, than to speak of certain things whose existence is neither demonstrable nor probable. The very fact that serious and conscientious men treat them as existing things brings them a step closer to existence and to the possibility of being born.”

Wednesday, October 22, 2008

Wednesday October 22, 2008

Filed under: General,Geometry — m759 @ 9:26 AM
Euclid vs. Galois

On May 4, 2005, I wrote a note about how to visualize the 7-point Fano plane within a cube.

Last month, John Baez
showed slides that touched on the same topic. This note is to clear up possible confusion between our two approaches.

From Baez’s Rankin Lectures at the University of Glasgow:

(Click to enlarge)

John Baez, drawing of seven vertices of a cube corresponding to Fano-plane points

Note that Baez’s statement (pdf) “Lines in the Fano plane correspond to planes through the origin [the vertex labeled ‘1’] in this cube” is, if taken (wrongly) as a statement about a cube in Euclidean 3-space, false.

The statement is, however, true of the eightfold cube, whose eight subcubes correspond to points of the linear 3-space over the two-element field, if “planes through the origin” is interpreted as planes within that linear 3-space, as in Galois geometry, rather than within the Euclidean cube that Baez’s slides seem to picture.

This Galois-geometry interpretation is, as an article of his from 2001 shows, actually what Baez was driving at. His remarks, however, both in 2001 and 2008, on the plane-cube relationship are both somewhat trivial– since “planes through the origin” is a standard definition of lines in projective geometry– and also unrelated– apart from the possibility of confusion– to my own efforts in this area. For further details, see The Eightfold Cube.

Tuesday, August 19, 2008

Tuesday August 19, 2008

Filed under: General,Geometry — Tags: , — m759 @ 8:30 AM
Three Times

"Credences of Summer," VII,

by Wallace Stevens, from
Transport to Summer (1947)

"Three times the concentred
     self takes hold, three times
The thrice concentred self,
     having possessed
The object, grips it
     in savage scrutiny,
Once to make captive,
     once to subjugate
Or yield to subjugation,
     once to proclaim
The meaning of the capture,
     this hard prize,
Fully made, fully apparent,
     fully found."

Stevens does not say what object he is discussing.

One possibility

Bertram Kostant, Professor Emeritus of Mathematics at MIT, on an object discussed in a recent New Yorker:

"A word about E(8). In my opinion, and shared by others, E(8) is the most magnificent 'object' in all of mathematics. It is like a diamond with thousands of facets. Each facet offering a different view of its unbelievable intricate internal structure."

Another possibility

The 4x4 square

  A more modest object —
the 4×4 square.

Update of Aug. 20-21 —

Symmetries and Facets

Kostant's poetic comparison might be applied also to this object.

The natural rearrangements (symmetries) of the 4×4 array might also be described poetically as "thousands of facets, each facet offering a different view of… internal structure."

More precisely, there are 322,560 natural rearrangements– which a poet might call facets*— of the array, each offering a different view of the array's internal structure– encoded as a unique ordered pair of symmetric graphic designs. The symmetry of the array's internal structure is reflected in the symmetry of the graphic designs. For examples, see the Diamond 16 Puzzle.

For an instance of Stevens's "three times" process, see the three parts of the 2004 web page Ideas and Art.

* For the metaphor of rearrangements as facets, note that each symmetry (rearrangement) of a Platonic solid corresponds to a rotated facet: the number of symmetries equals the number of facets times the number of rotations (edges) of each facet–

Platonic solids' symmetry groups

The metaphor of rearrangements as facets breaks down, however, when we try to use it to compute, as above with the Platonic solids, the number of natural rearrangements, or symmetries, of the 4×4 array. Actually, the true analogy is between the 16 unit squares of the 4×4 array, regarded as the 16 points of a finite 4-space (which has finitely many symmetries), and the infinitely many points of Euclidean 4-space (which has infinitely many symmetries).

If Greek geometers had started with a finite space (as in The Eightfold Cube), the history of mathematics might have dramatically illustrated Halmos's saying (Aug. 16) that

"The problem is– the genius is– given an infinite question, to think of the right finite question to ask. Once you thought of the finite answer, then you would know the right answer to the infinite question."

The Greeks, of course, answered the infinite questions first– at least for Euclidean space. Halmos was concerned with more general modern infinite spaces (such as Hilbert space) where the intuition to be gained from finite questions is still of value.

Wednesday, July 30, 2008

Wednesday July 30, 2008

Filed under: General,Geometry — m759 @ 11:48 AM
Theories of Everything

Ashay Dharwadker now has a Theory of Everything.
Like Garrett Lisi’s, it is based on an unusual and highly symmetric mathematical structure. Lisi’s approach is related to the exceptional simple Lie group E8.* Dharwadker uses a structure long associated with the sporadic simple Mathieu group M24.



by Ashay Dharwadker


“We show that the mathematical proof of the four colour theorem [1] directly implies the existence of the standard model, together with quantum gravity, in its physical interpretation. Conversely, the experimentally observable standard model and quantum gravity show that nature applies the mathematical proof of the four colour theorem, at the most fundamental level. We preserve all the established working theories of physics: Quantum Mechanics, Special and General Relativity, Quantum Electrodynamics (QED), the Electroweak model and Quantum Chromodynamics (QCD). We build upon these theories, unifying all of them with Einstein’s law of gravity. Quantum gravity is a direct and unavoidable consequence of the theory. The main construction of the Steiner system in the proof of the four colour theorem already defines the gravitational fields of all the particles of the standard model. Our first goal is to construct all the particles constituting the classic standard model, in exact agreement with t’Hooft’s table [8]. We are able to predict the exact mass of the Higgs particle and the CP violation and mixing angle of weak interactions. Our second goal is to construct the gauge groups and explicitly calculate the gauge coupling constants of the force fields. We show how the gauge groups are embedded in a sequence along the cosmological timeline in the grand unification. Finally, we calculate the mass ratios of the particles of the standard model. Thus, the mathematical proof of the four colour theorem shows that the grand unification of the standard model with quantum gravity is complete, and rules out the possibility of finding any other kinds of particles.”

* See, for instance, “The Scientific Promise of Perfect Symmetry” in The New York Times of March 20, 2007.

Thursday, May 8, 2008

Thursday May 8, 2008

Filed under: General — m759 @ 4:48 PM
Part Deux

Footprints at Log24 on the afternoon of May 8, 2008, including two from France

“On the Holy Trinity,”
the entry in the 3:20 PM
French footprint:

“…while the scientist sees
everything that happens
in one point of space,
the poet feels
everything that happens
in one point of time…
all forming an
instantaneous and transparent
organism of events….”

Vladimir Nabokov

“Angel in the Details,”
 the entry in the 3:59 PM
French footprint:

“I dwell in Possibility
A fairer House than Prose”

Emily Dickinson

These, along with this afternoon’s
earlier entry, suggest a review
of a third Log24 item, Windmills,
with an actress from France as…

Changing Woman:

“Kaleidoscope turning…

Juliette Binoche in 'Blue'  The 24 2x2 Cullinane Kaleidoscope animated images

Shifting pattern
within unalterable structure…”
— Roger Zelazny, Eye of Cat  

“When life itself seems lunatic,
who knows where madness lies?”

— For the source, see 
Joyce’s Nightmare Continues.

Wednesday, December 26, 2007

Wednesday December 26, 2007

Filed under: General — m759 @ 12:00 PM
A Wonderful Life

Part I:
Language Games

on December 19:


See also the noir entry on
“Nightmare Alley” for
Winter Solstice 2002,
as well as a solstice-related
commentary on I Ching
Hexagram 41, Decrease.

Part II:

Language Game
on Christmas Day

Pennsylvania Lottery
December 25, 2007:

PA Lottery Christmas Day: Mid-day 041 and 2911, Evening 173 and 0666

Part III:
A Wonderful Life

The Pennsylvania Lottery on Christmas at mid-day paired the number of the I Ching Hexagram 41, “Decrease,” with the number 2911, which may be interpreted as a reference to I Chronicles 29:11

“Thine, O LORD is the greatness, and the power, and the glory, and the victory, and the majesty: for all that is in the heaven and in the earth is thine; thine is the kingdom, O LORD, and thou art exalted as head above all.”

This verse is sometimes cited as influencing the Protestant conclusion of the Lord’s Prayer:

“Thine is the kingdom, and the power, and the glory, forever” (Mt 6.13b; compare 1 Chr 29.11-13)….

This traditional epilogue to the Lord’s prayer protects the petition for the coming of the kingdom from being understood as an exorcism, which we derive from the Jewish prayer, the Kaddish, which belonged at the time to the synagogical liturgy.

World Alliance of Reformed Churches

The Pennsylvania Lottery on Christmas evening paired 173 with the beastly number 0666.  The latter number suggests that perhaps being “understood as an exorcism” might not, in this case, be such a bad thing. What, therefore, might “173” have to do with exorcism?  A search in the context of the phrase “language games” yields a reference to Wittgenstein’s Zettel, section 173:


From Charles L. Creegan, Wittgenstein and Kierkegaard:

Language-games give general guidelines of the application of language. Wittgenstein suggests that there are innumerably many language-games: innumerably many kinds of use of the components of language.24 The grammar of the language-game influences the possible relations of words, and things, within that game. But the players may modify the rules gradually. Some utterances within a given language-game are applications; others are ‘grammatical remarks’ or definitions of what is or should be possible. (Hence Wittgenstein’s remark, ‘Theology as grammar’25 – the grammar of religion.)

The idea of the ‘form of life’ is a reminder about even more basic phenomena. It is clearly bound up with the idea of language. (Language and ‘form of life’ are explicitly connected in four of the five passages from the Investigations in which the term ‘form of life’ appears.) Just as grammar is subject to change through language-uses, so ‘form of life’ is subject to change through changes in language. (The Copernican revolution is a paradigm case of this.) Nevertheless, ‘form of life’ expresses a deeper level of ‘agreement.’ It is the level of ‘what has to be accepted, the given.’26 This is an agreement prior to agreement in opinions and decisions. Not everything can be doubted or judged at once.

This suggests that ‘form of life’ does not denote static phenomena of fixed scope. Rather, it serves to remind us of the general need for context in our activity of meaning. But the context of our meaning is a constantly changing mosaic involving both broad strokes and fine-grained distinctions.

The more commonly understood point of the ‘Private Language Argument’ – concerning the root of meaning in something public – comes into play here. But it is important to show just what public phenomenon Wittgenstein has in mind. He remarks: ‘Only in the stream of thought and life do words have meaning.’27

Investigations, sec. 23.
Investigations, sec. 373; compare Zettel, sec. 717.
Investigations, p. 226e.


Zettel, sec. 173. The thought is expressed many times in similar words.

And from an earlier chapter of Creegan:

The ‘possibility of religion’ manifested itself in considerable reading of religious works, and this in a person who chose his reading matter very carefully. Drury’s recollections include conversations about Thomas à Kempis, Samuel Johnson’s Prayers, Karl Barth, and, many times, the New Testament, which Wittgenstein had clearly read often and thought about.25 Wittgenstein had also thought about what it would mean to be a Christian. Some time during the 1930s, he remarked to Drury: ‘There is a sense in which you and I are both Christians.’26 In this context it is certainly worth noting that he had for a time said the Lord’s Prayer each day.27

Wittgenstein’s last words were: ‘Tell them I’ve had a wonderful life!’28

Drury (1981) ‘Conversations with Wittgenstein,’ in Ludwig Wittgenstein: Personal Recollections, pp. 112ff.
Drury, ‘Conversations,’ p. 130.
Drury, ‘Some notes,’ p. 109.
Reported by Mrs. Bevan, the wife of the doctor in whose house Wittgenstein was staying. Malcolm, Memoir, p. 81.

Part IV:

For more on the Christmas evening
number of the beast, see Dec. 3:
  “Santa’s Polar Opposite?” —

Did he who made the Lamb
make thee?

Saturday, August 18, 2007

Saturday August 18, 2007

Filed under: General — m759 @ 7:20 PM
A Concrete Universal

What on earth is
a ‘concrete universal’?

Said to be an annotation
(undated) by Robert M. Pirsig
of A History of Philosophy,
by Frederick Copleston,
Society of Jesus.

No matter how it’s done,
you won’t like it.

— Robert Redford to     
  Robert M. Pirsig in Lila    

“In chapters 19 and 20 of LILA there is a discussion about the possibility of making Zen and the Art into a movie. It opens with a scene where Robert Redford, who ‘really would like to have the film rights,’ comes to meet and negotiate with Phaedrus in his New York City hotel room. Phaedrus tells the famous actor that he can have the rights to the book, but maybe that’s just because he’s star-struck and doesn’t like to haggle. Under his excitement, Phaedrus has a bad feeling about it. He tells us that he’s been warned by several different people not to allow such a film to be made. Even Redford warned him not to do it. So what’s the problem? As it’s put at the end of that discussion, ‘Films are social media; his book was largely intellectual. That was the center of the problem.'”

David Buchanan at robertpirsig.org

“The insight is constituted precisely by ‘seeing’ the idea in the image, the intelligible in the sensible, the universal in the particular, the abstract in the concrete.”

— Fr. Brian Cronin‘s Foundations of Philosophy, Ch. 2, “Identifying Direct Insights,” quoted in Ideas and Art

See also Smiles of a Summer Evening, the current issue of TIME, the time of this entry (7:20:11 PM ET), and Plato, Pegasus, and the Evening Star.

Sunday, July 29, 2007

Sunday July 29, 2007

Filed under: General — m759 @ 7:59 AM
Nordic Truth: Jewish Fiction:
Snowball In Hell
From The New York Times in 2005:

Portrait of conductor
Arild Remmereit:

Arild Remmereit

April 24, 2005
Have Baton,
Will Travel

by James R. Oestreich


“HE’S the hottest conductor you’ve never heard of….

In music, as in most other pursuits, one person’s misfortune can be another’s opportunity. Many a podium career has been built on successful substitutions…. typically, the process is cumulative and measured.

In Mr. Remmereit’s case, it seems a sort of spontaneous combustion…. he seems destined for big things, and soon.

Regarding his sudden change in stature, he spoke as if from afar. ‘The snowball has reached such a size that it has started to roll,’ he said matter-of-factly….

‘It’s terrifying when it happens,’ he said, ‘but I can’t tell you how naively happy I am when it goes well. These are such major steps that I wasn’t even hoping for a few weeks ago.’

ARILD REMMEREIT (pronounced AHR-eeld REMM-uh-right, with the r’s heavily rolled) was born in a village in Norway, between Bergen and Trondheim, and has lived in Vienna since 1987. Slim and fresh-faced at 43, he has had a busy but low-level career in Europe….

So here he was, on April 15, conducting the Pittsburgh Symphony… in a vintage… Germanic program…. Wagner’s ‘Siegfried Idyll,’ Schumann’s Fourth Symphony and Brahms’s Second Piano Concerto….”


Württemberg Philharmonic February 2004
Nielsen, Sibelius, Grieg.

Reutlinger Nachrichten.
“Distant closeness, close distance.

Arild Remmereit as a guest conductor: ‘As when the sun rises in the North.’ The Philharmonics and their brilliant guest conductor fetched the mind-blowing, tempting and exciting Scandinavia.

It was like a lucky strike to see the Norwegian conductor on stage with the Philharmonic. When he conducts the Dane Nielsen, the Finn Sibelius and the Norwegian Grieg, one can really feel that this man has the locally marked music floating in his blood.”

From The New York Times today:

Discussion of
a new novel:
Variations on the Beast

Variations on
the Beast
by psychoanalyst
Henry Grinberg

An interview with Henry Grinberg conducted by James R. Oestreich:

“For those who find inspiration and edification in great art, it is always painful to be reminded that artists are not necessarily admirable as people and that art is powerless in the face of great evil. That truth was baldly evident in Nazi Germany and in the way the regime used and abused music and musicians, to say nothing of the way it used and abused human beings of all kinds.

[A new novel touches on] these issues…. In Variations on the Beast (Dragon Press), Henry Grinberg, a psychoanalyst, posits Hermann Kapp-Dortmunder, a powerful maestro, as a fictional rival of Wilhelm Furtwängler (whose qualms about working under the regime he does not share) and Herbert von Karajan (whose vaulting ambition he does).”


“And it soon occurred to me… that, my God, a lot of the famous, the notable, the moving, the magnificent composers in the 18th and 19th centuries and earlier were Germans. And I tried to understand, how did such a nation turn out to be so bestial and cruel, so indifferent to the suffering of others? And I have no explanation for it.

As a practicing psychoanalyst, I can see individual expressions of rage and their causes and their so-called justifications. But for a whole nation to be consumed, to be seduced by an overwhelming idea– well, there are rationalizations, I guess, but not explanations. There’s no forgiveness for this. And I tried to put together a story of a person who was a participant and a causer of these kinds of things….

So I sort of poured my feelings of contempt and rage into the character I was devising. And I have to admit, after having been psychoanalyzed myself in preparation for the training, that something of Hermann Kapp-Dortmunder exists in me. I shudder to think that this may be so, but I have to accept the possibility. Murderous thoughts may have occurred to me, but, thank God, I’ve never killed anyone.”

Tuesday, July 3, 2007

Tuesday July 3, 2007

Filed under: General — m759 @ 9:29 PM
The Ignorance
of Stanley Fish

(continued from
June 18, 2002)

The “ignorance” referred to
is Fish’s ignorance of the
philosophical background
of the words
“particular” and “universal.”

Postmodern Warfare:
The Ignorance of Our
Warrior Intellectuals,”
by Stanley Fish,
Harper’s Magazine,
July 2002, contains
the following passages:

“The deepest strain in a religion is the particular and particularistic doctrine it asserts at its heart, in the company of such pronouncements as ‘Thou shalt have no other Gods before me.’ Take the deepest strain of religion away… and what remains are the surface pieties– abstractions without substantive bite– to which everyone will assent because they are empty, insipid, and safe. It is this same preference for the vacuously general over the disturbingly particular that informs the attacks on college and university professors who spoke out in ways that led them to be branded as outcasts by those who were patrolling and monitoring the narrow boundaries of acceptable speech. Here one must be careful, for there are fools and knaves on all sides.”

“Although it may not at first be obvious, the substitution for real religions of a religion drained of particulars is of a piece with the desire to exorcise postmodernism.”

“What must be protected, then, is the general, the possibility of making pronouncements from a perspective at once detached from and superior to the sectarian perspectives of particular national interests, ethnic concerns, and religious obligations; and the threat to the general is posed by postmodernism and strong religiosity alike, postmodernism because its critique of master narratives deprives us of a mechanism for determining which of two or more fiercely held beliefs is true (which is not to deny the category of true belief, just the possibility of identifying it uncontroversially), strong religiosity because it insists on its own norms and refuses correction from the outside. The antidote to both is the separation of the private from the public, the establishing of a public sphere to which all could have recourse and to the judgments of which all, who are not criminal or insane, would assent. The point of the public sphere is obvious: it is supposed to be the location of those standards and measures that belong to no one but apply to everyone. It is to be the location of the universal. The problem is not that there is no universal–the universal, the absolutely true, exists, and I know what it is. The problem is that you know, too, and that we know different things, which puts us right back where we were a few sentences ago, armed with universal judgments that are irreconcilable, all dressed up and nowhere to go for an authoritative adjudication.

What to do? Well, you do the only thing you can do, the only honest thing: you assert that your universal is the true one, even though your adversaries clearly do not accept it, and you do not attribute their recalcitrance to insanity or mere criminality–the desired public categories of condemnation–but to the fact, regrettable as it may be, that they are in the grip of a set of beliefs that is false. And there you have to leave it, because the next step, the step of proving the falseness of their beliefs to everyone, including those in their grip, is not a step available to us as finite situated human beings. We have to live with the knowledge of two things: that we are absolutely right and that there is no generally accepted measure by which our rightness can be independently validated. That’s just the way it is, and we should just get on with it, acting in accordance with our true beliefs (what else could we do?) without expecting that some God will descend, like the duck in the old Groucho Marx TV show, and tell us that we have uttered the true and secret word.”

From the public spheres
of the Pennsylvania Lottery:

PA Lottery logo

PA Lottery July 3, 2007: Mid-day 105, Evening 268

105 —

Log24 on 1/05:

“‘From your lips
to God’s ears,’
 goes the old
Yiddish wish.

 The writer, by contrast,
tries to read God’s lips
and pass along
the words….”

— Richard Powers   

268 —

This is a page number
that appears, notably,
in my June 2002
journal entry on Fish
and again in an entry,
The Transcendent Signified,”
dated July 26, 2003,
that argues against
Fish’s school, postmodernism,
 and in favor of what the pomos
call “logocentrism.”

Page 268
of Simon Blackburn’s Think
(Oxford Univ. Press, 1999):

“It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy. It structures Plato’s (realist) reaction to the sophists (nominalists). What is often called ‘postmodernism’ is really just nominalism, colourfully presented as the doctrine that there is nothing except texts. It is the variety of nominalism represented in many modern humanities, paralysing appeals to reason and truth.”

Fish may, if he wishes,
regard the particular
page number 268 as
delivered– five years late,
but such is philosophy–
by Groucho’s
winged messenger
in response to
Fish’s utterance of the
  “true and secret word”–
namely, “universal.”

When not arguing politics,
Fish, though from
a Jewish background, is
 said to be a Milton scholar.
Let us therefore hope he
is by now, or comes to be,
aware of the Christian
approach to universals–
an approach true to the
philosophical background
sketched in 1999 by
Blackburn and made
particular in a 1931 novel
 by Charles Williams,
The Place of the Lion.

Wednesday, May 23, 2007

Wednesday May 23, 2007

Filed under: General — m759 @ 5:15 AM
Angel in the Details

See the Dickinson poem quoted here on May 15 (the date, as it happens, of Dickinson’s death) in the entry “A Flag for Sunrise.”  See also Zen and Language Games and a discussion of a detail in a Robert Stone novel.

“I dwell in Possibility
A fairer House than Prose”

Emily Dickinson

Monday, April 16, 2007

Monday April 16, 2007

Filed under: General — m759 @ 4:01 PM

The Abridgment of Hope

Part I: Framework

From Log24,
Here’s Your Sign,
Aug. 8, 2002–

“Paz also mentions the Christian concept of eternity as a realm outside time, and discusses what happened to modern thought after it abandoned the concept of eternity.

Naturally, many writers have dealt with the subject of time, but it seems particularly part of the Zeitgeist now, with a new Spielberg film about precognition.  My own small experience, from last night until today, may or may not have been precognitive.  I suspect it’s the sort of thing that many people often experience, a sort of ‘So that’s what that was about’ feeling.  Traditionally, such experience has been expressed in terms of a theological framework.”

Part II: Context

From Ann Copeland,
Faith and Fiction-Making:
The Catholic Context

“Each of us is living out a once-only story which, unlike those mentioned here, has yet to reveal its ending. We live that story largely in the dark. From time to time we may try to plumb its implications, to decipher its latent design, or at least get a glimmer of how parts go together. Occasionally, a backward glance may suddenly reveal implications, an evolving pattern we had not discerned, couldn’t have when we were ‘in’ it. Ah, now I see what I was about, what I was after.”

Part III: Context Sensitivity

From Log24’s
Language Game,
Jan. 14, 2004–

Ludwig Wittgenstein,
Philosophical Investigations:

373. Grammar tells what kind of object anything is. (Theology as grammar.)

From Wikipedia

Another definition of context-sensitive grammars defines them as formal grammars where all productions are of the form

a yields b where the length of a is less than or equal to the length of b

Such a grammar is also called a monotonic or noncontracting grammar because none of the rules decreases the size of the string that is being rewritten.

If the possibility of adding the empty string to a language is added to the strings recognized by the noncontracting grammars (which can never include the empty string) then the languages in these two definitions are identical.

 Part IV: Abridgment

“Know the one about the Demiurge and the Abridgment of Hope?”

— Robert Stone, A Flag for Sunrise, Knopf, 1981, the final page, 439

Also from Stone’s novel, quoted by Ann Copeland in the above essay:

You after all? Inside, outside, round and about. Disappearing stranger, trickster. Christ, she thought, so far. Far from where?

But why always so far?

Por qué?” she asked. There was a guy yelling.

Always so far away. You. Always so hard on the kid here, making me be me right down the line. You old destiny. You of Jacob, you of Isaac, of Esau.

Let it be you after all. Whose after all I am. For whom I was nailed.

So she said to Campos: “Behold the handmaid of the Lord.” (416)

Monday, January 29, 2007

Monday January 29, 2007

Filed under: General,Geometry — Tags: — m759 @ 9:00 AM

By Indirections
(Hamlet, II, i)

“Michael Taylor (1971)…. contends that the central conflict in Hamlet is between ‘man as victim of fate and as controller of his own destiny.'”– The Gale Group, Shakespearean Criticism, Vol. 71, at eNotes

Doonesbury today:

The image “http://www.log24.com/log/pix07/070129-Robot4A.gif” cannot be displayed, because it contains errors.

“Personality is a synthesis of possibility and necessity.”– Soren Kierkegaard

On Fate (Necessity),
Freedom (Possibility),
and Machine Personality–

Part I: Google as Skynet

George Dyson–
The Godel-to-Google Net [March 8, 2005]
A Cathedral for Turing [October 24, 2005]

Dyson: “The correspondence between Google and biology is not an analogy, it’s a fact of life.”

Part II: The Galois Connection

David Ellerman–
“A Theory of Adjoint Functors– with some Thoughts about their Philosophical Significance” (pdf) [November 15, 2005]

Ellerman: “Such a mechanism seems key to understanding how an organism can perceive and learn from its environment without being under the direct stimulus control of the environment– thus resolving the ancient conundrum of receiving an external determination while exercising self-determination.”

For a less technical version, see Ellerman’s “Adjoints and Emergence: Applications of a New Theory of Adjoint Functors” (pdf).

Ellerman was apparently a friend of, and a co-author with, Gian-Carlo Rota.  His “theory of adjoint functors” is related to the standard mathematical concepts known as profunctors, distributors, and bimodules. The applications of his theory, however, seem to be less to mathematics itself than to a kind of philosophical poetry that seems rather closely related to the above metaphors of George Dyson. For a less poetic approach to related purely mathematical concepts, see, for instance, the survey Practical Foundations of Mathematics by Paul Taylor (Cambridge University Press, 1999).  For less poetically appealing, but perhaps more perspicuous, extramathematical applications of category theory, see the work of, for instance, Joseph Goguen: Algebraic Semiotics and Information Integration, Databases, and Ontologies.

Tuesday, January 23, 2007

Tuesday January 23, 2007

Filed under: General — m759 @ 12:00 PM
Quine vs. Kierkegaard

“The most prominent critic
of the modal notions is Quine.
Throughout his career, he has
argued against the use of notions
like necessity and possibility.”

— Michael J. Loux,
Note 1 of Chapter 5,
“The Necessary and the Possible,”
in Metaphysics:
A Contemporary Introduction

(Routledge, second edition,
January 1, 2002)

Personality is a synthesis of
possibility and necessity.”

— Soren Kierkegaard,
The Sickness Unto Death

Related material:

Plato, Pegasus,
and the Evening Star

Diamonds Are Forever

Dream a Little Dream

Update of 3:45 PM:

From Arts & Letters Daily
this afternoon–

“Existentialism is not all gloom,
even if Heidegger looks pretty sour
in those photos. It’s a philosophy
that America needs now, says
the late Robert Solomon…

See also Jan. 2,
the date of
Solomon’s death
in Switzerland,
and click on the
following symbol
from that date:

The image “http://www.log24.com/log/pix07/070103-DoubleCross.jpg” cannot be displayed, because it contains errors.

Tuesday, January 9, 2007

Tuesday January 9, 2007

Filed under: General,Geometry — m759 @ 9:00 PM
Logos and Logic
(private, cut from prev. entry)

The diamond is used in modal logic to symbolize possibility.

  The 3×3 grid may also be used
to illustrate “possibility.”  It leads,
as noted at finitegeometry.org, to
the famed “24-cell,” which may be
pictured either as the diamond
figure from Plato’s Meno

The image “http://www.log24.com/theory/images/poly-24cell-sm.jpg” cannot be displayed, because it contains errors.

Click for details.

  — or as a figure
with 24 vertices:

The image “http://www.log24.com/theory/images/poly-24cell-02sm.jpg” cannot be displayed, because it contains errors.

Click for details.

The “diamond” version of the
24-cell seems unrelated to the
second version that shows all
vertices and edges, yet the
second version is implicit,
or hidden, in the first.
Hence “possibility.”

Neither version of the 24-cell
seems related in any obvious
way to the 3×3 grid, yet both
versions are implicit,
or hidden, in the grid.
Hence “possibility.”

Tuesday January 9, 2007

Filed under: General — Tags: — m759 @ 12:00 PM
For Balanchine's Birthday

(continued from
January 9, 2003)

George Balanchine

Encyclopædia Britannica Article

born January 22
[January 9, Old Style], 1904,
St. Petersburg, Russia
died April 30, 1983, New York,
New York, U.S.

Photograph:George Balanchine.
George Balanchine.
©1983 Martha Swope

original name 
Georgy Melitonovich Balanchivadze

most influential choreographer of classical ballet in the United States in the 20th century.  His works, characterized by a cool neoclassicism, include The Nutcracker (1954) and Don Quixote (1965), both pieces choreographed for the New York City Ballet, of which he was a founder (1948), the artistic director, and the…

Balanchine,  George… (75 of 1212 words)

"What on earth is
a concrete universal?"
— Robert M. Pirsig


From Wikipedia's
"Upper Ontology"
Epiphany 2007:

"There is no neutral ground
that can serve as
a means of translating between
specialized (lower) ontologies."

There is, however,
"the field of reason"–

the 3×3 grid:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

Click on grid
for details.

As Rosalind Krauss
has noted, some artists
regard the grid as

"a staircase to
  the Universal."

Other artists regard
Epiphany itself as an
approach to
the Universal:

"Epiphany signals the traversal
of the finite by the infinite,
of the particular by the universal,
of the mundane by the mystical,
of time by eternity.

Richard Kearney, 2005,
in The New Arcadia Review

The image “http://www.log24.com/log/pix07/070109-Kearney2.jpg” cannot be displayed, because it contains errors.

Kearney (right) with
Martin Scorsese (left)
and Gregory Peck
in 1997.

"… one of the things that worried me about traditional metaphysics, at least as I imbibed it in a very Scholastic manner at University College Dublin in the seventies, is that philosophy was realism and realism was truth. What disturbed me about that was that everything was already acquired; truth was always a systematic given and it was there to be learned from Creation onwards; it was spoken by Jesus Christ and then published by St. Thomas Aquinas: the system as perfect synthesis. Hence, my philosophy grew out of a hunger for the 'possible' and it was definitely a reaction to my own philosophical formation. Yet that wasn't my only reaction. I was also reacting to what I considered to be the deep pessimism, and even at times 'nihilism' of the postmodern turn."

— Richard Kearney, interview (pdf) in The Leuven Philosophy Newsletter, Vol. 14, 2005-2006

For more on "the possible," see Kearney's The God Who May Be, Diamonds Are Forever, and the conclusion of Mathematics and Narrative:


"We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."


Keith Allen Korcz 

The image “http://www.log24.com/log/pix05B/050802-Stone.gif” cannot be displayed, because it contains errors.

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity,
Christ Church College, Oxford
(the home of Lewis Carroll)

Friday, December 29, 2006

Friday December 29, 2006

Filed under: General — Tags: , — m759 @ 11:01 AM
of Christ Church

"For every kind of vampire,
there is a kind of cross."
— Thomas Pynchon

Cover of Thomas, by Shelley Mydans: Sword and its shadow, a cross

Click on picture for details.

Today is the feast
of St. Thomas Becket.

In his honor, a meditation
on tools and causation:

"Lewis Wolpert, an eminent developmental biologist at University College London, has just published Six Impossible Things Before Breakfast, a pleasant, though rambling, look at the biological basis of belief. While the book focuses on our ability to form causal beliefs about everyday matters (the wind moved the trees, for example), it spends considerable time on the origins of religious and moral beliefs. Wolpert defends the unusual idea that causal thinking is an adaptation required for tool-making. Religious beliefs can thus be seen as an odd extension of causal thinking about technology to more mysterious matters. Only a species that can reason causally could assert that 'this storm was sent by God because we sinned.' While Wolpert's attitude toward religion is tolerant, he's an atheist who seems to find religion more puzzling than absorbing."

Review by H. Allen Orr in
The New York Review of Books,
Vol. 54, No. 1, January 11, 2007    

"An odd extension"–

Wolpert's title is, of course,
from Lewis Carroll.

Related material:

"It's a poor sort of memory
that only works backwards."
Through the Looking-Glass

An event at the Kennedy Center
broadcast on
December 26, 2006
(St. Steven's Day):

"Conductor John Williams, a 2004 Honoree, says, 'Steven, sharing our 34-year collaboration has been a great privilege for me. It's been an inspiration to watch you dream your dreams, nurture them and make them grow. And, in the process, entertain and edify billions of people around the world. Tonight we'd like to salute you, musically, with a piece that expresses that spirit beautifully … It was written by Leonard Bernstein, a 1980 Kennedy Center Honoree who was, incidentally, the first composer to be performed in this hall.' Backed by The United States Army Chorus and The Choral Arts Society, soprano Harolyn Blackwell and tenor Gregory Turay sing the closing number for Spielberg's tribute and the gala itself. It's the finale to the opera 'Candide,' 'Make Our Garden Grow,' and Williams conducts."

CBS press release

See also the following,
from the conclusion to

"Mathematics and Narrative"

(Log24, Aug. 22, 2005):

Diamond on cover of Narrative Form, by Suzanne Keen

"At times, bullshit can
only be countered
   with superior bullshit."
Norman Mailer

Many Worlds and Possible Worlds in Literature and Art, in Wikipedia:

    "The concept of possible worlds dates back to at least Leibniz who in his Théodicée tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds.  Voltaire satirized this view in his picaresque novel Candide….
    Borges' seminal short story El jardín de senderos que se bifurcan ("The Garden of Forking Paths") is an early example of many worlds in fiction."

"Il faut cultiver notre jardin."
— Voltaire

"We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz 

Diamond in a square

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
 Regius Professor of Divinity,
  Christ Church College, Oxford
(the home of Lewis Carroll)

For further details,
click on the
Christ Church diamond.

Sunday, October 1, 2006

Sunday October 1, 2006

Filed under: General,Geometry — m759 @ 8:00 AM
Tales of Philosophy:

Recipe for Disaster
according to Jerome Kagan,
Harvard psychologist emeritus

From Log24 —

The Line

The image “http://www.log24.com/theory/images/GridCube165C3.jpg” cannot be displayed, because it contains errors.

The Cube

From Harvard's
Jerome Kagan —
"'Humans demand that there be a clear right and wrong,' he said. 'You've got to believe that the track you've taken is the right track. You get depressed if you're not certain as to what it is you're supposed to be doing or what's right and wrong in the world.'" "People need to divide the world into good and evil, us and them, Kagan continued. To do otherwise– to entertain the possibility that life is not black and white, but variously shaded in gray– is perhaps more honest, rational and decent. But it's also, psychically, a recipe for disaster."
The image “http://www.log24.com/log/pix06A/061001-epi3-w156.jpg” cannot be displayed, because it contains errors.

Black and White:

Log24 in
May 2005

The image “http://www.log24.com/log/pix06A/061001-Grays.jpg” cannot be displayed, because it contains errors.

Shades of Gray:

An affine space
Jerome Kagan


The above Kagan quotes are taken
from a New York Times essay by
Judith Warner as transcribed by
Mark Finkelstein on Sept. 29.

See also Log24 on
Sept. 29 and 30.

Related material:

Kagan's book

The image “http://www.log24.com/log/pix06A/SurpriseUncertainty.jpg” cannot be displayed, because it contains errors.

Surprise, Uncertainty,
and Mental Structures

(Harvard U. Press, April 2002)

and Werner Heisenberg–
discoverer of the
uncertainty principle
as Anakin Skywalker
being tempted by
the Dark Side:

The image “http://www.log24.com/log/pix05/050519-Anakin.jpg” cannot be displayed, because it contains errors.

(From Log24, May 2005)
George Lucas, who has profited
enormously from public depictions
of the clash between
good and evil, light and dark,
may in private life be inclined
to agree with Hercule Poirot:
"It is the brain, the little gray cells
on which one must rely.
One must seek the truth
within– not without."
(This is another version of the
"Descartes before dehors" principle–
See "A Table," Sept. 28.)

Friday, September 29, 2006

Friday September 29, 2006

Filed under: General — m759 @ 8:00 AM
for the High Holy Days

(Rosh Hashanah began at sundown September 22; Yom Kippur begins at sundown October 1.  —holidays.net)

Mark Finkelstein today:

"Today comes more evidence of the left's painful struggle to deal with its diminished standing and repeated rejection at the polls. In the subscription-required Why Voters Like Values, [New York] Times columnist Judith Warner claims that "the Christian right's ability to stir voter passions is based not on values, but on psychology." Warner describes having bravely gone inside the belly of the conservative beast, recently attending a Values Voters Summit in DC, and declaring it "imbued with so much intolerance and hate." This is presumably in contrast with liberal love-ins, where Bush & Co. are regularly depicted as liars, murderers, Hitlers, etc.

She later describes a schadenfreude-provoking scene of the day after Kerry's 2004 defeat, picking through the rubble with Harvard psychology professor emeritus, Jerome Kagan, who tried to console Warner and presumably himself. As she describes it:

"Our conversation drifted to the Republicans' 'values' [note scare quotes] agenda, and Kagan's belief that values sell because they're an antidote to the endemic mental health problem of our time: depression.

"'Humans demand that there be a clear right and wrong,' he said. 'You've got to believe that the track you've taken is the right track. You get depressed if you're not certain as to what it is you're supposed to be doing or what's right and wrong in the world."

"People need to divide the world into good and evil, us and them, Kagan continued. To do otherwise– to entertain the possibility that life is not black and white, but variously shaded in gray– is perhaps more honest, rational and decent. But it's also, psychically, a recipe for disaster."

Got it? Liberalism is "more honest, rational and decent" than conservativism, but that's just not what the benighted public wants. They're looking for political Prozac, a Manichean worldview they can cling to, and that's what conservatism cunningly offers.

Less controversial values are provided by yesterday evening's Pennsylvania lottery— namely, the values 4, 5, and 6.

For a discussion of these values under the guise of musical intervals, see Professor Kagan again, in a paper (pdf) he wrote with Marcel R. Zentner, "Infants' Perception of Consonance and Dissonance in Music" (Infant Behavior & Development, Vol. 21, No. 3, 1998):

Adults judge as most consonant either the octave (difference of 12 semitones) [or the unison, difference of 0 semitones], the fifth (7 semitones), or the major third (4 semitones).

Illustration (see also yesterday evening):

The image “http://www.log24.com/music/images/Keys-Values.gif” cannot be displayed, because it contains errors.

Notes and frequency ratios

The paper discusses consonant intervals
as an example of alleged
"perceptual universals."

Related material on universals
suitable for today, the Feast of
St. Michael and All Angels:

Shining Forth and
Midsummer Eve's Dream.

The material in Shining Forth
is also related, tangentially, to the
following presentation of the
Warner "values" essay
in today's online New York Times:

The image “http://www.log24.com/log/pix06A/060929-NYT.jpg” cannot be displayed, because it contains errors.

The above three Times items,
taken together, suggest that
those in search of "values"
should consult Betty Suarez:

The image “http://www.log24.com/log/pix06A/060929-BettyPoncho.gif” cannot be displayed, because it contains errors.

Click on picture for further details.

Sunday, June 4, 2006

Sunday June 4, 2006

Filed under: General — m759 @ 1:00 PM
and Words
for Baccalaureate
Day at Princeton

The image “http://www.log24.com/log/pix06A/060604-Weyl16.jpg” cannot be displayed, because it contains errors.

From Hermann Weyl’s
Princeton University
Press, page 140

The image �http://www.log24.com/log/pix03A/030909-SpiritWhole.jpg� cannot be displayed, because it contains errors.

Adapted from the
cover of Alan Watts’s
The Spirit of Zen

The image �http://www.log24.com/log/pix06A/060604-RomaniFlag.gif� cannot be displayed, because it contains errors.

Romani flag, courtesy of

The image “http://www.log24.com/log/pix06A/060604-Armando.jpg” cannot be displayed, because it contains errors.


Related material:

“The Scholar Gypsy”
in The Oxford Book
of English Prose
, 1923,
edited by
Sir Arthur Quiller-Couch

This is available online:

From The Vanity of Dogmatizing,
by Joseph Glanvill
(London, printed by E.C. for
Henry Eversden at the Grey-Hound
in St.Pauls-Church-Yard,  1661)

Pages 195-201:

That one man should be able to bind the thoughts of another, and determine them to their particular objects; will be reckon’d in the first rank of Impossibles: Yet by the power of advanc’d Imagination it may very probably be effected; and story abounds with Instances. I’le trouble the Reader but with one; and the hands from which I had it, make me secure of the truth on’t. There was very lately a Lad in the University of Oxford, who being of very pregnant and ready parts, and yet wanting the encouragement of preferment; was by his poverty forc’d to leave his studies there, and to cast himself upon the wide world for a livelyhood. Now, his necessities growing dayly on him, and wanting the help of friends to relieve him; he was at last forced to joyn himself to a company of Vagabond Gypsies, whom occasionally he met with, and to follow their Trade for a maintenance. Among these extravagant people, and by the insinuating subtilty of his carriage, he quickly got so much of their love, and esteem; as that they discover’d to him their Mystery: in the practice of which, by the pregnancy of his wit and parts he soon grew so good a proficient, as to be able to out-do his Instructors. After he had been a pretty while exercis’d in the Trade; there chanc’d to ride by a couple of Scholars who had formerly bin of his acquaintance. The Scholars had quickly spyed out their old friend, among the Gypsies; and their amazement to see him among such society, had well-nigh discover’d him: but by a sign he prevented their owning him before that Crew: and taking one of them aside privately, desired him with his friend to go to an Inn, not far distant thence, promising there to come to them. They accordingly went thither, and he follows: after their first salutations, his friends enquire how he came to lead so odd a life as that was, and to joyn himself with such a cheating beggarly company. The Scholar-Gypsy having given them an account of the necessity, which drove him to that kind of life; told them, that the people he went with were not such Impostours as they were taken for, but that they had a traditional kind of learning among them, and could do wonders by the power of Imagination, and that himself had learnt much of their Art, and improved in further than themselves could. And to evince the truth of what he told them, he said, he’d remove into another room, leaving them to discourse together; and upon his return tell them the sum of what they had talked of: which accordingly he perform’d, giving them a full acount of what had pass’d between them in his absence. The Scholars being amaz’d at so unexpected a discovery, ernestly desir’d him to unriddle the mystery. In which he gave them satisfaction, by telling them, that what he did was by the power of Imagination, his Phancy binding theirs; and that himself had dictated to them the discourse, they held together, while he was from them: That there were warrantable wayes of heightening the Imagination to that pitch, as to bind anothers; and that when he had compass’d the whole secret, some parts of which he said he was yet ignorant of, he intended to give the world an account of what he had learned.

Now that this strange power of the Imagination is no Impossibility; the wonderful signatures in the Foetus caus’d by the Imagination of the Mother, is no contemptible Item. The sympathies of laughing & gaping together, are resolv’d into this Principle: and I see not why the phancy of one man may not determine the cogitation of another rightly qualified, as easily as his bodily motion. This influence seems to be no more unreasonable, then [sic] that of one string of a Lute upon another; when a stroak on it causeth a proportionable motion in the sympathizing confort, which is distant from it and not sensibly touched. Now if this notion be strictly verifiable; ’twill yeeld us a good account of how Angels inject thoughts into our minds, and know our cogitations: and here we may see the source of some kinds of fascination. If we are prejudic’d against the speculation, because we cannot conceive the manner of so strange an operation; we shall indeed receive no help from the common Philosophy: But yet the Hypothesis of a Mundane soul, lately reviv’d by that incomparable Platonist and Cartesian, Dr. H. More, will handsomely relieve us. Or if any would rather have a Mechanical account; I think it may probably be made out some such way as follow. Imagination is inward Sense. To Sense is required a motion of certain Filaments of the Brain; and consequently in Imagination there’s the like: they only differing in this, that the motion of the one proceeds immediately from external objects; but that of the other hath its immediate rise within us. Now then, when any part of the Brain is stringly agitated; that, which is next and most capable to receive the motive Impress, must in like manner be moved. Now we cannot conceive any thing more capable of motion, then the fluid matter, that’s interspers’d among all bodies, and contiguous to them. So then, the agitated parts of the Brain begetting a motion in the proxime Aether; it is propagated through the liquid medium, as we see the motion is which is caus’d by a stone thrown into the water. Now, when the thus moved matter meets with anything like that, from which it received its primary impress; it will proportionably move it, as it is in Musical strings tuned Unisons. And thus the motion being convey’d, from the Brain of one man to the Phancy of another; it is there receiv’d from the instrument of conveyance, the subtil matter; and the same kind of strings being moved, and much of whay after the same manner as in the first Imaginant; the Soul is awaken’d to the same apprehensions, as were they that caus’d them. I pretend not to any exactness or infallibility in this account, fore-seeing many scruples that must be removed to make it perfect: ‘Tis only a hint of the possibility of mechanically solving the Phaenomenon; though very likely it may require many other circumstances completely to make it out. But ’tis not my business here to follow it: I leave it therefore to receive accomplishment from maturer Inventions.

Tuesday, May 23, 2006

Tuesday May 23, 2006

Filed under: General — m759 @ 10:18 AM

Exhibit A:
A science vulgarizer in today’s New York Times–

“Somewhere out there, more elusive than a snow leopard, more vaunted in its imagined cultural oomph than an Oprah book blurb, is the Science Movie.

You know, the film that finally does for science and scientists what ‘The Godfather’ did for crime and what ‘The West Wing’ did for politics, accurately reproducing the grandeur and grit of science while ushering its practitioners into the ranks of coolness.”

Dennis Overbye

Exhibit B:
John Updike’s review in the May 22 New Yorker of a new novel by Michel Houellebecq, The Possibility of an Island

“Nor is Houellebecq…. entirely without literary virtue.  His four novels– Whatever (1994), The Elementary Particles (1998), and Platform (2001) are the three others– display a grasp of science and mathematics beyond that of all but a few non-genre novelists.”

A character in the new novel– “a lengthy exercise in futuristic science fiction”– writes that

“The dream of all men is to meet little sluts who are innocent but ready for all forms of depravity– which is what, more or less, all teenage girls are.”

Exhibit C:
A mathematician hopes for more exciting vulgarizations of his subject–

“I would hope that clever writers might point out how mathematics is altering our lifestyles and do it in a manner that would not lead Garfield the Cat to say ‘ho hum.'”

— Philip J. Davis, “The Media and Mathematics Look at Each Other” (pdf), Notices of the American Mathematical Society, March 2006

Exhibit D:
Today’s Garfield

The image “http://www.log24.com/log/pix06A/060523-Garfield2.gif” cannot be displayed, because it contains errors.

Exhibit E:
Log24 entry of May 18, a parody of “Contact,” a 1997 film that vulgarized science–

Space Cadet

“They should have
sent a poet.”

The image “http://www.log24.com/log/pix06A/060518-SpaceCadet2.jpg” cannot be displayed, because it contains errors.

Exhibit F:
Gilbert and Sullivan, “The Mikado“–

“(With great effort) How de do, little girls, how de do? (Aside) Oh, my protoplasmal ancestor!”


“It might be asking too much
to make us cool.”
— Science vulgarizer   
Dennis Overbye

The image “http://www.log24.com/log/pix06A/060523-Godfather2.jpg” cannot be displayed, because it contains errors.

Robert De Niro as the
young Vito Corleone

Sunday, February 5, 2006

Sunday February 5, 2006

Filed under: General — m759 @ 11:00 AM

Catholic Schools Sermon

For those who might be tempted today, following yesterday’s conclusion of Catholic Schools Week, to sing (for whatever reason) “Ding Dong, the Witch is Dead”–

Here, from his classic Witchcraft (first published by Faber and Faber, London, 1941, reprinted by Apocryphile Press, Berkeley, CA, Oct. 1, 2005) is Charles Williams on the strong resemblance between witchcraft and the rituals of the Church:

Charles Williams on
Witchcraft and the Church

From Witchcraft, 2005 Apocryphile edition, pages 77-80–

[77] … The predisposition towards the idea of magic might be said to begin with a moment which seems to be of fairly common experience– the moment when it seems that anything might turn into anything else.  We have grown used– and properly used– to regarding this sensation invalid because, on the whole, things do not turn into other things except by processes which we realize, or else at least so frequently that we appreciate the probability.  But the occasional sensation remains.  A room, a street, a field becomes unsure.  The edge of a possibility of utter alteration intrudes.  A door, untouched, might close; a picture might walk; a tree might speak; an animal might not be an animal; a man might not be a man.  One may be with a friend, and a terror will take one even while his admirable voice is speaking; one will be with a lover and the hand will become a different and terrifying thing, moving in one’s own like a malicious intruder, too real for anything but fear.  All this may be due to racial memories or to any other cause; the point is that it exists.  It exists and can be communicated; it can even be shared.  There is, in our human centre, a heart-gripping fear of irrational change, of perilous and malevolent change.
    Secondly, there is the human body, and the movements of the human body.  Even now, when, as a general rule, the human body is not supposed to mean [78] anything, there are moments when it seems, in spite of ourselves, packed with significance.  This sensation is almost exactly the opposite of the last.  There, one was aware that any phenomenon might alter into another and truer self.  Here, one is aware that a phenomenon, being wholly itself, is laden with universal meaning.  A hand lighting a cigarette is the explanation of everything; a foot stepping from a train is the rock of all existence.  If the first group of sensations are due to racial fear, I do not know to what the second group are due– unless indeed to the Mercy of God, who has not left us without a cloud of witnesses.  But intellectually they are both as valid or invalid as each other; any distinction must be a matter of choice.  And they justify each other, at least to this extent, that (although the first suggests irrationality and the second rationality) they both at first overthrow a simple trust that phenomena are what phenomena seem.
    But if the human body is capable of seeming so, so are the controlled movements of the human body– ritual movements, or rather movements that seem like ritual.  A finger pointing is quite capable of seeming not only a significant finger, but a ritual finger; an evocative finger; not only a finger of meaning, but a finger of magic.  Two light dancing steps by a girl may (if one is in that state) appear to be what all the Schoolmen were trying to express; they are (only one cannot quite catch it) an intellectual statement of beatitude.  But two quiet steps by an old man may seem like the very speech of hell.  Or the other way round.  Youth and age have nothing to do with it, nor did the ages that defined and [79] denounced witchcraft think so.  The youngest witch, it is said, that was ever burned was a girl of eleven years old.
    Ordered movement, ritual, is natural to men.  But some ages are better at it, are more used to it, and more sensitive to it, than others.  The Middle Ages liked great spectacle, and therefore (if for no other reasons– but there were many) they liked ritual.  They were nourished by ritual– the Eucharist exhibited it.  They made love by ritual– the convention of courtly love preserved it.  Certainly also they did all these things without ritual– but ritual (outside the inner experience) was the norm.  And ritual maintains and increases that natural sense of the significance of movement.  And, of course, of formulae, of words.
    The value of formulae was asserted to be very high.  The whole religious life ‘as generally necessary to salvation’ depended on formulae.  The High God had submitted himself to formulae.  He sent his graces.  He came Himself, according to ritual movements and ritual formulae.  Words controlled the God.  All generations who have believed in God have believed that He will come on interior prayer; not all that He will come, if not visibly yet in visible sacraments, on exterior incantation.  But so it was.  Water and a Triune formula concentrated grace; so did oil and other formulae; so– supremely– did bread and wine and yet other formulae.   Invocations of saints were assumed, if less explicitly guaranteed, to be effective.  The corollaries of the Incarnation had spread, in word and gesture, very far.
    The sense of alteration, the sense of meaning, the [80] evocation of power, the expectation of the God, lay all about the world.  The whole movement of the Church had, in its rituals, a remarkable similarity to the other rites it denounced.  But the other rites had been there first, both in the Empire and outside the Empire.  In many cases the Church turned them to its own purposes.  But also in many cases it entirely failed to turn them to its own purposes.  In many cases it adopted statues and shrines.  But in others it was adopted by, at least, the less serious spells and incantations.  Wells and trees were dedicated to saints.  But the offerings at many wells and trees were to something other than the saint; had it not been so they would not have been, as we find they often were, forbidden.  Within this double and intertwined life existed those other capacities, of which we know more now, but of which we still know little– clairvoyance, clairaudience, foresight, telepathy.

Monday, January 23, 2006

Monday January 23, 2006

Filed under: General — Tags: — m759 @ 12:00 PM

The Case

An entry suggested by today's New York Times story by Tom Zeller Jr., A Million Little Skeptics:

From The Hustler, by Walter Tevis:

The only light in the room was from the lamp over the couch where she was reading.
    He looked at her face.  She was very drunk.  Her eyes were swollen, pink at the corners.  "What's the book?" he said, trying to make his voice conversational. But it sounded loud in the room, and hard.
    She blinked up at him, smiled sleepily, and said nothing.
    "What's the book?"  His voice had an edge now.
    "Oh," she said.  "It's Kierkegaard.  Soren Kierkegaard."  She pushed her legs out straight on the couch, stretching her feet.  Her skirt fell back a few inches from her knees.  He looked away.
    "What's that?" he said.
    "Well, I don't exactly know, myself."  Her voice was soft and thick.
    He turned his face away from her again, not knowing what he was angry with.  "What does that mean, you don't know, yourself?"
    She blinked at him.  "It means, Eddie, that I don't exactly know what the book is about.  Somebody told me to read it, once, and that's what I'm doing.  Reading it."
    He looked at her, tried to grin at her– the old, meaningless, automatic grin, the grin that made everybody like him– but he could not.  "That's great," he said, and it came out with more irritation than he had intended.
    She closed the book, tucked it beside her on the couch.  "I guess this isn't your night, Eddie.  Why don't we have a drink?"
    "No."  He did not like that, did not want her being nice to him, forgiving.  Nor did he want a drink.
    Her smile, her drunk, amused smile, did not change.  "Then let's talk about something else," she said.  "What about that case you have?  What's in it?"  Her voice was not prying, only friendly.  "Pencils?"
    "That's it," he said.  "Pencils."
    She raised her eyebrows slightly.  Her voice seemed thick.  "What's in it, Eddie?"
    "Figure it out yourself."  He tossed the case on the couch.


Related material:

Soren Kierkegaard on necessity and possibility
in The Sickness Unto Death, Chapter 3,

The Diamond of Possibility,

The image “http://www.log24.com/theory/images/Modal-diamondinbox.gif” cannot be displayed, because it contains errors.

the Baseball Almanac,

The image “http://www.log24.com/log/pix06/060123-BaseballLogo75.gif” cannot be displayed, because it contains errors.

and this morning's entry, "Natural Hustler."

Wednesday, November 30, 2005

Wednesday November 30, 2005

Filed under: General,Geometry — Tags: — m759 @ 8:20 PM


Brian Davies is a professor of mathematics at King’s College London.  In the December Notices of the American Mathematical Society, he claims that arithmetic may, for all we know, be inconsistent:

“Gödel taught us that it is not possible to prove that Peano arithmetic is consistent, but everyone has taken it for granted that in fact it is indeed consistent.
    Platonistically-inclined mathematicians would deny the possibility that Peano arithmetic could be flawed.  From Kronecker onwards many consider that they have a direct insight into the natural numbers, which guarantees their existence. If the natural numbers exist and Peano’s axioms describe properties that they possess then, since the axioms can be instantiated, they must be consistent.”

“It is not possible to prove that Peano arithmetic is consistent”…?!

Where did Gödel say this?  Gödel proved, in fact, according to a well-known mathematician at Princeton, that (letting PA stand for Peano Arithmetic),

“If PA is consistent, the formula expressing ‘PA is consistent’ is unprovable in PA.”

— Edward Nelson,
   Mathematics and Faith (pdf)

Remarkably, even after he has stated correctly Gödel’s result, Nelson, like Davies, concludes that

“The consistency of PA cannot be concretely demonstrated.”

I prefer the argument that the existence of a model ensures the consistency of a theory.

For instance, the Toronto philosopher William Seager writes that

“Our judgement as to the consistency of some system is not dependent upon that system’s being able to prove its own consistency (i.e. generate a formula that states, e.g. ‘0=1’ is not provable). For if that was the sole basis, how could we trust it? If the system was inconsistent, it could generate this formula as well (see Smullyan, Gödel’s Incompleteness Theorems, (Oxford, 1992, p. 109)). Furthermore, [George] Boolos allows that we do know that certain systems, such as Peano Arithmetic, are consistent even though they cannot prove their own consistency. Presumably, we know this because we can see that a certain model satisfies the axioms of the system at issue, hence that they are true in that model and so must be consistent.”

Yesterday’s Algorithm:
    Penrose and the Gödel Argument

The relationship between consistency and the existence of a model is brought home by the following weblog entry that neatly summarizes a fallacious argument offered in the AMS Notices by Davies:

The following is an interesting example that I came across in the article “Whither Mathematics?” by Brian Davies in the December issue of Notices of the American Mathematical Society.

Consider the following list A1 of axioms.

(1) There is a natural number 0.
(2) Every natural number a has a successor, denoted by S(a).
(3) There is no natural number whose successor is 0.
(4) Distinct natural numbers have distinct successors: a = b if and only if S(a) = S(b).
(5) If a property is possessed by 0 and also by the successor of every natural number which possesses it, then it is possessed by all the natural numbers.

Now consider the following list A2 of axioms.

(1) G is a set of elements and these elements obey the group axioms.
(2) G is finite but not isomorphic to any known list of finite simple groups.
(3) G is simple, in other words, if N is a subset of G satisfying certain properties then N=G.

We can roughly compare A2 with A1. The second axiom in A2 can be thought of as analogous to the third axiom of A1. Also the third axiom of A2 is analogous to the fifth axiom of A1, insofar as it refers to an unspecified set with cetain properties and concludes that it is equal to G.

Now, as is generally believed by most group theorists, the system A2 is internally inconsistent and the proof its inconsistency runs for more than 10000 pages.

So who is to deny that the system A1 is also probably internally inconsistent! Particularly since Godel proved that you can not prove it is consistent (staying inside the system). May be the shortest proof of its inconsistency is one hundred million pages long!

— Posted by Krishna,
   11/29/2005 11:46:00 PM,
   at his weblog,
  “Quasi-Coherent Ruminations”

An important difference between A1 (the set of axioms of Peano arithmetic) and A2 (a set of axioms that describe a new, unknown, finite simple group) is that A1 is known to have a model (the nonnegative integers) and A2 is not known to have a model.

Therefore, according to Seager’s argument, A1 is consistent and A2 may or may not be consistent.

The degree to which Seager’s argument invokes Platonic realism is debatable.  Less debatable is the quasireligious faith in nominalism proclaimed by Davies and Nelson.  Nelson’s own account of a religious experience in 1976 at Toronto is instructive.

I must relate how I lost my faith in Pythagorean numbers. One morning at the 1976 Summer Meeting of the American Mathematical Society in Toronto, I woke early. As I lay meditating about numbers, I felt the momentary overwhelming presence of one who convicted me of arrogance for my belief in the real existence of an infinite world of numbers, leaving me like an infant in a crib reduced to counting on my fingers. Now I live in a world in which there are no numbers save those that human beings on occasion construct.

— Edward Nelson,
   Mathematics and Faith (pdf)

Nelson’s “Mathematics and Faith” was written for the Jubilee for Men and Women from the World of Learning held at the Vatican, 23-24 May 2000.  It concludes with an invocation of St. Paul:

During my first stay in Rome I used to play chess with Ernesto Buonaiuti. In his writings and in his life, Buonaiuti with passionate eloquence opposed the reification of human abstractions. I close by quoting one sentence from his Pellegrino di Roma.  “For [St. Paul] abstract truth, absolute laws, do not exist, because all of our thinking is subordinated to the construction of this holy temple of the Spirit, whose manifestations are not abstract ideas, but fruits of goodness, of peace, of charity and forgiveness.”

— Edward Nelson,
   Mathematics and Faith (pdf)

Belief in the consistency of arithmetic may or may not be foolish, and therefore an Emersonian hobgoblin of little minds, but bullshit is bullshit, whether in London, in Princeton, in Toronto, or in Rome.

Wednesday, October 5, 2005

Wednesday October 5, 2005

Filed under: General — m759 @ 5:00 PM

New Page for Harvard’s President

From today’s Harvard Crimson:

“University President Lawrence H. Summers said yesterday that he will marry his longtime partner, Professor of English Elisa New.”

“I dwell in Possibility
A fairer House than Prose”

— Emily Dickinson, quoted in
    The Regenerate Lyric:
    Theology and Innovation
    in American Poetry, by
    Elisa New, page 162

Related material:
Log24 entries for Jan. 24 and 25, 2005.

Monday, August 22, 2005

Monday August 22, 2005

Filed under: General — Tags: , — m759 @ 4:07 PM
The Hole

Part I: Mathematics and Narrative

The image “http://www.log24.com/log/pix05B/050822-Narr.jpg” cannot be displayed, because it contains errors.

Apostolos Doxiadis on last month's conference on "mathematics and narrative"–

Doxiadis is describing how talks by two noted mathematicians were related to

    "… a sense of a 'general theory bubbling up' at the meeting… a general theory of the deeper relationship of mathematics to narrative…. "

Doxiadis says both talks had "a big hole in the middle."  

    "Both began by saying something like: 'I believe there is an important connection between story and mathematical thinking. So, my talk has two parts.  [In one part] I’ll tell you a few things about proofs.  [And in the other part] I’ll tell you about stories.' …. And in both talks it was in fact implied by a variation of the post hoc propter hoc, the principle of consecutiveness implying causality, that the two parts of the lectures were intimately related, the one somehow led directly to the other."
  "And the hole?"
  "This was exactly at the point of the link… [connecting math and narrative]… There is this very well-known Sidney Harris cartoon… where two huge arrays of formulas on a blackboard are connected by the sentence ‘THEN A MIRACLE OCCURS.’ And one of the two mathematicians standing before it points at this and tells the other: ‘I think you should be more explicit here at step two.’ Both… talks were one half fascinating expositions of lay narratology– in fact, I was exhilarated to hear the two most purely narratological talks at the meeting coming from number theorists!– and one half a discussion of a purely mathematical kind, the two parts separated by a conjunction roughly synonymous to ‘this is very similar to this.’  But the similarity was not clearly explained: the hole, you see, the ‘miracle.’  Of course, both [speakers]… are brilliant men, and honest too, and so they were very clear about the location of the hole, they did not try to fool us by saying that there was no hole where there was one."

Part II: Possible Worlds

"At times, bullshit can only be countered with superior bullshit."
Norman Mailer

Many Worlds and Possible Worlds in Literature and Art, in Wikipedia:

    "The concept of possible worlds dates back to a least Leibniz who in his Théodicée tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds.  Voltaire satirized this view in his picaresque novel Candide….
    Borges' seminal short story El jardín de senderos que se bifurcan ("The Garden of Forking Paths") is an early example of many worlds in fiction."



Modal Logic in Wikipedia

Possible Worlds in Wikipedia

Possible-Worlds Theory, by Marie-Laure Ryan
(entry for The Routledge Encyclopedia of Narrative Theory)

The God-Shaped Hole

Part III: Modal Theology

  "'What is this Stone?' Chloe asked….
  '…It is told that, when the Merciful One made the worlds, first of all He created that Stone and gave it to the Divine One whom the Jews call Shekinah, and as she gazed upon it the universes arose and had being.'"

  — Many Dimensions, by Charles Williams, 1931 (Eerdmans paperback, April 1979, pp. 43-44)

"The lapis was thought of as a unity and therefore often stands for the prima materia in general."

  — Aion, by C. G. Jung, 1951 (Princeton paperback, 1979, p. 236)

"Its discoverer was of the opinion that he had produced the equivalent of the primordial protomatter which exploded into the Universe."

  — The Stars My Destination, by Alfred Bester, 1956 (Vintage hardcover, July 1996, p. 216)
"We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz 

The image “http://www.log24.com/log/pix05B/050802-Stone.gif” cannot be displayed, because it contains errors.

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)

Saturday, August 13, 2005

Saturday August 13, 2005

Filed under: General,Geometry — m759 @ 2:00 PM

Kaleidoscope, continued:

Austere Geometry

From Noel Gray, The Kaleidoscope: Shake, Rattle, and Roll:

“… what we will be considering is how the ongoing production of meaning can generate a tremor in the stability of the initial theoretical frame of this instrument; a frame informed by geometry’s long tradition of privileging the conceptual ground over and above its visual manifestation.  And to consider also how the possibility of a seemingly unproblematic correspondence between the ground and its extrapolation, between geometric theory and its applied images, is intimately dependent upon the control of the truth status ascribed to the image by the generative theory.  This status in traditional geometry has been consistently understood as that of the graphic ancilla– a maieutic force, in the Socratic sense of that term– an ancilla to lawful principles; principles that have, traditionally speaking, their primary expression in the purity of geometric idealities.*  It follows that the possibility of installing a tremor in this tradition by understanding the kaleidoscope’s images as announcing more than the mere subordination to geometry’s theory– yet an announcement that is still in a sense able to leave in place this self-same tradition– such a possibility must duly excite our attention and interest.

* I refer here to Plato’s utilisation in the Meno of graphic austerity as the tool to bring to the surface, literally and figuratively, the inherent presence of geometry in the mind of the slave.”

See also

Noel Gray, Ph.D. thesis, U. of Sydney, Dept. of Art History and Theory, 1994:

“The Image of Geometry: Persistence qua Austerity– Cacography and The Truth to Space.”

Sunday, July 17, 2005

Sunday July 17, 2005

Filed under: General — m759 @ 7:59 PM


Yesterday’s AP “Thought for Today”–

“In some sort of crude sense which no vulgarity, no humor, no overstatement can quite extinguish, the physicists have known sin; and this is a knowledge which they cannot lose.” – J. Robert Oppenheimer, American physicist (1904-1967).

From Log24 on Dec. 17, 2002:

The Dancing Wu Li Masters,
by Gary Zukav, Harvard ’64:

“The Wu Li Masters know that physicists are doing more than ‘discovering the endless diversity of nature.’ They are dancing with Kali [or Durga], the Divine Mother of Hindu mythology.”

“Eastern religions have nothing to say about physics, but they have a great deal to say about human experience. In Hindu mythology, Kali, the Divine Mother, is the symbol for the infinite diversity of experience. Kali represents the entire physical plane. She is the drama, tragedy, humor, and sorrow of life. She is the brother, father, sister, mother, lover, and friend. She is the fiend, monster, beast, and brute. She is the sun and the ocean. She is the grass and the dew. She is our sense of accomplishment and our sense of doing worthwhile. Our thrill of discovery is a pendant on her bracelet. Our gratification is a spot of color on her cheek. Our sense of importance is the bell on her toe.

This full and seductive, terrible and wonderful earth mother always has something to offer. Hindus know the impossibility of seducing her or conquering her and the futility of loving her or hating her; so they do the only thing that they can do. They simply honor her.”

How could I dance with another….?

— John Lennon and Paul McCartney, 1962-1963  

See also yesterday‘s entry.

Sunday, July 3, 2005

Sunday July 3, 2005

Filed under: General — m759 @ 2:28 PM


1. Blue Ridge meets Black Mountain,

2. Vertical meets horizontal in music,

3. The timeless meets time in religion.


1. Blue Ridge, Black Mountain

Montreat College is located in the beautiful Blue Ridge Mountains of Western North Carolina…. The Black Mountain Campus is… three miles from the main campus in the historic town of Black Mountain.”

Black Mountain College was “established on the Blue Ridge Assembly grounds outside the town of Black Mountain in North Carolina in the fall of 1933.”

USA Today, May 15, 2005, on Billy Graham

“MONTREAT, N.C. — … It’s here at his… homestead, where the Blue Ridge meets the Black Mountain range east of Asheville, that Graham gave a rare personal interview.”

See also the following from June 24:

The image “http://www.log24.com/log/pix05A/050624-Cross.jpg” cannot be displayed, because it contains errors.

“No bridge reaches God, except one…
God’s Bridge: The Cross.”

— Billy Graham Evangelistic Association,
according to messiahpage.com

For some remarks more in the spirit of Black Mountain than of the Blue Ridge, see today’s earlier entry on pianist Grete Sultan and composer Tui St. George Tucker.

2. Vertical, Horizontal in Music

Richard Neuhaus on George Steiner’s
Grammars of Creation

 “… the facts of the world are not and will never be ‘the end of the matter.’ Music joins grammar in pointing to the possibility, the reality, of more. He thinks Schopenhauer was on to something when he said music will continue after the world ends.

‘The capacity of music to operate simultaneously along horizontal and vertical axes, to proceed simultaneously in opposite directions (as in inverse canons), may well constitute the nearest that men and women can come to absolute freedom.  Music does “keep time” for itself and for us.'”

3. Timeless, Time

A Trinity Sunday sermon quotes T. S. Eliot:

“… to apprehend
The point of intersection of the timeless
With time, is an occupation for the saint.”

See also The Diamond Project.

Update of July 8, 2005, 3 AM:

A Bridge for Private Ryan

The image “http://www.log24.com/log/pix05A/050708-RyansBridge.jpg” cannot be displayed, because it contains errors.

In memory of actor
Harrison Richard Young, 75,
who died on Sunday, July 3, 2005

Sunday, May 22, 2005

Sunday May 22, 2005

Filed under: General — Tags: — m759 @ 4:09 PM

The Diamond in the Labyrinth

From the labyrinth of Solitude:

  1. An Invariant Feast
  2. Columbia News obituary of Robert D. Cumming
  3. Solitude

    (Phenomenology and Deconstruction, Vol 4
    by Robert Denoon Cumming)

    On page 13 of Solitude —

    From Heidegger’s “Letter on Humanism” —
    “… so long as philosophy merely busies itself with continually obstructing the possibility of admission to the subject of thinking– that is, the truth of being– it escapes the danger of ever being broken against the hardness of that subject.  Thus ‘philosophizing’ about the shattering is separated by an abyss from a thinking that is shattered.”

    This suggests a search for
    “Heidegger” + “diamond,” which yields —

  4. The Diamond at the End of Time,
    which leads to
  5. Orson Welles Interviews Jilly Dybka,
    which leads to
  6. Poetry Hut Blog,
    which leads to

  7. Fair Territory, by Jilly Dybka,
    which contains the following —
  8. The Quickening

    I hold my breath, the plane’s
       wheels under me
    still suspended in the minutes after
    takeoff, when the planet’s brute gravity
    statistically can cause a disaster.
    We are flying low enough that I scan
    civilization in miniature.
    Blue pill swimming pools, and
       roadways that fan
    out like ribbons in the wind. On the sure
    crust, too, a baseball diamond.
       Young boys race
    across the tilted surface, mute and small,
    kicking up red dust. First base, Second base,
    Third Base, Home. We ascend into nightfall
    and beneath the broken stars one kid bunts.
    I remember I was a rookie once.

  9. From yesterday’s online New York Times:

    The image “http://www.log24.com/log/pix05/050521-ConeyIslandCrash.gif” cannot be displayed, because it contains errors.

Nine is a Vine.

Tuesday, March 29, 2005

Tuesday March 29, 2005

Filed under: General — Tags: — m759 @ 4:01 PM


The stranglehold of the Wiener Kreis on Harvard philosophy may at last be breaking:

"… imagination and belief are related….  belief presupposes imagination…."

"To negate the actual is to move imaginatively into the realm of modality.  Logic is all about the entertaining of possibilities."

"… imagination is central to an account of linguistic understanding. To understand a sentence is to imaginatively grasp the possibility it represents."

— Colin McGinn, excerpt (pdf) from Mindsight: Image, Dream, Meaning, published by Harvard University Press on November 22, 2004

From November 22, 2004:

Photo by Gerry Gantt

From Four Quartets:

And the pool was filled
with water out of sunlight,
And the lotos rose, quietly, quietly,
The surface glittered out of heart of light…

Thursday, March 3, 2005

Thursday March 3, 2005

Filed under: General — Tags: — m759 @ 3:26 PM
Necessity, Possibility, Symmetry

The image “http://www.log24.com/log/pix05/050303-Symmetry.gif” cannot be displayed, because it contains errors.

Matrix group actions,
March 26, 1985

"We symbolize logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz,
(Log24.net, 1/25/05)

And what do we           
   symbolize by  The image “http://www.log24.com/theory/images/Modal-diamondbox.gif” cannot be displayed, because it contains errors. ?

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)

Sunday, February 20, 2005

Sunday February 20, 2005

Filed under: General,Geometry — Tags: , , — m759 @ 2:20 PM

Relativity Blues

Today, February 20, is the 19th anniversary of my note The Relativity Problem in Finite Geometry.  Here is some related material.

In 1931, the Christian writer Charles Williams grappled with the theology of time, space, free will, and the many-worlds interpretation of quantum mechanics (anticipating by many years the discussion of this topic by physicists beginning in the 1950's).

(Some pure mathematics — untainted by physics or theology — that is nevertheless related, if only by poetic analogy, to Williams's 1931 novel, Many Dimensions, is discussed in the above-mentioned note and in a generalization, Solomon's Cube.)

On the back cover of Williams's 1931 novel, the current publisher, William B. Eerdmans Publishing Company of Grand Rapids, Michigan, makes the following statement:

"Replete with rich religious imagery, Many Dimensions explores the relation between predestination and free will as it depicts different human responses to redemptive transcendence."

One possible response to such statements was recently provided in some detail by a Princeton philosophy professor.  See On Bullshit, by Harry G. Frankfurt, Princeton University Press, 2005.

A more thoughtful response would take into account the following:

1. The arguments presented in favor of philosopher John Calvin, who discussed predestination, in The Death of Adam: Essays on Modern Thought, by Marilynne Robinson

2. The physics underlying Einstein's remarks on free will, God, and dice
3. The physics underlying Rebecca Goldstein's novel Properties of Light and Paul Preuss's novels  Secret Passages and Broken Symmetries

4. The physics underlying the recent so-called "free will theorem" of John Conway and Simon Kochen of Princeton University

5. The recent novel Gilead, by Marilynne Robinson, which deals not with philosophy, but with lives influenced by philosophy — indirectly, by the philosophy of the aforementioned John Calvin.

From a review of Gilead by Jane Vandenburgh:  

"In The Death of Adam, Robinson shows Jean Cauvin to be the foremost prophet of humanism whose Protestant teachings against the hierarchies of the Roman church set in motion the intellectual movements that promoted widespread literacy among the middle and lower classes, led to both the American and French revolutions, and not only freed African slaves in the United States but brought about suffrage for women. It's odd then that through our culture's reverse historicism, the term 'Calvinism' has come to mean 'moralistic repression.'"

For more on what the Calvinist publishing firm Eerdmans calls "redemptive transcendence," see various July 2003 Log24.net entries.  If these entries include a fair amount of what Princeton philosophers call bullshit, let the Princeton philosophers meditate on the summary of Harvard philosophy quoted here on November 5 of last year, as well as the remarks of November 5, 2003,  and those of November 5, 2002.

From Many Dimensions (Eerdmans paperback, 1963, page 53):

"Lord Arglay had a suspicion that the Stone would be purely logical.  Yes, he thought, but what, in that sense, were the rules of its pure logic?"

A recent answer:

Modal Theology

"We symbolize logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz,
(Log24.net, 1/25/05)

And what do we           
   symbolize by  The image “http://www.log24.com/theory/images/Modal-diamondbox.gif” cannot be displayed, because it contains errors. ?

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)

Thursday, February 17, 2005

Thursday February 17, 2005

Filed under: General,Geometry — Tags: — m759 @ 1:00 PM
Modal Theology

"We symbolize logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz,
(Log24.net, 1/25/05)

And what do we           
   symbolize by  The image “http://www.log24.com/theory/images/Modal-diamondbox.gif” cannot be displayed, because it contains errors. ?

On the Lapis Philosophorum,
the Philosophers' Stone –

"'What is this Stone?' Chloe asked….
'…It is told that, when the Merciful One
made the worlds, first of all He created
that Stone and gave it to the Divine One
whom the Jews call Shekinah,
and as she gazed upon it
the universes arose and had being.'"
Many Dimensions,
by Charles Williams, 1931
(Eerdmans paperback,
April 1979, pp. 43-44)

"The lapis was thought of as a unity
and therefore often stands for
the prima materia in general."
Aion, by C. G. Jung, 1951
(Princeton paperback,
1979, p. 236)

"Its discoverer was of the opinion that
he had produced the equivalent of
the primordial protomatter
which exploded into the Universe."
The Stars My Destination,
by Alfred Bester, 1956
(Vintage hardcover,
July 1996, p. 216)

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)

See also
The Diamond Archetype.

For more on modal theology, see

Kurt Gödel's Ontological Argument

 The Ontological Argument
 from Anselm to Gödel.

Tuesday, January 25, 2005

Tuesday January 25, 2005

Filed under: General — Tags: — m759 @ 12:00 PM

Diamonds Are Forever

The image “http://www.log24.com/theory/images/Modal-diamondinbox.gif” cannot be displayed, because it contains errors.


Robert Stone,
A Flag for Sunrise:

" 'That old Jew gave me this here.'  Egan looked at the diamond.  'I ain't giving this to you, understand?  The old man gave it to me for my boy.  It's worth a whole lot of money– you can tell that just by looking– but it means something, I think.  It's got a meaning, like.'

'Let's see,' Egan said, 'what would it mean?'  He took hold of Pablo's hand cupping the stone and held his own hand under it.  '"The jewel is in the lotus," perhaps that's what it means.  The eternal in the temporal.  The Boddhisattva declining nirvana out of compassion.   Contemplating the ignorance of you and me, eh?  That's a metaphor of our Buddhist friends.'

Pablo's eyes glazed over.  'Holy shit,' he said.  'Santa Maria.'  He stared at the diamond in his palm with passion.

'Hey,' he said to the priest, 'diamonds are forever!  You heard of that, right?  That means something, don't it?'

'I have heard it,' Egan said.  'Perhaps it has a religious meaning.' "

"We symbolize logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz



Nythamar Fernandes de Oliveira

Pontifical Catholic University
at Porto Alegre, Brazil

"Such is the paradoxical 'encounter' of the eternal with the temporal. Just like the Moment of the Incarnation, when the Eternal entered the temporal, Kierkegaard refers to the category of the Instant (Danish Ojeblikket, 'a glance of the eye, eyeblink,' German Augenblick) as the dialectical kernel of our existential consciousness:

If the instant is posited, so is the eternal –but also the future, which comes again like the past … The concept around which everything turns in Christianity, the concept which makes all things new, is the fullness of time, is the instant as eternity, and yet this eternity is at once the future and the past.

Although I cannot examine here the Kierkegaardian conception of time, the dialectical articulation of time and existence, as can be seen, underlies his entire philosophy of existence, just as the opposition between 'eternity' and 'temporality': the instant, as 'an atom of eternity,' serves to restructure the whole synthesis of selfhood into a spiritual one, in man’s 'ascent' toward its Other and the Unknown. In the last analysis, the Eternal transcends every synthesis between eternity and time, infinity and finiteness, preserving not only the Absolute Paradox in itself but above all the wholly otherness of God. It is only because of the Eternal, therefore, that humans can still hope to attain their ultimate vocation of becoming a Chistian. As Kierkegaard writes in Works of Love (1847),

The possibility of the good is more than possibility, for it is the eternal. This is the basis of the fact that one who hopes can never be deceived, for to hope is to expect the possibility of the good; but the possibility of the good is eternal. …But if there is less love in him, there is also less of the eternal in him; but if there is less of the eternal in him, there is also less possibility, less awareness of possibility (for possibility appears through the temporal movement of the eternal within the eternal in a human being)."

Monday, January 24, 2005

Monday January 24, 2005

Filed under: General — Tags: — m759 @ 10:23 PM

The Diamond
of Possibility

by  Keith Allen Korcz

"We symbolize logical necessity with the box (box.gif (75 bytes)) and logical possibility with the diamond (diamond.gif (82 bytes)).  I first discuss combining negations with the box and diamond, noting that logical possibility and logical necessity are inter-definable with the help of negation: box.gif (75 bytes)p = ~diamond.gif (82 bytes)~p and diamond.gif (82 bytes)p = ~box.gif (75 bytes)~p. Thus, possibility and necessity are two sides of the same coin."

And what do we           
 symbolize by  The image “http://www.log24.com/theory/images/Modal-diamondbox.gif” cannot be displayed, because it contains errors. ?

Sunday, July 25, 2004

Sunday July 25, 2004

Filed under: General — Tags: — m759 @ 8:30 AM

Keeping Time

Richard Neuhaus on George Steiner's
Grammars of Creation

 "… the facts of the world are not and will never be 'the end of the matter.' Music joins grammar in pointing to the possibility, the reality, of more. He thinks Schopenhauer was on to something when he said music will continue after the world ends.

'The capacity of music to operate simultaneously along horizontal and vertical axes, to proceed simultaneously in opposite directions (as in inverse canons), may well constitute the nearest that men and women can come to absolute freedom.  Music does "keep time" for itself and for us.'"

"Goin' to Carolina in my mind…."

Thursday, June 3, 2004

Thursday June 3, 2004

Filed under: General — Tags: — m759 @ 3:17 PM


Today’s New York Times story on Richard Helms, together with my reminiscences in the entry that follows it below, suggest the following possibility for symbol-mongering:

Compare the 16-point star of the C.I.A.
with the classic 8-point star of Venus:

From today’s New York Times:

The image “http://www.log24.com/log/pix04A/040603-Tenet.jpg” cannot be displayed, because it contains errors.

Not even the most powerful
can alter the alignment
of the stars.

In a related story….

The Good Bad Boy
By Alison Lurie

“Today, many people have the illusion that they know who Pinocchio is. They think that he is a wooden marionette who becomes a human boy; that he was swallowed by a huge fish; and that when he told lies his nose grew longer. These people are right, but often in a very limited way. They know Pinocchio only from the sentimentalized and simplified Disney cartoon, or the condensed versions of his story that are thought more suitable for children. The original novel by Carlo Collodi, which today survives mainly in scholarly editions, is much longer, far more complex and interesting, and also much darker.”

The New York Review of Books, June 24, 2004


Thursday, May 27, 2004

Thursday May 27, 2004

Filed under: General — Tags: — m759 @ 10:10 AM


On the poetry of Geoffrey Hill:

"… why read him? Because of the things he writes about—war and peace and sacrifice, and the search for meaning and the truths of the heart, and for that haunting sense that, in spite of war and terror and the indifferences that make up our daily hells, there really is some grander reality, some ineluctable presence we keep touching. There remains in Hill the daunting possibility that it may actually all cohere in the end, or at least enough of it to keep us searching for more.

There is a hard edge to Hill, a strong Calvinist streak in him, and an intelligence that reminds one of Milton….."

— Paul Mariani, review in America of Geoffrey Hill's The Orchards of Syon

"Hello! Kinch here. Put me on to Edenville. Aleph, alpha: nought, nought, one." 

"A very short space of time through very short times of space…. Am I walking into eternity along Sandymount strand?"

James Joyce, Ulysses, Proteus chapter

"Time has been unfolded into space."

James O. Coplien, Bell Labs

"Pattern and symmetry are closely related."

James O. Coplien on Symmetry Breaking

"… as the critic S. L. Goldberg puts it, 'the chapter explores the Protean transformations of matter in time . . . apprehensible only in the condition of flux . . . as object . . . and Stephen himself, as subject. In the one aspect Stephen is seeking the principles of change and the underlying substance of sensory experience; in the other, he is seeking his self among its temporal manifestations'….

— Goldberg, S.L. 'Homer and the Nightmare of History.' Modern Critical Views: James Joyce. Ed. Harold Bloom. New York: Chelsea House, 1986. 21-38."

from the Choate site of David M. Loeb

In summary:


James Joyce


See also Time Fold.

(By the way, Jorn Barger seems
to have emerged from seclusion.)


Thursday, May 20, 2004

Thursday May 20, 2004

Filed under: General,Geometry — m759 @ 7:00 AM


“A comparison or analogy. The word is simply a transliteration of the Greek word: parabolé (literally: ‘what is thrown beside’ or ‘juxtaposed’), a term used to designate the geometric application we call a ‘parabola.’….  The basic parables are extended similes or metaphors.”


“If one style of thought stands out as the most potent explanation of genius, it is the ability to make juxtapositions that elude mere mortals.  Call it a facility with metaphor, the ability to connect the unconnected, to see relationships to which others are blind.”

Sharon Begley, “The Puzzle of Genius,” Newsweek magazine, June 28, 1993, p. 50

“The poet sets one metaphor against another and hopes that the sparks set off by the juxtaposition will ignite something in the mind as well. Hopkins’ poem ‘Pied Beauty’ has to do with ‘creation.’ “

Speaking in Parables, Ch. 2, by Sallie McFague

“The Act of Creation is, I believe, a more truly creative work than any of Koestler’s novels….  According to him, the creative faculty in whatever form is owing to a circumstance which he calls ‘bisociation.’ And we recognize this intuitively whenever we laugh at a joke, are dazzled by a fine metaphor, are astonished and excited by a unification of styles, or ‘see,’ for the first time, the possibility of a significant theoretical breakthrough in a scientific inquiry. In short, one touch of genius—or bisociation—makes the whole world kin. Or so Koestler believes.”

— Henry David Aiken, The Metaphysics of Arthur Koestler, New York Review of Books, Dec. 17, 1964

For further details, see

Speaking in Parables:
A Study in Metaphor and Theology

by Sallie McFague

Fortress Press, Philadelphia, 1975

Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7

“Perhaps every science must start with metaphor and end with algebra; and perhaps without metaphor there would never have been any algebra.”

— attributed, in varying forms (1, 2, 3), to Max Black, Models and Metaphors, 1962

For metaphor and algebra combined, see

“Symmetry invariance in a diamond ring,” A.M.S. abstract 79T-A37, Notices of the Amer. Math. Soc., February 1979, pages A-193, 194 — the original version of the 4×4 case of the diamond theorem.

Friday, May 14, 2004

Friday May 14, 2004

Filed under: General — m759 @ 6:36 PM

Moral Hazard —
The Devil and Wallace Stevens,
continued from May 1-2 entries:

Law Day,
Readings for Law Day,
Fallen from Heaven, and
The Script

University of Southern California, Department of Economics — Industrial Organization ECN 680 – Autumn 2002 — Introduction to Contract and Organization Theory —

Professor Jean-Jacques Laffont
(September 4October 21):

“The purpose of this course is to introduce the student to modern contract and organization theory. Part 1 of the course focuses upon models with moral hazard and adverse selection.”

From the insurance page at 


“The size of the insurance industry indicates that people are eager to pay to avoid risk. They pay and get nothing if fortune smiles on them, whereas if misfortune strikes, they break even because the insurance should just pay back the value lost in the misfortune.

Sometimes, however, people do better than break even when misfortune strikes, and this possibility has greatly interested economists. If, for example, the misfortune costs a person $1000, but insurance will pay $2000, the insured person has no incentive to avoid the misfortune and may act to bring it on. This tendency of insurance to change behavior is called moral hazard.

Sometimes moral hazard is dramatic….

People who know that they face large risks are more likely to buy insurance than people who face small risks. Insurance companies try to minimize the problem that only the people with big risks will buy their product, which is the problem of adverse selection ….”

From today’s New York Times:

“Jean-Jacques Laffont, an economist known for developing mathematical models to estimate what something is worth in situations of deep uncertainty, died on May 1 in Toulouse, France. He was 57….

…Jerry R. Green of Harvard said he was ‘an architect of systems’ and ‘a very original figure.’

Eric Maskin, a professor at the Institute for Advanced Study in Princeton, N.J., called Dr. Laffont ‘simply one of the major figures of our time.’

‘Many people would say he was the leading economist in Europe,’ he added, ‘and that wouldn’t be an unfair judgment.’

Although Dr. Laffont’s models were abstruse enough to satisfy the most theoretical economists, Dr. Green said they were adapted for practical purposes by companies, as well as by public television for scheduling programs.”

Sunday, April 11, 2004

Sunday April 11, 2004

Filed under: General,Geometry — m759 @ 3:28 PM

Good Friday and
Descartes’s Easter Egg

“The use of z, y, x . . . to represent unknowns is due to René Descartes, in his La géometrie (1637)…. In a paper on Cartesian ovals, prepared before 1629, x alone occurs as unknown…. This is the earliest place in which Descartes used one of the last letters of the alphabet to represent an unknown.”

— Florian Cajori, A History of Mathematical Notations. 2 volumes. Lasalle, Illinois: The Open Court Publishing Co., 1928-1929. (Vol. 1, page 381)

This is from


Descartes’s Easter Egg is found at

EggMath: The Shape of an Egg —
Cartesian Ovals

An Easter Meditation
on Humpty Dumpty

The following is excerpted from a web page headed “Catholic Way.”  It is one of a series of vicious and stupid Roman Catholic attacks on Descartes.  Such attacks have been encouraged by the present Pope, who today said “may the culture of life and love render vain the logic of death.”

The culture of life and love is that of the geometry (if not the philosophy) of Descartes.  The logic of death is that of Karol Wojtyla, as was made very clear in the past century by the National Socialist Party, which had its roots in Roman Catholicism.

Humpty Dumpty sat on a wall.
Humpty Dumpty had a great fall

“In the century just completed, the human race found itself in a position not unlike the scrambled mess at the base of an imaginary English wall….

… we are heirs to a humanity that is broken, fractured, confused, unsure of what to make of itself….

 … ‘postmodernism’ is merely the articulation of the fractured, dissipated state of the human being…. 

Without relating a history of modern philosophy, our unfortunate human shell has suffered a continual fragmentation for a period of roughly 500 years. (You philosophers out there will recognize immediately that I am referring to the legacy of René Descartes.) And this fragmentation has been a one-way street: one assault after another on the integrity and dignity of the human person until you have, well, the 20th Century.

But now it’s the 21st Century.

The beauty … the marvel … the miracle of our time is the possibility that gravity will reverse itself: Humpty Dumpty may be able, once again, to assume his perch.”

—  Ted Papa,
Raising Humpty Dumpty


The upper part
of the above icon
is from EggMath.
For the lower part,
see Good Friday.

Monday, February 9, 2004

Monday February 9, 2004

Filed under: General — m759 @ 6:36 PM

Hermes and Folded Time

Yesterday’s entry on painter Ward Jackson and the philosopher Gadamer involved what is called hermeneutics, or the art of interpretation.  Gadamer was a leader in this field.  The following passage perhaps belabors the obvious, but it puts hermeneutics clearly in context.

From Daniel Chandler’s Semiotics for Beginners:

“The ‘tightness’ of semiotic codes themselves varies from the rule-bound closure of logical codes (such as computer codes) to the interpretative looseness of poetic codes. Pierre Guiraud notes that ‘signification is more or less codified,‘ and that some systems are so ‘open’ that they ‘scarcely merit the designation ‘code’ but are merely systems of “hermeneutic” interpretation’ (*Guiraud 1975, 24). Guiraud makes the distinction that a code is ‘a system of explicit social conventions’ whilst ‘a hermeneutics’ is ‘a system of implicit, latent and purely contingent signs,’ adding that ‘it is not that the latter are neither conventional nor social, but they are so in a looser, more obscure and often unconscious way’ (*ibid., 41). His claim that (formal) codes are ‘explicit’ seems untenable since few codes would be likely to be widely regarded as wholly explicit. He refers to two ‘levels of signification,’ but it may be more productive to refer to a descriptive spectrum based on relative explicitness, with technical codes veering towards one pole and interpretative practices veering towards the other. At one end of the spectrum are what Guiraud refers to as ‘explicit, socialized codes in which the meaning is a datum of the message as a result of a formal convention between participants’ (*ibid., 43-4). In such cases, he argues, ‘the code of a message is explicitly given by the sender’ (*ibid., 65). At the other end of the spectrum are ‘the individual and more or less implicit hermeneutics in which meaning is the result of an interpretation on the part of the receiver’ (*ibid., 43-4). Guiraud refers to interpretative practices as more ‘poetic,’ being ‘engendered by the receiver using a system or systems of implicit interpretation which, by virtue of usage, are more or less socialized and conventionalized’ (*ibid., 41). Later he adds that ‘a hermeneutics is a grid supplied by the receiver; a philosophical, aesthetic, or cultural grid which he applies to the text’ (*ibid., 65).”

* Pierre Guiraud, Semiology (trans. George Gross), London: Routledge & Kegan Paul, 1975

Related material:

From Michalinos Zembylas on Michel Serres:

“Serres’ use of Hermes is reminiscent of hermeneutics. The word derives from Hermes and implies that the idea of hermeneutics as a theory of interpretation (and consequently of communication) is necessary when there is a possibility for misunderstanding. Hermes translated the ‘word of Gods’; an interpreter translates the written text, and a teacher ‘translates’ the literature….  Understanding then is aided by the mediation of a hermeneut…. According to Gadamer (1975), the pleasure such understanding elicits is the joy of knowledge (which does not operate as an enchantment but as a kind of transformation). It is worth exploring this idea a bit more since there are interesting connections with Serres’ work.”

There is also an interesting connection with Guiraud’s work.  As quoted above, Guiraud wrote that

“…a hermeneutics is a grid supplied by the receiver; a philosophical, aesthetic, or cultural grid which he applies to the text.”

Serres describes Hermes as passing through “folded time.”  Precisely how time can be folded into a grid is the subject of my note The Grid of Time, which gives the context for the Serres phrase “folded time.”

For more on hermeneutics and Gadamer’s “joy of knowledge,” see Ian Lee in The Third Word War on “understanding the J.O.K.E.” (the Joy of Knowledge Encyclopedia).

Saturday, November 15, 2003

Saturday November 15, 2003

Filed under: General — Tags: , — m759 @ 12:00 PM

Aes Triplex

The title, from a Robert Louis Stevenson essay, means “triple brass” (or triple bronze):

From the admirable site of J. Nathan Matias:

Aes Triplex means Triple Bronze, from a line in Horace’s Odes that reads ‘Oak and triple bronze encompassed the breast of him who first entrusted his frail craft to the wild sea.’ ”

From Philip K. Dick’s The Man in the High Castle:

Juliana said, “Oracle, why did you write The Grasshopper Lies Heavy? What are we supposed to learn?”

“You have a disconcertingly superstitious way of phrasing your question,” Hawthorne said. But he had squatted down to witness the coin throwing. “Go ahead,” he said; he handed her three Chinese brass coins with holes in the center. “I generally use these.”

This passage, included in my earlier entry of Friday, combined with the opening of yet another major motion picture starring Russell Crowe, suggests three readings for that young man, who is perhaps the true successor to Marlon Brando.

Oracle, for Crowe as John Nash (A Beautiful Mind):

Understanding the I Ching

Mutiny, for Crowe as Jack Aubrey (Master and Commander):

Bartleby, the Scrivener

Storm, for Crowe as Maximus (Gladiator):

Pharsalia, Book V:
The Oracle, the Mutiny, the Storm

As background listening, one possibility is Sinatra’s classic “Three Coins”:

“Three hearts in the fountain,
Each heart longing for its home.
There they lie in the fountain
Somewhere in the heart of Rome.*” 

Personally, though, I prefer, as a tribute to author Joan Didion (who also wrote of coins and the Book of Transformations), the even more classic Sinatra ballad

Angel Eyes.”

 * Horace leads to “Acroceraunian shoals,” which leads to Palaeste, which leads to Pharsalia and to the heart of Rome.  (With a nod to my high school Latin teacher, the late great John Stachowiak.)

Tuesday, September 2, 2003

Tuesday September 2, 2003

Filed under: General,Geometry — Tags: — m759 @ 1:11 PM

One Ring to Rule Them All

In memory of J. R. R. Tolkien, who died on this date, and in honor of Israel Gelfand, who was born on this date.

Leonard Gillman on his collaboration with Meyer Jerison and Melvin Henriksen in studying rings of continuous functions:

“The triple papers that Mel and I wrote deserve comment. Jerry had conjectured a characterization of beta X (the Stone-Cech compactification of X) and the three of us had proved that it was true. Then he dug up a 1939 paper by Gelfand and Kolmogoroff that Hewitt, in his big paper, had referred to but apparently not appreciated, and there we found Jerry’s characterization. The three of us sat around to decide what to do; we called it the ‘wake.’  Since the authors had not furnished a proof, we decided to publish ours. When the referee expressed himself strongly that a title should be informative, we came up with On a theorem of Gelfand and Kolmogoroff concerning maximal ideals in rings of continuous functions. (This proved to be my second-longest title, and a nuisance to refer to.) Kolmogoroff died many years ago, but Gelfand is still living, a vigorous octogenarian now at Rutgers. A year or so ago, I met him at a dinner party in Austin and mentioned the 1939 paper. He remembered it very well and proceeded to complain that the only contribution Kolmogoroff had made was to point out that a certain result was valid for the complex case as well. I was intrigued to see how the giants grouse about each other just as we do.”

Leonard Gillman: An Interview

This clears up a question I asked earlier in this journal….

Wednesday, May 14, 2003

Common Sense

On the mathematician Kolmogorov:

“It turns out that he DID prove one basic theorem that I take for granted, that a compact hausdorff space is determined by its ring of continuous functions (this ring being considered without any topology) — basic discoveries like this are the ones most likely to have their origins obscured, for they eventually come to be seen as mere common sense, and not even a theorem.”

Richard Cudney, Harvard ’03, writing at Xanga.com as rcudney on May 14, 2003

That this theorem is Kolmogorov’s is news to me.


The above references establish that Gelfand is usually cited as the source of the theorem Cudney discusses.  Gelfand was a student of Kolmogorov’s in the 1930’s, so who discovered what when may be a touchy question in this case.  A reference that seems relevant: I. M. Gelfand and A. Kolmogoroff, “On rings of continuous functions on topological spaces,” Doklady Akad. Nauk SSSR 22 (1939), 11-15.  This is cited by Gillman and Jerison in the classic Rings of Continuous Functions.

There ARE some references that indicate Kolmogorov may have done some work of his own in this area.  See here (“quite a few duality theorems… including those of Banaschewski, Morita, Gel’fand-Kolmogorov and Gel’fand-Naimark”) and here  (“the classical theorems of M. H. Stone, Gelfand & Kolmogorov”).

Any other references to Kolmogorov’s work in this area would be of interest.

Naturally, any discussion of this area should include a reference to the pioneering work of M. H. Stone.  I recommend the autobiographical article on Stone in McGraw-Hill Modern Men of Science, Volume II, 1968.

A response by Richard Cudney:

“In regard to your entry, it is largely correct.  The paper by Kolmogorov and Gelfand that you refer to is the one that I just read in his collected works.  So, I suppose my entry was unfair to Gelfand.  You’re right, the issue of credit is a bit touchy since Gelfand was his student.  In a somewhat recent essay, Arnol’d makes the claim that this whole thread of early work by Gelfand may have been properly due to Kolmogorov, however he has no concrete proof, having been but a child at the time, and makes this inference based only on his own later experience as Kolmogorov’s student.  At any rate, I had known about Gelfand’s representation theorem, but had not known that Kolmogorov had done any work of this sort, or that this theorem in particular was due to either of them. 

And to clarify-where I speak of the credit for this theorem being obscured, I speak of my own experience as an algebraic geometer and not a functional analyst.  In the textbooks on algebraic geometry, one sees no explanation of why we use Spec A to denote the scheme corresponding to a ring A.  That question was answered when I took functional analysis and learned about Gelfand’s theorem, but even there, Kolmogorov’s name did not come up.

This result is different from the Gelfand representation theorem that you mention-this result concerns algebras considered without any topology(or norm)-whereas his representation theorem is a result on Banach algebras.  In historical terms, this result precedes Gelfand’s theorem and is the foundation for it-he starts with a general commutative Banach algebra and reconstructs a space from it-thus establishing in what sense that the space to algebra correspondence is surjective, and hence by the aforementioned theorem, bi-unique.  That is to say, this whole vein of Gelfand’s work started in this joint paper.

Of course, to be even more fair, I should say that Stone was the very first to prove a theorem like this, a debt which Kolmogorov and Gelfand acknowledge.  Stone’s paper is the true starting point of these ideas, but this paper of Kolmogorov and Gelfand is the second landmark on the path that led to Grothendieck’s concept of a scheme(with Gelfand’s representation theorem probably as the third).

As an aside, this paper was not Kolmogorov’s first foray into topological algebra-earlier he conjectured the possibility of a classification of locally compact fields, a problem which was solved by Pontryagin.  The point of all this is that I had been making use of ideas due to Kolmogorov for many years without having had any inkling of it.”

Posted 5/14/2003 at 8:44 PM by rcudney

Sunday, August 10, 2003

Sunday August 10, 2003

Filed under: General — m759 @ 8:35 AM

Death of a Holy Man

Part I:  An American Religion

Hiroshima Mayor Says
US Worships Nukes

“HIROSHIMA — Hiroshima Mayor Tadatoshi Akiba warned that the world is moving toward war and accused Washington of ‘worshipping’ nuclear weapons during Wednesday’s ceremony marking the 58th anniversary of the atomic bombing of the city….

… the Hiroshima mayor blamed the United States for making the world a more uncertain place through its policy of undermining the Treaty on the Non-Proliferation of Nuclear Weapons.

‘A world without nuclear weapons and war that the victims of the atomic bomb have long sought for is slipping into the shadows of growing black clouds that could turn into mushroom clouds at any moment,’ Akiba said. ‘The chief cause of this is the United States’ nuclear policy which, by openly declaring the possibility of a pre-emptive nuclear strike and by starting research into small ‘useable’ nuclear weapons, appears to worship nuclear weapons as God.’ “

Mainichi Shimbun, Aug. 6, 2003

Part II: Holy Men and
             Sons of Bitches

“I am become Death, the Destroyer of Worlds.”

Dr. J. Robert Oppenheimer,
    Director of Los Alamos

John Steinbeck describing Cannery Row in Monterey:

“Its inhabitants are, as the man once said, ‘whores, pimps, gamblers, and sons of bitches,’ by which he meant Everybody. Had the man looked through another peephole he might have said, ‘Saints and angels and martyrs and holy men,’ and he would have meant the same thing.”  

“Now we are all sons of bitches.”

Dr. Kenneth Bainbridge,
    Director of Trinity Test

Part III: Death of a Holy Man

The New York Times, Aug. 10, 2003:

Atom-Bomb Physicist Dies at 98

“Henry A. Boorse, a physicist who was one of the original scientists who worked on the Manhattan Project in the development of the atomic bomb, died on July 28 in Houston, where he lived….

Dr. Boorse was a consultant to the United States Atomic Energy Commission from 1946 to 1958 and to the Brookhaven National Laboratory from 1951 to 1955.

He and Lloyd Motz wrote a two-volume work, The World of the Atom (1966), and — with Jefferson Hane Weaver — a one-volume book, The Atomic Scientists (1989).”

From a review of The Atomic Scientists:

“… the authors try to add a personal element that can excite the reader about science.”

For more excitement, see Timequake, by Kurt Vonnegut, Jr.

Sunday, June 29, 2003

Sunday June 29, 2003

Filed under: General — m759 @ 11:00 PM

The sequel to
Every Boy Has a Daddy“:

Hepburn’s Mass
at Heaven’s Gate

Katharine Hepburn died at 2:50 PM EDT
on the Feast of St. Peter

“The Consecration and Sacrifice effected by the priest (standing in the place of Christ) is, then, the visible manifestation of an eternal and timeless act. After the Consecration, as Gueranger says in The Liturgical Year, ‘the divine Lamb is lying on our altar!’ Thus we see that the Mass is the visible reality, here and now, of the timeless eternal Mass of Heaven, described in the Apocalypse. Through it we participate in the Celestial Liturgy; through it the gates of Heaven are opened to us and the possibility of eternal life is made available to us.”

The Source:

The Church Militant recommends
Defense of the Inquisitions.

For a different viewpoint,
see my 
May 12 entries.

Sunday, April 20, 2003

Sunday April 20, 2003

Filed under: General — m759 @ 2:30 PM

Hall of Shame

“You belong with the cowards and ideologues in a hall of infamy and shame.”

— Actor Tim Robbins, who played pitcher Nuke LaLoosh in “Bull Durham,” in a letter to baseball Hall of Fame president Dale Petroskey.  Petroskey cancelled a scheduled April 26-27 Hall of Fame celebration of the Bull film due to the possibility of political remarks.

In further remarks at the National Press Club on April 15, Robbins said

“Sportswriters across the country reacted with such overwhelming fury at the Hall of Fame that the president of the Hall admitted he made a mistake and Major League Baseball disavowed any connection to the actions of the Hall’s president. A bully can be stopped, and so can a mob. It takes one person with the courage and a resolute voice.”

 Wonder Boy

Shoe, Easter 2003

Update of 2:00 AM April 21, 2003:

A belated Easter greeting from Durham, North Carolina.


Tuesday, January 7, 2003

Tuesday January 7, 2003

Filed under: General — m759 @ 2:45 AM

Can You See?

I finally got around to watching “Minority Report” on DVD.  My favorite part is scene 16, which takes place in a sort of high-tech fantasy park — rather like Hollywood itself.  Rufus T. Riley, the hacker who works there, asks Anderton, “You brought a precog… here?”   When the reality sinks in, he exclaims “Jesus Christ!,” falls to his knees, crosses himself, and asks “Are you reading my mind right now?”

A Brief History of Time

Time present and time past
Are both perhaps present
      in time future,
And time future contained
      in time past.
If all time is eternally present
All time is unredeemable.
What might have been is
      an abstraction
Remaining a perpetual
Only in a world of
What might have been and 
      what has been
Point to one end,
      which is always present.

— T. S. Eliot, “Burnt Norton”

Anderton and Agatha

Is it now?”
Good question, Agatha.


Tuesday, December 17, 2002

Tuesday December 17, 2002

Filed under: General — m759 @ 12:00 AM


Just Seventeen


Today's site music*
is in honor of
a memorable date.

Northern Songs.
Quiet may be restored by using
the midi control box at the top right
of this page.  Please let me know
if your browser is not showing
this control box.



From a June/July 1997
Hadassah Magazine article:

"Plato is obviously Jewish."

— Rebecca Goldstein

Readings on the Dark Lady  

From a July 27, 1997
New York Times article
by Holland Cotter:

"The single most important and sustained model for Khmer culture was India, from which Cambodia inherited two religions, Buddhism and Hinduism, and an immensely sophisticated art. This influence announces itself early in this exhibition in a spectacular seventh-century figure of the Hindu goddess Durga, whose hip-slung pose and voluptuous torso, as plush and taut as ripe fruit, combine the naturalism and idealism of the very finest Indian work."

From The Dancing Wu Li Masters,
by Gary Zukav, Harvard '64:

"The Wu Li Masters know that physicists are doing more than 'discovering the endless diversity of nature.' They are dancing with Kali [or Durga], the Divine Mother of Hindu mythology."

"Eastern religions have nothing to say about physics, but they have a great deal to say about human experience. In Hindu mythology, Kali, the Divine Mother, is the symbol for the infinite diversity of experience. Kali represents the entire physical plane. She is the drama, tragedy, humor, and sorrow of life. She is the brother, father, sister, mother, lover, and friend. She is the fiend, monster, beast, and brute. She is the sun and the ocean. She is the grass and the dew. She is our sense of accomplishment and our sense of doing worthwhile. Our thrill of discovery is a pendant on her bracelet. Our gratification is a spot of color on her cheek. Our sense of importance is the bell on her toe.

This full and seductive, terrible and wonderful earth mother always has something to offer. Hindus know the impossibility of seducing her or conquering her and the futility of loving her or hating her; so they do the only thing that they can do. They simply honor her."

How could I dance with another….?

— John Lennon and Paul McCartney, 1962-1963  

Wednesday, October 23, 2002

Wednesday October 23, 2002

Filed under: General — m759 @ 8:00 PM

Bright Star

From the website of Karey Lea Perkins:

“The truth is that man’s capacity for symbol-mongering in general and language in particular is…intimately part and parcel of his being human, of his perceiving and knowing, of his very consciousness…”

Walker Percy, The Message in the Bottle, Farrar, Strauss, and Giroux, 1975

Today’s New York Times story on Richard Helms, together with my reminiscences in the entry that follows it below, suggest the following possibility for symbol-mongering:

Compare the 16-point star of the C.I.A.

with the classic 8-point star of Venus:

This comparison is suggested by the Spanish word “Lucero” (the name, which means “Bright Star,” of the girl in Cuernavaca mentioned two entries down) and by the following passage from Robert A. Heinlein‘s classic novel, Glory Road:

    “I have many names. What would you like to call me?”

    “Is one of them ‘Helen’?”

    She smiled like sunshine and I learned that she had dimples. She looked sixteen and in her first party dress. “You are very gracious. No, she’s not even a relative. That was many, many years ago.” Her face turned thoughtful. “Would you like to call me ‘Ettarre’?”

    “Is that one of your names?”

    “It is much like one of them, allowing for different spelling and accent. Or it could be ‘Esther’ just as closely. Or ‘Aster.’ Or even ‘Estrellita.’ ”

    ” ‘Aster,’ ” I repeated. “Star. Lucky Star!”

The C.I.A. star above is from that organization’s own site.  The star of Venus (alias Aster, alias Ishtar) is from Symbols.com, an excellent site that has the following variations on the Bright Star theme:

Ideogram for light Alchemical sign
Greek “Aster” Babylonian Ishtar
Phoenician Astarte Octagram of Venus
Phaistos Symbol Fortress Octagram

See also my notes The Still Point and the Wheel and Midsummer Eve’s Dream.  Both notes quote Robinson Jeffers:

“For the essence and the end
Of his labor is beauty…
one beauty, the rhythm of that Wheel,
and who can behold it is happy
and will praise it to the people.”

— Robinson Jeffers, “Point Pinos and Point Lobos,”
quoted at the end of The Cosmic Code,
by Heinz Pagels, Simon & Schuster, 1982

Place the eightfold star in a circle, and you have the Buddhist Wheel of Life:

Sunday, September 29, 2002

Sunday September 29, 2002

Filed under: General — m759 @ 10:18 PM

New from Miracle Pictures

Pi in the Sky
for Michaelmas 2002

“Fear not, maiden, your prayer is heard.
Michael am I, guardian of the highest Word.”

A Michaelmas Play

Contact, by Carl Sagan:

Chapter 1 – Transcendental Numbers

  In the seventh grade they were studying “pi.” It was a Greek letter that looked like the architecture at Stonehenge, in England: two vertical pillars with a crossbar at the top. If you measured the circumference of a circle and then divided it by the diameter of the circle, that was pi. At home, Ellie took the top of a mayonnaise jar, wrapped a string around it, straightened the string out, and with a ruler measured the circle’s circumference. She did the same with the diameter, and by long division divided the one number by the other. She got 3.21. That seemed simple enough.

  The next day the teacher, Mr. Weisbrod, said that pi was about 22/7, about 3.1416. But actually, if you wanted to be exact, it was a decimal that went on and on forever without repeating the pattern of numbers. Forever, Ellie thought. She raised her hand. It was the beginning of the school year and she had not asked any questions in this class.
  “How could anybody know that the decimals go on and on forever?”
  “That’s just the way it is,” said the teacher with some asperity.
  “But why? How do you know? How can you count decimals forever?”
  “Miss Arroway” – he was consulting his class list – “this is a stupid question. You’re wasting the class’s time.”

  No one had ever called Ellie stupid before and she found herself bursting into tears….

  After school she bicycled to the library at the nearby college to look through books on mathematics. As nearly as she could figure out from what she read, her question wasn’t all that stupid. According to the Bible, the ancient Hebrews had apparently thought that pi was exactly equal to three. The Greeks and Romans, who knew lots of things about mathematics, had no idea that the digits in pi went on forever without repeating. It was a fact that had been discovered only about 250 years ago. How was she expected to know if she couldn’t ask questions? But Mr. Weisbrod had been right about the first few digits. Pi wasn’t 3.21. Maybe the mayonnaise lid had been a little squashed, not a perfect circle. Or maybe she’d been sloppy in measuring the string. Even if she’d been much more careful, though, they couldn’t expect her to measure an infinite number of decimals.

  There was another possibility, though. You could calculate pi as accurately as you wanted. If you knew something called calculus, you could prove formulas for pi that would let you calculate it to as many decimals as you had time for. The book listed formulas for pi divided by four. Some of them she couldn’t understand at all. But there were some that dazzled her: pi/4, the book said, was the same as 1 – 1/3 + 1/5 – 1/7 + …, with the fractions continuing on forever. Quickly she tried to work it out, adding and subtracting the fractions alternately. The sum would bounce from being bigger than pi/4 to being smaller than pi/4, but after a while you could see that this series of numbers was on a beeline for the right answer. You could never get there exactly, but you could get as close as you wanted if you were very patient. It seemed to her

a miracle

 Cartoon by S.Harris

that the shape of every circle in the world was connected with this series of fractions. How could circles know about fractions? She was determined to learn


  The book said something else: pi was called a “transcendental” number. There was no equation with ordinary numbers in it that could give you pi unless it was infinitely long. She had already taught herself a little algebra and understood what this meant. And pi wasn’t the only transcendental number. In fact there was an infinity of transcendental numbers. More than that, there were infinitely more transcendental numbers that ordinary numbers, even though pi was the only one of them she had ever heard of. In more ways than one, pi was tied to infinity.

  She had caught a glimpse of something majestic.

Chapter 24 – The Artist’s Signature

  The anomaly showed up most starkly in Base 2 arithmetic, where it could be written out entirely as zeros and ones. Her program reassembled the digits into a square raster, an equal number across and down. Hiding in the alternating patterns of digits, deep inside the transcendental number, was a perfect circle, its form traced out by unities in a field of noughts.

  The universe was made on purpose, the circle said. In whatever galaxy you happen to find yourself, you take the circumference of a circle, divide it by its diameter, measure closely enough, and uncover

a miracle

— another circle, drawn kilometers downstream of the decimal point. There would be richer messages farther in. It doesn’t matter what you look like, or what you’re made of, or where you come from. As long as you live in this universe, and have a modest talent for mathematics, sooner or later you’ll find it. It’s already here. It’s inside everything. You don’t have to leave your planet to find it. In the fabric of space and in the nature of matter, as in a great work of art, there is, written small, the artist’s signature. Standing over humans, gods, and demons… there is an intelligence that antedates the universe. The circle had closed. She found what she had been searching for.

Song lyric not in Sagan’s book:

Will the circle be unbroken
by and by, Lord, by and by?
Is a better home a-waitin’
in the sky, Lord, in the sky?

“Contact,” the film: 


Columbia 37669

Date Issued:





Can The Circle Be Unbroken


Carter Family

Recording Date:

May 6, 1935



Music courtesy of honkingduck.com.
For bluegrass midi version, click here.

The above conclusion to Sagan’s book is perhaps the stupidest thing by an alleged scientist that I have ever read.  As a partial antidote, I offer the following.

Today’s birthday: Stanley Kramer, director of “On the Beach.”

From an introduction to a recording of the famous Joe Hill song about Pie in the Sky:

“They used a shill to build a crowd… You know, a carny shill.”


Powered by WordPress