Sunday, January 24, 2016

Long Line

Filed under: General,Geometry — Tags: — m759 @ 6:00 PM

"The ideal of a complete mathematical theory of beauty
lies on the same long line of distinguished fantasies of
mathematical wisdom as the number mysticism of
Pythagoras and Plato, the Ars Magna  of Ramon Llull
(whom Agrippa studied) and Giordano Bruno
(who studied Llull and Agrippa), the vision of Mathesis
  that Descartes and Leibniz shared, and the
Ars Combinatoria  of Leibniz. Dürer does not deny the
existence of absolute beauty but despairs of knowing it."

— The late David Ritz Finkelstein in 2007.
     He reportedly died today.

Saturday, January 26, 2013

Nine Years

Filed under: General — m759 @ 12:00 PM

IMAGE- Yahoo CEO Marissa Mayer and the ontology of entities

Excerpt from an essay cached nine years ago:

"The current dominant conceptual framework
which pictures the self as an inner entity
is slowly breaking up. And I am convinced that
some, if not all, of the approaches to the self
sketched here will form the basis for a new
conceptual framework…."

Context for the essay: 

A journal issue titled "The Opening of Narrative Space" (pdf, 475 KB)

For one sort of narrative space, see Giordano Bruno in this journal.

See also Nine Years.

Tuesday, January 8, 2013

Nine is a Vine (continued)

Filed under: General — m759 @ 9:00 AM

In honor of a famed architecture critic,
here is a link to Bruno's Atria.

See also Giordano Bruno  in this journal.

Friday, September 4, 2009

Friday September 4, 2009

Filed under: General — m759 @ 2:02 PM
Closing the Circle

Continued from Monday

“This is a chapel 
 of mischance;
ill luck betide it, ’tis
the cursedest kirk
  that ever I came in!”

Philip Kennicott on
Kirk Varnedoe in
The Washington Post:

“Varnedoe’s lectures were
ultimately about faith,
about his faith in
the power of abstraction,
 and abstraction as a kind of
    anti-religious faith in itself….”

Kennicott’s remarks were
 on Sunday, May 18, 2003.
They were subtitled
“Closing the Circle
on Abstract Art.”

Also on Sunday, May 18, 2003:

 “Will the circle be unbroken?
  As if some southern congregation
  is praying we will come to understand.”

Princeton University Press

Empty canvas on cover of Varnedoe's 'Pictures of Nothing'

See also

  Giordano Bruno

Parmiggiani's Bruno: empty canvas with sculpture of Durer's solid

Dürer’s Melencolia I

Durer, Melencolia I

and Log24 entries
of May 19-22, 2009,
ending with
    “Steiner System” —

Diamond-shaped face of Durer's 'Melencolia I' solid, with  four colored pencils from Diane Robertson Design

George Steiner on chess
(see yesterday morning):

“There are siren moments when quite normal creatures otherwise engaged, men such as Lenin and myself, feel like giving up everything– marriage, mortgages, careers, the Russian Revolution– in order to spend their days and nights moving little carved objects up and down a quadrate board.”

Steiner continues

“Allegoric associations of death with chess are perennial….”

Yes, they are.

April is Math Awareness Month.
This year’s theme is “mathematics and art.”

Mathematics and Art: Totentanz from Seventh Seal

Cf. both of yesterday’s entries.

Thursday, April 23, 2009

Thursday April 23, 2009

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


The Geometry
of Language

(continued from April 16)


Professor Arielle Saiber with chess set

Click on the image for an
interview with the author of
Giordano Bruno and
the Geometry of Language

Related material:

Joyce on language —

The sigla of 'Finnegans Wake'

Bruno, Joyce, and coincidentia oppositorum

Cullinane on geometry —

Geometry of the I Ching (for comparison to Joyce's 'sigla')

Click on images for details.

Friday, April 17, 2009

Friday April 17, 2009

Filed under: General,Geometry — Tags: — m759 @ 10:31 AM

Begettings of
the Broken Bold

Thanks for the following
quotation (“Non deve…
nella testa“) go to the
weblog writer who signs
himself “Conrad H. Roth.”

of Goethe

(Vol. II, London, Bell & Daldy,
1868, at Google Books):

… Yesterday I took leave of my Captain, with a promise of visiting him at Bologna on my return. He is a true


representative of the majority of his countrymen. Here, however, I would record a peculiarity which personally distinguished him. As I often sat quiet and lost in thought he once exclaimed “Che pensa? non deve mai pensar l’uomo, pensando s’invecchia;” which being interpreted is as much as to say, “What are you thinking about: a man ought never to think; thinking makes one old.” And now for another apophthegm of his; “Non deve fermarsi l’uomo in una sola cosa, perche allora divien matto; bisogna aver mille cose, una confusione nella testa;” in plain English, “A man ought not to rivet his thoughts exclusively on any one thing, otherwise he is sure to go mad; he ought to have in his head a thousand things, a regular medley.”

Certainly the good man could not know that the very thing that made me so thoughtful was my having my head mazed by a regular confusion of things, old and new. The following anecdote will serve to elucidate still more clearly the mental character of an Italian of this class. Having soon discovered that I was a Protestant, he observed after some circumlocution, that he hoped I would allow him to ask me a few questions, for he had heard such strange things about us Protestants that he wished to know for a certainty what to think of us.

Notes for Roth:

Roth and Corleone in Havana

The title of this entry,
“Begettings of the Broken Bold,”
is from Wallace Stevens’s
“The Owl in the Sarcophagus”–

This was peace after death, the brother of sleep,
The inhuman brother so much like, so near,
Yet vested in a foreign absolute,

Adorned with cryptic stones and sliding shines,
An immaculate personage in nothingness,
With the whole spirit sparkling in its cloth,

Generations of the imagination piled
In the manner of its stitchings, of its thread,
In the weaving round the wonder of its need,

And the first flowers upon it, an alphabet
By which to spell out holy doom and end,
A bee for the remembering of happiness.

Peace stood with our last blood adorned, last mind,
Damasked in the originals of green,
A thousand begettings of the broken bold.

This is that figure stationed at our end,
Always, in brilliance, fatal, final, formed
Out of our lives to keep us in our death....

Related material:

  • Yesterday’s entry on Giordano Bruno and the Geometry of Language
  • James Joyce and Heraldry
  • “One might say that he [Joyce] invented a non-Euclidean geometry of language; and that he worked over it with doggedness and devotion….” —Unsigned notice in The New Republic, 20 January 1941
  • Joyce’s “collideorscape” (scroll down for a citation)
  • “A Hanukkah Tale” (Log24, Dec. 22, 2008)
  • Stevens’s phrase from “An Ordinary Evening in New Haven” (Canto XXV)

Some further context:

Roth’s entry of Nov. 3, 2006–
Why blog, sinners?“–
and Log24 on that date:
First to Illuminate.”

Thursday, April 16, 2009

Thursday April 16, 2009

Filed under: General,Geometry — m759 @ 1:00 PM
Happy Birthday,
Benedict XVI:

A Game for Bishops
continued from April 3

Professor Arielle Saiber with chess set

Click on the image for an
interview with the author of
Giordano Bruno and
the Geometry of Language

Saturday, June 26, 2004

Saturday June 26, 2004

Filed under: General — m759 @ 3:03 AM
Deep Game

The entry Ado of June 25, 2004 contains a link to an earlier entry, A Form, continued, of June 5, 2004.  This in turn contains a link to a site by Wolfgang Wildgen which contains the following:

“Historically, we may say that the consequence of Bruno’s parallel work on cosmology and artificial memory is a new model of semantic fields which was so radical in its time that the first modern followers (although ignorant of this tradition) are the Von-Neumann automata and the neural net systems of the 1980s (cf. Wildgen 1998: 39, 237f).”

Wildgen, W. 1998. Das kosmische Gedächtnis. Kosmologie, Semiotik und Gedächtniskunst im Werke von Giordano Bruno. Frankfurt/Bern: Lang.

For an applet illustrating
the above remarks, see


The image “http://www.log24.com/log/pix04A/040626-Neighbors.gif” cannot be displayed, because it contains errors. 
Figure A

Neighborhood in a
Cellular Automaton
by Adam Campbell

For more of the Gedächtnis
in this Kunst, see the following
Google search on shc759:

The image “http://www.log24.com/log/pix04A/040626-Search.jpg” cannot be displayed, because it contains errors.

Figure B

Note that the reference to “forerunners” in fig. B occurs in a journal entry of June 12, 2002. See also the reference to a journal entry of the following day, June 13, 2002, in last Tuesday’s Dirty Trick.

Those who have viewed Campbell’s applet (see  fig. A) may appreciate the following observation of poet and Dante translator Robert Pinsky:

“… a grid, and a flow–
that is the essence of terza rima….”

Poetry, Computers, and Dante’s Inferno

For some related remarks
on the muses and epic poetry,
see a paper on Walter Benjamin:

“Here the memory (Gedächtnis) means
‘the epic faculty par excellence.’ “
(Benjamin, Der Erzähler, 1936: in
Gesammelte Schriften, 1991, II.2, 453)

Benjamin on Experience,
Narrative, and History

One possible connection to the muses is, as noted in a link in yesterday’s Ado, via George Balanchine.

An apt link to epic poetry (aside from the reference to Dante above) is, via the June 12, 2002, entry, to the epic The Gameplayers of Zan (the third reference in fig. B above).

The applet linked below fig. A very nicely illustrates the “structured chaos” of a space described by automata theory.  For a literary approach to such a space, see the Gameplayers entry.

For the benefit of art critic Robert Hughes, who recently made a distinction between “fast art” and “slow art,” the Campbell applet has a convenient speed control.

Sunday, June 6, 2004

Sunday June 6, 2004

Filed under: General,Geometry — Tags: — m759 @ 1:28 PM

“I confess I do not believe in time.
I like to fold my magic carpet,
after use, in such a way
as to superimpose
one part of the pattern
upon another.”

(Nabokov, Speak, Memory)

From a review of On the Composition of Images, Signs & Ideas, by Giordano Bruno:

Proteus in the House of Mnemosyne (which is the fifth chapter of the Third Book) relies entirely on familiarity with Vergil’s Aeneid (even when the text shifts from verse to prose). The statement, “Proteus is, absolutely, that one and the same subject matter which is transformable into all images and resemblances, by means of which we can immediately and continually constitute order, resume and explain everything,” reads less clear than the immediate analogy, “Just as from one and the same wax we awaken all shapes and images of sensate things, which become thereafter the signs of all things that are intelligible.”

From an interview with Vladimir Nabokov published in Wisconsin Studies in Contemporary Literature, vol. VIII, no. 2, Spring 1967:

When I was your student, you never mentioned the  Homeric parallels in discussing Joyce’s Ulysses  But you did supply “special information” in introducing many of the masterpieces: a map of Dublin for Ulysses….  Would you be able to suggest some equivalent for your own readers?

Joyce himself very soon realized with dismay that the harping on those essentially easy and vulgar “Homeric parallelisms” would only distract one’s attention from the real beauty of his book. He soon dropped these pretentious chapter titles which already were “explaining” the book to non-readers.  In my lectures I tried to give factual data only. A map of three country estates with a winding river and a figure of the butterfly Parnassius mnemosyne for a cartographic cherub will be the endpaper in my revised edition of Speak, Memory.

For more on Joyce and Proteus,
see the May 27 entry

Saturday, June 5, 2004

Saturday June 5, 2004

Filed under: General,Geometry — m759 @ 11:11 AM
A Form,

Some cognitive uses
of the 3×3 square
are discussed in

From Lullus to Cognitive Semantics:
The Evolution of a Theory of Semantic Fields

by Wolfgang Wildgen and in

Another Page in the Foundation of Semiotics:
A Book Review of On the Composition of Images, Signs & Ideas, by Giordano Bruno
by Mihai Nadin

“We have had a gutful of fast art and fast food. What we need more of is slow art: art that holds time as a vase holds water: art that grows out of modes of perception and whose skill and doggedness make you think and feel; art that isn’t merely sensational, that doesn’t get its message across in 10 seconds, that isn’t falsely iconic, that hooks onto something deep-running in our natures. In a word, art that is the very opposite of mass media. For no spiritually authentic art can beat mass media at their own game.”

Robert Hughes, speech of June 2, 2004

Whether the 3×3 square grid is fast art or slow art, truly or falsely iconic, perhaps depends upon the eye of the beholder.

For a meditation on the related 4×4 square grid as “art that holds time,” see Time Fold.

Monday, February 17, 2003

Monday February 17, 2003

Filed under: General — m759 @ 3:36 PM

Saint Faggot’s Day

“During the European Inquisitions, faggot referred to the sticks used to set fires for burning heretics, or people who opposed the teachings of the Catholic Church. Heretics were required to gather bundles of sticks (‘faggots’) and carry them to the fire that was being built for them. Heretics who changed their beliefs to avoid being killed were forced to wear a faggot design embroidered on their sleeve, to show everyone that they had opposed the Church.”

— Handout

Cover illustration
by Stephen Savage

N.Y. Times Feb. 2, 2003

‘A Box of Matches’:
A Miniaturist’s
Novel of Details

In Nicholson Baker’s novel,
things not worth noticing
eventually become
all there is to notice.

Head White House speechwriter Michael Gerson:

“In the last two weeks, I’ve been returning to Hopkins.  Even in the ‘world’s wildfire,’ he asserts that ‘this Jack, joke, poor potsherd, patch, matchwood, immortal diamond,/Is immortal diamond.’ A comfort.”
— Vanity Fair, May 2002, page 162

“At midnight on the Emperor’s pavement flit
Flames that no faggot feeds….”

— William Butler Yeats, “Byzantium”

On this date in 1600, Saint Giordano Bruno was burned at the stake for heresy by the Roman Catholic Church.

He was resurrected by Saint Frances Yates, who went to her reward on the feast day of Saint Michael and All Angels, 1981.

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