Tuesday, November 3, 2015

Logic at Harvard

Filed under: General — m759 @ 11:30 AM

A review of the Log24 posts on Oct. 29, 2015,
yields the following image relevant to remarks at
the Harvard Graduate School of Design yesterday:

Branding at Harvard

Filed under: General — m759 @ 11:00 AM

From the Harvard Graduate School of Design's introduction
to a lecture on All Souls' Day 2015 —

"Calvin Klein is an award-winning fashion icon.
He is recognized globally as a master of minimalism
and has spent his career distilling things to
their very essence. His name ranks among the
best-known brands in the world, with Calvin Klein, Inc.
reaching over seven billion dollars in global retail sales."

A Klein icon I prefer —

The Klein Four-Group, illustration by Steven H. Cullinane

Click the above image for some backstory.

Tuesday, May 5, 2015

Harvard Cinco de Mayo

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

… And Some Not So Live —

"Here was finality indeed, and cleavage!" — Under the Volcano

Monday, September 4, 2017

Up to Date

Filed under: General — m759 @ 12:31 PM

The obituary for Sekler is somewhat surprising, given that he
reportedly died on May 1, 2017. His burial is also rather late,
according to the Globe  

"A service has been held for Dr. Sekler . . . .
 He will be buried Sept. 29 in a cemetery
 in Vienna, in his family’s plot."

"A memorial lecture in his honor is planned for November
at the Harvard Graduate School of Design." — The Globe

"All in good time, my little pretty."

Another design note related to May Day 2017 —

Related material —

A Vanderbilt University article titled "The significance of Sheriff Bell’s
dreams at the end of No Country for Old Men
," and an obituary from
a Log24 post, "Extreme Aesthetic Distance," of August 27, 2017 . . .

Tuesday, December 22, 2015

How Deep the Darkness

Filed under: General — m759 @ 10:29 AM


See Bauhaus remarks on space and Devil's Night Eve.

See also Klein Group and, for the Harvard Graduate
School of Design, an appropriate Calvin Klein label —

Wednesday, December 9, 2015

Eternity (Not by Calvin Klein*)

Filed under: General — m759 @ 10:18 AM

The two symbols on the monolith

Images of time and eternity in a 1x4x9 black monolith

may, if one likes, be interpreted 
as standing for Damnation Morning 
and for the Windmill of Time.

* "Award-winning fashion icon."
Harvard Graduate School of Design

Friday, October 23, 2015

Retro or Not?

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

Happy birthday to the late Michael Crichton (Harvard '64).

See also Diamond Theory Roulette —

Part of the ReCode Project (http://recodeproject.com).
Based on "Diamond Theory" by Steven H. Cullinane,
originally published in "Computer Graphics and Art" 
Vol. 2 No. 1, February 1977.
Copyright (c) 2013 Radames Ajna 
— OSI/MIT license (http://recodeproject/license).

Related remarks on Plato for Harvard's
Graduate School of Design

See also posts from the above publication date, March 31,
2006, among posts now tagged "The Church in Philadelphia."

Sunday, May 3, 2015

In Memoriam

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

For the author of Dances with Wolves —

'Winter Count,' by Barry Holstun Lopez, cover with shades of gray

Saturday, May 2, 2015

Die Scheinung

Filed under: General — Tags: , , — m759 @ 11:00 PM

See also Die Scheinung  in this journal.

Wednesday, April 22, 2015

ART WARS continued

Filed under: General — Tags: — m759 @ 8:29 PM

The previous post mentioned a new mobile, "Triangle Constellation,"
commissioned for the Harvard Art Museums.

Related material (click to enlarge) —

The above review is of an exhibition by the "Constellation" artist,
Carlos Amorales, that opened on Sept. 26, 2008 — "just in time for
Halloween and the Day of the Dead."

See also this  journal on that date.

Purely Aesthetic

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

G. H. Hardy in A Mathematician's Apology —

What ‘purely aesthetic’ qualities can we distinguish in such theorems as Euclid’s or Pythagoras’s?

I will not risk more than a few disjointed remarks. In both theorems (and in the theorems, of course, I include the proofs) there is a very high degree of unexpectedness, combined with inevitability and economy. The arguments take so odd and surprising a form; the weapons used seem so childishly simple when compared with the far-reaching results; but there is no escape from the conclusions. There are no complications of detail—one line of attack is enough in each case; and this is true too of the proofs of many much more difficult theorems, the full appreciation of which demands quite a high degree of technical proficiency. We do not want many ‘variations’ in the proof of a mathematical theorem: ‘enumeration of cases’, indeed, is one of the duller forms of mathematical argument. A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way. 

Related material:

Tuesday, October 21, 2014


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

(Night at the Museum continues.)

"Strategies for making or acquiring tools

While the creation of new tools marked the route to developing the social sciences,
the question remained: how best to acquire or produce those tools?"

— Jamie Cohen-Cole, “Instituting the Science of Mind: Intellectual Economies
and Disciplinary Exchange at Harvard’s Center for Cognitive Studies,”
British Journal for the History of Science  vol. 40, no. 4 (2007): 567-597.

Obituary of a co-founder, in 1960, of the Center for Cognitive Studies at Harvard:

"Disciplinary Exchange" —

In exchange for the free Web tools of HTML and JavaScript,
some free tools for illustrating elementary Galois geometry —

The Kaleidoscope Puzzle,  The Diamond 16 Puzzle
The 2x2x2 Cube, and The 4x4x4 Cube

"Intellectual Economies" —

In exchange for a $10 per month subscription, an excellent
"Quilt Design Tool" —

This illustrates not geometry, but rather creative capitalism.

Related material from the date of the above Harvard death:  Art Wars.

Thursday, August 28, 2014

Source of the Finite

Filed under: General,Geometry — Tags: — m759 @ 10:20 AM

"Die Unendlichkeit  ist die uranfängliche Tatsache: es wäre nur
zu erklären, woher das Endliche  stamme…."

— Friedrich Nietzsche, Das Philosophenbuch/Le livre du philosophe
(Paris: Aubier-Flammarion, 1969), fragment 120, p. 118

Cited as above, and translated as "Infinity is the original fact;
what has to be explained is the source of the finite…." in
The Production of Space , by Henri Lefebvre. (Oxford: Blackwell,
1991 (1974)), p.  181.

This quotation was suggested by the Bauhaus-related phrase
"the laws of cubical space" (see yesterday's Schau der Gestalt )
and by the laws of cubical space discussed in the webpage
Cube Space, 1984-2003.

For a less rigorous approach to space at the Harvard Graduate
School of Design, see earlier references to Lefebvre in this journal.

Tuesday, December 18, 2012

Monkey Grammar

Filed under: General,Geometry — Tags: , — m759 @ 2:29 AM

For a modern Adam and Eve—

W. Tecumseh Fitch and Gesche Westphal Fitch,
editors of a new four-volume collection titled
Language Evolution  (Feb. 2, 2012, $1,360)—

Related material—

"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth. 
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by
Helen Lane (Kindle edition of
2011-11-07, Kindle locations

The "play of mirrors" link above is my own.

Click on W. Tecumseh Fitch for links to some
examples of mirror-play in graphic design—
from, say, my own work in a version of 1977, not from
the Fitches' related work published online last June—

See also Log24 posts from the publication date
of the Fitches' Language Evolution

Groundhog Day, 2012.

Happy birthday to the late Alfred Bester.

Saturday, December 8, 2012

Defining the Contest…

Filed under: General,Geometry — Tags: , , , , — m759 @ 5:48 AM

Chomsky vs. Santa

From a New Yorker  weblog yesterday—

"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."

See Meno Diamond in this journal. For instance, from 
the Feast of Saint Nicholas (Dec. 6th) this year—

The Meno Embedding


For related truths about geometry, see the diamond theorem.

For a related contest of language theory vs. geometry,
see pattern theory (Sept. 11, 16, and 17, 2012).

See esp. the Sept. 11 post,  on a Royal Society paper from July 2012
claiming that

"With the results presented here, we have taken the first steps
in decoding the uniquely human  fascination with visual patterns,
what Gombrich* termed our ‘sense of order.’ "

The sorts of patterns discussed in the 2012 paper —

IMAGE- Diamond Theory patterns found in a 2012 Royal Society paper

"First steps"?  The mathematics underlying such patterns
was presented 35 years earlier, in Diamond Theory.

* See Gombrich-Douat in this journal.

Monday, September 17, 2012

Pattern Conception

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

( Continued from yesterday's post FLT )

Context Part I —

"In 1957, George Miller initiated a research programme at Harvard University to investigate rule-learning, in situations where participants are exposed to stimuli generated by rules, but are not told about those rules. The research program was designed to understand how, given exposure to some finite subset of stimuli, a participant could 'induce' a set of rules that would allow them to recognize novel members of the broader set. The stimuli in question could be meaningless strings of letters, spoken syllables or other sounds, or structured images. Conceived broadly, the project was a seminal first attempt to understand how observers, exposed to a set of stimuli, could come up with a set of principles, patterns, rules or hypotheses that generalized over their observations. Such abstract principles, patterns, rules or hypotheses then allow the observer to recognize not just the previously seen stimuli, but a wide range of other stimuli consistent with them. Miller termed this approach 'pattern conception ' (as opposed to 'pattern perception'), because the abstract patterns in question were too abstract to be 'truly perceptual.'….

…. the 'grammatical rules' in such a system are drawn from the discipline of formal language theory  (FLT)…."

— W. Tecumseh Fitch, Angela D. Friederici, and Peter Hagoort, "Pattern Perception and Computational Complexity: Introduction to the Special Issue," Phil. Trans. R. Soc. B  (2012) 367, 1925-1932 

Context Part II —

IMAGE- Wikipedia article 'Formal language'

Context Part III —

A four-color theorem describes the mathematics of
general  structures, not just symbol-strings, formed from
four kinds of things— for instance, from the four elements
of the finite Galois field GF(4), or the four bases of DNA.

Context Part IV —

A quotation from William P. Thurston, a mathematician
who died on Aug. 21, 2012—

"It may sound almost circular to say that
what mathematicians are accomplishing
is to advance human understanding of mathematics.
I will not try to resolve this
by discussing what mathematics is,
because it would take us far afield.
Mathematicians generally feel that they know
what mathematics is, but find it difficult
to give a good direct definition.
It is interesting to try. For me,
'the theory of formal patterns'
has come the closest, but to discuss this
would be a whole essay in itself."

Related material from a literate source—

"So we moved, and they, in a formal pattern"

Formal Patterns—

Not formal language theory  but rather
finite projective geometry  provides a graphic grammar
of abstract design

IMAGE- Harvard Crimson ad, Easter Sunday, 2008: 'Finite projective geometry as a graphic grammar of abstract design'

See also, elsewhere in this journal,
Crimson Easter Egg and Formal Pattern.

Sunday, September 16, 2012


Filed under: General,Geometry — Tags: , , — m759 @ 8:28 PM

The "FLT" of the above title is not Fermat's Last Theorem,
but Formal Language Theory (see image below).

In memory of George A. Miller, Harvard cognitive psychologist, who
reportedly died at 92 on July 22, 2012, the first page of a tribute
published  shortly before his death

IMAGE- Design and Formal Language Theory

The complete introduction is available online. It ends by saying—

"In conclusion, the research discussed in this issue
breathes new life into a set of issues that were raised,
but never resolved, by Miller 60 years ago…."

Related material: Symmetry and Hierarchy (a post of 9/11), and
Notes on Groups and Geometry, 1978-1986 .

Happy Rosh Hashanah.

Tuesday, June 19, 2012


Filed under: General — m759 @ 12:00 PM

The New York Times online front page last night

"Microsoft introduced its own tablet computer,
called Surface, illustrating the pressure
Apple's success has put on it to marry
software and hardware more tightly."


IMAGE- The Marriage of Heaven and Hell-- Swedenborg Chapel and the Harvard Graduate School of Design

Google Maps image

Related material

"Was ist Raum, wie können wir ihn
 erfassen und gestalten?"

Walter Gropius,

The Theory and
Organization of the

Update of Feb. 3, 2013:
See also The Perception of Doors in this journal.

Friday, February 27, 2009

Friday February 27, 2009

Filed under: General,Geometry — Tags: , — m759 @ 7:35 PM
Time and Chance

Today's Pennsylvania lottery numbers suggest the following meditations…

Midday:  Lot 497, Bloomsbury Auctions May 15, 2008– Raum und Zeit (Space and Time), by Minkowski, 1909. Background: Minkowski Space and "100 Years of Space-Time."*

Evening: 5/07, 2008, in this journal– "Forms of the Rock."

Related material:

A current competition at Harvard Graduate School of Design, "The Space of Representation," has a deadline of 8 PM tonight, February 27, 2009.

The announcement of the competition quotes the Marxist Henri Lefebvre on "the social production of space."

A related quotation by Lefebvre (cf. 2/22 2009):

"… an epoch-making event so generally ignored that we have to be reminded of it at every moment. The fact is that around 1910 a certain space was shattered… the space… of classical perspective and geometry…."

— Page 25 of The Production of Space (Blackwell Publishing, 1991)

This suggests, for those who prefer Harvard's past glories to its current state, a different Raum from the Zeit 1910.

In January 1910 Annals of Mathematics, then edited at Harvard, published George M. Conwell's "The 3-space PG(3, 2) and Its Group." This paper, while perhaps neither epoch-making nor shattering, has a certain beauty. For some background, see this journal on February 24, 2009.†

    * Ending on Stephen King's birthday, 2008
     † Mardi Gras

Sunday, February 22, 2009

Sunday February 22, 2009

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

Design at Harvard:
Natural or Unnatural?

Logo of Harvard Graduate School of Design compared to the 'natural' sign

From the Harvard Graduate School of Design

Call for Entries: The Space of Representation


"According to Henri Lefebvre, the social production of space has three components: spatial practice, the representation of space, and the space of representation. The latter two are integral to both design and the review process."

Also according to Henri Lefebvre:

An 'epoch-making event' from Lefebvre, 'The Production of Space'

This is clearly nonsense.
It is also, like much else at Harvard,
damned Marxist  nonsense.

I recommend instead  
James Joyce on space —

Dagger Definitions

From 'Ulysses,' 1922 first edition, page 178-- 'dagger definitions'

Saturday, July 5, 2003

Saturday July 5, 2003

Filed under: General,Geometry — m759 @ 4:17 AM


In memory of Walter Gropius, founder of the Bauhaus and head of the Harvard Graduate School of Design.  Gropius died on this date in 1969.  He said that

"The objective of all creative effort in the visual arts is to give form to space. … But what is space, how can it be understood and given a form?"

"Alle bildnerische Arbeit will Raum gestalten. … Was ist Raum, wie können wir ihn erfassen und gestalten?"


— "The Theory and Organization
of the Bauhaus
" (1923)

I designed the following logo for my Diamond Theory site early this morning before reading in a calendar that today is the date of Gropius's death.  Hence the above quote.

"And still those voices are calling
from far away…"
— The Eagles


("Stoicheia," Elements, is the title of
Euclid's treatise on geometry.)

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