… And Some Not So Live —
"Here was finality indeed, and cleavage!" — Under the Volcano
Tuesday, May 5, 2015
Harvard Cinco de Mayo
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Thursday, May 26, 2011
For the Class of ’11
But leave the wise to wrangle, and with me
the quarrel of the universe let be;
and, in some corner of the hubbub couched,
make game of that which makes as much of thee.
Related material: Harvard Treasure, Favicon, and Crimson Tide.
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Thursday, May 5, 2011
Beyond Forgetfulness
From this journal on July 23, 2007—
| It is not enough to cover the rock with leaves. We must be cured of it by a cure of the ground Or a cure of ourselves, that is equal to a cure Of the ground, a cure beyond forgetfulness. And if we ate the incipient colorings – Wallace Stevens, “The Rock” |
This quotation from Stevens (Harvard class of 1901) was posted here on when Daniel Radcliffe (i.e., Harry Potter) turned 18 in July 2007.
Other material from that post suggests it is time for a review of magic at Harvard.
On September 9, 2007, President Faust of Harvard
“encouraged the incoming class to explore Harvard’s many opportunities.
‘Think of it as a treasure room of hidden objects Harry discovers at Hogwarts,’ Faust said.”
That class is now about to graduate.
It is not clear what “hidden objects” it will take from four years in the Harvard treasure room.
Perhaps the following from a book published in 1985 will help…
The March 8, 2011, Harvard Crimson illustrates a central topic of Metamagical Themas , the Rubik’s Cube—
Hofstadter in 1985 offered a similar picture—
Hofstadter asks in his Metamagical introduction, “How can both Rubik’s Cube and nuclear Armageddon be discussed at equal length in one book by one author?”
For a different approach to such a discussion, see Paradigms Lost, a post made here a few hours before the March 11, 2011, Japanese earthquake, tsunami, and nuclear disaster—
Whether Paradigms Lost is beyond forgetfulness is open to question.
Perhaps a later post, in the lighthearted spirit of Faust, will help. See April 20th’s “Ready When You Are, C.B.“
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Sunday, May 3, 2015
Saturday, May 2, 2015
Wednesday, April 22, 2015
ART WARS continued
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.
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Purely Aesthetic
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:
-
A post at noon on Sunday, April 19, 2015, with a link,
"Ageometretos medeis eisito," to an image search
for "large Desargues configuration" that includes …
-
A review, dated April 20, 2015, of "After Hours at the
Harvard Art Museums" in The Harvard Crimson -
An article, also dated April 20, 2015, in Harvard Magazine
titled "Harvard Installs 'Triangle Constellation'"
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Tuesday, October 21, 2014
Tools
(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.
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Tuesday, December 18, 2012
Monkey Grammar
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
by Octavio Paz, translated by |
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—
Happy birthday to the late Alfred Bester.
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Saturday, December 8, 2012
Defining the Contest…
… 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 —
"First steps"? The mathematics underlying such patterns
was presented 35 years earlier, in Diamond Theory.
* See Gombrich-Douat in this journal.
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Monday, September 17, 2012
Pattern Conception
( 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 —
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—
See also, elsewhere in this journal,
Crimson Easter Egg and Formal Pattern.
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Sunday, September 16, 2012
FLT
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—
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 .
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Friday, October 12, 2007
Friday October 12, 2007
Ceremonies marking the installation of Drew Gilpin Faust as the President of Hogwarts will begin in Hogwarts Yard at 2 PM ET today.
Faust has actually been Hogwarts’s president since July 1. Last month she welcomed the Class of 2011:
Faust “encouraged the incoming class to explore [the school’s] many opportunities. ‘Think of it as a treasure room of hidden objects Harry discovers at Hogwarts,’ Faust said.”
— The Hogwarts Crimson, Sept. 10, 2007
From Faust’s website today:
“As a historian, I am proud to lead an institution with such a rich and storied past. Hogwarts began in colonial days with a handful of students, little property and limited power and prestige, but a determined mission: ‘To advance Learning and perpetuate it to Posterity,’ as a 1643 brochure put it. That bold vision has guided Hogwarts for the past four centuries….”
The rest of the story —
From The Hogwarts Guide:
“An early brochure, published in 1643, justified the College’s existence: ‘To advance Learning and perpetuate it to Posterity; dreading to leave an illiterate Ministry to the Churches.'”
Related material:
The Crimson Passion,
Midnight Drums for Larry,
and Primitive Roots.
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Monday, September 10, 2007
Monday September 10, 2007
The Story Theory
of Truth —
of Truth —
“I’m a gun for hire,
I’m a saint, I’m a liar,
because there are no facts,
there is no truth,
just data to be manipulated.”
Data
The data in more poetic form:
Commentary:
23: See
The Prime Cut Gospel.
16: See
Happy Birthday, Benedict XVI.
Related material:
The remarks yesterday
of Harvard president
Drew G. Faust
to incoming freshmen.
Faust “encouraged
the incoming class
to explore Harvard’s
many opportunities.
‘Think of it as
a treasure room
of hidden objects
Harry discovers
at Hogwarts,’
Faust said.”
For a less Faustian approach,
see the Harvard-educated
philosopher Charles Hartshorne
at The Harvard Square Library
and the words of another
Harvard-educated Hartshorne:
“Whenever one
approaches a subject from
two different directions,
there is bound to be
an interesting theorem
expressing their relation.”
— Robin Hartshorne
Saturday, January 11, 2003
Saturday January 11, 2003
METROPOLITAN ART WARS:
The First Days of Disco
Some cultural milestones, in the order I encountered them today:
From Dr. Mac’s Cultural Calendar:
- “On this day in 1963, Whiskey-A-Go-Go—believed to be the first discotheque in the world—opened on Sunset Boulevard in Los Angeles with extraordinary hype and fanfare.”
From websites on Whit Stillman’s film, “The Last Days of Disco”:
Scene: Manhattan in the very early 1980’s.
Alice and her friend Charlotte are regulars at a fashionable disco.
“Charlotte is forever giving poor Alice advice about what to say and how to behave; she says guys like it when a girl uses the word ‘sexy,’ and a few nights later, when a guy tells Alice he collects first editions of Scrooge McDuck comic books, she…”
“… looks deep into his eyes and purrs ‘I think Scrooge McDuck is sexy!’ It is a laugh-out-loud funny line and a shrewd parody, but is also an honest statement.”
(Actually, to be honest, I encountered Thomson first and Ebert later, but the narrative sequence demands that they be rearranged.)
The combination of these cultural landmarks suggested that I find out what Scrooge McDuck was doing during the first days of disco, in January 1963. Some research revealed that in issue #40 of “Uncle Scrooge,” with a publication date of January 1963, was a tale titled “Oddball Odyssey.” Plot summary: “A whisper of treasure draws Scrooge to Circe.”
Further research produced an illustration:
Desiring more literary depth, I sought more information on the story of Scrooge and Circe. It turns out that this was only one of a series of encounters between Scrooge and a character called Magica de Spell. The following is from a website titled
“Magica’s first appearance is in ‘The Midas Touch’ (US 36-01). She enters the Money Bin to buy a dime from Scrooge. Donald tells Scrooge that she is a sorceress, but Scrooge sells her a dime anyway. He sells her his first dime by accident, but gets it back. The fun starts when Scrooge tells her that it is the first dime he earned. She is going to make an amulet….”
with it. Her pursuit of the dime apparently lasts through a number of Scrooge episodes.
“…in Oddball Odyssey (US 40-02). Magica discovers Circe’s secret cave. Inside the cave is a magic wand that she uses to transform Huey, Dewey and Louie to pigs, Donald to a goat (later to a tortoise), and Scrooge to a donkey. This reminds us of the treatment Circe gave Ulysses and his men. Magica does not succeed in transforming Scrooge after stealing the Dime, and Scrooge manages to break the spell (de Spell) by smashing the magic wand.”
At this point I was reminded of the legendary (but true) appearance of Wallace Stevens’s wife on another historic dime. This was discussed by Charles Schulz in a cartoon of Sunday, May 27, 1990:
Here Sally is saying…
Who, me?… Yes, Ma’am, right here.
This is my report on dimes and pennies…
“Wallace Stevens was a famous poet…
His wife was named Elsie…”
“Most people do not know that Elsie was the model for the 1916 ‘Liberty Head’ dime.”
“Most people also don’t know that if I had a dime for every one of these stupid reports I’ve written, I’d be a rich person.”
Finally, sitting outside the principal’s office:
I never got to the part about who posed for the Lincoln penny.
I conclude this report on a note of synchronicity:
The above research was suggested in part by a New York Times article on Ovid’s Metamorphoses I read last night. After locating the Scrooge and Stevens items above, I went to the Times site this afternoon to remind myself of this article. At that point synchronicity kicked in; I encountered the following obituary of a Scrooge figure from 1963… the first days of disco:
|
The New York Times, January 12, 2003 (So dated at the website on Jan. 11) C. Douglas Dillon Dies at 93;
|
. Douglas Dillon, a versatile Wall Street financier who was named secretary of the Treasury by President Kennedy and ambassador to France under President Eisenhower, and was a longtime executive of the Metropolitan Museum of Art, died Friday [Jan. 10, 2003] at New York Presbyterian Hospital in Manhattan. Mr. Dillon, who lived with his wife on Jupiter Island in Hobe Sound, Fla., was 93.
Et cetera, et cetera, and so forth.
(See yesterday’s two entries, “Something Wonderful,” and “Story.”)
Two reflections suggest themselves:
“I need a photo opportunity.
I want a shot at redemption.
Don’t want to end up a cartoon
In a cartoon graveyard.”
— Paul Simon
Ending up in a cartoon graveyard is indeed an unhappy fate; on the other hand…
It is nice to be called “sexy.”
Added at 1:50 AM Jan. 12, 2003:
Tonight’s site music, in honor of Mr. Dillon
and of Hepburn, Holden, and Bogart in “Sabrina” —
“Isn’t It Romantic?”
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