"Google Gone Haywire" Continues.
See as well a long complete list of the many Google search results
on combinatorial mathematics that contain the above phrase as
part of a fake "abstract" quoted by Google.
"Google Gone Haywire" Continues.
See as well a long complete list of the many Google search results
on combinatorial mathematics that contain the above phrase as
part of a fake "abstract" quoted by Google.
The "large language model" approach to AI has yielded
startlingly good results for programmers, but is not so good
for finding out facts . . .
A Google search for harvard mathematician h.s.m. coxeter yields . . .
Readers able to use Google can easily find out who wrote the above
gestalt passage. It was not Coxeter.
Further investigation via Google yields the O'Toole source:
O'Toole, Michael, The Language of Displayed Art ,
Leicester University Press, 1994, p. 4.
From a song discussed in yesterday’s online NY Times :
“Blue, blue, my love is blue.”*
Trigger warning from SNL’s Weekend Update on April 12, 2014:
“It was announced this week that in an upcoming issue of
Life With Archie , the main character Archie Andrews
will die, following a lifelong struggle with blue balls.”
* Misheard version of Bryan Blackburn‘s “blue, blue, my world is blue”
translation of the Pierre Cour lyric “bleu, bleu, l’amour est bleu “
Or: Being There
(A sequel to last night's Lyric Intelligence )
William Deresiewicz reviews Kurt Vonnegut's 1952 novel Player Piano :
The novel’s prescience is chilling. Six years before the left-wing English
sociologist Michael Young published The Rise of the Meritocracy ,
a dystopian satire that coined that now-ubiquitous final word,
Vonnegut was already there.
Related material:
Intelligence Test , Gombrich, and, more generally, Stupidity.
""Against stupidity the gods themselves contend in vain."
("Mit der Dummheit kämpfen Götter selbst vergebens.")
— Friedrich Schiller (1759-1805) German poet, playwright, critic,
Die Jungfrau von Orleans [The Maid of Orleans], Act III, sc. vi (1801)
To be fair and balanced, we also offer a contrary view–
"Weird Science—Why Editors Must Dare to be Dumb,"
by K.C. Cole, Columbia Journalism Review, 2006
For fans of the "story theory of truth" —
An example of artificial stupidity:
The phrases "midpoints of opposite faces" and "essentially
creating a smaller cube" are hallucinated bullshit.
The above AI description was created by inanely parroting
verbiage from the Wikipedia article "Diamond cubic" —
which it credits as a source. (See wider view of search.)
That article contains neither the word "theorem" nor the
phrase "unit cube " from the search-request prompt.
AI, like humans, is likely to fall victim to the notorious
"story theory of truth" purveyed by Richard J. Trudeau.
A real "diamond shape formed within a unit cube" is the
octahedron, one of the five classical Platonic solids.
Fans of the opposing "diamond theory of truth" rejected by
Trudeau may prefer . . .
(Log24, July 1, 2019).
From Sunday evening's In Memoriam post —
The "from Princeton" remark in the previous post came from
Princeton, but originated with a retired professor in Rochester,
NY, one Joseph Neisendorfer.
Another remark by Neisendorfer, from his weblog —
Those familiar with the chapter on Galois in the
Eric Temple Bell classic Men of Mathematics
will know that the words quoted above by
Neisendorfer are definitely not those of Albert Einstein.
Galois and Abel vs. Rubik
"Abel was done to death by poverty, Galois by stupidity.
In all the history of science there is no completer example
of the triumph of crass stupidity…."
— Eric Temple Bell, Men of Mathematics
Gray Space (Continued)
… For The Church of Plan 9.
"Buckle up!" — Harlan Kane, in the spirit of strategic stupidity.
Part I: Timothy Gowers on equivalence relations
Part II: Martin Gardner on normal subgroups
Part III: Evariste Galois on normal subgroups
"In all the history of science there is no completer example
of the triumph of crass stupidity over untamable genius…."
— Eric Temple Bell, Men of Mathematics
See also an interesting definition and Weyl on Galois.
Update of 6:29 PM EDT Oct. 30, 2011—
For further details, see Herstein's phrase
"a tribute to the genius of Galois."
Evariste Galois, 1811-1832 (Vita Mathematica, V. 11)
Awarded 5 stars by Christopher G. Robinson (Cambridge, MA USA).
See also other reviews by Robinson.
Galois was shot in a duel on today's date, May 30, in 1832. Related material for those who prefer entertainment to scholarship—
"It is a melancholy pleasure that what may be [Martin] Gardner’s last published piece, a review of Amir Alexander’s Duel at Dawn: Heroes, Martyrs & the Rise of Modern Mathematics, will appear next week in our June issue." —Roger Kimball of The New Criterion, May 23, 2010.
Today is, incidentally, the feast day of St. Joan of Arc, Die Jungfrau von Orleans. (See "against stupidity" in this journal.)
The Fano Plane
by Ed Pegg Jr.,
“One thing in the Fano plane that bothered me for years (for years, I say) is that it had a circle – and it was described as a line. For me, a line was a straight line, and I didn’t trust curved or wriggly lines. This distrust kept me away from understanding projective planes, designs, and finite geometries for a awhile (for years).”
|
— Schiller,* quoted as
the epigraph to the
chapter on Galois in
Men of Mathematics,
by E. T. Bell
Related material:
Galois Geometry
* From Die Jungfrau von Orleans
(The Maid of Orleans), Act III, sc. vi.
Today is the feast of that Jungfrau.
— Foucault’s Pendulum
by Umberto Eco,
Professor of Semiotics at
Europe’s oldest university,
the University of Bologna.
The Club Dumasby Arturo Perez-Reverte
|
“In 1603, at Monte Paderno, outside Bologna, an alchemist (by day a cobbler) named Vicenzo Cascariolo discovered the Philosopher’s Stone, catalyst in the transformation of base metals into gold, focus of the imagination, talisman for abstruse thought. Silver in some lights, white in others, it glowed blue in darkness, awesome to behold.”
“For the University of Bologna hosting an International Conference on Bioluminescence and Chemiluminescence has a very special significance. Indeed, it is in our fair City that modern scientific research on these phenomena has its earliest roots….
‘After submitting the stone
to much preparation, it was not
the Pluto of Aristophanes
that resulted; instead, it was
the Luciferous Stone’ ”
From one of the best books
of the 20th century: The Hawkline Monsterby Richard Brautigan
|
Presbyterian Poets Society
The Wrinkle in Time link in my previous entry led to a sermon for St. Andrew’s day, 2003, at the Riviera Presbyterian Church in Miami.
I belong to no church, but have a vague recollection of being confirmed in the Presbyterian church in early adolescence. That ceremony meant nothing to me then, and means nothing to me now. It was the culmination of fitful attendance at Presbyterian Sunday School, which I recall, reluctantly, only as a course of training in ugliness, lies, and stupidity.
There seems, however, to be a paradox here. The same religion I so detested seems to have inspired in others works of beauty, truth, and intelligence.
To wit, three poets, each with a Presbyterian background:
It may be that I am becoming reconciled to the religion that was urged upon me in my youth… becoming, at last, a Riviera Presbyterian.
For more details,
click on the above picture.
Intelligence Test
At left: |
Today’s British Intelligence Award
goes to Reuters news agency:
Key Phrase Was Dropped LONDON (Reuters) – The British intelligence chief responsible for a pre-war dossier on Iraq’s weapons dropped a key sentence from it days before publication after prompting from Downing Street, an inquiry heard Tuesday. He did it at the suggestion of Jonathan Powell, chief of staff to Prime Minister Tony Blair, the inquiry heard. The offending sentence stated that former Iraqi President Saddam Hussein was prepared to use chemical and biological weapons “if he believes his regime is under threat.” Powell argued that phrase suggested Iraq was only a threat if attacked. The revelation that Powell ordered the sentence to be omitted raises fresh doubts over the intervention of Blair’s office in the compilation of the September dossier. |
Today’s British Stupidity Award goes,
of course, to Jonathan Powell.
In memory of Cécile de Brunhoff, discoverer of
Babar, who died yesterday at the age of 99.
“Here we see the imagined universe of Babar’s Dream by Jean de Brunhoff. In an archetypal battle between good and evil, the graceful winged elephants — the angels of kindness, intelligence, courage, patience, perseverance, knowledge, work, hope, love, health, joy, and happiness — drive out the demons of misfortune, anger, stupidity, discouragement, sickness, spinelessness, despair, fear, ignorance, cowardice, laziness.”
— Source cited: Edward R. Tufte, Visual Explanations
Today is Buddha’s birthday. For the
connection with elephants, click here.
Daimon Theory
Today is allegedly the anniversary of the canonization, in 1622, of two rather important members of the Society of Jesus (Jesuits):
Ignatius Loyola…
Click here for Loyola’s legacy of strategic intelligence.
Francis Xavier…
Click here for Xavier’s legacy of strategic stupidity.
We can thank (or blame) a Jesuit (Gerard Manley Hopkins) for the poetic phrase “immortal diamond.” He may have been influenced by Plato, who has Socrates using a diamond figure in an argument for the immortality of the soul. Confusingly, Socrates also talked about his “daimon” (pronounced dye-moan). Combining these similar-sounding concepts, we have Doctor Stephen A. Diamond writing about daimons — a choice of author and topic that neatly combines the strategic intelligence of Loyola with the strategic stupidity of Xavier.
The cover illustration is perhaps not of Dr. Diamond himself.
A link between diamond theory and daimon theory is furnished by the charitable legacy of the non-practicing Jew Walter Annenberg.
For Annenberg and diamond theory, see this site on the elementary geometry of quilt blocks, which credits the Annenberg Foundation for support.
For Annenberg and daimon theory, see this site on Socrates, which has a similar Annenberg support credit.
Advanced disciples of Annenberg can learn much from the Perseus site about daimon theory. Let us pray that Abrahamic religious bigotry does not stand in their way. Less advanced disciples of Annenberg may find fulfillment in teaching children the beauty of elementary 4×4 quilt-block symmetry. Let us pray that academic bigotry does not prevent these same children, when they have grown older, from learning the deeper, and more difficult, beauties of diamond theory.
A Logocentric Archetype
Today we examine the relativist, nominalist, leftist, nihilist, despairing, depressing, absurd, and abominable work of Samuel Beckett, darling of the postmodernists.
One lens through which to view Beckett is an essay by Jennifer Martin, "Beckettian Drama as Protest: A Postmodern Examination of the 'Delogocentering' of Language." Martin begins her essay with two quotations: one from the contemptible French twerp Jacques Derrida, and one from Beckett's masterpiece of stupidity, Molloy. For a logocentric deconstruction of Derrida, see my note, "The Shining of May 29," which demonstrates how Derrida attempts to convert a rather important mathematical result to his brand of nauseating and pretentious nonsense, and of course gets it wrong. For a logocentric deconstruction of Molloy, consider the following passage:
"I took advantage of being at the seaside to lay in a store of sucking-stones. They were pebbles but I call them stones…. I distributed them equally among my four pockets, and sucked them turn and turn about. This raised a problem which I first solved in the following way. I had say sixteen stones, four in each of my four pockets these being the two pockets of my trousers and the two pockets of my greatcoat. Taking a stone from the right pocket of my greatcoat, and putting it in my mouth, I replaced it in the right pocket of my greatcoat by a stone from the right pocket of my trousers, which I replaced by a stone from the left pocket of my trousers, which I replaced by a stone from the left pocket of my greatcoat, which I replaced by the stone which was in my mouth, as soon as I had finished sucking it. Thus there were still four stones in each of my four pockets, but not quite the same stones….But this solution did not satisfy me fully. For it did not escape me that, by an extraordinary hazard, the four stones circulating thus might always be the same four."
Beckett is describing, in great detail, how a damned moron might approach the extraordinarily beautiful mathematical discipline known as group theory, founded by the French anticleric and leftist Evariste Galois. Disciples of Derrida may play at mimicking the politics of Galois, but will never come close to imitating his genius. For a worthwhile discussion of permutation groups acting on a set of 16 elements, see R. D. Carmichael's masterly work, Introduction to the Theory of Groups of Finite Order, Ginn, Boston, 1937, reprinted by Dover, New York, 1956.
There are at least two ways of approaching permutations on 16 elements in what Pascal calls "l'esprit géométrique." My website Diamond Theory discusses the action of the affine group in a four-dimensional finite geometry of 16 points. For a four-dimensional euclidean hypercube, or tesseract, with 16 vertices, see the highly logocentric movable illustration by Harry J. Smith. The concept of a tesseract was made famous, though seen through a glass darkly, by the Christian writer Madeleine L'Engle in her novel for children and young adults, A Wrinkle in Tme.
This tesseract may serve as an archetype for what Pascal, Simone Weil (see my earlier notes), Harry J. Smith, and Madeleine L'Engle might, borrowing their enemies' language, call their "logocentric" philosophy.
For a more literary antidote to postmodernist nihilism, see Archetypal Theory and Criticism, by Glen R. Gill.
For a discussion of the full range of meaning of the word "logos," which has rational as well as religious connotations, click here.
Double Day… August 2, 2002
“Time cannot exist without a soul (to count it).” — Aristotle
The above quotation appears in my journal note of August 2, 1995, as an epigraph on the reproduced title page of The Sense of an Ending, by Frank Kermode (Oxford University Press, 1967).
August 2, 1995, was the fortieth anniversary of Wallace Stevens’s death. On the same date in 1932 — seventy years ago today — actor Peter O’Toole was born. O’Toole’s name appears, in a suitably regal fashion, in my journal note of August 2, 1995, next to the heraldic crest of Oxford University, which states that “Dominus illuminatio mea.” Both the crest and the name appear below the reproduced title page of Kermode’s book — forming, as it were, a foundation for what Harvard professor Marjorie Garber scornfully called “the Church of St. Frank” (letters to the editor, New York Times Book Review, July 30, 1995).
Meditations for today, August 2, 2002:
From page 60 of Why I Am a Catholic, by Gary Wills (Houghton Mifflin, 2002):
“Was Jesus teasing Peter when he called him ‘Rocky,’ naming him ab opposito, as when one calls a not-so-bright person Einstein?”
From page 87 of The Third Word War, by Ian Lee (A&W Publishers, Inc., New York, 1978):
“Two birds… One stone (EIN STEIN).”
From “Seventy Years Later,” Section I of “The Rock,” a poem by Wallace Stevens:
A theorem proposed between the two —
Two figures in a nature of the sun….
From page 117 of The Sense of an Ending:
“A great many different kinds of writing are called avant-garde…. The work of William Burroughs, for instance, is avant-garde. His is the literature of withdrawal, and his interpreters speak of his hatred for life, his junk nihilism, his treatment of the body as a corpse full of cravings. The language of his books is the language of an ending world, its aim… ‘self-abolition.'”
From “Today in History,” by The Associated Press:
“Five years ago: ‘Naked Lunch’ author William S. Burroughs, the godfather of the ‘Beat generation,’ died in Kansas City, Mo., at age 83.”
Part of the above statement is the usual sort of AP disinformation, due not to any sinister intent but to stupidity and carelessness. Burroughs actually died in Lawrence, Kansas. For the location of Lawrence, click on the link below. Location matters.
From page 118 of The Sense of an Ending:
“Somewhere, then, the avant-garde language must always rejoin the vernacular.”
From the Billie Holiday songbook:
“Good mornin’, heartache.”
From page 63 of The New Yorker issue dated August 5, 2002:
“Birthday, death-day — what day is not both?” — John Updike
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