See the title in this journal.
See too . . .
and, exploring Burroway's "nature of identity" …
Wednesday, August 21, 2019
Language Evolution
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Saturday, July 12, 2014
Sequel
A sequel to the 1974 film
Thunderbolt and Lightfoot :
Contingent and Fluky
Some variations on a thunderbolt theme:
These variations also exemplify the larger
Verbum theme:
A search today for Verbum in this journal yielded
a Georgetown University Chomskyite, Professor
David W. Lightfoot.
"Dr. Lightfoot writes mainly on syntactic theory,
language acquisition and historical change, which
he views as intimately related. He argues that
internal language change is contingent and fluky,
takes place in a sequence of bursts, and is best
viewed as the cumulative effect of changes in
individual grammars, where a grammar is a
'language organ' represented in a person's
mind/brain and embodying his/her language
faculty."
Some syntactic work by another contingent and fluky author
is related to the visual patterns illustrated above.
See Tecumseh Fitch in this journal.
For other material related to the large Verbum cube,
see posts for the 18th birthday of Harry Potter.
That birthday was also the upload date for the following:
See esp. the comments section.
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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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Thursday, August 5, 2004
Thursday August 5, 2004
In the beginning
was…
the recursion?
"Words are events."
— The Walter J. Ong Project,
quoted in Log24 on Aug. 25, 2003
"Words are events."
— The Walter J. Ong Project,
quoted in the Heckler & Coch weblog
on July 17, 2004 as part of a section
titled "Recursive, Wide, and Loopy"
Walter J. Ong was a Jesuit. The Feast of St. Ignatius Loyola, founder of the Jesuit order, is celebrated on July 31 each year.
"Recursive, Wide, and Loopy 2", a Heckler & Coch entry dated July 31, 2004, leads to the following:
|
How humans got
Why do other primates
lag behind in language? "New research may help scientists dissect just what it is about the human brain that endows us with language. Researchers have found that tamarin monkeys have some distinctly languagelike abilities but that they can’t quite master the more complex rules of human grammar. The findings appear in Friday’s issue of the journal Science, published by AAAS, the non-profit science society. The grammatical toolkit 'A relatively open question concerning language evolution is, "What aspects of the language faculty are shared with other animals, and what aspects are unique to humans?" ' said study author Marc Hauser of Harvard University. To investigate, Hauser and W. Tecumseh Fitch of the University of St. Andrews, in Scotland, devised tests for cotton-top tamarin monkeys and human volunteers. Tamarins have been evolving separately from humans for approximately 40 million years –suggesting that any shared machinery in human and tamarin brains is old enough to be relatively common among primates. Instead of trying to teach the monkeys real words, Hauser and Fitch generated strings of one-syllable words that followed various grammatical rules. According to linguistics expert Noam Chomsky, the simplest type of grammar is a 'finite state grammar' or 'FSG,' which dictates which types of words go near each other in a sentence. In English, for example, an adjective like 'fast' must go directly in front of 'car,' the noun it's describing. Building on previous experiments, Hauser and Fitch recorded word-strings that obeyed a specific FSG, in which any syllable spoken by a female voice was automatically followed by one from a male voice.
Audio: Listen to an FSG word-string. After listening to a series of word-strings, the monkeys were able to distinguish between those that followed this rule and others that didn't. Human test subjects could tell the difference as well, implying that tamarins and humans may share at least some components of what Hauser called 'the universal toolkit underlying all languages.' Mastering this type of grammar represents the ability to compute some simple statistics, something human infants accomplish early on as they learn to speak. This ability may not be specific to language, however. 'Either the same mechanism or some approximation of it is used in mathematics, vision, music and other activities,' Hauser said. Upping the Complexity The grammatical rules of real languages govern more than just the placement of neighboring words, as anyone who had to diagram sentences in English class may remember all too well. One of the more complex types of grammar is known as a 'phrase structure grammar,' or PSG. These grammars involve relationships between words that aren't next to each other in a sentence and thus allow for a more complex range of expression. The 'if … then' construction is an example of a PSG. The researchers generated a second set of word-strings that followed a PSG in which a pairing of syllables spoken by a female and a male could be embedded within another pairing. This grammar produces structures like [female [female, male] male].
Audio: Listen to a PSG word-string. After playing these recordings repeatedly to the monkeys, the researchers found that the animals didn't seem to notice the difference between word strings that obeyed the PSG and other strings that did not. In contrast, the human volunteers did notice the difference." — Kathleen Wren |
"The grammar or syntax of human language is certainly unique. Like an onion or Russian doll, it is recursive: One instance of an item is embedded in another instance of the same item. Recursion makes it possible for the words in a sentence to be widely separated and yet dependent on one another. 'If-then' is a classic example…. Are animals capable of such recursion? Fitch and Hauser have reported that tamarin monkeys are not capable of recursion. Although the monkeys learned a nonrecursive grammar, they failed to learn a grammar that is recursive. Humans readily learn both."
— David Premack (Science 2004 303:318, quoted in ScienceWeek)
These citations by Heckler & Coch show that inability to understand complex language is not limited to monkeys.
The examples given by Wren in the audio samples are of alternating female (Hi) and male (Lo) voices, thus —
FSG: Hi Lo Hi Lo Hi Lo
PSG: Hi Hi Hi Lo Lo Lo
As these examples show, neither monkeys nor humans heard the sound of parentheses (or square brackets) as Wren describes them:
"structures like [female [female, male] male]."
There of course is, in ordinary language (which does not include the monologues of Victor Borge), no such thing as the sound of parentheses.
Thus the research of Hauser and Fitch is not only invalid, but ridiculous.
This point is driven strongly home by the following two articles:
Greg Kochanski, Research Fellow,
Oxford University Phonetics Lab:
Is a Phrase Structure Grammar
the Important Difference
between Humans and Monkeys?,
and
Mark Liberman, Professor,
University of Pennsylvania
Departments of Linguistics
and of Computer Science,
and co-director of the
Institute for Research
in Cognitive Science,
in his
Language Log,
January 17, 2004:
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Thursday, June 30, 2016
Rubik vs. Galois: Preconception vs. Pre-conception
From Psychoanalytic Aesthetics: The British School ,
by Nicola Glover, Chapter 4 —
|
In his last theoretical book, Attention and Interpretation (1970), Bion has clearly cast off the mathematical and scientific scaffolding of his earlier writings and moved into the aesthetic and mystical domain. He builds upon the central role of aesthetic intuition and the Keats's notion of the 'Language of Achievement', which
… includes language that is both Bion distinguishes it from the kind of language which is a substitute for thought and action, a blocking of achievement which is lies [sic ] in the realm of 'preconception' – mindlessness as opposed to mindfulness. The articulation of this language is possible only through love and gratitude; the forces of envy and greed are inimical to it.. This language is expressed only by one who has cast off the 'bondage of memory and desire'. He advised analysts (and this has caused a certain amount of controversy) to free themselves from the tyranny of the past and the future; for Bion believed that in order to make deep contact with the patient's unconscious the analyst must rid himself of all preconceptions about his patient – this superhuman task means abandoning even the desire to cure . The analyst should suspend memories of past experiences with his patient which could act as restricting the evolution of truth. The task of the analyst is to patiently 'wait for a pattern to emerge'. For as T.S. Eliot recognised in Four Quartets , 'only by the form, the pattern / Can words or music reach/ The stillness'.30. The poet also understood that 'knowledge' (in Bion's sense of it designating a 'preconception' which blocks thought, as opposed to his designation of a 'pre -conception' which awaits its sensory realisation), 'imposes a pattern and falsifies'
For the pattern is new in every moment The analyst, by freeing himself from the 'enchainment to past and future', casts off the arbitrary pattern and waits for new aesthetic form to emerge, which will (it is hoped) transform the content of the analytic encounter. 29. Attention and Interpretation (Tavistock, 1970), p. 125 30. Collected Poems (Faber, 1985), p. 194. 31. Ibid., p. 199. |
See also the previous posts now tagged Bion.
Preconception as mindlessness is illustrated by Rubik's cube, and
"pre -conception" as mindfulness is illustrated by n×n×n Froebel cubes
for n= 1, 2, 3, 4.
Suitably coordinatized, the Froebel cubes become Galois cubes,
and illustrate a new approach to the mathematics of space .
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Sunday, August 10, 2014
Sermon
From The Mathematics of Language:
10th and 11th Biennial Conference….
Berlin, Springer, 2010 —
“Creation Myths of Generative Grammar
and the Mathematics of Syntactic Structures”
by Geoffrey K. Pullum, University of Edinburgh
Abstract
“Syntactic Structures (Chomsky [6]) is widely believed to have laid
the foundations of a cognitive revolution in linguistic science, and
to have presented (i) the first use in linguistics of powerful new ideas
regarding grammars as generative systems, (ii) a proof that English
was not a regular language, (iii) decisive syntactic arguments against
context-free phrase structure grammar description, and (iv) a
demonstration of how transformational rules could provide a formal
solution to those problems. None of these things are true. This paper
offers a retrospective analysis and evaluation.”
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Saturday, February 19, 2011
Paradigms Lost
Harvard Science Review (Winter 1997) on Thomas Kuhn's
The Structure of Scientific Revolutions —
"…his language often portrays paradigms as cults
and the battle between paradigms as quasi-religious wars."
Related material: This journal's "Paradigms" on February 17th
and the following notes—
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Thursday, February 18, 2010
Theories: An Outline
Truth, Geometry, Algebra
The following notes are related to A Simple Reflection Group of Order 168.
1. According to H.S.M. Coxeter and Richard J. Trudeau
“There is a pleasantly discursive treatment of Pontius Pilate’s unanswered question ‘What is truth?’.”
— Coxeter, 1987, introduction to Trudeau’s The Non-Euclidean Revolution
1.1 Trudeau’s Diamond Theory of Truth
1.2 Trudeau’s Story Theory of Truth
2. According to Alexandre Borovik and Steven H. Cullinane
2.1 Coxeter Theory according to Borovik
2.1.1 The Geometry–
Mirror Systems in Coxeter Theory
2.1.2 The Algebra–
Coxeter Languages in Coxeter Theory
2.2 Diamond Theory according to Cullinane
2.2.1 The Geometry–
Examples: Eightfold Cube and Solomon’s Cube
2.2.2 The Algebra–
Examples: Cullinane and (rather indirectly related) Gerhard Grams
Summary of the story thus far:
Diamond theory and Coxeter theory are to some extent analogous– both deal with reflection groups and both have a visual (i.e., geometric) side and a verbal (i.e., algebraic) side. Coxeter theory is of course highly developed on both sides. Diamond theory is, on the geometric side, currently restricted to examples in at most three Euclidean (and six binary) dimensions. On the algebraic side, it is woefully underdeveloped. For material related to the algebraic side, search the Web for generators+relations+”characteristic two” (or “2“) and for generators+relations+”GF(2)”. (This last search is the source of the Grams reference in 2.2.2 above.)
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Wednesday, October 8, 2008
Wednesday October 8, 2008
Serious Numbers
A Yom Kippur
Meditation
"When times are mysterious
Serious numbers
Will always be heard."
— Paul Simon,
"When Numbers Get Serious"
"There is a pleasantly discursive treatment of Pontius Pilate's unanswered question 'What is truth?'"
— H. S. M. Coxeter, introduction to Richard J. Trudeau's remarks on the "story theory" of truth as opposed to the "diamond theory" of truth in The Non-Euclidean Revolution
Trudeau's 1987 book uses the phrase "diamond theory" to denote the philosophical theory, common since Plato and Euclid, that there exist truths (which Trudeau calls "diamonds") that are certain and eternal– for instance, the truth in Euclidean geometry that the sum of a triangle's angles is 180 degrees. As the excerpt below shows, Trudeau prefers what he calls the "story theory" of truth–
"There are no diamonds. People make up stories about what they experience. Stories that catch on are called 'true.'"
(By the way, the phrase "diamond theory" was used earlier, in 1976, as the title of a monograph on geometry of which Coxeter was aware.)
Excerpt from
The Non-Euclidean Revolution
What does this have to do with numbers?
Pilate's skeptical tone suggests he may have shared a certain confusion about geometric truth with thinkers like Trudeau and the slave boy in Plato's Meno. Truth in a different part of mathematics– elementary arithmetic– is perhaps more easily understood, although even there, the existence of what might be called "non-Euclidean number theory"– i.e., arithmetic over finite fields, in which 1+1 can equal zero– might prove baffling to thinkers like Trudeau.
Trudeau's book exhibits, though it does not discuss, a less confusing use of numbers– to mark the location of pages. For some philosophical background on this version of numerical truth that may be of interest to devotees of the Semitic religions on this evening's High Holiday, see Zen and Language Games.
For uses of numbers that are more confusing, see– for instance– the new website The Daily Beast and the old website Story Theory and the Number of the Beast.
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Wednesday, December 26, 2007
Wednesday December 26, 2007
A Wonderful Life
Part I:
Language Games
on December 19:
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:
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.
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
- 24
- Investigations, sec. 23.
- 25
- Investigations, sec. 373; compare Zettel, sec. 717.
- 26
- Investigations, p. 226e.
- 27
- 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
- 25
- Drury (1981) 'Conversations with Wittgenstein,' in Ludwig Wittgenstein: Personal Recollections, pp. 112ff.
- 26
- Drury, 'Conversations,' p. 130.
- 27
- Drury, 'Some notes,' p. 109.
- 28
- 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?" —
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Monday, December 4, 2006
Monday December 4, 2006
180, 932 –
The Musical!
“You gotta be
true to your code.”
— Sinatra
JSTOR: A Theophany
The Musical!
“You gotta be
true to your code.”
— Sinatra
NY Lottery, 2006:
Dec. 3 Mid-day – 180
Dec. 3 Evening – 932
Yesterday’s entry suggested that
the date, December 3, might be
appropriate for some sort of
Broadway production.
Yesterday evening’s NY lottery
number, 932, suggests*
(via Google) that a visit to
the castle Wildeck
is in order.
This castle is now the home
of the Buchdruck-Museum
honoring Johannes Gutenberg.
For an appropriate Broadway
production, see today’s
New York Times:
Yesterday’s mid-day NY lottery
number, 180, suggests, in the
above context, the German term
Umkehrung. A casual web search
on this term (+ “reversal,”
then, refining the search,
+ “Theocritus”) leads
to the following material,
which I personally find of
much greater interest than
the above Broadway production.
(Such web searches are made
possible by a technological
revolution comparable to that
of Gutenberg… Broadway may
perhaps look forward to…
“Google! The Musical!“)
| Google Search 12/4/06 |
| Results 1 – 2 of about 14 for umkehrung theocritus. (0.07 seconds) |
JSTOR: Theocritus
| I12: on ‘transference’ by Theocritus of refined motifs to uncouth peasants, … is in reality a parody, a devastating ‘Umkehrung‘ of the real thing, … |
JSTOR: A Theophany
in Theocritus
| A THEOPHANY IN THEOCRITUS IN a masterly study of the language and motifs of … epithet I The completeness and precision of the Umkehrung (for this term cf. … |
* “ZSCHOPAU, a town in the kingdom of Saxony, on the left bank of the Zschopau…. It contains… a castle (Wildeck), built by the Emperor Henry I in 932.” —From the classic 11th edition of the Encyclopaedia Britannica (1911)
(The date 932 may or may not be accurate, but still serves nicely as what has been called elsewhere “an instance of the fingerpost.”)
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Sunday, August 6, 2006
Sunday August 6, 2006
Zen and the Art
of Definition
of Definition
"Good is a noun. That was it. That was what Phaedrus had been looking for. That was the homer over the fence that ended the ballgame." —Robert M. Pirsig
"How should we define goodness?"
— Title of an article (pdf) available online from Harvard.
This article (Journal of Theoretical Biology 231 (2004) 107–120), examines goodness in the light of evolutionary dynamics as it involves altruism and social reputation, and concludes that goodness as an evolved social trait has two characteristics: those with good reputations are helped, those with bad reputations are not helped. This is expressed as follows. (English is apparently not the native language of the authors, from Kyushu University in Japan.)
"One [feature of goodness] is that a player interacting with good persons are assessed by what he does. Cooperation with good individuals should be good and defection against good ones should be bad. The second feature should we consider with much emphasis: a good player who refused to help a bad person must be labeled good. This enables players facing cheaters to refuse help without worrying about the influence of the action on their own good reputation."
In other words,
"… a person in good standing falls into bad if and only if he fails to cooperate with an opponent in good standing. Even if he refuses to help an individual in bad standing, he does not lose his good standing. This is because the refusal is interpreted as punishment against a selfish individual (for studies on punishment, see Brandt and Sigmund (2003), Fehr and Gachter (2000), Fehr and Rockenbach (2003), and Henrich and Boyd (2001))."
See also Harry Truman and Hiroshima, on this date in 1945.
Related material:
Hitler's Still Point:
A Hate Speech for Harvard
The 5 Log24 entries ending
with "Three in One" on
December 30, 2002
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Tuesday, April 25, 2006
Tuesday April 25, 2006
Mathematics and Narrative, continued
“There is a pleasantly discursive treatment
of Pontius Pilate’s unanswered question
‘What is truth?'”
— H. S. M. Coxeter, 1987, introduction to
Richard J. Trudeau’s remarks on
the “Story Theory” of truth
as opposed to
the “Diamond Theory” of truth
in The Non-Euclidean Revolution
A Serious Position
“‘Teitelbaum,’ in German,
is ‘date palm.'”
— Generations, Jan. 2003
“In Hasidism, a mystical brand
of Orthodox Judaism, the grand rabbi
is revered as a kinglike link to God….”
— Today’s New York Times obituary
of Rabbi Moses Teitelbaum,
who died on April 24, 2006
(Easter Monday in the
Orthodox Church)
From Nextbook.org, “a gateway to Jewish literature, culture, and ideas”:
NEW BOOKS: 02.16.05
Proofs and Paradoxes
Alfred Teitelbaum changed his name to Tarski in the early 20s, the same time he changed religions, but when the Germans invaded his native Poland, the mathematician was in California, where he remained. His “great achievement was his audacious assault on the notion of truth,” says Martin Davis, focusing on the semantics and syntax of scientific language. Alfred Tarski: Life and Logic, co-written by a former student, Solomon Feferman, offers “remarkably intimate information,” such as abusive teaching and “extensive amorous involvements.”
Proofs and Paradoxes
Alfred Teitelbaum changed his name to Tarski in the early 20s, the same time he changed religions, but when the Germans invaded his native Poland, the mathematician was in California, where he remained. His “great achievement was his audacious assault on the notion of truth,” says Martin Davis, focusing on the semantics and syntax of scientific language. Alfred Tarski: Life and Logic, co-written by a former student, Solomon Feferman, offers “remarkably intimate information,” such as abusive teaching and “extensive amorous involvements.”
From Wikipedia, an unsigned story:
“In 1923 Alfred Teitelbaum and his brother Wacław changed their surnames to Tarski, a name they invented because it sounded very Polish, was simple to spell and pronounce, and was unused. (Years later, he met another Alfred Tarski in northern California.) The Tarski brothers also converted to Roman Catholicism, the national religion of the Poles. Alfred did so, even though he was an avowed atheist, because he was about to finish his Ph.D. and correctly anticipated that it would be difficult for a Jew to obtain a serious position in the new Polish university system.”
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Sunday, November 20, 2005
Sunday November 20, 2005
“There is a pleasantly discursive treatment of Pontius Pilate’s unanswered question ‘What is truth?'”
— H. S. M. Coxeter, 1987, introduction to Richard J. Trudeau’s remarks on the “Story Theory” of truth as opposed to the “Diamond Theory” of truth in The Non-Euclidean Revolution
“A new epistemology is emerging to replace the Diamond Theory of truth. I will call it the ‘Story Theory’ of truth: There are no diamonds. People make up stories about what they experience. Stories that catch on are called ‘true.’ The Story Theory of truth is itself a story that is catching on. It is being told and retold, with increasing frequency, by thinkers of many stripes*….”
— Richard J. Trudeau in
The Non-Euclidean Revolution
“‘Deniers’ of truth… insist that each of us is trapped in his own point of view; we make up stories about the world and, in an exercise of power, try to impose them on others.”
— Jim Holt in The New Yorker.
(Click on the box below.)
Exercise of Power:
Show that a white horse–
a figure not unlike the
symbol of the mathematics
publisher Springer–
is traced, within a naturally
arranged rectangular array of
polynomials, by the powers of x
modulo a polynomial
irreducible over a Galois field.
This horse, or chess knight–
“Springer,” in German–
plays a role in “Diamond Theory”
(a phrase used in finite geometry
in 1976, some years before its use
by Trudeau in the above book).
Related material
On this date:
In 1490, The White Knight
(Tirant lo Blanc 
)–
a major influence on Cervantes–
was published, and in 1910
the Mexican Revolution began.
Illustration:
Zapata by Diego Rivera,
Museum of Modern Art,
New York
“First published in the Catalan language in Valencia in 1490…. Reviewing the first modern Spanish translation in 1969 (Franco had ruthlessly suppressed the Catalan language and literature), Mario Vargas Llosa hailed the epic’s author as ‘the first of that lineage of God-supplanters– Fielding, Balzac, Dickens, Flaubert, Tolstoy, Joyce, Faulkner– who try to create in their novels an all-encompassing reality.'”
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Tuesday, May 31, 2005
Tuesday May 31, 2005
Subject and Predicates
“A Chu space is a set X of subjects and a set A of predicates on those subjects. These stand in a symbiotic relationship in which the nature of each is determined by the other. Each subject is characterized by the values the predicates take on it, while each predicate is characterized by its values on subjects.”
— Vaughan Pratt, Chu Spaces
Click here for Sambin’s paper (ps).
It would seem that Pratt and Sambin need to reconcile their similar predicates for the same subject.
For some background on Sambin’s approach to the subject, see
Mathematical Modal Logic:
A View of its Evolution (pdf),
by Robert Goldblatt at
Victoria University of Wellington’s
Centre for Logic, Language,
and Computation
A View of its Evolution (pdf),
by Robert Goldblatt at
Victoria University of Wellington’s
Centre for Logic, Language,
and Computation
For some background on Pratt’s approach to the subject, see
Information Transfer
Across Chu Spaces (pdf),
by Johan van Benthem
at the University of Amsterdam’s
Institute for Logic, Language,
and Computation
For a gloss on Sambin’s words
see the Log24 entry of Epiphany, 2005.
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Thursday, November 6, 2003
Thursday November 6, 2003
Legacy Codes:
The Most Violent Poem
Lore of the Manhattan Project:
From The Trinity Site —
“I imagined Oppenheimer saying aloud,
‘Batter my heart, three person’d God,”
unexpectedly recalling John Donne’s ‘Holy Sonnet [14],’
and then he knew, ‘ “Trinity” will do.’
Memory has its reasons.
‘Batter my heart’ — I remember these words.
I first heard them on a fall day at Duke University in 1963.
Inside a classroom twelve of us were
seated around a long seminar table
listening to Reynolds Price recite this holy sonnet….
I remember Reynolds saying, slowly, carefully,
‘This is the most violent poem in the English language.’ ”
Related Entertainment
Today’s birthday:
director Mike Nichols
From a dead Righteous Brother:
“If you believe in forever
Then life is just a one-night stand.”
— Bobby Hatfield, found dead
in his hotel room at
7 PM EST Wednesday, Nov. 5, 2003,
before a concert scheduled at
Western Michigan University, Kalamazoo.
From a review of The Matrix Revolutions:
“You’d have to be totally blind at the end
to miss the Christian symbolism….
Trinity gets a glimpse of heaven…. And in the end…
God Put A Rainbow In The Clouds.”
Moral of the
Entertainment:
According to Chu Hsi [Zhu Xi],
“Li” is
“the principle or coherence
or order or pattern
underlying the cosmos.”
— Smith, Bol, Adler, and Wyatt,
Sung Dynasty Uses of the I Ching,
Princeton University Press, 1990
Related Non-Entertainment
Symmetry and a Trinity
(for the dotting-the-eye symbol above)
Introduction to Harmonic Analysis
(for musical and historical background)
Mathematical Proofs
(for the spirit of Western Michigan
University, Kalamazoo)
Moral of the
Non-Entertainment:
“Many kinds of entity
become easier to handle
by decomposing them into
components belonging to spaces
invariant under specified symmetries.”
— The importance of
mathematical conceptualisation
by David Corfield,
Department of History and
Philosophy of Science,
University of Cambridge
See, too,
Symmetry of Walsh Functions and
Geometry of the I Ching.
Comments Off on Thursday November 6, 2003
Monday, March 24, 2003
Monday March 24, 2003
Orwell’s question, according to
an admirer of leftist Noam Chomsky:
“When so much of the BS is right out in the open,
why is it that we know so little about it?
Why don’t we see what’s right in front of our eyes?”
 Oscar |
Lying, Truth-Telling, and the Social Order |
 Michael Moore |
“First of all, I’d like to thank the Academy….”
— Quotation attributed to Plato
The New Yorker of March 31, 2003, discusses leftist academic Noam Chomsky. The online edition provides a web page listing pro-Chomsky links.
Chomsky’s influence is based in part on the popularity of his half-baked theories on linguistics, starting in the 1950’s with “deep structure” and “transformational,” or “generative,” grammar.
Chomsky has abandoned many of his previous ideas and currently touts what he calls The Minimalist Program.
For some background on Chomsky’s recent linguistic notions, see the expository essay “Syntactic Theory,” by Elly van Gelderen of the Arizona State University English Department. Van Gelderen lists her leftist political agenda on her “Other Interests” page. Her department may serve as an example of how leftists have converted many English departments in American universities to propaganda factories.
Some attacks on Chomsky’s scholarship:
Forty-four Reasons Why the Chomskians Are Mistaken
Chomsky’s (Mis)Understanding of Human Thinking
Anatomy of a Revolution… Chomsky in 1962
…Linguistic Theory: The Rationality of Noam Chomsky
Some attacks on Chomsky’s propaganda:
Destructive Generation excerpt
Partners in Hate: Noam Chomsky and the Holocaust Deniers
Chomsky and Plato’s Diamond
Like another purveyor of leftist nonsense, Jacques Derrida, Chomsky is fond of citing Plato as a precedent. In particular, what Chomsky calls “Plato’s problem” is discussed in Plato’s Meno. For a look at the diamond figure that plays a central role in that dialogue, see Diamond Theory. For an excellent overview of related material in Plato, see Theory of Forms.