Sunday, October 8, 2017

Patterns at Oxford

Filed under: Uncategorized — m759 @ 7:59 PM

See also W. Tecumseh Fitch in this journal.

From the publisher (click to enlarge) —

The above publication date, 01 September 2015, suggests a review
of posts now tagged A Mirror Darkly.

Friday, July 1, 2016

Transparent Core

Filed under: Uncategorized — m759 @ 2:28 PM

"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 

A more specific "transparent core" —

See all references to this figure
in this journal.

For a more specific "monkey grammarian," 
see W. Tecumseh Fitch in this journal.

Saturday, July 12, 2014


Filed under: Uncategorized — Tags: — m759 @ 9:00 AM

A sequel to the 1974 film
Thunderbolt and Lightfoot :

Contingent and Fluky

Some variations on a thunderbolt  theme:

Design Cube 2x2x2 for demonstrating Galois geometry

These variations also exemplify the larger
Verbum  theme:

Image-- Escher's 'Verbum'

Escher’s Verbum

Image-- Solomon's Cube

Solomon’s Cube

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

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.

Tuesday, December 18, 2012

Monkey Grammar

Filed under: Uncategorized — 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.

Sunday, December 9, 2012

Adam in Eden

Filed under: Uncategorized — Tags: , — m759 @ 7:00 PM


"… we have taken the first steps
in decoding the uniquely human
fascination with visual patterns…."

W. Tecumseh Fitch et al. ,  July 2012

Fitch cites the following as a reference:

IMAGE- Washburn and Crowe, 'Symmetries of Culture' (1988)

Washburn and Crowe discuss symmetries in general, but
not the Galois geometry underlying patterns like some of
those shown on their book's cover.

Deep Structure

Filed under: Uncategorized — Tags: , — m759 @ 10:18 AM

The concept of "deep structure," once a popular meme,
has long been abandoned by Chomskians.

It still applies, however, to the 1976 mathematics, diamond theory  ,
underlying the formal patterns discussed in a Royal Society paper
this year.

A review of deep structure, from the Wikipedia article Cartesian linguistics

[Numbers in parentheses refer to pages in the original 1966 Harper edition of Chomsky's book Cartesian Linguistics .]

Deep structure vs. surface structure

"Pursuing the fundamental distinction between body and mind, Cartesian linguistics characteristically assumes that language has two aspects" (32). These are namely the sound/character of a linguistic sign and its significance (32). Semantic interpretation or phonetic interpretation may not be identical in Cartesian linguistics (32). Deep structures are often only represented in the mind (a mirror of thought), as opposed to surface structures, which are not.

Deep structures vary less between languages than surface structures. For instance, the transformational operations to derive surface forms of Latin and French may obscure common features of their deep structures (39). Chomsky proposes, "In many respects, it seems to me quite accurate, then, to regard the theory of transformational generative grammar, as it is developing in current work, as essentially a modern and more explicit version of the Port-Royal theory" (39).

Summary of Port Royal Grammar

The Port Royal Grammar is an often cited reference in Cartesian Linguistics  and is considered by Chomsky to be a more than suitable example of Cartesian linguistic philosophy. "A sentence has an inner mental aspect (a deep structure that conveys its meaning) and an outer, physical aspect as a sound sequence"***** This theory of deep and surface structures, developed in Port Royal linguistics, meets the formal requirements of language theory. Chomsky describes it in modern terms as "a base system that generates deep structures and a transformational system that maps these into surface structures", essentially a form of transformational grammar akin to modern studies (42).

The corresponding concepts from diamond theory are

"Deep structure"— The line diagrams indicating the underlying
structure of varying patterns

"A base system that generates deep structures"—
Group actions on square arrays for instance, on the 4×4 square

"A transformational system"— The decomposition theorem 
that maps deep structure into surface structure (and vice-versa)

Saturday, December 8, 2012

Defining the Contest…

Filed under: Uncategorized — 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: Uncategorized — 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.

Tuesday, September 11, 2012

Symmetry and Hierarchy

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

A followup to Intelligence Test (April 2, 2012).

Philosophical Transactions of the Royal Society
B  (2012) 367, 2007–2022
(theme issue of July 19, 2012

Gesche Westphal-Fitch [1], Ludwig Huber [2],
Juan Carlos Gómez [3], and W. Tecumseh Fitch [1]
[1]  Department of Cognitive Biology, University of Vienna,
      Althanstrasse 14, 1090 Vienna, Austria
[2]  Messerli Research Institute, University of Veterinary Medicine Vienna,
      Medical University of Vienna and University of Vienna,
      Veterinärplatz 1, 1210 Vienna, Austria
[3]  School of Psychology, St Mary’s College, University of St Andrews,
      South Street, St Andrews, KY16 9JP, UK
Excerpt (added in an update on Dec. 8, 2012) —
Conclusion —
"…  We believe that applying the theoretical
framework of formal language theory to two-dimensional
patterns offers a rich new perspective on the
human capacity for producing regular, hierarchically
organized structures. Such visual patterns may actually
prove more flexible than music or language for probing
the full extent of human pattern processing abilities.
      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’.
      Although the patterns we studied are most similar
to tilings or mosaics, they are examples of a much
broader type of abstract plane pattern, a type found
in virtually all of the world’s cultures [4]. Given that
such abstract visual patterns seem to represent
human universals, they have received astonishingly
little attention from psychologists. This neglect is particularly
unfortunate given their democratic nature,
their popular appeal and the ease with which they
can be generated and analysed in the laboratory.
With the current research, we hope to spark renewed
scientific interest in these ‘unregarded arts’, which
we believe have much to teach us about the nature of
the human mind."
[4]  Washburn, D. K. & Crowe, D. W.,1988
      Symmetries of Culture
      Theory and Practice of Plane Pattern Analysis
      Seattle, WA: University of Washington Press.
Commentary —
For hierarchy , see my assessment of Gombrich.
For culture , see T. S. Eliot and Russell Kirk on Eliot.

Thursday, August 5, 2004

Thursday August 5, 2004

Filed under: Uncategorized — Tags: — m759 @ 4:06 PM

In the beginning
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:

MSNBC, Jan. 15, 2004:

How humans got
the gift of gab

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.
(Requires Windows Media Player.)

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.
(Requires Windows Media Player)

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?


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:

Hi Lo Hi Lo,
it's off to
formal language theory
we go

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