From a discussion about "loss of generality" on the Funknet discussion list (http://lloyd.emich.edu/cgi-bin/wa?A2=ind0406&L=funknet&D=0&P=3622):

'The particular analysis which interests me is one I found in a historical

retrospective by Fritz Newmeyer and others "Chomsky's 1962 programme for

linguistics" (in Newmeyer's "Generative Linguistics -- A Historical

Perspective", Routledge, 1996, and apparently also published in "Proc. of the

XVth International Congress of Linguists".)

Newmeyer is talking mostly about Chomsky's "Logical basis of linguistic

"One of the most brilliant mathematicians of the last and current century is John Horton Conway. Near the middle of the last century he formalized a notion of game in terms of a certain recursive data structure. He went on to show that every notion of number that has made it into the canon of numerical notions could be given representations in terms of this data structure. These ideas are documented in his delightful On Numbers and Games. Knuth popularized some of these ideas in his writings on surreal numbers."

http://biosimilarity.blogspot.com/2008/03/naming-as-dialectic.html

Rudy Rucker on cellular automata: "I was first hooked on modern cellular automata by [Wolfram84]. In this article, Wolfram suggested that many physical processes that seem random are in fact the deterministic outcome of computations that are simply so convoluted that they cannot be compressed into shorter form and predicted in advance. He spoke of these computations as "incompressible," and cited cellular automata as good examples."

"We have seen that the Glider Gun generates ordered gliders every 30 generations, and that the generation process is chaotic: it exhibits the butterfly effect."

http://www.upscale.utoronto.ca/GeneralInterest/Harrison/LifeEnergy/LifeA...

Work like the classic seminal work of Pawley and Syder demonstrate natural language is far from random, but is equally far from regular:

p.g. 2

"The problem we are addressing is that native speakers do not

exercise the creative potential of syntactic rules to anything like

their full extent, and that, indeed, if they did do so they would

not be accepted as exhibiting nativelike control of the language.

The fact is that only a small proportion of the total set of grammatical

sentences are nativelike in form - in the sense of being

Natural language appears to be random (c.f. from the Hutter Prize page):

"...in 1950, Claude Shannon estimated the entropy (compression limit)

of written English to be about 1 bit per character [3]. To date, no

compression program has achieved this level."

(http://cs.fit.edu/~mmahoney/compression/rationale.html)

The most successful contemporary natural language technologies are probabilistic.

The usual explanation is that something external selects between alternatives which are equally probable on linguistic grounds. Commonly this external factor is assumed to be "meaning".

From Heisenberg to Goedel via Chaitin

Authors: C.S. Calude, M.A. Stay

(Submitted on 26 Feb 2004 (v1), last revised 11 Jul 2006 (this version, v6))

"Conway conjectured on the existence of infinitely growing patterns, and offered a reward for an example. Gosper was the first to find such a pattern (specifically, the Glider gun), and won the prize."

From a discussion on the "Hutter-Prize" Google group (http://groups.google.com/group/Hutter-Prize/browse_thread/thread/bfea185...):

...If A_1, A_2,... A_n

are the contexts of A in some text, and X_1, X_2,...X_n are contexts of

other tokens, then the number of ways A can have common contexts with

other tokens in the text, and thus uniquely specify some new

paradigmatic class, are just Matt's "(n choose k) = n!/(k!(n-k)!)

possible sets", where k is the number of common contexts between A and

some other token.

The syntagmatic distribution of sequences AX_? specified by these