The Three Little Pigs : Chemistry of language acquisition

Yuri Tarnopolsky

 
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Abstract

While problems of emergence are often treated in terms of complexity reaching a certain threshold, a different
approach can be advocated in terms of simplicity. Inspired by fundamental principles of chemistry, it looks for
very simple systems in tiny phase spaces, governed by simple local rules and capable of increasing their complexity
by simple steps. It is hypothesized that the initial stage of language acquisition is a natural example of emergence
through simplicity.It might be difficult to reconcile evolving systems with the axiom of closure, which is the keystone
of mathematics butleaves no place to evolutionary novelty. Chemistry, however, accommodates the concept
of novelty quite well. This e-paper continues, in a freewheeling fashion, the examination of language as a quasi-molecular
system from the point of view of a chemist who happens to ask, “What if the words were atoms?”  It further explores
the parallel between cognitive and chemical systems. A unified conceptual groundwork for chemistry and linguistics,
as well as cognition and all other discrete combinatorial systems, is borrowed from the atomism of Pattern Theory
(Ulf Grenander). As an illustration, the text of The Three Little Pigs is decomposed into triplets of adjacent words
and some local principles of generator identification and categorization are examined. The principle of local equilibrium
between the category and its entries is discussed against the background of basic chemical ideas. 

CONTENTS

If words were atoms: an introduction                                                    3

PART 1.  The mind and the flask                                                           6

Name your friends                                                                      6 

Drowning by numbers                                                                11

            The language elephant                                                              13

A former child’s credo                                                               15

The New and the Different                                                        17

Go I don’t know where and bring me I don’t know what          19

Connections and collisions                                                         24

            Is the mind an enzyme?                                                              29

Equilibrium and emergence of mind                                          33

Small is big                                                                                  39

From thought to language                                                           41

Notes on locality                                                                         44

PART 2   The chemistry of the Three Little Pigs                                 47

Principles                                                                                    47

Illustrations                                                                                56

Conclusion                                                                                              72
References                                                                                             75

If words were atoms: an introduction         

This e-paper continues the examination of language as a quasi-molecular system from the point of view of a chemist who, inspired by the book by Mark C. Baker The Atoms of Language [1] , quite seriously asks, “What if the words were atoms?” 

The chemist happens to be myself. My motivation comes from the time when I, a student at a chemistry department in the mid-1950’s, learned for the first time about Norbert Wiener and his previously forbidden in the Soviet Russia cybernetics. By the same time, facing a large body of chemical publications and starting to develop some passive skills in foreign languages, I felt the pull of the linguistic cosmos. Thirty years later I had learned, by mere accident, about Ulf Grenander and his Pattern Theory (PT)  [2, 3] and the theory seemed to friendly embrace all available to me knowledge.

I want to look at cognition with the eyes of neither a mathematician, nor an engineer, nor a linguist, nor a cognitive scientist, but a chemist. My intuition tells me that chemistry may be relevant at least for one reason. Molecules and phrases, both observable, are configurations in PT.

What chemistry can contribute to the area is, first of all, the unique experience with discrete structural change over time, which hardly any other science possesses in comparably pure form. Another little used angle of vision, also inspired by chemistry, is the evolutionary one, but, again, not in the common sense. It is not that “everything evolves” but that everything grows on a historical scale from very simple structures by very simple steps up to an overwhelming complexity. Thirdly, the eye-catching but often misunderstood principle of catalysis has a very general extra-chemical meaning.

There is yet another subtle reason. We do not know whether it is essential for the brain and its cells to be a chemical system. If we knew, we could probably understand why human mind has been so stubbornly resisting any integral computer simulation for at least half a century of computer science.

Chemistry, as no other science, can efficiently master enormous complexity by simple means and a Spartan stock of ideas. Taking to account the chemical origin of life and tracing the origin of species, mind, and society back to the chemical cradle, we may expect to notice in the oblique light some new shadows invisible in the frontal glare of computer science.

I ended my previous e-paper [ 4] with a tentative Appendix as an illustration of some chemistry-inspired concepts regarding the first language acquisition by children and the Poverty of Stimulus argument. I decomposed a fragment of The Three Little Pigs into 1-neighborhoods of words, i.e., the word and its right and left neighbors, and tried to derive syntactic classification in a non-algorithmic manner through primitive local operations, ignoring the impressive achievements of Neural Networks, algorithmic Part-of-Speech tagging, corpus-based and context-based categorization, and other contemporary approaches to language processing. As before, I am interested here only in exploring the parallels between language and chemistry in the light of Pattern Theory, but always from the position and with habits of a chemist.  

Further pursuing the program If Words Were Atoms,  I am making here the next step within a larger program The Chemical View of the World, see  [ 4, 5 ] . where some relevant literature was collected from distant domains of knowledge.  It is the larger program that could be an excuse for numerous digressions from the immediate subject and references to distant times and places on the map of knowledge.   

            The main idea can be presented in the following way. The natural complex systems, especially, life, mind, language, society, and culture, all emerged at some elusive point. The dominating point of view is that order emerges in a dynamical system when its parameters exceed some threshold  [6]. This is certainly  true, as far as the origin of order in some physical and chemical systems is concerned, but there is no way to derive a particular kind of order, for example, origin and evolution of language, from the general systemic ideas about order. We can derive regularities from observing particular systems, but we cannot derive particular systems from the regularities, unless we have a conceptual bridge between particularities and regularities. This bridge naturally exists in chemistry and follows from the idea of atomism. Pattern Theory is, in this sense, a meta-chemistry, i.e., a mathematical foundation for the study of atomistic structure.

If the prevalent direction in the study of emergence starts with complexity, the alternative idea is advocated here in terms of simplicity. The science of simplicity, possibly complementary to the science of complexity, starts with very simple systems in tiny phase spaces, governed by simple local rules and capable of increasing their complexity by simple steps. On its progress toward complexity,  simplicity is not bound by the axiom of closure that makes mathematics and logic possible. Chemical systems, having served as the cradle of life and life’s subsequent expansions into mind and society, are the natural source of such ideas. It is hypothesized that language acquisition is one of possible illustrations, too. Unlike the origin of life and society, not to mention the universe, it is perfectly observable in small children.

I suggest that the simple origin is a necessary condition of unfolding of any complex system and it should be included into the definition of the complex open system and taken to account in designing realistic simulations of life, mind, and society.

The paper consists of two parts: one is about principles and the other one with illustrations. As far as the style of this paper is concerned, if it appears tousled, it tells about the excitement of the adventure.

©    Yuri Tarnopolsky, 2005