Answering The Finite Language, Infinite Thoughts Galileo Problem

The finite number of symbols and infinite number of thoughts problem raised by Galileo (and Descartes) refers to the concept that although the number of symbols or words we have at our disposal is limited, the number of thoughts and ideas we can express using those symbols seems to be limitless. Galileo Galilei, the famous Italian scientist, philosopher, and mathematician, pondered this issue. How can we effectively communicate complex and abstract thoughts using a limited set of symbols?

Chomsky, 94 years old, was asked in an interesting interview (however biased) what was the most fascinating unanswered question, and he pointed at that problem. The CHAT AI, that is traditional answer, is to list or blahblahblah the obvious various strategies to enhance communication: Context, metaphor and analogy, clarification and feedback, non-verbal communication: In addition to words, CHAT AI would add, we communicate using non-verbal cues such as gestures, facial expressions, and body language… or a drawing board for much of math, physics, engineering, let alone art. Visual representations, and multimedia. Iterative and adaptive communication: Communication is an iterative process that involves sending and receiving messages. For example Galileo was ordered to shut up and stay in his house. Descartes fled to the Netherlands (CHAT AI won’t tell you that).  

***

WHAT is it that we are trying to communicate? Brain geometry! Brain attitude!

Now brain geometry is made in the first approach of AXONAL paths. Each axonal path is made of a finite number of axons (one-simplex in 3 dim space to use math semantics). So the question is: how do we translate a bunch of one dimensional paths in 3 D space over? Simple! We describe them! How? 

The short and glib answer is that computers can describe any path in 3 dimensions using only two symbols: 0 and 1…because any base two number system is equivalent to any other base, and a fortiori the 26 + 10 Latin alphabet plus usual numerals…)

I give a different (mathematical) approach (of mine) in a (Math technical) appendix to come (perhaps). Anyway I am not surprised that Galileo and Descartes didn’t know about computers (their existence had been eradicated by Catholicism). But Chomsky? Chomsky didn’t know about neural paths, neural networks, and how to digitally model paths with just two symbols?

Let me chomp on that…

Patrice Ayme

 Random walk in 3 dimensions projected in 2 dimensions. Such a walk changes by +1 or -1 at every step in a 3 dimensional lattice

Tags: Chomsjy. Axonal paths, Galileo Finite Symbol problem, Neural Networks