Thursday, December 15, 2011

Language

I just woke up from a dream, where it seemed I was struggling with understanding/visualizing/solving some problem/idea, and something happens which switches my language/medium-of-thought and suddenly, a flood of things come into picture, and what seemed an impasse/stalemate bursts into motion. This reminds me how important "Language" or the "Medium of expression of conscious thought" is.
This also reminded me of two quotes one by a Turing-award winner and one by a Usenet-famous-lisp-hacker:

Besides a mathematical inclination, an exceptionally good mastery of one's native tongue is the most vital asset of a competent programmer.
- Edsger Dijkstra
[I never understood this quote until now]

languages shape the way we think, or don't.
- Erik Naggum

This gives rise to many questions, one of them is probably impossible to answer:
What is the language/medium-of-expression of the subconscious/unconscious if there is one?

Other questions are easier, but nonetheless interesting:
What is the optimum language for Mathematics? for Problem Solving?
I believe Hadamard (but I might be wrong) said that the solution/insight to a problem distilled from something he cannot describe (a mess of mental artifacts). Ramanujam would say that the solution came to him in his sleep where his village goddess would come and whisper it to him. This is probably related to the first question, but certainly if Ramanujam and Hadamard had a different language to visualize/understand prime numbers and other mathematical abstractions, then certainly it shaped their solutions. But what of us lesser mortals? I usually use a lot of formal machinery and concise notation to represent a problem, not too many diagrams. Some people use a lot of diagrams, some people have a whole solution of one piece of paper with random scribblings and no structure, some people might use linear structure, very much like a proof proceeds. Perhaps one has to just discover what his or her optimum medium of expression is and there is no one single ring to rule them all.
Note that I am not talking about how the final solution is written down, I am inspecting the creative/analytic process of solving a problem and its medium of creation/analysis. But what is about language that affects this process? Is it the form/appearance/syntax that affects it more? Is it the content/vocabulary/idioms? Is it the arsenal of problem-solving strategies that one as accumulated over time that are now in-built into your language?. Is it the association on form, association on content, association on form with content?
By association I mean the brain working at a meta-level on the expression (of the problem) itself and doing some computing such as associating, deriving implicit facts, connecting, recognizing structure in the expression, pattern recognition (with an inbuilt/stored solving strategy) etc. The bigger the language - slower the association? or the way brain works does it scale pretty well? ...

What about designing programs/software and then implementing it in some computer language? More on this in some other post.


ps: writing is hard, one has to organize a lot of ideas (and I had many good ideas to put into this post) into some structure, hold the whole structure of what you are going to say in your head and then like tetris let it fall (more organizing) into one coherent solid piece. I believe playing chess exercises your ability of holding a lot of things (moves) in your head and should improve ones writing. Knuth says writing software is even harder than writing books, I wonder what he meant by that.