Mr. Stephen Wolfram’s idea of ‘computational irreducibility’ has possessed my mind since I read it two days ago.
Here’s a definition he gives - ‘Computations that cannot be sped up by means of any shortcut are called computationally irreducible. The principle of computational irreducibility says that the only way to determine the answer to a computationally irreducible question is to perform. or simulate,
the computation.’
This idea is so important, and its implications are so deep, that it effectively gives an answer to the big questions of science and even philosophy.
First of all, it shows the limits of science.
Second, it answers some fundamental questions of science. And even explains what science is, what mathematics is, what scientific progress means,
and why do we do all these things.
Although. he’s not a philosopher, he’s a scientist, mathematician and physicist.
But his mother used to teach philosophy, so maybe the germs got transferred.
Why this theory he gave is so important, and so exciting to me, is because with its help we can not only explain much of the phenomenon, but also predict and see the future of science.
And most importantly, because in his writings he has tried to touch the topic of consciousness, in relation to this theory.
I am surprised to see how well thought of this theory is, that it can speak on consciousness in saner words, quite contrary to traditional science.
I would recall a sober guy quote, that said something like - ‘The web of māyā is more complex than our intellect. It can see through the web, but cannot get out of it.’
Here’s a link to his writings.
I first used Wolfram Alpha many many years ago, probably in college or school. And knew him as a great man with big ambitions.
But reading his writings (and possibly I will read his books too soon), I can conclude that he is quite a genius to be able to think so deeply as to come up with his theories to define ‘a new kind of science’.
And also I congratulate him to have taken up the task of creating, and continuously improving the wolfram language, and his dream of a computational language and its usage by people.
I certainly do not remember everything I read in last two days, but I understood in core arguments. And it really hit me, that he’s right!
Felt like I understood what science means. What progress is all about. What direction we ought to steer science and technology in, since AI models will soon change a lot about the nature of work we do currently.
Okay, on the ‘computational irreducibility’ thing again.
Last night I was writing all this but unexpectedly slept, so continuing now.
Mr. Stephen Wolfram has given the principle of computational irreduciblity that basically says that for some things you can’t find a formula or a shortcut. To be able to know the output, you will need to actually go through the computation itself.
And he has given many examples from natural sciences for same.
Now, let me come to why this is significant.
See, first of all, what is science? Why do we do science? What is scientific progress? Have we been progressing all this time?
Why science?
First, for the very sake of it. For knowledge. To know, it’s a natural desire to know.
Second, utility. To make use of it. Build technology with it to make things possible or possible more easily.
What is progress in this, then?
In our journey to ‘know’, we become more and more ‘higher level’ in our thinking. This means that we encapsulate certain concepts as one basic unit, and build higher things with these basic units. And keep on going higher. This is progress.
Example, take a programming language. There is machine code. We have hidden those details, and instead we use a higher language that translates into all that. Even in this higher language, we use built in libraries, so making our job even more higher level.
Whether a particular mathematical fact is significant or not, is decided by whether it helps us understand a deeper phenomenon than itself or not. If yes, then the fact is significant for us.
What is mathematics is actually the story built up by mathematical facts that we know. This story is called mathematics. The story is important because it helps us find more facts. And the facts are important because they help us know more of the story.
..to be continued