Book Review: Ludwig Wittgenstein: The Duty of Genius

His life is just legendary! His life is so legendary that I won’t use the word “legendary” to describe anybody anymore.¹ His life is like the combination of two journeys, one of which is the struggle of going beyond his family and society and make a living on his own in academia, and yes, since he works in academia he moves around a lot, the other one is the struggle of human mind in the bigger picture.

But since I have also read Philosophical Investigations and some reviews, let’s talk about how his ideas can be applied to physics. Or what I think about how “language is a game”.

What Kant said about how math gives us the concept of time is not true, because the math we do in a theory is actually existing at the same time, which is already there given the axioms. So what really matters is the axioms (or some supplement method we then added) in a theory, which defines how far we can go really. I agree with him on that “Math is a technique”, see Chap.15.

Thus in a theory, let’s say General Relativity, the barrier is already there, thus it can’t be combined with Quantum Physics (which is non-local, both for time and particles in infinite deep potential well). Because language does not work that way, language is a game, and we play different games by different rules, thus we can believe multiple contradictory things at the same time, which is something Kant called “Antinomy”. Also, it’s unbelievably hard to get the “overview”, it’s one thing to get the overview from simple cases or games, it’s another thing to get it from complicated theories.

For example, there are inconsistency and contradictions in math already, “Gödel’s incompleteness theorems”. Or there are inconsistency and contradictions in different math, Euclidean geometry and Riemannian geometry. All of these examples are the limits we meet when we are playing different games yet trying to play the same game.

We have no idea whether the universe plays the same game or not² (i.e. “Thing-in-itself can not be understood or reached”). Or, we can’t let the universe play the same game, because we don’t play the same game when facing different “aspects” of our world. If there is such a game, I would be more than happy, but so far we don’t have this game, and by the way we think, I don’t think we will. Although that would be really neat, just like the game ChatGPT plays.

So what we can really do is to excel in different games. And whatever works. And that, my friend, is how I convinced myself to use Monte Carlo models.