Question: Do you agree with wolfram, that mathematics is only able to explain a limited amount of the universe, and that the possibility of using other methods such as computer code will be necessary in the future? And WHAT THE HELL IS HE TALKING ABOUT

Asked By: Oli Charity


This is actually a rather huge question.


First of all, I would like to make it clear that Stephen Wolfram is really a mathematical genius, and that his Mathematica program and Wolfram Alpha engine are of exquisite construction and are of immediate and profound help to humanity.


However, I want to lament, with all due respect, that he might be more than just a bit philosophically challenged, and should study a bit more about the stuff he is conjecturing about.


Evidence is not far away. In "A New Kind of Science", he made a lot of conjectures, many of which are known to be false. If he made the simplest search for it, he would see this. He was not even the first to theorize, nor is there any evidence of his searching for prior work. We need to put in mind that it is more of an ego boost than real progress.


Then, we can proceed further and talk about the actual stuff he is talking about.


One of the most blatantly obvious examples of the nonsensical nature of all this is the inconsistency of his own statements.


1) He is saying that his computer code is the fundamental structure of the universe.

2) He is also saying that mathematics is incapable of doing the stuff his computer code can do.


This is already a big joke, because his computer code is built upon mathematics, and worse, classical notions of mathematics.


This is the single biggest kind of nonsense you can find in that book. But we can scrutinize the thesis a lot more.


It turns out that his computer code actually can simulate the entirety of the universe. But this is rather trivial. The thing is that, from mathematical analysis, it is well known that fractions can never represent, among other things, the square root of 2. It might seem irrelevant, but this is of importance.


It is of importance for two reasons. There are some things that mathematics cannot do. Cantor's proof of there being more than one type of infinity leads to Godel's incompleteness theorem, which later leads to the Turing machines being unable to solve the decidability problem. But the problem is universal -- the computers cannot hope to do it any better than mathematics can.


The other reason is that, despite the fact that the end point is unreachable, you can get forever better approximations that may, in the end, reach it. Although the square root of 2, or pi, or e cannot be expressed in full, you can always get as close to them as you like.


This means that mathematics can simulate the physical reality with as much precision as you would like. It is also because of this that Wolfram's computer stuff can simulate the universe we live in.


In short, he found one of the (infinitely many) possibilities to simulate the world. And a very inefficient one at that. Big deal.


In fact, we already know from the philosophy of physics that you cannot insist upon one representation of the universe as being the correct one if there is more than one representation available for that job.


So, as you can see, I would very much like the education system to treat philosophy and logic in more detail, so that brilliant minds can waste less time on silly things like that. If he did not spend the time writing the gigantic book of silliness, things might be better for us, no matter how little that change would be. At least more trees would be left alive.




Sources / Further readings:


There are many sources on the internet that refute his claims, for he is a famous target and an idol to many nerds. You can read these:


Or better, this is a collection of reviews:


But the argument I gave would not make sense if you do not already know about how we constructed the real number system for mathematical analysis, which any first undergraduate textbook on mathematics starts with. The smallest is Baby Rudin, but that is particularly difficult.


Godel's Completeness and Incompleteness theorems are a lot more involved, and the standard treatment people recommend is the "Godel, Escher, Bach", which has its own wikipedia page too.,_Escher,_Bach


Godel is indisputable -- because he knew in advance how controversial it would be, he made sure to construct every little thing he needed to present the proof, so that any system of mathematics capable of those operations will necessarily be incomplete. For those that stick onto incompleteness, however, he first shows that a mathematical system that does not seek to do so much is complete. Mind explodes.


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