[loudouncodes]

This alsp pissed me off. He is totally ignoring Benoit Mandel brot’s work in the 1950’s and John Conways work in the 1970’s. He sounds like a petulent child who takes himself too seriously and expects others do the same. It distracts from an otherwise interesting classification paradigm.

I do not see much difference between his 4th paradigm and a breadth-first search through an np (nondeterministic polynomial) problem. I’d love to know what other mathemeticians that work on dynamical systems (Dr Krieger, anyone?) think of his work…

[t_mann]

I may have actually given him a bit too much credit initially (I'll admit, I didn't read the full article). Even if I acknowledge that Wolfram probably knows a lot more graduate-level math than me, sentences like these raise some eyebrows:

"There are regions of 'metamathematical space' (the slices of proof space) that might have higher 'densities of proofs' corresponding to more interconnected fields of mathematics - or more 'metamathematical energy'. And as part of the generic behavior of multicomputational systems we can expect an analog of Einstein’s equations, and we can expect that 'proof geodesics' will be 'gravitationally attracted' to regions of higher 'metamathematical energy'. (...) In the presence of large amounts of 'metamathematical energy' there’ll effectively be a metamathematical black hole formed. And where there’s a 'singularity in metamathematical space' there’ll be a whole collection of proof paths that just end—effectively corresponding to a decidable area of mathematics."

Is this for real? Is this a legit mathematical theory that leads to new mathematical discoveries? Are these conjectures that he expects to be rigorously provable? Or are these just ramblings of someone who left the game a long time ago and who thinks that he still 'has it'?

[FrozenVoid]

It seems to make sense, if you view that as current math theories treated as "windows" into a space of possible mathematics, like e.g. quantum string theory possibility space(10^500) vs "accepted string theories" https://www.dummies.com/article/academics-the-arts/science/p...

[tinco]

Not to give any credence to Wolfram's theories, I'm wholly unqualified, but why not? Mathematics extends all the way into algorithms and complexity. We have already established that for example machine learning could lead to new mathematical discoveries, and machine learning is easily described by math.

Of course whether such a space is in any way practically computable or of a scale that could even reasonably comprehendable to a human being or even to some machine is an unanswered question.

[t_mann]

Sure, in principle it's interesting, and I can fathom that statements like these could in principle be provable. This 'graphical' perspective could lead to interesting insights eg in proof theory (I actually wouldn't be surprised if things like that had already been done).

My point was rather: making any statement in modern mathematics is hard. I was wondering how serious he is about formally establishing any insights about his ideas, eg a connection between proof spaces and Einstein's equations (presumably general relativity).

[eximius]

Theorising about a structure behind proofs made of an alphabet isnt new - its part of theorems like Godels Incompleteness, etc.

Actually exploring or evaluating objects in this space has always (and continues to be) intractable due to the high complexity and computational power required.

[whodunnit]

The big ego stuff and always needing to feed it with claiming credit for everything reminds me a lot of narcissistic personality disorder, which is caused by childhood emotional abuse, so I think we should just humor his ego and recognize it for what it is, that is be kind and understand what causes that sort of thing, while not letting it distract us from the value of the research he’s doing. Intellectually Wolfram is clearly a very intelligent person; emotionally he is underdeveloped.

[Bostonian]

I doubt that any personality disorder has as its sole cause "childhood emotional abuse", so I would not want to indirectly someone's parents because of their perceived personality flaws.

[whodunnit]

Good point. I encourage you to read up on the personality disorders, they are fascinating.

[andrewpolidori]

I think a fairer reading of the paragraph isn't that he's claiming to have initiated work in cellular automata as a whole but that he's claiming to have been the initiator of the "burst of productivity" in the 80s.

[t_mann]

But he does call it a new idea, directly followed by three strong words (ultimately, primary, initiator). I'm not saying the only reasonable interpretation of the sentence is that he's overstating his role. But what does make me cringe is that it can easily mislead readers who aren't familiar with the history of this specific idea, and that this confusion would have been easy to avoid.