For one, it discusses other possibilities for FTL beyond 'wormholes'; for another, 'wormhole' is mostly a mysterious label for the possibility of the 'locality' of space being more complicated than our intuitive understanding.

The linked post is part of a larger project exploring the possibility of a 'hypergraph physics' – it's not asserting that the universe is a hypergraph but 'assuming' it for the sake of explication.

I wish Wolfram would do less of "if my theory is right, then X" and more of "if X, then my theory is right".

I am not going to repeat my objections at length (1, 2), but in a nutshell, Wolfram's entire trick seems to be noticing that a system is Turing-complete, and then impressing people how X is possible in the system. Which, if you understand what "Turing-complete" means, is like: well, duh. (But as far as I know, he never uses the words "Turing-complete", which makes it difficult to notice for people not familiar with this.)

I'm not pretending to even remotely understand the math in question, but, subjectively, his team is doing novel research. The initial results look promising and it looks like they are constantly making progress even though they started pretty recently. The papers are being peer reviewed and they are actively engaging with community.

I know that they are constantly trying to find areas which could generate novel predictions, but maybe it's a bit too early to demand so much rigor at this point?

Not directly related to your comment, but I don't understand why there is so much negativity coming from our community and I don't see why objections could not be respectful.

I agree – it seems perfectly fine research, and, as you mention, novel.

I also think it's not only too early but besides the point to demand rigor at all. Or, it's fine to demand rigor, but no one's obligated to supply it – not even Wolfram or his team or the wider 'community'. It's fine to ignore them too!

But yes, it's unreasonable to expect a lot of rigor given how young this 'field' is.

I also thank that – *reasonably – our priors regarding the computational, i.e. practical, difficulty of simulating our universe (or something similar) at the level of 'space quanta' is immense. String theory seems to have run into similar problems – and it's been one of the premier fields in physics for decades.

AFAIK, our simulations of the Standard Model, or other quantum mechanical models, are extremely limited too. Why would we expect any more fundamental theory to be even that much more difficult to compute/simulate/analyze?

I think that, given the extremely young age of this topic of research, the kind of qualitative 'eyeball or ad-hoc program' analysis Wolfram provides in his published work is eminently sensible and reasonable. It should be very much exploratory at such an early stage.

The math is a bit advanced at times but the 'raw' research is much simpler – basically very simple computer programs, but lots of them.

This is Wolfram's big/unique trick (IMO): just enumerate literally all of the possibilities for some class or set of simple programs and, often first, look at some visualizations of the programs, e.g. their evolution, and look for patterns, first with your eyes/brain and then, incrementally, with more and more 'search' programs. If possible, one might find good 'mathematical' compressions of the data/info/behavior of the programs, and, more rarely, a good 'mechanistic' understanding as well.

He wrote and published a book – available free online here – that's a massive infodump of basically all of his thoughts and speculations after having performed his trick – and diligently recorded all kinds of interesting findings – on a whole bunch of different kinds of 'simple programs'. (And this apparently happened over decades.) He came up with a bunch of interesting and, to me, very plausible ideas about computation and its implications for a lot of other sciences. I found, and continue to find, it to be a hugely impressive intellectual achievement.

But the book – and now Wolfram as a person – has very much not been received as I did and have. Academics in particular have a number of objections, some (IMO) reasonable – e.g. Wolfram seems to claim originality for some ideas that definitely had been published earlier (in the 'academic literature') – and some (again, IMO) unreasonable – e.g. Wolfram doesn't write in a typical academic style or format.

Wolfram also is widely considered to be generally arrogant and self-centered. I don't find those charges to be that persuasive, or that significant or serious regardless.

(He's certainly not, on any scale, particularly bad along these dimensions. But I also don't have any personal problem that, e.g. Steve Jobs, was also arrogant, self-centered, and seemingly an extreme 'asshole'. It does seem like the kind of people that are like this are over-represented among people that are both (relatively and extremely, as well as publicly) 'successful' or 'important'. And this doesn't seem that unintuitive either.)

And that is my theory/model of the "negativity" that Wolfram elicits. (And the examples here on this post are pretty mild based on what I've found elsewhere.)

Wolfram doesn't write in a typical academic style or format.

If this is the main problem, it seems like an opportunity for arbitrage -- someone should take Wolfram's ideas, translate them into academic language, and publish. With proper citations there is nothing wrong about doing it, and it should be easier than doing your own research.

I think this is a waste of his time tho. Academia is nice and all (tho not as much as we once thought) but it actively resists its members publishing big accessible books. That seems tragic to me.

With his latest 'hypergraph physics' project, that's exactly what his 'team' is doing.

His company hosts some kind of math/science/computation summer camp (for high school students and older I think) and I'm pretty sure he's mentioned several times that research has been published based on the camp activities. (That's much less directly connected to him or his own personal ideas or research tho.)

I don't think he has literally one trick but you're right that a lot of his recent public work has been exploring his ideas instead of falsifying them.

I'd describe his 'main trick' as trying to find a simple computable system that mostly mimics the 'dynamics' of some other system.

And – or so I think – exploring, at considerable length, the idea that 'everything is space' and '(maybe) space is a hypergraph evolving according to a simple rule' is an extremely interesting endeavor. It doesn't seem particularly crazy compared to other niche 'theories of everything' for one.

And, yes, he talks and writes about 'universal computation', his own phrase, instead of 'Turing-complete' – that's a somewhat lamentable phenomena, but pretty understandable. We all – as individuals and groups – do that too tho, so I don't really 'ding' him for those 'excesses'. This is an extremely common complaint about him and his work, but it's mostly irrelevant to determining whether his ideas are interesting, let alone true.

(Arguably we – the LessWrong users – have done the same thing repeatedly!)

I think the bigger thing that he has – not demonstrated exactly – but accumulated tantalizing evidence for, is that Turing-completeness ('universal computation') is both easy and, surprisingly, common. I still think that's an under-appreciated point.

His recent 'hypergraph' work seems promising to me – it seems like a (very mildly or weakly) plausible (tho rough) idea of how one might formulate everything else in terms of 'space quanta' and his ideas about what 'time' and 'causality' could mean based on an example formulation seem very interesting. I certainly don't begrudge him, or anyone else, spending their time this doing this. And I definitely don't think him, or anyone else, owes me a falsifiable theory! (I might feel a little differently if I was involuntarily supporting his efforts, e.g. via taxes, like I am with string theory.)

The practical obstacles to actually start to test how well his ideas or theories work seem insurmountable, but that's still true of string theory as well – and maybe you feel similarly about it!

I think the bigger thing that he has – not demonstrated exactly – but accumulated tantalizing evidence for, is that Turing-completeness ('universal computation') is both easy and, surprisingly, common. I still think that's an under-appreciated point.

Yes.

I'd describe his 'main trick' as trying to find a simple computable system that mostly mimics the 'dynamics' of some other system.

The analogies seem very superficial to me. I mean, I would be impressed if he could derive the equation for Lorentz contraction, but I am unimpressed if he merely shows that "something can get shorter". Etc. Could you give me the best example of mimicking some specific law of physics?

He in fact did derive (approximately) both special and general relativity for the 'hypergraph physics' project – I think. I'll look for a link but it should be on the same site as the link for this post.

Have you read his previous book "A New Kind of Science"? It's available for free online here. I think the "analogies" he presents are surprisingly good given how simple they are, e.g. the fluid dynamics stuff seems 'right', even if it's not (nearly) as accurate as standard numerical approximations/simulations based on the standard differential equations.

And here is a review, written by an expert on physics and computation. It does not address all claims in the book, specifically not the ones you mentioned. But I think it explains why people who know a lot about these things are not necessarily impressed by "the new kind of science".

In the second paragraph of the introduction in the review by Aaronson:

As a popularization, A New Kind of Science is an impressive accomplishment.

With regard to Aaronson's criticisms with respect to the content in NKS about quantum mechanics, I'm pretty sure Wolfram has addressed some of them in his newer work, e.g. (previously) ignoring 'multiway systems'.

One thing that jumps out at me, in Aaronson's 'not compatible with both special relativity and Bell inequality violations' argument against Wolfram's (earlier version of his) 'hypergraph physics':

A technicality is that we need to be able to identify which vertices correspond to x_a, y_a, and so on, even as G evolves over time.

Funnily enough, it's Aaronson's 'computation complexity for philosophers' paper that now makes me think such an 'identification' routine is possibly (vastly far) from "a technicality", especially given that the nodes in the graph G are expected to represent something like a Planck length (or smaller) and x_a and y_a are "input bits", i.e. some two-level quantum mechanical system (?). The idea of identifying the same x_a and y_a as G doesn't seem obvious or trivial from a computational complexity perspective.

Tho, immediately following what I quoted above, Aaronson writes:

We could do this by stipulating that (say) "the x_a vertices are the ones that are roots of complete binary trees of depth 3", and then choosing the rule set to guarantee that, throughout the protocol, exactly two vertices have this property.

That doesn't make sense to me as even a reasonable example of how to identify 'the same' qubits as G evolves. Aaronson seems to be equating vertices in G with a qubit but Wolfram's idea is that a qubit is something much much bigger inside G.

I can't follow the rest of that particular argument with any comprehensive understanding.

I wonder how much 'criticism' of Wolfram is a result of 'independent discovery'. Aaronson points out that a lot of Wolfram's 'hypergraph physics' is covered in work on loop quantum gravity. While Wolfram was a 'professional physicist' at one point, he hasn't been a full-time academic in decades so it's understandable that he isn't familiar with all of the possibly relevant literature.

It's also (still) possible that Wolfram's ideas will revolutionize other sciences as he claims. I'm skeptical of this too tho!

Thanks! I just read another Aaronson paper recently – his 'computation complexity for philosophers' – and thought it was fantastic. (I've been following his blog for awhile now.)

I definitely appreciate, not even having (yet) read the paper to which you linked, that Wolfram might not be entirely up-to-date with the frontier of computation complexity. (I'm pretty sure he knows some, if not a lot, of the major less-recent results.)

Wolfram's also something of a 'quantum computing' skeptic, which I think satisfyingly explains why he doesn't discuss it much in NKS or elsewhere. (He also does somewhat explain his skepticism, and that he is skeptical of it, in NKS (IIRC).)

I can also understand and sympathize with experts not being impressed with the book, or his work generally. But Robin Hanson has expressed similar complaints about the reception of his own work, and interdisciplinary work more widely, and I think those complaints are valid and (sadly) true.

I don't personally model academia as (effectively) producing truth or even insight as a particularly high priority.

Short version: "If wormholes exist, FLT movement is possible."

Long version: Like the short version, but between each two consecutive words insert several pages of assertions that universe is a hypergraph.

This is extremely uncharitable.

For one, it discusses other possibilities for FTL beyond 'wormholes'; for another, 'wormhole'

ismostly a mysterious label for the possibility of the 'locality' of space being more complicated than our intuitive understanding.The linked post is part of a larger project exploring the possibility of a 'hypergraph physics' – it's not

assertingthat the universe is a hypergraph but 'assuming' it for the sake of explication.I wish Wolfram would do less of "if my theory is right, then X" and more of "if X, then my theory is right".

I am not going to repeat my objections at length (1, 2), but in a nutshell, Wolfram's entire trick seems to be noticing that a system is Turing-complete, and then impressing people how X is possible in the system. Which, if you understand what "Turing-complete" means, is like: well, duh. (But as far as I know, he never uses the words "Turing-complete", which makes it difficult to notice for people not familiar with this.)

I'm not pretending to even remotely understand the math in question, but, subjectively, his team is doing novel research. The initial results look promising and it looks like they are constantly making progress even though they started pretty recently. The papers are being peer reviewed and they are actively engaging with community.

I know that they are constantly trying to find areas which could generate novel predictions, but maybe it's a bit too early to demand so much rigor at this point?

Not directly related to your comment, but I don't understand why there is so much negativity coming from our community and I don't see why objections could not be respectful.

I agree – it seems perfectly fine research, and, as you mention, novel.

I also think it's not only too early but

besides the pointto demand rigor at all. Or, it's fine to demand rigor, but no one's obligated to supply it – not even Wolfram or his team or the wider 'community'. It's fine to ignore them too!But yes, it's

unreasonableto expect a lot of rigor given how young this 'field' is.I also thank that – *reasonably – our priors regarding the computational, i.e. practical, difficulty of simulating our universe (or something similar)

at the level of 'space quanta'is immense. String theory seems to have run into similar problems – and it's been one of thepremierfields in physics fordecades.AFAIK, our simulations of the Standard Model, or other quantum mechanical models, are extremely limited too. Why would we expect any more fundamental theory to be even that much more difficult to compute/simulate/analyze?

I think that, given the extremely young age of this topic of research, the kind of qualitative 'eyeball or ad-hoc program' analysis Wolfram provides in his published work is eminently sensible and reasonable. It

shouldbe very much exploratory at such an early stage.The math

isa bit advanced at times but the 'raw' research is much simpler – basically very simple computer programs, but lots of them.This is Wolfram's big/unique trick (IMO): just enumerate literally all of the possibilities for some class or set of simple programs and, often first, look at some visualizations of the programs, e.g. their evolution, and look for patterns, first with your eyes/brain and then, incrementally, with more and more 'search' programs. If possible, one might find good 'mathematical'

compressionsof the data/info/behavior of the programs, and, more rarely, a good 'mechanistic' understanding as well.He wrote and published a book – available free online here – that's a massive infodump of basically all of his thoughts and speculations after having performed his trick – and

diligentlyrecorded all kinds of interesting findings – on a whole bunch of different kinds of 'simple programs'. (And this apparently happened overdecades.) He came up with a bunch of interesting and, to me, very plausible ideas about computation and its implications for a lot of other sciences. I found, and continue to find, it to be a hugely impressive intellectualachievement.But the book – and now Wolfram as a person – has very much

notbeen received as I did and have. Academics in particular have a number of objections, some (IMO) reasonable – e.g. Wolframseemsto claim originality for some ideas that definitely had been published earlier (in the 'academic literature') – and some (again, IMO) unreasonable – e.g. Wolfram doesn't write in a typical academic style or format.Wolfram also is widely considered to be generally arrogant and self-centered. I don't find those charges to be that persuasive, or that significant or serious regardless.

(He's certainly not, on any scale,

particularlybad along these dimensions. But I also don't have any personal problem that, e.g. Steve Jobs, was also arrogant, self-centered, and seemingly an extreme 'asshole'. Itdoesseem like the kind of people that are like this are over-represented among people that are both (relatively and extremely, as well as publicly) 'successful' or 'important'. And this doesn't seem that unintuitive either.)And that is my theory/model of the "negativity" that Wolfram elicits. (And the examples here on this post are pretty mild based on what I've found elsewhere.)

If this is the main problem, it seems like an opportunity for arbitrage -- someone should take Wolfram's ideas, translate them into academic language, and publish. With proper citations there is nothing wrong about doing it, and it should be easier than doing your own research.

I think this is a waste of his time tho. Academia is nice and all (tho not as much as we once thought) but it actively resists its members publishing big

accessiblebooks. That seems tragic to me.With his latest 'hypergraph physics' project, that's exactly what his 'team' is doing.

His company hosts some kind of math/science/computation summer camp (for high school students and older I think) and I'm pretty sure he's mentioned several times that research has been published based on the camp activities. (That's much less directly connected to him or his own personal ideas or research tho.)

Ahh – I can understand and sympathize with that!

I don't think he has literally

onetrick but you're right that a lot of his recent public work has been exploring his ideas instead of falsifying them.I'd describe his 'main trick' as trying to find a simple computable system that mostly

mimicsthe 'dynamics' of some other system.And – or so I think – exploring, at considerable length, the idea that 'everything is space' and '(maybe) space is a hypergraph evolving according to a simple rule' is an

extremelyinteresting endeavor. It doesn't seem particularly crazy compared to other niche 'theories of everything' for one.And, yes, he talks and writes about 'universal computation', his own phrase, instead of 'Turing-complete' – that's a somewhat lamentable phenomena, but pretty understandable. We all – as individuals and groups – do that too tho, so I don't really 'ding' him for those 'excesses'. This is an

extremelycommon complaint about him and his work, but it's mostly irrelevant to determining whether his ideas are interesting, let alone true.(Arguably we – the LessWrong users – have done the same thing repeatedly!)

I think the bigger thing that he has – not

demonstratedexactly – but accumulated tantalizing evidence for, is that Turing-completeness ('universal computation') is botheasyand, surprisingly,common. I still think that's an under-appreciated point.His recent 'hypergraph' work seems

promisingto me – it seems like a (very mildly or weakly)plausible(tho rough) idea of how one might formulate everything else in terms of 'space quanta' and his ideas about what 'time' and 'causality' could mean based on an example formulation seem very interesting. I certainly don't begrudge him, or anyone else, spending their time this doing this. And I definitely don't think him, or anyone else, owes me a falsifiable theory! (I might feel a little differently if I was involuntarily supporting his efforts, e.g. via taxes, like I am with string theory.)The practical obstacles to actually start to test how well his ideas or theories work

seeminsurmountable, but that's still true of string theory as well – and maybe you feel similarly about it!Yes.

The analogies seem very superficial to me. I mean, I would be impressed if he could derive the equation for Lorentz contraction, but I am unimpressed if he merely shows that "something can get shorter". Etc. Could you give me the

best exampleof mimicking some specific law of physics?He in fact did derive (approximately) both special and general relativity for the 'hypergraph physics' project – I think. I'll look for a link but it should be on the same site as the link for this post.

Have you read his previous book "A New Kind of Science"? It's available for free online here. I think the "analogies" he presents are surprisingly good given how simple they are, e.g. the fluid dynamics stuff seems 'right', even if it's not (nearly) as accurate as standard numerical approximations/simulations based on the standard differential equations.

And here is a review, written by an expert on physics and computation. It does not address all claims in the book, specifically not the ones you mentioned. But I think it explains why people who know a lot about these things are not necessarily impressed by "the new kind of science".

In the second paragraph of the introduction in the review by Aaronson:

With regard to Aaronson's criticisms with respect to the content in NKS about quantum mechanics, I'm pretty sure Wolfram has addressed some of them in his newer work, e.g. (previously) ignoring 'multiway systems'.

One thing that jumps out at me, in Aaronson's 'not compatible with both special relativity and Bell inequality violations' argument against Wolfram's (earlier version of his) 'hypergraph physics':

Funnily enough, it's Aaronson's 'computation complexity for philosophers' paper that now makes me think such an 'identification' routine is possibly (vastly far) from "a technicality", especially given that the nodes in the graph G are expected to represent something like a Planck length (or smaller) and x_a and y_a are "input bits", i.e. some two-level quantum mechanical system (?). The idea of identifying

the samex_a and y_a as G doesn't seem obvious or trivial from a computational complexity perspective.Tho, immediately following what I quoted above, Aaronson writes:

That doesn't make sense to me as even a reasonable example of how to identify 'the same' qubits as G evolves. Aaronson

seemsto be equating vertices in G with a qubit but Wolfram's idea is that a qubit is something much much bigger inside G.I can't follow the rest of that particular argument with any comprehensive understanding.

I wonder how much 'criticism' of Wolfram is a result of 'independent discovery'. Aaronson points out that a lot of Wolfram's 'hypergraph physics' is covered in work on loop quantum gravity. While Wolfram was a 'professional physicist' at one point, he hasn't been a full-time academic in decades so it's understandable that he isn't familiar with all of the possibly relevant literature.

It's also (still) possible that Wolfram's ideas

willrevolutionize other sciences as he claims. I'm skeptical of this too tho!Thanks! I just read another Aaronson paper recently – his 'computation complexity for philosophers' – and thought it was

fantastic. (I've been following his blog for awhile now.)I definitely appreciate, not even having (yet) read the paper to which you linked, that Wolfram might not be entirely up-to-date with the frontier of computation complexity. (I'm pretty sure he knows some, if not a lot, of the major less-recent results.)

Wolfram's also something of a 'quantum computing' skeptic, which I think satisfyingly explains why he doesn't discuss it much in NKS or elsewhere. (He also

doessomewhat explain his skepticism, and that heisskeptical of it, in NKS (IIRC).)I can also understand and sympathize with experts not being impressed with the book, or his work generally. But Robin Hanson has expressed similar complaints about the reception of his own work, and interdisciplinary work more widely, and I think those complaints are valid and (sadly) true.

I don't personally model academia as (effectively) producing truth or even insight as a particularly high priority.