Tegmark's mathematical universe hypothesis

[James R]

Sarkus:

It appears to be, given what I know of the MUH, but then I am not an expert in his arguments. I find comparing to the SH helps, though. What are his arguments for either ignoring or accepting what you perceive to be this category error? I assume you know, to be able to assert his hypothesis as being based on this error?

I assumed you knew, if you're telling me that I am wrong.

It seems that neither you nor I have read Tegmark's book, so we're on an approximately equal footing when it comes to commenting on his claims and reasons. I have been going by what I have read about the specifics of his claims from various sources on the internet. How about you?

I'm always happy to learn more, and to be corrected if you can demonstrate that I've made a mistake. If you can show me I'm not fairly assessing Tegmark's arguments, fine. Go to it.

Just above you refer to the MUH as being "about our universe - the universe we perceive and have access to". No disagreement there. But now here, with regard the SH, you're not giving the same benefit. Yet you say specifically that any substrate "is not part of our measurable universe". Both the MUH and the SH are about the universe that those within the universe experience. Therefore any substrate of the SH is an irrelevant consideration. All that is relevant is whether the universe under consideration is mathematical or not. The SH universe would seem to be - the abstract 1s and 0s and the maths that guides their interactions. All abstract. All maths.

Tegmark's MUH is about the "ultimate nature of reality". He says that if we keep digging down, we'll discover that, at the bottom, our universe is nothing but mathematics.

The simulation hypothesis is not consistent with the base level of our universe being mathematics because it posits another undiscovered layer - the one which is doing the simulating.

I do not think the 1s and 0s in the computer in front of me are mathematics. The characters in a video game on my computer are not "made of mathematics". If they can think for themselves, they should not conclude that they are made of mathematics, even though they, in universe A (inside the simulated computer game) can't access universe B (our universe, in which my computer exists). The fact of the matter, in this example, is that the relevant information that makes up those simulated people in my computer, is encoded in a physical substrate that involves silicon chips, electrons and such.

So, no, to me at least, and perhaps to others, the SH is not an unhelpful distraction, but rather a parallel idea that can help people wrap their heads around what Tegmark might be trying to argue for, even if not entirely the same. That you don't find it helpful, sure, I get that. Then feel free to not reply to it. Don't let it distract you.

Don't worry about me. I'll be fine.

Whether you understand the fundamental difference I'm trying to explain to you or not is actually irrelevant to the wider discussion. So I won't push it.

Good of you to allow for my mental deficiency. You're clearly much cleverer than I am, as usual.

I'll ask again: have you read and understood his MUH sufficiently to be able to assert this?

Read his book? No. Understood sufficiently what his argument is? I think so. But I could be wrong. I've heard him talk, so I do have some direct access from the horse's mouth, so to speak.

How about you?

Or do you mean that you are not aware of how he has distinguished it, if he has?

I don't know whether he has addressed the issue or not. I hope he is aware of it. It seems like an obvious and important objection.

Certainly, some of his reviewers, who have read his book, don't think that he has dealt with the matter.

I'm just trying to see whether you're saying you think the flaw is definitely with the MUH, or perhaps that you don't know enough about it, about his arguments, to understand how he has distinguished, if he has?

There's only one way to find out for sure if I'm wrong about what he says. Happy reading, Sarkus!

 

[Sarkus]

I assumed you knew, if you're telling me that I am wrong.

I'm not telling you that you're wrong, so please don't misrepresent what I have said. Speaking of which, nor I have I said the the SH is important to the MUH, as you have otherwise implied me to have said (see your post #99). As stated, I don't know Tegmark's arguments sufficiently to be able to say that he is committing a category error, although I have agreed that it intuitively seems like that. But intuition isn't sufficient.

It seems that neither you nor I have read Tegmark's book, so we're on an approximately equal footing when it comes to commenting on his claims and reasons. I have been going by what I have read about the specifics of his claims from various sources on the internet. How about you?

Similarly, thanks.

I'm always happy to learn more, and to be corrected if you can demonstrate that I've made a mistake. If you can show me I'm not fairly assessing Tegmark's arguments, fine. Go to it.

Blind leading the blind? I do think that if you start with the assumption of category error when diving deeper then that is all you will find. So maybe not start with that assumption, even if based on your initial assessment at a high level? Then see where you get.

Tegmark's MUH is about the "ultimate nature of reality". He says that if we keep digging down, we'll discover that, at the bottom, our universe is nothing but mathematics.

Yes. Our universe.

The simulation hypothesis is not consistent with the base level of our universe being mathematics because it posits another undiscovered layer - the one which is doing the simulating.

Yes, it is consistent. Our universe is mathematics in the SH - or at least programming that is analagous.

I do not think the 1s and 0s in the computer in front of me are mathematics.

What is a "1" and "0" if not part of mathematics?

The characters in a video game on my computer are not "made of mathematics".

Surely they are nothing but 1s and 0s interacting according to the program that they follow? What else do you think they are? If you're thinking of the screen, then this is just our means of observing it. Switch off your monitor and the game is still running, is it not?

If they can think for themselves, they should not conclude that they are made of mathematics, even though they, in universe A (inside the simulated computer game) can't access universe B (our universe, in which my computer exists).

Why not? What if they reach the same conclusion that they are inside a simulation, and thus nothing but mathematics/programming, just as some have done in suggested to be the case for our universe? Why is there a "should not conclude"? Is that not simply asserting the correctness of your view a priori?

The fact of the matter, in this example, is that the relevant information that makes up those simulated people in my computer, is encoded in a physical substrate that involves silicon chips, electrons and such.

That is irrelevant to the universe in question. The universe that those people experience as "our universe" is purely programming/mathematical. If it is a simulation then the physical substrate exists whether the program is running or not, right? Unless you think your computer disappears when you switch it off? As such, the universe is not the substrate. The substrate is irrelevant to the universe being experienced.
As for the thinking that the SH just pushes the issue a layer up/down, think about whether a simulated universe could simulate a universe, and that simulated universe simulate another universe... "it's turtles all the way down!"
But, as stated, if you don't find this a helpful analogy, there's no need for you to pursue it, especially if you find it a distraction. And that is all I'm saying it is: helpful. Not important to the MUH. Just helpful in understanding the idea that a universe can, at least in some analagous way, be mathematical.

Good of you to allow for my mental deficiency. You're clearly much cleverer than I am, as usual.

If you say so, but note that at no point have I asserted it, or implied it. Clever people aren't always able to understand everything thrown at them. Don't assume that just because you can't understand something means you're being called stupid. As and when I think you are being stupid please rest assured that I will let you know.

Read his book? No. Understood sufficiently what his argument is? I think so.

I'm sure you think you do.

But I could be wrong. I've heard him talk, so I do have some direct access from the horse's mouth, so to speak.

This does smack of Write4U claiming to understand what Tegmark says by posting videos of him talking. Be careful.

How about you?

I understand very little of it, to be honest. About as much as you, I'm guessing. I'm still trying to understand how his MUH would enable us to consider something as "physical" while still being a mathematical structure. I'm not dismissing it as a category mistake, though, or asserting that there is necessarily a distinction. For example:
“I think that consciousness is the way information feels when being processed in certain complex ways.” ― Max Tegmark, Our Mathematical Universe: My Quest for the Ultimate Nature of Reality
Here he sstates that consciousness is simply a property of information being processed. i.e. it is itself an emergent property of information. If we couple this with the idea that what we think of as "matter" and what is deemed "physical" are just interpretations from our consciousess, then you might be able to see a path where his MUH possibly survives cries of "category error". But perhaps not. I'm still playing around with it, though.

I don't know whether he has addressed the issue or not. I hope he is aware of it. It seems like an obvious and important objection.
Certainly, some of his reviewers, who have read his book, don't think that he has dealt with the matter.

I have little doubt he understands the issue, and that he feels his MUH, once understood sufficiently, answers it (or perhaps shows it to be moot). It is possibly frustrating for many reviewers that he has not come out and explicitly responded to it in a manner that they can understand, though. Maybe he can't.

There's only one way to find out for sure if I'm wrong about what he says.

I strongly doubt that Tegmark will sit down with anyone here and address our questions, or confirm our understandings. But we live in hope, eh.

 

[Pinball1970]

I'm not telling you that you're wrong, so please don't misrepresent what I have said. Speaking of which, nor I have I said the the SH is important to the MUH, as you have otherwise implied me to have said (see your post #99). As stated, I don't know Tegmark's arguments sufficiently to be able to say that he is committing a category error, although I have agreed that it intuitively seems like that. But intuition isn't sufficient.
Similarly, thanks.
Blind leading the blind? I do think that if you start with the assumption of category error when diving deeper then that is all you will find. So maybe not start with that assumption, even if based on your initial assessment at a high level? Then see where you get.
Yes. Our universe.
Yes, it is consistent. Our universe is mathematics in the SH - or at least programming that is analagous.
What is a "1" and "0" if not part of mathematics?
Surely they are nothing but 1s and 0s interacting according to the program that they follow? What else do you think they are? If you're thinking of the screen, then this is just our means of observing it. Switch off your monitor and the game is still running, is it not?
Why not? What if they reach the same conclusion that they are inside a simulation, and thus nothing but mathematics/programming, just as some have done in suggested to be the case for our universe? Why is there a "should not conclude"? Is that not simply asserting the correctness of your view a priori?
That is irrelevant to the universe in question. The universe that those people experience as "our universe" is purely programming/mathematical. If it is a simulation then the physical substrate exists whether the program is running or not, right? Unless you think your computer disappears when you switch it off? As such, the universe is not the substrate. The substrate is irrelevant to the universe being experienced.
As for the thinking that the SH just pushes the issue a layer up/down, think about whether a simulated universe could simulate a universe, and that simulated universe simulate another universe... "it's turtles all the way down!"
But, as stated, if you don't find this a helpful analogy, there's no need for you to pursue it, especially if you find it a distraction. And that is all I'm saying it is: helpful. Not important to the MUH. Just helpful in understanding the idea that a universe can, at least in some analagous way, be mathematical.
If you say so, but note that at no point have I asserted it, or implied it. Clever people aren't always able to understand everything thrown at them. Don't assume that just because you can't understand something means you're being called stupid. As and when I think you are being stupid please rest assured that I will let you know.
I'm sure you think you do.
This does smack of Write4U claiming to understand what Tegmark says by posting videos of him talking. Be careful.
I understand very little of it, to be honest. About as much as you, I'm guessing. I'm still trying to understand how his MUH would enable us to consider something as "physical" while still being a mathematical structure. I'm not dismissing it as a category mistake, though, or asserting that there is necessarily a distinction. For example:
“I think that consciousness is the way information feels when being processed in certain complex ways.” ― Max Tegmark, Our Mathematical Universe: My Quest for the Ultimate Nature of Reality
Here he sstates that consciousness is simply a property of information being processed. i.e. it is itself an emergent property of information. If we couple this with the idea that what we think of as "matter" and what is deemed "physical" are just interpretations from our consciousess, then you might be able to see a path where his MUH possibly survives cries of "category error". But perhaps not. I'm still playing around with it, though.
I have little doubt he understands the issue, and that he feels his MUH, once understood sufficiently, answers it (or perhaps shows it to be moot). It is possibly frustrating for many reviewers that he has not come out and explicitly responded to it in a manner that they can understand, though. Maybe he can't.
I strongly doubt that Tegmark will sit down with anyone here and address our questions, or confirm our understandings. But we live in hope, eh.

I have downloaded his paper and I will read through it this weekend.

 

[C C]

My guess is that W4U is arguing (perhaps without realizing it) for a currently popular idea in the philosophy of science called Structural Realism.

https://plato.stanford.edu/entries/structural-realism

[...] And I take Tegmark as basically publishing a publicly accessable version of a rather Platonic (and Kantian?) sort of idea that is known in the literature as Ontic Structural Realism. [...]

Yah, Tegmark's MUH seems to be affiliated with or crouched in it.

But based on the first items below, MUH might arguably sport an eternalism view of time. Whereas W4U may independently be drifting into a presentism or "procedural outputting of short-lived nows" view, what with it sounding like his proto-intelligent mathematical "principles" are regulating such a process of changes or how the universe behaves through those incremental developments.

Why the Flow of Time Is an Illusion
https://nautil.us/why-the-flow-of-time-is-an-illusion-237380/

INTRO: In his book Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, Max Tegmark writes that “time is not an illusion, but the flow of time is.” In this month’s issue of Nautilus, which looks at the concept of flow through various portals in science, we revisited our 2014 video interview with Tegmark...

Max Tegmark (from a SciAm article published in the early 2000s): A mathematical structure is an abstract, immutable entity... If history were a movie, the structure would correspond not to a single frame of it but to the entire videotape.

Consider, for example, a world made up of pointlike particles moving around in three-dimensional space. In four-dimensional spacetime --the bird perspective-- these particle trajectories resemble a tangle of spaghetti. If the frog [perspective] sees a particle moving with constant velocity, the bird sees a straight strand of uncooked spaghetti.

If the frog sees a pair of orbiting particles, the bird sees two spaghetti strands intertwined like a double helix. To the frog, the world is described by Newton's laws of motion and gravitation. To the bird, it is described by the geometry of the pasta --a mathematical structure.

The frog itself is merely a thick bundle of pasta, whose highly complex intertwining corresponds (in its view) to a cluster of particles that store and process information. Our universe is far more complicated than this [non-multiverse, single block-universe] example, and scientists do not yet know to what, if any, mathematical structure it corresponds. --Parallel Universes​

Back to the structural realism issue...

Ontic Structural Realism
https://en.wikipedia.org/wiki/Structuralism_(philosophy_of_science)#Ontic_structural_realism

"Max Tegmark takes this concept even further with the mathematical universe hypothesis, which proposes that, if our universe is only a particular structure, then it is no more real than any other structure."​

RELATED:

Cat Gillen advocating structural realism (article)
https://iai.tv/articles/hossenfelder-vs-goff-do-electrons-exist-auid-2681?_auid=2020

--> video link ... Cat Gillen (guest) discussion about scientific realism

 

[Halc]

Does an observer have to be conscious or does the wave function just collapse when encountering something physical?

I never mentioned the word 'observer'. But again you reference Wigner interpretation, the only one which posits that consciousness has anything to do with ontic wave function collapse. It is a solipsistic interpretation, meaning other minds do not exist.
All that said, wave functions are not objects that 'encounter' things.

This whole topic was opened by James R seemingly to get a real discussion about MUH going, but people (well, James at least) seem to shy from actual discussion and would seemingly prefer just to rag on you about your assertions of understanding things that you clearly don't. I guess you really do constitute the entertainment around here. One does not assert an understanding of a subject, one demonstrates it. So your posts continue to confirm the accusations against you.

Pretty picture posted, but there's no duck, so is it relevant?

 

[Sarkus]

This whole topic was opened by James R seemingly to get a real discussion about MUH going, but people (well, James at least) seem to shy from actual discussion and would seemingly prefer just to rag on you about your assertions of understanding things that you clearly don't. I guess you really do constitute the entertainment around here. One does not assert an understanding of a subject, one demonstrates it. So your posts continue to confirm the accusations against you.

Well, there's two issues at play here. One is the actual subject of Tegmark's MUH. I would have thought that if James R's aim was for an actual discussion of that he would have split this into one of the other sub-forums than "Site Feedback". "Alternative Theories", or "Physics & Maths", or possibly even "Philosophy". Putting it here is almost as if he's asking the question of whether we should have more discussion on it or not, not necessarily to actually discuss it.
The second issue is pretty much an effort to address Write4U's approach to "discussion". I use the term loosely here, as it's open to debate whether what transpires with him is an actual discussion, or whether it is just an exercise in him never addressing the questions you ask while appealing to science videos and links as if they answer them. Oh, and the "Tegmark!!1!" and "microtubules!!11!1!" fixation he seems to have. In their place, not an issue. Everywhere else, well, we get this.

Pretty picture posted, but there's no duck, so is it relevant?

He also has the habit, as above, of posting links and images as if they are relevant. I mean, we all know what a wave is, right? His question refers to wavefunction, so he posts a picture of a wave (okay, sure, whatever) but then some added irrelevancies of types of waves. "Ooh. It's shiny!" and "Look, ma! I know how to post pictures!"

Anyhoo - I would actually suggest that this thread has been answered - in that there do seem to be people willing to have a fuller and sensible discussion on the MUH, and as such the actual ongoing discussion be split off from here into a new thread in the Physics&Maths, Philosophy, or whichever thread is deemed appropriate - or merged into an existing one if more sensible. I'm not sure "Site Feedback" lends itself to sticking to the actual MUH.

 

[Halc]

Max Tegmark (from a SciAm article published in the early 2000s): A mathematical structure is an abstract, immutable entity... If history were a movie, the structure would correspond not to a single frame of it but to the entire videotape.

OK, this verifies what I said above: MUH is an eternalist view. It does surprise me to see the word 'abstract', which implies something more fundamental doing the abstracting. If that were the case, the whole hypothesis collapses.

The rest of the quote seems to be him trying to get the reader to visualize spacetime and worldlines and such, as opposed to the 3D presentist view.

Nobody has commented on my critique of MUH, and I have no idea how to search for what Tegmark might has said about it

 

[C C]

OK, this verifies what I said above: MUH is an eternalist view. It does surprise me to see the word 'abstract', which implies something more fundamental doing the abstracting. If that were the case, the whole hypothesis collapses.

He was probably addressing "mathematical structure" in a conventional context rather than one where he reifies the concept as physical, since he wasn't discussing MUH directly in that old article.

Though, for all I know, in his writings somewhere he might do the same when he is discussing MUH. Or maybe he flips back and forth between the two orientations at times with little concern for the reader's confusion.

The rest of the quote seems to be him trying to get the reader to visualize spacetime and worldlines and such, as opposed to the 3D presentist view.

Nobody has commented on my critique of MUH, and I have no idea how to search for what Tegmark might has said about it

He's only responded to a few common questions on his his website. He's got interviews and videos scattered all over the internet, but similarly I don't know to what extent (if any) he has addressed the specific scrutiny of others in them.

The SEP seems to have no entry devoted to MUH, though bits of details slash commentary about it are scattered around under different topics.
_

 

[Yazata]

Perhaps part of the problem in this thread is that that everyone is trying to understand what Tegmark is about through W4U's interpretation of him. That might be a bit like peering through a kaleidoscopic fun-house distorting mirror.

Here's a shorter-than-booklength 31 page account of the "MUH" by Tegmark himself, published in 2007 in Foundations of Physics:

https://arxiv.org/pdf/0704.0646/

I have to admit that I haven't read it yet and it seems to me to perhaps be too filled with physics and mathematics jargon to be comprehensible as metaphysical philosophy (which is what it ultimately is) by a physics and mathematics layman like me. But I believe that he does address the question of why some mathematics is tangible and physical in his 'MUH' view, while so much of the rest of mathematics is purely conceptual.

Maybe this represents a fundamental difference between Tegmark and me. My scientific background (such as it is) is in biological science. I conceive of the reality posited by science as a biologist might, not through the perhaps excessively mathematical lens of theoretical physics. I've long suspected that many theoretical physicists think that the mathematics they scrawl all over their chalkboards is more real to them than the physical reality that it's supposedly meant to describe. What really exists (in some strong ontological sense) in their minds is seemingly the mathematics on the chalkboard, and all that physical reality does is exemplify and instantiate it somehow.

I'm reminded of Plato's cave imagery in the Republic, where physical reality is just an imperfect shadow of the true reality of the Eternal Forms. It seems to me that what Tegmark might be doing is trying to create a more physically informed and sophisticated version of Plato's 'cave' image.

 

[C C]

Perhaps part of the problem in this thread is that that everyone is trying to understand what Tegmark is about through W4U's interpretation of him. That might be a bit like peering through a kaleidoscopic fun-house distorting mirror.

Here's a shorter-than-booklength 31 page account of the "MUH" by Tegmark himself, published in 2007 in Foundations of Physics:

https://arxiv.org/pdf/0704.0646/

I have to admit that I haven't read it yet and it seems to me to perhaps be too filled with physics and mathematics jargon to be comprehensible as metaphysical philosophy (which is what it ultimately is) by a physics and mathematics layman like me. But I believe that he does address the question of why some mathematics is tangible and physical in his 'MUH' view, while so much of the rest of mathematics is purely conceptual.

Maybe this represents a fundamental difference between Tegmark and me. My scientific background (such as it is) is in biological science. I conceive of the reality posited by science as a biologist might, not through the perhaps excessively mathematical lens of theoretical physics. I've long suspected that many theoretical physicists think that the mathematics they scrawl all over their chalkboards is more real to them than the physical reality that it's supposedly meant to describe. What really exists (in some strong ontological sense) in their minds is seemingly the mathematics on the chalkboard, and all that physical reality does is exemplify and instantiate it somehow.

I'm reminded of Plato's cave imagery in the Republic, where physical reality is just an imperfect shadow of the true reality of the Eternal Forms. It seems to me that what Tegmark might be doing is trying to create a more physically informed and sophisticated version of Plato's 'cave' image.

From that paper:

EXCERPTS: . . . By insisting on a complete description of reality, the MUH banishes not only the classical notion of initial conditions, but also the classical notion of randomness.

The traditional view of randomness (viewed either classically or as in the Copenhagen interpretation of quantum mechanics) is only meaningful in the context of an external time, so that one can start with one state and then have something random “happen”, causing two or more possible outcomes. In contrast, the only intrinsic properties of a mathematical structure are its relations, timeless and unchanging.

In a fundamental sense, the MUH thus implies Einstein’s dictum “God does not play dice”. This means that if the MUH is correct, the only way that randomness and probabilities can appear in physics is via the presence of ensembles, as a way for observers to quantify their ignorance about which element(s) of the ensemble they are in...

[...] Parallel universes are now all the rage... They are also a source of confusion, since many forget to distinguish between different types of parallel universes that have been proposed, whereas argued that the various proposals form a natural four-level hierarchy of multiverses allowing progressively greater diversity.

[...] The key question is therefore not whether there is a multiverse (since Level I is the rather uncontroversial cosmological standard model), but rather how many levels it has. ... Level I, II and III parallel universes are all part of the same mathematical structure, but from the frog perspective, they are for all practical purposes causally disconnected. Level II, is currently a very active research area...

[...] In summary, many mathematical structures contain defacto parallel universes at levels I through III, so the possibility of a multiverse is a direct and obvious implication of the MUH. We will therefore not dwell further on these levels, and devote the remainder of this section to Level IV...

[...] Long a staple of science fiction, the idea that our external reality is some form of computer simulation has gained prominence with recent blockbuster movies like "The Matrix".

[...] Lloyd has advanced the intermediate possibility that we live in an analog simulation performed by a quantum computer, albeit not a computer designed by anybody — rather, because the structure of quantum field theory is mathematically equivalent to that of a spatially distributed quantum computer. In a similar spirit, Schmidhuber, Wolfram and others have explored the idea that the laws of physics correspond to a classical computation. Below we will explore these issues in the context of the MUH.

[...] Suppose that our universe is indeed some form of computation. A common misconception in the universe simulation literature is that our physical notion of a one-dimensional time must then necessarily be equated with the step-by-step one-dimensional flow of the computation. I will argue below that if the MUH is correct, then computations do not need to evolve the universe, but merely describe it (defining all its relations).

[...] The temptation to equate time steps with computational steps is understandable, given that both form a one-dimensional sequence where (at least for the non-quantum case) the next step is determined by the current state. However, this temptation stems from an outdated classical description of physics: there is generically no natural and well-defined global time variable in general relativity, and even less so in quantum gravity where time emerges as an approximate semiclassical property of certain “clock” subsystems. Indeed, linking frog perspective time with computer time is unwarranted even within the context of classical physics.

The rate of time flow perceived by an observer in the simulated universe is completely independent of the rate at which a computer runs the simulation. Moreover, as emphasized by Einstein, it is arguably more natural to view our universe not from the frog perspective as a 3-dimensional space where things happen, but from the bird perspective as a 4-dimensional spacetime that merely is.

There should therefore be no need for the computer to compute anything at all — it could simply store all the 4-dimensional data, i.e., encode all properties of the mathematical structure that is our universe. Individual time slices could then be read out sequentially if desired, and the “simulated” world should still feel as real to its inhabitants as in the case where only 3-dimensional data is stored and evolved. In conclusion, the role of the simulating computer is not to compute the history of our universe, but to specify it.

[...] This paper has explored the implications of the Mathematical Universe Hypothesis (MUH) that our external physical reality is a mathematical structure (a set of abstract entities with relations between them). I have argued that the MUH follows from the external reality hypothesis (ERH) that there exists an external physical reality completely independently of us humans, and that it constitutes the opposite extreme of the Copenhagen interpretation and other “many words interpretations” of physics where human-related notions like observation are fundamental.

In Section III, we discussed the challenge of deriving our perceived everyday view (the “frog’s view”) of our world from the formal description (the “bird’s view”) of the mathematical structure, and argued that although much work remains to be done here, promising first steps include computing the automorphism group and its subgroups, orbits and irreducible actions...
- - - - - - -

The "frog" and "bird" analogies as well as "multiverse levels" also go back to this 2003 SciAm article called "Parallel Universes": https://space.mit.edu/home/tegmark/multiverse.pdf

And again, he also discusses the "timeless and unchanging" mathematical structure or "time is not an illusion, but the flow of time is" here: https://nautil.us/why-the-flow-of-time-is-an-illusion-237380/

_

 

[Pinball1970]

Perhaps part of the problem in this thread is that that everyone is trying to understand what Tegmark is about through W4U's interpretation of him. That might be a bit like peering through a kaleidoscopic fun-house distorting mirror.

I am absolutely not doing that.
I summized pretty quickly that Write4U knows next to nothing about Tegmark's thesis. This is because the Tegmark video that he keeps posting says next to nothing about it.

The actual paper is 26 pages including references so I am going to have a crack at it today, see how far I get.

 

[C C]

[...] Here's a shorter-than-booklength 31 page account of the "MUH" by Tegmark himself, published in 2007 in Foundations of Physics:

https://arxiv.org/pdf/0704.0646/ [...]

Visiting this again, with respect to what it signifies, rather than offering excerpts...

Apparently, the whole venture into mathematicism is a distraction from a narrower ontological agenda.

What Tegmark is actually advocating is a multiverse version of eternalism. The simplistic block-universe concept cannot accommodate the complexity of that, thus his broadening to a discussion or fixation on mathematical structures in general.
_

 

[Pinball1970]

Setting up a thread for the actual discussion would be good, rather than keep it here. However, I'm not sure Write4U should be excluded from posting there. I'm not a fan of limiting one's activity so specifically (didn't even know it was possible), but rather they face the consequences of their actions (cumulative warnings etc). It may require a bit more active moderation to keep it on track, removing off-topic posts etc, but we have the capability of ignoring him, actively or passively, and of reporting off-topic posts. I mean, if people simply choose not to respond to his off-topic posts, would that not be sufficient? Just my two-pence worth.

Write4u cannot discuss the paper, the one I have at least.
It would dilute this discussion or people would just have to ignore it.
Like his video, Tegmark is breaking down mathematics to its component parts and it's relevance to physics.
TBH I still don't know what I am reading, it is like broad over view of the philosophy of mathematics with the add on that every operation or object IS physical.
He has not mentioned Gödel yet but this is a long paper.

 

[gmilam]

From the PDF that Yazata posted a link to: https://arxiv.org/pdf/0704.0646/

Whereas the customary terminology in physics textbooks is that the external reality is described by mathematics, the MUH states that it is mathematics (more specifically, a mathematical structure).

This makes no sense to me. I don't have a clue as to what this means. How can our external reality BE mathematics?

 

[Pinball1970]

From the PDF that Yazata posted a link to: https://arxiv.org/pdf/0704.0646/



This makes no sense to me. I don't have a clue as to what this means. How can our external reality BE mathematics?

The paper is outlining mathematical foundations but I am yet to get the part where a square root can be found in the universe.

 

[James R]

Sarkus:

A couple of things came up in your replies to Write4U that I think are best addressed to you, lest they get lost in the mess of attempts to get Write4U to engage in a rational discussion.

Nothing you have posted here has any bearing on the notion of "mathematical object" that James R mentioned. He said "DNA is not a 'mathematical object'". This, I'm presuming given the context and the thread title, is in reference to what Tegmark argues for - the "everything is a mathematical structure" idea.

Yes. As you know, I am not on board with Tegmark's claim that mathematics is all there is. I do not, for instance, accept that things that are made of matter are mathematics, for reasons I have given previously.

Needless to say, what you posted is just more pretty much irrelevant stuff about things behaving in a mathematical manner. None of which is disputed. Did James R mean that DNA does not behave in a manner that could be modelled by mathematics, for example? No. He said that it was not a "mathematical object", which in context is referencing Tegmark's notion that it is nothing but mathematics. I.e. no underlying fundamental physical stuff - just mathematics.

Yes.

.... you have a pet idea, that everything is governed by / behaves according to mathematics. This in itself is absolutely fine. It is also, I wager, something that is not disputed at all by anyone here, and probably not by any scientist - the laws of physics suggest that the universe is mathematical in nature. It is, in essence, a rather trivial idea, a given, if you will. Axiomatic, perhaps.

My own view is a little different.

I tend to take a more instrumentalist view of mathematics. I am quite happy to agree that mathematics is a very useful tool for describing how our physical universe works and for predicting what physical systems will do in the future. But when it comes to saying something like "the universe is governed by mathematics", whether I take issue with that claim really depends on what the person who is making it means by it.

If all that is meant is that mathematics is very effective in describing how the universe is operating, how it has operated in the past and how it is likely to operate in the future, then there's no major problem. All that is being said, there, is that mathematics is a useful tool in the human toolbox.

If, on the other hand, what is meant is that mathematics has some sort of Platonic existence which interfaces - somehow - with the physical universe to determine how physical things behave and interact, then I think somebody might be making a more profound claim than is supported by the available evidence.

Saying "the universe is governed by mathematics" and saying "the laws of physics, as expressed in human physics textbooks, are mathematical" are two different claims. I accept the latter; I'm not so sure about the former.

It is notable that mathematics is as effective as it is when it comes to describing our physical world. Clearly, something important is going on with mathematics. I don't deny that. But I'm an empiricist, not an idealist. I don't really subscribe to the idea of Plato's eternal forms.

I have never said that Tegmark is a charlatan. You do know that posters here are not sockpuppets of a single person, right? If James R has referred to Tegmark as a charlatan, that is for you to raise with James R.

I have not referred to Tegmark as a charlatan. But while we're talking about that, I do think he is rather showy. I haven't seen enough of him to conclude that he's dishonest, so I'm happy to give him the benefit of the doubt on that, for now.

 

[Sarkus]

My own view is a little different.

I tend to take a more instrumentalist view of mathematics. I am quite happy to agree that mathematics is a very useful tool for describing how our physical universe works and for predicting what physical systems will do in the future. But when it comes to saying something like "the universe is governed by mathematics", whether I take issue with that claim really depends on what the person who is making it means by it.

To be clear: when I say that "the universe is governed by mathematics" I mean that the universe is governed by physical laws that can be expressed mathematically.

If all that is meant is that mathematics is very effective in describing how the universe is operating, how it has operated in the past and how it is likely to operate in the future, then there's no major problem. All that is being said, there, is that mathematics is a useful tool in the human toolbox.

I do think mathematics is more than just a tool, though. I don't think it is a "real" object, but I do think that interactions behave in line with the laws, which can be expressed exactly via maths. To me this makes the universe inherently "mathematical in nature", at least as far as we currently understand it. This, however, introduces its own issues, in the manner of some form of selection bias. I.e. we improve our understanding of the universe through science, and maths, which would otherwise tend to ignore that which is not mathematical. Hence our understanding is driven by maths. etc.
But we share the view that maths is not a real/physical thing in and of itself. Unlike that which Tegmark is espousing.

If, on the other hand, what is meant is that mathematics has some sort of Platonic existence which interfaces - somehow - with the physical universe to determine how physical things behave and interact, then I think somebody might be making a more profound claim than is supported by the available evidence.

Agreed, but I accept this mostly on intuition, and probably some form of reinforcement bias... i.e. we're taught the way the universe is, therefore we're likely to interpret everything to support that, etc.

Saying "the universe is governed by mathematics" and saying "the laws of physics, as expressed in human physics textbooks, are mathematical" are two different claims. I accept the latter; I'm not so sure about the former.

I don't see them as different claims, because I'm not aware of anything that governs the universe that is not a law of physics. And they are mathematical. Hence I think it's okay to say that the universe is governed by mathematics. But, sure, in the debate about whether mathematics has a separate reality, I guess it's important to clarify.

It is notable that mathematics is as effective as it is when it comes to describing our physical world. Clearly, something important is going on with mathematics. I don't deny that. But I'm an empiricist, not an idealist. I don't really subscribe to the idea of Plato's eternal forms.

Ok.

I have not referred to Tegmark as a charlatan. But while we're talking about that, I do think he is rather showy. I haven't seen enough of him to conclude that he's dishonest, so I'm happy to give him the benefit of the doubt on that, for now.

Ditto. He is one of the "celebrity physicists" of the 2000+ era, along with Michio Kaku etc. I feel their "celebrity" status may tend to give their ideas more newsorthiness, and more credence among the following, than is appropriate. For example, if the MUH was a paper/book by any other non-celebrity physicist would it have ever been given the same publicity?

 

[James R]

I do think mathematics is more than just a tool, though. I don't think it is a "real" object, but I do think that interactions behave in line with the laws, which can be expressed exactly via maths.

I'm not sure that we're expressing the physical laws exactly with our maths.

Physical laws are constantly being revised. We had Newton's law of gravity, which was good enough for 400 years, but then we found that it couldn't account for certain observations. Then we had Einstein's general relativity for 100 years. But there are good reasons to expect that GR is not the be all and end all when it comes to theories of gravity. So, now people are proposing string theories and the like which, so far, have not been confirmed to be an improvement on GR.

Pick any area of physics you like. What tends to happen over time is that the mathematical laws get repeatedly tweaked so that they are in accordance with new experiments or observations. On occasion, laws are thrown away and replaced by new laws, although often those new laws include the old ones as some sort of special case or approximation.

It is fair to say that our physical laws are good enough for many purposes. I just don't think it's right to claim that they govern the way the universe works. They are descriptive, not prescriptive.

 

[exchemist]

I'm not sure that we're expressing the physical laws exactly with our maths.

Physical laws are constantly being revised. We had Newton's law of gravity, which was good enough for 400 years, but then we found that it couldn't account for certain observations. Then we had Einstein's general relativity for 100 years. But there are good reasons to expect that GR is not the be all and end all when it comes to theories of gravity. So, now people are proposing string theories and the like which, so far, have not been confirmed to be an improvement on GR.

Pick any area of physics you like. What tends to happen over time is that the mathematical laws get repeatedly tweaked so that they are in accordance with new experiments or observations. On occasion, laws are thrown away and replaced by new laws, although often those new laws include the old ones as some sort of special case or approximation.

It is fair to say that our physical laws are good enough for many purposes. I just don't think it's right to claim that they govern the way the universe works. They are descriptive, not prescriptive.

Agree. It should also be borne in mind that the practical utility of mathematics in science is limited to comparatively simple or idealised physical systems, of the kind that is often dealt with in physics. In most of the other sciences mathematical models, where they exist at all, give only approximate predictions, due to the complexity of real systems. This is not to deny that one can imagine, at least in principle*, that the complexities could potentially be modelled mathematically, but the effort would be a waste of time.

*As Walter J Moore memorably stated in the undergraduate physical chemistry textbook I had at university, "from en principe oui, a French expression meaning non".

For this reason I am a bit suspicious of attempts to raise mathematics on too high a pedestal in science, and in particular of the claim, which I have sometimes come across, that until you have a mathematical model you have not got a proper scientific theory.

 

[Sarkus]

I'm not sure that we're expressing the physical laws exactly with our maths.

Perhaps not at the moment, but the principle is that those absolute laws can be expressed exactly with mathematics. Whether we have the full understanding of the laws at present is neither here nor there, I'd suggest.

Physical laws are constantly being revised. We had Newton's law of gravity, which was good enough for 400 years, but then we found that it couldn't account for certain observations. Then we had Einstein's general relativity for 100 years. But there are good reasons to expect that GR is not the be all and end all when it comes to theories of gravity. So, now people are proposing string theories and the like which, so far, have not been confirmed to be an improvement on GR.

Sure. And how many of these are non-mathematical? All improvements are still mathematical - i.e. can be expressed exactly as understood by maths.

Pick any area of physics you like. What tends to happen over time is that the mathematical laws get repeatedly tweaked so that they are in accordance with new experiments or observations. On occasion, laws are thrown away and replaced by new laws, although often those new laws include the old ones as some sort of special case or approximation.

Not disputed. But let's dispense with what our understanding of them is, and look at the objective laws. The principle is that these laws can still be expressed exactly by mathematics. Is that contentious? What would be an alternative?

It is fair to say that our physical laws are good enough for many purposes. I just don't think it's right to claim that they govern the way the universe works. They are descriptive, not prescriptive.

Sure - no dispute between descriptive and prescriptive. By "governed by" I simply mean that things act in accordance with. I don't intend it as presuming a causal relationship, that maths somehow causes.