We need more discussion of Tegmark's mathematical universe hypothesis

[Sarkus]

And your job does not involve numbers and values and functions? Science is a mathematical discipline.

Please quote me where I have indicated that I am a scientist? You keep making stuff up and then cry foul when someone calls you out on it. Please stop it.

I don't claim any superior intellect, that is your projection. I claim that I can count and use mathematical formula (algebra).

Whoop-di-doo. You can count. Then why did you feel the need to boast that you used to be a bookkeeper, doing accounts for 7 non-profits, and specifically implied that this gave you a special insight into "balancy and symmetry"? This is not my projection, this is what you posted. It is boasting, even if you don't recognise it as such, and is also irrelevant, especially if all you were trying to claim was that you can count and use mathematical formula.

Note that I never accuse someone else of being stupid or a moron. I don't feel I have that superiority. You do.

Please link to where I have quoted you as being stupid or a moron? If you can't then please apologise for misrepresenting what I have said. You do yourself no favours, Write4U. Making stuff up, and posting irrelevancies really isn't going to get you far. So please stop it.

 

[Sarkus]

So three threads?

Such is the ability of Write4U to introduce numerous irrelevant strands into a topic that it needs three more threads to untangle them. And even in those he struggles to keep it on topic. Ah, well.

I watched the video and wondered what the hell it was!
Probably because he did not really mention mathematics till 25 minutes into a 45 minute video.
We got a brief summary of where we are in current cosmology including sped up video of a radio telescope for the first 25 minutes.
The last ten minutes was a discussion of the future, what we may make of it.
All good stuff BUT what did he actually say about the universe and mathematics? What was his overall thesis? The Universe IS mathematics....Is that it?
Right, how does that work? What does that mean?

Congratulations on sitting through the video. You're a better man than me. I'll wait for the precis from the person who seems to expect us to do so, so that he can demonstrate that he at least understands what the video is about etc.

 

[exchemist]

So three threads? This on mathematics to

I watched the video and wondered what the hell it was!
Probably because he did not really mention mathematics till 25 minutes into a 45 minute video.
We got a brief summary of where we are in current cosmology including sped up video of a radio telescope for the first 25 minutes.
The last ten minutes was a discussion of the future, what we may make of it.
All good stuff BUT what did he actually say about the universe and mathematics? What was his overall thesis? The Universe IS mathematics....Is that it?
Right, how does that work? What does that mean?
We can always buy his book of course (available at most reputable bookstores...)

Thanks for sitting through this on our behalf. I would not have had the patience.

This is why some people suspect Tegmark (whose real name is Shapiro but which he changed to his mother's maiden name, as Shapiros are two a penny on the US East Coast) is more of a showman and self-publicist than a serious metaphysician.

I posted Massimo's criticism of Tegmark/Shapiro in post 50. Peter Woit gives a thoroughly damning review of his ideas, as expresed in a recent book, here: https://www.math.columbia.edu/~woit/wordpress/?p=6551

These people seems to me to talk sense. Teggers, not so much.

 

[Write4U]

Universe IS mathematics....Is that it?

It is not difficult. I did not say "the universe is mathematics", that's Tegmark.

My personal POV is that the universe is a mathematical object, a pattern, and all universal functions are based on and guided by generic logical mathematical laws based on relational values and functions that humans have observed and been able to symbolize and codify.

AFAIK, most scientists stipulate that parts of the universe and universal mechanics have "some" generic mathematical properties, no?
So there is at least consensus of the presence of some mathematical properties, such as quantity and quality.
I am only supporting Tegmark's POV when he asks why the entire universe cannot be a mathematical construct?.

If that makes a wholeness that is fundamentally all mathematical, I leave that to Tegmark. Perceptronium?

Universe IS mathematics....Is that it?
Right, how does that work? What does that mean?
We can always buy his book of course (available at most reputable bookstores...)

Yep, Capitalism, a result of mathematical values and functions, runs deep. IMO, it's a good thing when serious science is available to the general public. Knowledge must spread to become effective in decision-making, right?
As far as merchandising "knowledge", you can find a bible in every motel. How's that for spreading knowledge?
But you can also go online and listen to his personally delivered live lectures, leaving peer review of the proofs to his peers in theoretical mathematics

Do you know what I as a reductionist, like about Tegmark's hypothesis? He thinks that in the end, the pattern of the Universe can be represented with an equation requiring some 32 relational properties (values) interacting via a handful of equations.
Its simple elegance requires a minimal quantity of mathematical symbols to address the absolute fundamentals of the "Wholeness".

Say the universe turns out to be a hologram, a very persuasive model. Clearly, that function would rest on the mathematical precision of the action, even at an abstract level.
(Or as David Bohm would say, the "Implicate" or "Enfolded" order.)

p.s.(awaiting moderation)

 

[Pinball1970]

more of a showman and self-publicist than a serious metaphysician

Yes there is that because popular science sells books and videos.
Some cameras like these scientists and i am sure that their publicist jumped on that.
Brian Cox, Jim Al Kalili, Sabine Hossenfelder, Krauss, Turok, Kaku and personal favourite Sean Carroll.
Do not get me wrong, some of these guys are top notch published scientists but the persona and ideas they put out in pop sci books is nothing like what they discuss in conferences.
Tegmark's presentation is very see through,he said virtually nothing regarding his ideas. Are they even his ideas?
Feynman discussed this issue (see his 'onion' analogy)
Penrose too although he was a lot more humble, "we do not know why the universe seems to be governed by mathematics."
This idea is hardly original.

 

[Pinball1970]

I posted Massimo's criticism of Tegmark/Shapiro in post 50. Peter Woit gives a thoroughly damning review of his ideas, as expresed in a recent book, here: https://www.math.columbia.edu/~woit/wordpress/?p=6551

Thanks for the reference. I will check that out, Woit and Smolin have written some decent books and articles regarding string theory. Ten years or so on from those books regarding the experimental evidence, it is still lacking. W.r.t. beyond SM physics? Besides that little G2 wobble! Save that for another thread!

 

[exchemist]

Yes there is that because popular science sells books and videos.
Some cameras like these scientists and i am sure that their publicist jumped on that.
Brian Cox, Jim Al Kalili, Sabine Hossenfelder, Krauss, Turok, Kaku and personal favourite Sean Carroll.
Do not get me wrong, some of these guys are top notch published scientists but the persona and ideas they put out in pop sci books is nothing like what they discuss in conferences.
Tegmark's presentation is very see through,he said virtually nothing regarding his ideas. Are they even his ideas?
Feynman discussed this issue (see his 'onion' analogy)
Penrose too although he was a lot more humble, "we do not know why the universe seems to be governed by mathematics."
This idea is hardly original.

Ah but “governed by” mathematics, which is just a fancy way of saying it displays ordered behaviour, is not at all the same as saying it IS mathematics. That is where Teggers loses people like Pigliucci - and, at a much more humble level, people like me. It does not seem to follow at all and doesn’t even make sense, if one sees mathematics as a structure of quantitative logic, i.e. essentially abstract.

I like Sabine and I don’t know Sean Carroll. I’m rather suspicious of Cox, Al Khalili and especially Krauss, who is silly enough to dismiss philosophy, thereby showing a poor grasp of the foundations of his own subject.

 

[Sarkus]

Ah but “governed by” mathematics, which is just a fancy way of saying it displays ordered behaviour, is not at all the same as saying it IS mathematics. That is where Teggers loses people like Pigliucci - and, at a much more humble level, people like me. It does not seem to follow at all and doesn’t even make sense, if one sees mathematics as a structure of quantitative logic, i.e. essentially abstract.

I struggle with the "is mathematics" as well, but then sometimes I think it does sort of make some sense (in the way that a refelction in a hall of mirrors sort of looks like the person).
There's the whole "map v territory" category fallacy that it seems to be, or "model v reality" to put it in a more mathematical scenario. So my thinking about it is that the more detailed the mathematical model, the more closely the output reflects reality. This isn't novel. We all aspire, when we make such models - be they financial or otherwise - to make them as reflective of reality as possible. So, to mix analogies, at what point does a working model of a duck actually become a duck? How detailed must the model be to reflect reality perfectly? And if something is a perfect model of reality, then surely it ceases being a model at all, and actually is the reality that you're modelling, right?
So, my thinking is that if you can create a mathematical model that perfectly represents reality, then that mathematical model must be that reality. And hence reality could be considered mathematical. And that's my sticking point in this line of thinking (as woolly and unscientificly simple as I've tried to make it) - is it actually possible to create a mathematical model that perfectly reflects reality?
If you create a model of a duck that perectly looks, walks, smells, quacks, and does everything else a duck does and does them exactly like a duck... is it not a duck?

A similar line of thinking - and excuse the slight sidetrack - seems to be with regard the "Simulation Hypothesis", the idea that we, and our universe, are actually nothing more than a simulation being run in a (albeit rather powerful) computer. It has serious probabilistic arguments for it, but the point is not whether it's true or not, but that if true then it would also suggest that our universe is nothing more than a series of 0s and 1s, or whatever computational system the computer is running on. I.e. something akin to it being mathematical.
One could argue that with regard the MUH, the Simulation Hypothesis really just pushes the issue back a layer, but I thought it sufficiently worthy of comparison.
Anyhoo - just a side note.

 

[Write4U]

This is why some people suspect Tegmark (whose real name is Shapiro but which he changed to his mother's maiden name, as Shapiros are two a penny on the US East Coast) is more of a showman and self-publicist than a serious metaphysician.

I posted Massimo's criticism of Tegmark/Shapiro in post 50. Peter Woit gives a thoroughly damning review of his ideas, as expresed in a recent book, here: https://www.math.columbia.edu/~woit/wordpress/?p=6551

Interesting critique without a shred of hard science.
This is in one of the replies to the critique:

I mean, when modern physics points to fact that solid, physical matter is in fact vast amount of empty space linked together by interactions of profoundly small particles that seem to have an ephemeral existence all their own, is Platonism or realism about abstract structures and mathematical relations underlying the physical world really so outlandish? I agree it could probably never be tested, making it more philosophical than empirical, but do you think it a reasonable view?

I do.

By the way Frenkel’s book, Love and Math, is brilliant so far and its clear from the reading that he, along with a long list of other mathematicians, wholeheartedly embraces the Platonic view without the slightest bit of crackpot “mysticism.”

 

[exchemist]

I struggle with the "is mathematics" as well, but then sometimes I think it does sort of make some sense (in the way that a refelction in a hall of mirrors sort of looks like the person).
There's the whole "map v territory" category fallacy that it seems to be, or "model v reality" to put it in a more mathematical scenario. So my thinking about it is that the more detailed the mathematical model, the more closely the output reflects reality. This isn't novel. We all aspire, when we make such models - be they financial or otherwise - to make them as reflective of reality as possible. So, to mix analogies, at what point does a working model of a duck actually become a duck? How detailed must the model be to reflect reality perfectly? And if something is a perfect model of reality, then surely it ceases being a model at all, and actually is the reality that you're modelling, right?
So, my thinking is that if you can create a mathematical model that perfectly represents reality, then that mathematical model must be that reality. And hence reality could be considered mathematical. And that's my sticking point in this line of thinking (as woolly and unscientificly simple as I've tried to make it) - is it actually possible to create a mathematical model that perfectly reflects reality?
If you create a model of a duck that perectly looks, walks, smells, quacks, and does everything else a duck does and does them exactly like a duck... is it not a duck?

A similar line of thinking - and excuse the slight sidetrack - seems to be with regard the "Simulation Hypothesis", the idea that we, and our universe, are actually nothing more than a simulation being run in a (albeit rather powerful) computer. It has serious probabilistic arguments for it, but the point is not whether it's true or not, but that if true then it would also suggest that our universe is nothing more than a series of 0s and 1s, or whatever computational system the computer is running on. I.e. something akin to it being mathematical.
One could argue that with regard the MUH, the Simulation Hypothesis really just pushes the issue back a layer, but I thought it sufficiently worthy of comparison.
Anyhoo - just a side note.

Yes but this is where the error comes in, it seems to me. You can't build a mathematical model of something physical without first defining certain entities and their attributes, which you have to do in words. "An electron." "Energy." Momentum." etc.

None of these things can be defined by an equation without some words behind, to explain the physical concepts the equation relates together. This is where people can lose track of the physical nature of models in their worship of the maths.

 

[Write4U]

Yes but this is where the error comes in, it seems to me. You can't build a mathematical model of something physical without first defining certain entities and their attributes, which you have to do in words. "An electron." "Energy." Momentum." etc.

None of these things can be defined by an equation without some words behind, to explain the physical concepts the equation relates together. This is where people can lose track of the physical nature of models in their worship of the maths.

But does what humans say affect how the universe works?
What if the word is an equation?

 

[Write4U]

Ah but “governed by” mathematics, which is just a fancy way of saying it displays ordered behaviour, is not at all the same as saying it IS mathematics.

"Is governed" by, or guided by is the proof that mathematics is an underlying principle.
"Ordered behaviour" is by definition mathematical in essence, no? Are there any other ordering mechanics?

 

[C C]

It is not difficult. I did not say "the universe is mathematics", that's Tegmark.

My personal POV is that the universe is a mathematical object, a pattern, and all universal functions are based on and guided by generic logical mathematical laws based on relational values and functions that humans have observed and been able to symbolize and codify. [...]

Mathematical universe hypothesis: Tegmark's MUH is the hypothesis that our external physical reality is a mathematical structure. That is, the physical universe is not merely described by mathematics, but is mathematics — specifically, a mathematical structure. Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Observers, including humans, are "self-aware substructures (SASs)". In any mathematical structure complex enough to contain such substructures, they "will subjectively perceive themselves as existing in a physically 'real' world".​

This seems redundant at first glance. What's the difference between declaring the universe a "physical structure" and declaring it a "mathematical structure"?

If the latter is completely disassociated from graphics or pictures, then "mathematical structure" might become radically different by consisting purely of technical description.

But that's the point where few, if anybody, can fathom what mathematical realists (in general) are claiming with respect to their abstract entities being "real", or how they exist. If they're not the redundancy of "physical forms" or spatial configurations, and they obviously can't be our artificially invented symbols (which are also impotent in terms of generating slash governing anything on their own).

All I can see that's left is some fuzzy idea that mathematical entities are nomological or immaterial "generative principles" that output and regulate phenomenal or physical "stuff". Thereby turning the universe into a continuing process rather than a complex, higher-dimensional physical structure where all its "developing" states co-exist.

Which seems to be an obscured way of mathematical realists claiming (without the directness) that the universe is a simulation. Where one configuration of the world is created and replaces the last one according to rules, maintaining inter-consistency of such states over time. But not a simulation residing within a computer (which would just be a fallacious repeat of the nature of this world). But riding atop whatever that weird, immutable realm of "mathematical" generative principles is whose only [supposed] evidence is its creative/governing effects on this universe (simulation, process).

Even advocates of philosophical presentism might dismiss that as a superfluous add-on, akin to the old-fashioned supernatural. Preferring instead that the order -- the "lawfulness" in their view of the universe as a process -- just happens or is "magically" maintained without an extraneous or underlying nomological domain (stratum of laws or generative principles -- whether dubbed mathematical or otherwise).
_

 

[Write4U]

This seems redundant at first glance. What's the difference between declaring the universe a "physical structure" and declaring it a "mathematical structure"?

Exchemist has a problem with that.

 

[Sarkus]

Yes but this is where the error comes in, it seems to me. You can't build a mathematical model of something physical without first defining certain entities and their attributes, which you have to do in words. "An electron." "Energy." Momentum." etc.

None of these things can be defined by an equation without some words behind, to explain the physical concepts the equation relates together. This is where people can lose track of the physical nature of models in their worship of the maths.

Ultimately the issue may not be one of category error, but rather semantics. i.e. Tegmark may be defining things (I don't know if he is, I haven't examined his work that closely) such that their equivalence is assumed.
I also have no doubt he has an argument for asserting their equivalence (the model of the duck, and the duck etc), but also one must consider that if a "physical" object is so perfectly described by mathematics that one can simply conclude that the object thus is mathematics. The particles, the sub-atomic particles, are all perfectly described by mathematics, as are their interactions. Our experiences of something as "solid" or "wet" are then just interpretations of the mathematics, with meaning only in the conscious mind, which is itself simply a mathematical process / structure / whatever.
I would be interested to hear someone's summary of how he does argue their equivalence, ideally from someone who seems to name-drop Tegmark as if they actually understand this work of his, if just to save me time of wading through hours of videos to find such a thing.

 

[exchemist]

Ultimately the issue may not be one of category error, but rather semantics. i.e. Tegmark may be defining things (I don't know if he is, I haven't examined his work that closely) such that their equivalence is assumed.
I also have no doubt he has an argument for asserting their equivalence (the model of the duck, and the duck etc), but also one must consider that if a "physical" object is so perfectly described by mathematics that one can simply conclude that the object thus is mathematics. The particles, the sub-atomic particles, are all perfectly described by mathematics, as are their interactions. Our experiences of something as "solid" or "wet" are then just interpretations of the mathematics, with meaning only in the conscious mind, which is itself simply a mathematical process / structure / whatever.
I would be interested to hear someone's summary of how he does argue their equivalence, ideally from someone who seems to name-drop Tegmark as if they actually understand this work of his, if just to save me time of wading through hours of videos to find such a thing.

Yet it seems to me maths cannot describe a physical object. All it can do is describe the object and its properties in relation to others, which need definition by means other than maths. To give an example, what equation defines an electron? Or energy? There are no such equations. The maths relies on the concepts being defined first, and then tells you the relationships between these.

 

[Write4U]

Yet it seems to me maths cannot describe a physical object. All it can do is describe the object and its properties in relation to others, which need definition by means other than maths. To give an example, what equation defines an electron? Or energy? There are no such equations. The maths relies on the concepts being defined first, and then tells you the relationships between these.

The smallest possible size for anything in the universe is the Planck Length, which is 1.6 x10-35 m across.

What is the Value of Electrons?

An electron is a subatomic particle commonly represented as e– or e. It possesses negative polarity. An electron inherits the properties like – Charge, Mass, Spin, etc. The values of electrons imply the value of the charge of an electron, the mass of the electron, and a quantum mechanical property- spin of the electron along with corresponding units.

Value of electron Unit
Electron charge 1.60217662 × 10-19 Coulombs
Electron charge in e V1.60217662 × 10-19 Joule
Electron mass9. 10938356 × 10-31 Kg
Electron mass in amu 0.00054858 Atomic Mass Unit(amu)
Sep 17, 2020

https://byjus.com/physics/value-of-electron/

 

[James R]

We can always buy his book of course (available at most reputable bookstores...)

That will only encourage him.

 

[James R]

I think there is room for confusion concerned Tegmark's hypothesis and more general philosophical ideas.

The big philosophical problem is the question of what is the true nature of existence. In the context of the present discussion, there are two ideas that I think we should exclude upfront.

The first idea is the problem of hard solipcism. Solipcism is the claim that we cannot be sure that anything exists, apart from our own minds. Actually, you can't be sure that my mind exists, except as some notion in your mind. This means that there's no way to know whether ducks - or anything else normally considered external to your mind - actually exist separately from your mind.

It seems to me that solipcism is, by its nature, an unfalsifiable hypothesis. No conceivable test could ever show that it is false. Therefore, we should leave it to one side when we ask questions like "what is the ultimate nature of our universe?" Not discount it - because it can't be disproved - but just put it aside as something that we can't investigate further. The universe may be an illusion created by your mind, but to make any progress, we have to adopt as a working assumption that things other than your mind have some reality of their own.

The second idea is the "simulation hypothesis". This is the claim that the outside world that you are aware of is generated entirely by some external agency pumping sensations into your head, which you take as real. You might, for example, be a brain in a vat, fed sensory information directly into your neurons by some sort of computer. This idea is different from solipcism because it does not assume that your mind and everything else in the (apparent) universe are one. It contemplates the existence of other beings or entities ourself of yourself, which have their own, separate existence beyond your ability to perceive.

This, too, is an unfalsifiable hypothesis. There is nothing you can do to disprove that you are in a simulation. Therefore, this is another useless avenue for speculation (by us) about the nature of the universe we actually perceive.

We come, then, to Tegmark's claim that the universe is mathematics. One thing to note, before we go on, is that if the simulation hypothesis is correct, that doesn't support Tegmark's hypothesis. If you and are I just digital data in some kind of machine run by aliens, it still does not follow that we and our universe are "made of mathematics". A simulation would need to run on something - just something is inaccessible to our senses.

So, let's step away now from these unfalsifiable philosophical hypotheses and accept, for the sake of argument, that you really do exist separately from ducks (that they aren't just things in your head) and that, as far as we can tell, our universe is "real", in the sense that it will go on existing after you're no longer aware of it. Let us also agree that, even if we are in a simulation, there appear to be certain rules and regularities that we can investigate from inside the simulation, even if we can never look outside it. Let's do what we can do.

Now we're into the realm of observation and science. We observe that that there are two types of things in our world - physical objects and ideas. Put simply, physical objects are things that can be touched or otherwise sensed. They exist outside our minds which, for the sake of argument, we are accepting as separate from one another and from the universe at large. Ideas, on the other hand, are thoughts in our heads. They are information. We can communicate them to other people, to a certain extent using physical media, but they cannot be touched or otherwise sensed.

What is mathematics? Is it a physical object (or collection of physical objects) that we can touch or otherwise sense? I say: it is not. It is a collection of ideas. Tegmark, on the other hand, says that mathematics and physical objects are one and the same. He wants to abolish the distinction. In Tegmark's world, the number 3 is on the same ontological footing as a real-life duck. Tegmark says that mathematics is the ultimate reality: the duck is mathematics, along with every other thing that you and I would normally call a "physical object".

The main problem I have with Tegmark's hypothesis is that I think it's a dead end in terms of suggesting any useful programme of research to better understand the universe in which we find ourselves (simulated or otherwise, as the case may be). Worse, I think Tegmark has lost his grip on what for (most of) the rest of us is the common-sense appreciation that concepts are different from physical objects. We recognise that the idea of an apple is not an apple. But for Tegmark, both the idea of the apple and the apple itself are the same thing, in essence. That is, both the idea of the apple and the apple itself are, he claims, mathematics.

Another way to explain this is using the analogy of the map and the territory. The idea of an apple is like a map. It is what allows us to recognise physical apples when we encounter them. The physical apples themselves are the territory that the map describes. Similarly, Einstein's theory of general relativity is an idea - it describes the "territory" of the physical space and time that we experience. Einstein's theory is a set of ideas which can be expressed partly using mathematics, but it is a category error to mistake a description of spacetime for spacetime itself. It is a category error to mistake the idea of a duck for a duck.

Suppose we accept Tegmark's hypothesis, and hold that everything is mathematics - indeed, there is only mathematics. What follows? Having abolished the distinction between ideas and physical objects, it seems to me that we're in for a whole lot of problems. It might be okay to accept that the idea of an apple is not very different from an apple, at a stretch, but the idea of Godzilla appears to be very different from Godzilla, in an important way. Even when it comes to mathematics itself, we immediately run into difficulties. The idea of a tesseract is perfectly valid mathematics, but we observe no tesseracts in our physical world. Yet Tegmark would have to say that tesseracts are on an equal footing with apples (not to mention apples and Godzilla) when it comes to appreciating what is real in our world.

Tegmark's hypothesis also appears to be unfalsifiable. How could we test to find the difference between the idea of an apple and an apple? In Tegmark's universe, there can be no such test. Maybe the idea of an apple involves slightly different mathematics than the physical apple, but Tegmark would hold that both are mathematics none the less. Also: at what level of probing will a physical apple be seen to be nothing but mathematics? At what point does it become apparent that the physical things and the ideas have become one and the same? Because, from where I'm standing right now, those two things look very different.

None of this proves that Tegmark is wrong, of course. But I wonder whether Tegmark himself would concede that it's important to maintain a distinction between things and ideas, regardless of whether he believes, in the end, that they are one and the same. I don't think think I could take him seriously if he said that he wouldn't concede that.

To summarise: I just think that Tegmark's hypothesis makes a horrible mess of basic ontology and is practically useless in that it doesn't help to advance any actual knowledge that we have about our world. I also suspect that Tegmark hasn't really thought it through. I would suggest that maybe he should have taken a few classes in philosophy, alongside his physics.

 

[Write4U]

None of this proves that Tegmark is wrong, of course. But I wonder whether Tegmark himself would concede that it's important to maintain a distinction between things and ideas, regardless of whether he believes, in the end, that they are one and the same. I don't think I could take him seriously if he said that he wouldn't concede that.

Perhaps it is a matter of "resistance" on your part?