Perhaps.

I disagree with your interpretation, Gnomon, because Max Tegmark explicitly says – which I point out in my previous post – that he is not proposing the "MU" merely as "a mental construct". Read The Mathematical Universe or stream video of one of Tegmark's lectures on this thesis.
Reality. Ironically, Tegmark has been called a "radical Platonist". So, I would be surprised if that was compatible with your own (Realist?) worldview.
I don't agree with that common misconception either.
[Tegmark's MUH] looks like hyper-Platonism to many but more like Spinozism to me. — 180 Proof
I answer favorably to being called an "Epicurean-Spinozist". — 180 Proof

OK. I guess we'll have to agree to disagree on Tegmark's Platonic inclinations. But maybe we can at least agree on the "Spinozist" half of your "Epicurean-Spinozist" label. If I was to choose such a hyphenated label, I'd probably make it "Stoic-Spinozist". But then, I'm not really comfortable with butterfly pin labels. So, you can just call me a "gnarly-Gnomonist". :grin:

:smirk:

It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. I know why the universe is mathematical. I have discovered a truly marvelous proof of this, which this margin is too narrow to contain. — Pierre de Fermat(ized) TheMadFool

:sweat:

Well math is the application of numbers to some kind of structure. What this structure is, isn't clear.

But I don't understand the notion that there is only structure. It seems to me that a structure must be structure of something.

So if the universe is essentially mathematical and we don't really know what the structure math describes is, then I don't see Tegmark's hypothesis making much sense.

Yeah, yeah. The universe has no obligation to make sense to us. Doesn't mean we shouldn't try to give it some sense, otherwise, why bother learning about it? It's a strange proposition on the whole, not very convincing.

Having to create an infinitum of universes to explain our one universe is suspect.

True. Perhaps that's why Tegmark isn't doing what you mistaken believe he's doing re: .

He's a many worlds proponent. Simply put, many worlds posits that is the explanation of our universe.

Tegmark's a proponent of MUH which indirectly implies MWI, etc, and not as an "explanation of the universe" but for explaining (E. Wigner's) unreasonable effectiveness of mathematics in fundamental physics, etc.

MUH (Mathematical Universe Hypothesis) is just Pythagoreanism (vide infra) resurrected! What if Jesus was an idea?, but that's another story.

All is number — Pythagoras

Lemme see...

Take prime numbers. Yep, they're mathematical but they're patternless and hence, no known formula to generate them. Math is the study of patterns. There's something nonmathematical about mathematics viz. primes. It's kinda like saying all is good but there's something bad about all is good. :chin:

Every prime number can be written as 6n+1 or 6n-1. Where do these formulaticals exist in the MU? How does an integral exist? Near a summation? What about functions or complex numbers? Is there a big book in which the mathematician can look? Written in mathematical heaven? Are the spherical harmonics existing in the hydrogen atom? Or is it just a way nature can answer if we ask questions in the language of math? What about the infinity of Feynman diagrams, negative energy frequencies in quantum fields, or the operators, and their distributions in space? What about space itself? Is it pseudo Euclidean or a manifold? Who am I? If all is math then so are we. Is a thought about the long line and Hausdorff spaces, Julia sets, and Lebesque measures, are these thoughts mathematical stuff? It's a belief, like the thought of charged interactions can be a charged process itself, or the thought about God can be God itself.

Every prime number can be written as 6n+1 or 6n-1. Where do these formulaticals exist in the MU? How does an integral exist? Near a summation? What about functions or complex numbers? Is there a big book in which the mathematician can look? Written in mathematical heaven? Are the spherical harmonics existing in the hydrogen atom? Or is it just a way nature can answer if we ask questions in the language of math? What about the infinity of Feynman diagrams, negative energy frequencies in quantum fields, or the operators, and their distributions in space? What about space itself? Is it pseudo Euclidean or a manifold? Who am I? If all is math then so are we. Is a thought about the long line and Hausdorff spaces, Julia sets, and Lebesque measures, are these thoughts mathematical stuff? It's a belief, like the thought of charged interactions can be a charged process itself, or the thought about God can be God itself.

Tegmark's views are in part the logical corollary of swallowing the subjective-objective distinction, according to which perspective isn't real and only "inter-subjective" laws for translating Lockean primary qualities are real.

His views are also funny, not only for abusing Occam's razor in such a crackpot fashion, but that a parameter-less "model" of physics is a contradiction in terms; for it is the parameters of a model that correspond to the model's falsifiable propositions, that are revised via fitting the model to data. An infinitely adaptable model that has no parameters makes no predictions and is functionally similar to the largest possible fishing net.

The general thrux of Tegmark's remarks can be interpreted as a Modus-Tollens argument against scientific realism. i.e. that his argument is valid, but that his conclusion is false, implying that his premise of a mind-independent universe is false - which is already an empirically obvious false premise to those who aren't blinded by a dogmatic understanding of scientific jargon.

Both idealists and realists can agree with the Ontic-Structural Realism of Tegmark. For example, British idealism's doctrine of internal relations is in logical agreement with OSR, without jumping the shark to conclude that only unthinkable and unperceivable mathematical structure exists in a way that is divorced from the Lockean secondary qualities of perception.

Both idealists and realists can agree with the Ontic-Structural Realism of Tegmark. For example, British idealism's doctrine of internal relations is in logical agreement with OSR, without jumping the shark to conclude that only unthinkable and unperceivable mathematical structure exists in a way that is divorced from the Lockean secondary qualities of perception — sime

Whatever. As I mentioned in another thread, a simple isomorphism between physical reality and mathematical structures provides a way of saying they are the "same" without being identical. But if this is truly what Tegmark had in mind he overdid his arguments - as do some posters on this forum. :cool:

Since it doesn't seem to me that philosophy of mathematics is getting close to converging to a satisfying answer any time soon (I think we are in some areas of philosophy, like metaethics), I just see this as intriguing speculative thought and that's perhaps the best kind of contribution that can be made at this point. I have no clue what type of evidence or piece of reasoning will leave the matter at rest, it's at the stage of the Pre-Socratics (whose atomic speculations were actually not entirely without basis at the time, although obviously not sufficient. See Schrodinger's book "Nature and the Greeks" So maybe someone today is right.)

Btw 's reading seems correct based on a summary given by Tegmark in his exchange with Scott Aaronson in the comments here:

https://scottaaronson.blog/?p=1753

"Physicalist: I think there’s no “secret life sauce” distinguishing living from non-living things.
Critic: That’s an unscientific theory, since you can’t experimentally prove there’s no secret life sauce!

Integrated information theorist: I think there’s no “secret consciousness sauce” distinguishing conscious information processing systems from unconscious “zombie” ones.
Critic: That’s an unscientific theory, since you can’t experimentally prove there’s no secret consciousness sauce!

MUH advocate: I think there’s no “secret existence sauce” distinguishing physically existing mathematical structures from other mathematical structures.
Critic: That’s an unscientific theory, since you can’t experimentally prove there’s no secret existence sauce!

I think that in all three cases, the first person makes a simple Occam-style claim, and the the onus should be on critic to experimentally detect the sauce!"

From the Aaronson blog:

But Tegmark goes further. He doesn’t say that the universe is “isomorphic” to a mathematical structure; he says that it is that structure, that its physical and mathematical existence are the same thing

I'm with him up to an isomorphism. Beyond that is the absurd IMHO.

I agree with the absurdity of it:

Where is there motion (in the philosophical sense of change - such as causation requires) within maths themselves? Without mathematics consisting of the causation by which we live - or, at the very least, accounting for why we hold the illusion of constantly changing, in a temporally unidirectional manner at that, within a mathematical 4D block universe - mathematics cannot be equivalent to the world.

Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe? — Stephen Hawking

... or, in this case, the universe as we know it.

Both idealists and realists can agree with the Ontic-Structural Realism of Tegmark. For example, British idealism's doctrine of internal relations is in logical agreement with OSR, without jumping the shark to conclude that only unthinkable and unperceivable mathematical structure exists in a way that is divorced from the Lockean secondary qualities of perception — sime

This sounds like nuking the fridge.

or, in this case, the universe as we know it. — javra

The fire that breathes life in the physìcal theory describing the fundamental physical/mathematical structure ĺies in the content of what they describe. The structure of the two basic fields in nature, interacting on an evolving background of spacetime, can be described mathematically exactly only in a very limited area of nature. If we apply that theory to the atom, the theory is non-applicable, as it describes only free fields that interact shortly (asymptotically free is a misnomer, as the fields are free all of the time, except for a short interaction, which can be described by an infinity of ďiagrams, all happening simultaneously, so the story goes. Do all these diagrams to describe the interaction exist there in spacetime? Is spacetime itself a mathematical structure? Who knows. The wavefunction to describe the hydrogen atom is a harmonic function. It seems to exist truly and it can be depicted. It can't be describe by quantum field theory though. Do mathematical structures exist which are not exact and which can be described by an approximation only? And what about the mathematical structure of the human face and its connection to emotion, the face laughing or talking?
The fire left out of the mathematical structures is that what is inside of them, so I think wholeheartedly. It could be the concept of charge, be it electrical or color and the mass describing the evolution of particle fields. Nobody knows exactly what a particle is. Only on the inside of the particle (the field of all its simultaneous paths or the bath of hidden variables it finds itself in, which could form space itself) the fire can be known. It's called charge. Maybe all charges interacting give holistically rise to new charges, leading to structures with forrest fires, or exploding fires, inside of them. I can feel this fire within. It's hot.
I think Hawking referred to the fire of charge. Near the big bang, massless charges were waiting for the moment to get real and form massive structures, to interact with each other, form bodies and run through the forrest of trees and plants (silently charged structures, just wanting to wave their leaves in the wind). Are they mathematical structures? Dunno. I Tegmark thinks so, it's a reality for him. I wonder if he could find a mathematical structure of people. If there isn't a mathematical structure to be found of an isolated iron atom (there exist approximations only), I doubt it. There is no exact mathematical structure if we can't find it. If there exists an approximation only, then what's the real, exact structure?

I think Hawking referred to the fire of charge. — Raymond

Could of course be. My thought is that he was referring to fire in the Heraclitan sense: flux, change, becoming, the philosophical notion of motion.

Which would be in line with the as of yet unanswered question I posed in regard to this subject.

If there exists an approximation only, then what's the real, exact structure? — Raymond

You're talking to one who is a mysterianist in relation to any self's understanding of awareness's core essence while also upholding this same core essence of awareness to be ontically primary. :wink: It's not a mainstream view, and other views of course abound. From any such point of view, however, I'd think your question here is quite complex.

For instance, if Platonic realism in relation to at least the most basic of mathematical ideas/forms, then basic mathematical ideas/forms such as that of a circle and of Pi are the real, exact structure in an of themselves ... with empirically perceived circles being the approximation of these ideas/forms. But even here, what is it that gives these real ideas/forms the motion/becoming/change/flux of the world we know?

Then there's the view that all maths are only human concoctions ... and, hence, approximations of what in fact is real. This view however has nothing to do with the topic this thread addresses.

At any rate, I don't find it an easy question to answer. But I do what to emphasize: E pur si muove.

Edit: Just in case I need to clarify this: the ideas/forms of a circle and of Pi - as with all other mathematics that I know of, be it math's rules, its eqasions, its relations, and so forth - are perfectly static of themselves. So, for example, when granting their Platonic realism, the reality of these static forms does not in and of itself explain the dynamic nature of the world which we know and live in.

I think Plato's idea of the metaphysical domain of mathematical objects was a domain of unchanging objects, indeed as you described. The 5 Platonic bodies, like the cube or the isocahedron. There was an over 100 year physical model discovered in a university basement. A paper mache partial model of a special function, I can't remember which one. Beautiful, a true piece of art, made without computers. Would fit in Plato's realm. But what are these structures made off? Plato said we can't know them an Sich. Every math formula or physical realization, say a cube, is an approximation, even an exact formula. They are the shadows on the walls of a cave. They are lit by light, and the shadows can be investigated, with a model or a formula. Aristotle said the cube is just the construction of clay, and the formula an abstraction without real existence. Now who is right? Plato says the real cube exists, and can never be known, only approximated, while Aristotle says the dirty cube is the real cube and the mathematical cube a unreachable abstraction. Somehow, Tegmark is sandwiched between the both. The cube, or any other form, is real, and all forms are mathematical. So, the formula of the cube refers to a shape present in the world. At least, potentially, because nobody has seen a perfect cube. Like in general, no perfect mathematical forms can be found. Particular cases can be found though. The archetypal example being the hydrogen atom. The wavefunction has an exact 3D shape and the electron conforms to this. It depends on your view of particles what the shape actually is. A shape without substance is, well, an empty shape. There has to be something that is in shape. Tegmark conjectures tha the shape is devoid of substance. People too are complicated mathematical shapes, and contrary to Platonic objects they can shape-shift. He misses an essential part of reality. My reality, that is.

He misses an essential part of reality. My reality, that is. — Raymond

:up: :cool:

I don’t in any way consider myself intelligent in mathematics. I’ve got a weird kind of dyslexia, mistaking p’s with b’s or b’s with d’s in what I handwrite so that – unless I reread what I’ve written say weeks later – I don’t register these mistakes even after repeated re-readings of what I’ve written. Well, its sometimes better and sometimes worse. Spellchecks help. But re: mathematics. In my high school AP calculus class I’d place +’s instead of -‘s and vice versa in proofs and have no idea of how I got the proof wrong even after repeated reappraisals of it. Didn’t flunk but I got a measly C-. Terrible. I’m only OK with maths when it comes to certain abstractions regarding them, but by no means all.

Long story short, I’m not mathematically savvy. I say this because I notice that your savviness in at least this respect far exceeds mine.

That said, from my simpleton view, all maths are static, non-motional. I’m familiar with there being maths such as causal calculus. But as far as I can tell, these maths are fully static as well. If you or any other mathematically savvy person know of any exception to maths being non-motional, I’d be very wanting to be familiarized with them.

To shift the subject slightly to something that has traditionally irked me, music. Its rhythms and, when applicable, its rhymes. I know it can be represented by maths, such as octaves. But I’ve always been bothered when people say that music is mathematical - i.e., that its equivalent to the maths it is constituted of. Its of course a metaphysical issue, and my reaction has always been that it’s not. There’s a lot that could be argued either way in this. But here going back to what I’ve previously expressed, the maths lack the motion that is requisite for the music to be. Ergo, I’m thinking, the maths that can describe music cannot be equated to the music itself. Music has that “extra [?] stuff” that the maths lack.

Also, want to point out that the Platonic notion of forms does not translate into shapes. Physical forms, for example, do have shapes. Yet, for example, the forms that cultures can take are shape-devoid. More Platonically addressed, the form of “the good”, for example, is shapeless. But maybe this isn’t central to the issue.

But I’ve always been bothered when people say that music is mathematical - — javra

Consider me on your side mate! Many physicists, mathematicians, and computer scientists, are fan of Bach. Because of the beauty of the mathematical structure. Well, I dunno. If that's the reason you like it, you seem to miss the point of music somehow. However much structure it may contain, however difficult is to play, somehow I feel they like it to pat their ability of abstract mathematical thought on the back.
I have a friend who can't distinguish between p and q. He got mad after I told him the q and p were mixed up on a shopping list. I tried to imagine what's it like. Of course I can't. Maybe it's me who perceives wrongly! Do p and q , or b, look the same to you? Are the three the same? Is ppp the same as pqq or qpq? Just curious. I'm raised in a society that stimulates curiosity...

Just curious. I'm raised in a society that stimulates curiosity.. — Raymond

Hey, no worries! No, they certainly look different to me. But its as if I cognitively - sometimes and only to some extent - separate the meaning I intend from the phenomena that serves as a vehicle for the meaning’s expression. Like in a slip of the tongue where one knows what one is actively meaning to say, says something that doesn’t convey the meaning one intends, and recognizes this only after the fact. It’s weird and interesting to me at the same time, though I’ve had my entire lifetime to get used to it: has a lot to do with notions of metacognition such as the knowing of knowing (like knowing a word that’s on the tip of one’s tongue whose phenomenal form one momentarily doesn’t known … but knowing that one knows the word all the same). So when I immediately reread a “d” when I in fact wrote a “b” (say rereading dog when the written word is bog) I’m grasping the meaning I intended to impart into the writing (dog) without becoming consciously aware that the phenomena which conveys this meaning is different from what it ought to have been. It’s by no means constant or else debilitating in general, but, yea, happens every now and then.

:up:

See Schrodinger's book "Nature and the Greeks" ... — Saphsin

I prefer instead the much more informed, contemporary God and the Atom by the late, eminent, particle physicist and philosopher Victor J. Stenger, which thoroughly refutes all of the immaterialist, dualist woo-of-the-gaps, antirealist, supernaturalist perennial dogmas inconsistently based on misappropriating 'fundamental physics' to sophistically propagandize against philosophical atomism (which they confuse, or fail to distinguish from, methodological materialism).

If the magical thinker uses quantum physics to piggy bag on quantum mechanics or quantum fields he is fully justified in doing so. The expert Brian Cox advocates the idea that when QM is used in the magical realm and the person uttering the language used in QM, one only has to ask if the person in question knows about the mathematics involved, a typical attitude covering up a misunderstanding of what quantum field theory actually stands for. Nobody knows the true nature of quantum fields because only their outside appearance is described by mathematics without even a speck of inside understanding. No physicist in the world understands the nature of the charges and the particles these are contained in. The concept of a point particle is problematic, and the way they interact, by virtual or real fields of intermediaries, can be perfectly described by the mathematical language, but any question about what's really going on is countered with a vague reply hiding a basic ignorance using math to justify ignorance. For whatever math is used, the ingredients described by the math remain a magical mystery, which forms the foundation of consciousness and will. The dualism is not between reality and the mind, with the mind never being able to make direct contact with reality. The true dualism is the dualism between the outside description and the inside ingredients. Every outside description of a material creates a direct knowledge of and a direct contact with the material studied. There is no gap. But the inside nature of the material (not the Ding an Sich, as this doesn't exist), will remain unknown. Only by eating it material reveals its inside nature.

I didn't read that yet, I'll take your recommendation. Note I cited Schrodinger's book not because I hold his worldview, but because I learned from it the interesting historical tid-bit that Pre-Socratic atomism borrowed from Anaximenes's observation of changes of states of matter, that condensation and rarefaction wouldn't make sense if materials were just a continuum.

In my humble opinion, mathematics is (entirely?) about precision (definition-wise, measurement-wise). An example should illustrate my point.

A reconstruction of Newton's thoughts:

An apple falls, the moon revolves around the earth. :chin: Maybe it's the same force (gravity) that does both. [Note, there's still as yet no math at all in Newton's theory].

Time to be precise. Enter math (arithmetic, geometry, algebra, calculus, to name a few). — Isaac Newton

That's to say, mathematics only brings high levels of exactitude to what's actually a nonmathematical idea/theory/hypothesis. Would you call a stick "micrometrical" (mathematical) just because you measured it with greater precision using a micrometer (mathematics)? :chin:

Whatever. As I mentioned in another thread, a simple isomorphism between physical reality and mathematical structures provides a way of saying they are the "same" without being identical. But if this is truly what Tegmark had in mind he overdid his arguments - as do some posters on this forum. :cool: — jgill

But if meaning is use - which is essentially a structuralist standpoint - then it isn't clear to me that maths and physics aren't identical, at least partially, in a tautological sense. From the perspective of use, the meaning of Newtons Laws of motion, for instance, includes the mathematical activities which are used in their application. Conversely, the meaning of "2 + 2 = 4" can be understood to include the physical experiments that verify it.

What i was mostly objecting to earlier was Tegmark's aperpsectival take on the conceptual overlap that is a consequence of his scientific and metaphysical realism.

I knew if! Peoqle who bon'f see fhe qitterrence detmeen q, t, f, p, q, and p, are zecrefely fruing fo tree thewselwez trow fhe consfraints ot vriffen synpolz! What a great quality! :smile: