That's to say, mathematics only brings high levels of exactitude to what's actually a nonmathematical idea/theory/hypothesis — Agent Smith

An exactitude that that can only be reached in a very limited practice though. An approximation is not exact, for there is no real thing corresponding to an approximation. What is the real form of that approximated? There is no exact form. Is the mathematical approximation of the electron orbitals in an iron atom the real thing? Or an approximation of them when together a zillion-fold?

An exactitude that that can only be reached in a very limited practice though. An approximation is not exact, for there is no real thing corresponding to an approximation. What is the real form of that approximated? There is no exact form. Is the mathematical approximation of the electron orbitals in an iron atom the real thing? Or an approximation of them when together a zillion-fold? — Raymond

I see it from a missile guidance angle. Some have poor guidance systems (precision hundreds of meters), others are super-precise (lands within meters of the target).

I see it from a missile guidance angle. Some have poor guidance systems (precision hundreds of meters), others are super-precise (lands within meters of the target). — Agent Smith

The filled balloon that's let loose with open mouth, the virus falling in static air, or leaves in the wind, where do they touch the Earth?

Btw ↪Pfhorrest
'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!" — Saphsin

Thank you for that link, it was a fun read, and nice to know that I understand Tegmark's position correctly. :-)

M = The universe is mathematical (Max Tegmark et al).

What does M mean?

We can do the most/squeeze every last drop with/out of reality if we apply math to the universe (reality). Please include, inter alia, comprehensibility to that - the universe can be understood (only if) viewed through a mathematical lens.

To cut to the chase, we can extract the maximum bits of information from the universe if we use math.

Oddly many people claim, with great pride I might add, that they're bad at math! :chin:

There's a wonderful isomorphism between mathematical thought and the physical world. To go beyond that is metaphysical hogwash. IMHO. :roll:

According to physicist Max Tegmark, there are nothing but mathematical structures and 'the physical world' is just a nested network of mathematical structures to which we (observers) happen to belong, or inhabit. . . . This looks like hyper-Platonism to many but more like Spinozism to me. — 180 Proof

I've only read one of Tegmark's books, but I have a general idea of "what he's talking about". I'm not sure I agree with all his speculations, but his basic notion that Reality is fundamentally mathematical makes sense to me, especially in light of Quantum Physics, where the structure of reality is a mathematical Field.

Personally, I prefer the more inclusive term "Information" (Matter + Energy + Mind) to the austere abstract ideality of a pure mathematical structure underlying the messy concrete material world. My view combines a bit of Plato's Idealism (LOGOS) with a smidgen of Spinoza's universal substance Monism (G*D). Consequently, my world model consists of both Material objects (known by senses) and Mathematical (Mental) structures (known by reason). :nerd:

Substance or Structure :
Baruch Spinoza denied Descartes' "real distinction" between mind and matter. Substance, according to Spinoza, is one and indivisible, but has multiple "attributes". . . . . The single essence of one substance can be conceived of as material and also, consistently, as mental.
https://en.wikipedia.org/wiki/Substance_theory

Our Mathematical Universe :
My Quest for the Ultimate Nature of Reality
___Max Tegmark, theoretical physicist
Note to self -- The basic element of my Information Universe is the "Re-El" (reality element) which is a ratio between existence and non-existence (1 or 0). The universe as a whole, is continuous, but its constituent parts are discrete.

but his basic notion that Reality is fundamentally mathematical makes sense to me, especially in light of Quantum Physics, where the structure of reality is a mathematical Field — Gnomon

That idea seems to predict well, but it models phenomena that are poorly understood.

Reality is fundamentally mathematical makes sense to me, especially in light of Quantum Physics, where the structure of reality is a mathematical Field — Gnomon

But what

constitues

a mathematical "Field" (why do you write it with a capital F?). If we are a collection of mathematical formulas, is there an isomorphism between the world of formulas as encountered around us and the mathematical formulas constituting us? Is this isomorphism a mathematical structure?

Note to self -- The basic element of my Information Universe is the "Re-El" (reality element) which is a ratio between existence and non-existence (1 or 0). The universe as a whole, is continuous, but its constituent parts are discrete. — Gnomon

I think that here you conflate reality with fantasy, as Tegmark seems to do.

But what constitutes a mathematical "Field" (why do you write it with a capital F?). — Cornwell1

Hypothetical Quantum Fields consist of abstract relationships (ratios ; vectors) that are not real things but ideal mathematical "points" & "links". When those points have measurable values, the field can be assumed to be real. I capitalize the word "field" to emphasize that it is not a real object, but an abstract model of some feature of Reality. I capitalize "Reality" to emphasize that it's a mental model of what's outside your skull, not necessarily the ding an sich. :nerd:

A field is a mathematical abstraction. ... Vector fields are not real, for the same reasons vectors are not real; the electric field is real ..
https://physics.stackexchange.com/questions/322983/how-real-are-fields

Ding An Sich : (in Kant's philosophy) a thing as it is in itself, not mediated through perception by the senses or conceptualization, and therefore unknowable.

I think that here you conflate reality with fantasy, as Tegmark seems to do. — Cornwell1

No. I don't conflate "Reality" with "Ideality", I merely compare them as hypothetical mental models, not the actual " totality of real things and events". Our models of reality are not necessarily "fantasies", but they are inherently "imaginary". So, I'd be careful about labeling Tegmark's speculations as "fantasy". It's possible that he knows something you don't. As I said in the post, I don't agree with all of his conjectures, but they seem to be based on a deep insight into Reality (objects : things) and Ideality (models ; ideas). :smile:

Reality Is Not What It Seems :
book by physicist Carlo Rovelli
https://en.wikipedia.org/wiki/Reality_Is_Not_What_It_Seems

A model of reality explains how the universe was created and how it operates. You might think that this is a definition of reality itself, but it isn't, which can be illustrated by looking at the most popular model, known as naïve realism. In a nutshell, naïve realism says that what you see is what you get.
https://www.sfgate.com/opinion/chopra/article/The-Most-Popular-Model-of-Reality-Is-Wrong-14842693.php

That idea seems to predict well, but it models phenomena that are poorly understood. — jgill

Yes. Tegmark's mathematical model of the world is an attempt to describe the "poorly understood" phenomena on the Quantum level of reality. We know pretty well what Quarks do, but have no idea what they are. We can't compare them to anything in our sensory experience of the world. The definition of a Quark, or of Superposition, sounds about as counter-intuitive as the Catholic Trinity. :joke:

We know pretty well what Quarks do, but have no idea what they are. We can't compare them to anything in our sensory experience of the world. — Gnomon

Don't think so. Quarks can be viewed as triplets. An up-quark is TTV. A down quark tvv. An electron is ttt and a neutrino VVV. Small letters anti particles. The three families are excitations. A particle is just an object moving through space. That's not so difficult to imagine. Point-like is different to imagine. The particles jumping madly between paths is quite weird as is their interaction. Somehow they are consciousness and long for other particles. Or wanna stay away from each other. Already at fundamental level love and hate rule! :razz:

Don't think so. Quarks can be viewed as triplets — Cornwell1

I'd like to "view" that unitary triplet. Can you post a picture? :wink:

Quarks appear to be true elementary particles; that is, they have no apparent structure and cannot be resolved into something smaller.
https://www.britannica.com/science/quark
Note -- For over two thousand years the Atom was defined as the true elementary indivisible particle. If Quarks have no structure, why are they hypothetically portrayed with internal parts? The Holy Trinity is also described as One deity with three forms : up, down, and yummy. :joke:

ONE QUARK IN THREE FLAVORS blueberry, strawberry and lemon-lime

ONE QUARK IN THREE FLAVORS blueberry, strawberry and lemon-lime — Gnomon

Tasty flavors! I think there are two flavors of tasty stuff. They are pure kinetic energy. Let's call them L(iquorice), and S(ugar). And let's call their anti's l and s. The L has electric charge 1/3 and S has charge 0, and two kinds of color charges (a strong one to form colorless triplets and a normal one to form colored ones).

Electron (muon tau)
lll
Up quark (charm quark, top quark)
LLS
Down quark (strange quark, bottom quark)
lss
Electron neutrino (muon neutrino, and tau neutrino)
SSS

In an electron, proton (uud), neutron (anti-(udd)), and electron neutrino reside equal amounts of matter and antimatter! No asymmetry between matter and antimatter. Excitations of the triplets are the three particle families. Excited liquorices and sugars. And they are massless, explaining the relation between mass and energy. How bout that?

It would seem another physicist has entered the room :clap:

The universe is mathematical (Max Tegmark et al) simply means that if you mathematize the universe, it becomes comprehensible.

What does it mean, mathematize the universe?

Translate the universe into numbers (arithmetic) and shapes (geometry) and we're gonna make (a whole lot of) progress towards apprehending what the universe is all about.

Mathematics, of course, has a much broader definition - study of patterns - but, from what I know of mathematicians (not much), numericizing/geometrizing patterns makes them more mind-friendly (eaiser to grasp).

It would seem another physicist has entered the room — jgill

You are the "father of modern bouldering"? And a mathematician too? That's quite something! I saw quite an impressive picture of you. You hang on one arm with stretched horizontal body! Is the device you hang on a mathematical structure?

The universe is mathematical (Max Tegmark et al) simply means that if you mathematize the universe, it becomes comprehensible. — Agent Smith

Most things in the universe have no corresponding mathematical structure. Only approximations will do. What's the mathematical structure of a piece of music?

Most things in the universe have no corresponding mathematical structure. Only approximations will do. What's the mathematical structure of a piece of music? — Cornwell1

There usually is a pattern. Patterns are best studied/understood mathematically. At least that's what I've been told.

Most things in the universe have no corresponding mathematical structure — Cornwell1

Perhaps they do and we are incapable of understanding them.

Only approximations will do — Cornwell1

All of life are approximations. A right triangle is a Platonic ideal, but its approximations in the physical world have been overwhelmingly of benefit to humankind.

Some structures though don't even have an approximation. What's the functional form of the motion of gas particles that carry the information òf a piece of music? The particle oscillates at the rythm of the music. It can't be reduced to sine terms. Is a particle a mathematical structure?

There is a pattern on my face toò. A math structure with a laugh? What's the structure made up?

What's the mathematical structure of a piece of music? — Cornwell1

In theory, everything in the universe can be analyzed down to its mathematical structure (conceptual inter-relationships). Math is not a physical object. It is instead the logical order (organization) of things and ideas. Since Logic is not made of matter, it is only knowable to a rational mind. Even "un-cuttable" atoms & in-divisible quarks have an internal or fundamental mathematical structure. The emotional sonic structure of music is intuitive for most minds, but only rational minds can infer the logical mathematical organization of music. :nerd:

What is Mathematical Music Theory? Mathematical music theory uses modern mathematical structures to 1. analyze works of music (describe and explain them), 2. study, characterize, and reconstruct musical objects such as the consonant triad, the diatonic scale, the Ionian mode, the consonance/dissonance dichotomy...
http://www-personal.umd.umich.edu/~tmfiore/1/FioreWhatIsMathMusTheoryBasicSlides.pdf

What Is A Mathematical Structure? :
A mathematical structure is nothing but a (more or less) complicated organization of smaller, more fundamental mathematical substructures. Numbers are one kind of structure, and they can be used to build bigger structures like vectors and matrices
https://truebeautyofmath.com/what-is-a-mathematical-structure/

Logic and mathematics are two sister-disciplines, because logic is this very general theory of inference and reasoning, and inference and reasoning play a very big role in mathematics,
http://serious-science.org/logic-and-mathematics-7243

Prishon, I started a discussion entitled Ethics as a method, not an artifact that has been utterly over run by this guy's idea that reality is mathematical. It's a discussion about how ethics is a method for formulating moral conclusions, just as math is a method by which we track value and change patterns in reality. You aught to stop by and help me with these people. It's completely absurd. They've derailed the entire discussion for the insistence on making Tegmarks ridiculous and completely disregarded argument. I suspect it's because they don't actually want to discuss ethics. But, yeah, come on through if you feel up to it.

-G