Is Everything in the Universe Truly a Mathematical Structure?

[Demystifier]

http://arxiv.org/abs/0704.0646

I predict that this paper will become famous and frequently cited, not only by those who will like it, but also by those who will not.
Does anyone wants to take a bet?

By the way, I am not one of those who will particularly like it.

 

[marcus]

http://arxiv.org/abs/0704.0646
will like it, but also by those who will not.
...

cited, that is, by those who think it is a load of baloney, and, perhaps
mildly envious of Tegmark as a fashionable influential young
preacher to the cool science congregation,
may be outraged by his launching such speculation

(I am trying to explicate your post here, which is a bit mysterious. I am not committing to an opinion of my own. I will reserve judgment)

Does anyone wants to take a bet?

hmmm. I think I will not take the bet

Tegmark is head of the FQXi foundation which has a lot of Templeton money to distribute in support of longshot research into foundational questions---the Big questions---as I think you know. that makes his paper worth inspecting and possibly worth citing regardless of whether one likes it or does not like it. FQXi is an important operation because, AFAIK in the US, nobody else does what they do. (the Feds play safe)

 

[jal]

He did not go far enough. He needs another level. Level V is the level that would produce an increasing entropy.
In order to achieve maximum entropy there has to be a lot of room for movement. No movement no entropy. It would be homogeneous, therefore the entropy would be zero. However, there would be maximum potential to do anything.
The multi-universe can only work when there exist the conditions that permit multi movements and maximum entropy.
jal

 

[MeJennifer]

Tegmark is head of the FQXi foundation which has a lot of Templeton money to distribute in support of longshot research into foundational questions---the Big questions---as I think you know. that makes his paper worth inspecting and possibly worth citing regardless of whether one likes it or does not like it. FQXi is an important operation because, AFAIK in the US, nobody else does what they do. (the Feds play safe)

I think that citing a document should be related to the scientific importance of it (or to contradict it). Just quoting a paper because of the writer's title or affiliation, membership of some old boys network, or by the amount of money behind it is just wrong IMHO.

 

[garrett]

I see two neat ideas in this paper that extend -- or rather, constrain -- his original mathematical universe hypothesis. The first idea is that, in order to avoid Godel incompleteness, our universe may be a computable structure. The second (more of an observation) is that there may be some "weight" favoring structures that are simple rather than complex. Both of these ideas give hope to finding a TOE -- so, I'm biased to like them for that. ;)

 

[setAI]

He did not go far enough. He needs another level. Level V is the level that would produce an increasing entropy.
jal

entropy emerges from Level III- the quantum multiverse and the natural computation of the quantum field- [level IV is a structure that contains all possible states as a block/ phase space] in quantum information theory entropy is the propagation of ignorance of bit values that spreads through a computation- if a bit register's value is unknown any bits it interacts with also become unknown-

this understanding of entropy as information entropy is very promising- some have computed the information entropy of the observable universe and the result shows the 'dark energy'/ the cosmolical constant- so the conjecture is that the increasing information entropy of the universe is the source of dark energy and accelerating expansion:

http://arxiv.org/abs/astro-ph/0603084
http://arxiv.org/abs/hep-th/0701199

 

[jal]

this understanding of entropy as information entropy is very promising

The problems of quantum computing will not be overcome until there is a better understanding of mnimum length, and quantum structures which should give a better understanding of how to deal with uncertainties.

We got to figure out what is going in, select the part that we want, and make it go to where we want.

Simple to say...hard to do.
jal

 

[Mike2]

http://arxiv.org/abs/0704.0646

I predict that this paper will become famous and frequently cited, not only by those who will like it, but also by those who will not.
Does anyone wants to take a bet?

By the way, I am not one of those who will particularly like it.

Between pages 7 and 8, Tegmark suggests that all of QFT and QM can be derived from the S(3)XS(2)XU(1) symmetry group. He seems to indicate that these symmetries can be derived from nothing but the U(1) symmetry and the Poincare group. Is this true, and if so where can I find an elegant demonstration of this? Thanks.

I seem to have stumbled across a way of getting a Path Intergral formulation of QM from nothing but classical logic. In the process I insert e^iL(x',x) only because its absolute value is 1 and does not change the probabilities. But I haven't gotten any physics out of it. So now if I get physics out of this path integral by means of symmetry consideration only, then I will have gotten physics from logic alone. Thus the above quest. Thanks again.

 

[christianjb]

It's not my field, but I find Tegmark's speculations to be very exciting.

I suspect that in the same way we now appreciate that the brain is nothing more than a fantastically complicated interaction of atoms and electrical signals- we will come to accept that ultimately fields- and subatomic particles are 'made of math' and nothing more.

It also explains the origin of the universe! We exist as part of the eternal Platonic realm of all possible equations and their solutions. Our existence was no more created than PI, the Mandelbrot Set or De Moivre's theorem was created.

 

[Demystifier]

"Shut up and calculate":
http://xxx.lanl.gov/abs/0709.4024

 

[marcus]

Sabine Hossenfelder replies to Tegmark

http://backreaction.blogspot.com/2007/09/imaginary-part.html

 

[MathematicalPhysicist]

I see two neat ideas in this paper that extend -- or rather, constrain -- his original mathematical universe hypothesis. The first idea is that, in order to avoid Godel incompleteness, our universe may be a computable structure. The second (more of an observation) is that there may be some "weight" favoring structures that are simple rather than complex. Both of these ideas give hope to finding a TOE -- so, I'm biased to like them for that. ;)

perhpas I am ignorant but what does godels' incompleteness theorems has got to do with the theory of everything in physics?
it only deals with mathematical theories in first order logic.

 

[marcus]

http://backreaction.blogspot.com/2007/09/imaginary-part.html
a sequence of eight photographs with thought-balloon captions
here's a sample

 

[MathematicalPhysicist]

well she's sub-structure, to be precise.

 

[marcus]

"My brain is invariant under action of this thought."

---Bee

 

[garrett]

perhpas I am ignorant but what does godels' incompleteness theorems has got to do with the theory of everything in physics?
it only deals with mathematical theories in first order logic.

Yah, I mostly agree with you. Just because it's a neat idea doesn't mean it's true. I'm fine with there being things in physics that are true but not provable. So I doubt Gödelian incompleteness has anything to say about fundamental physics -- but it's a cute idea to ponder. And I do like the mathematical universe hypothesis, since why else would math work to describe the universe so well if the universe wasn't intrinsically mathematical?

P.S. The Perimeter Institute is very nice. ;)

 

[MathematicalPhysicist]

garrett you are confused between identify our mathmetical models of nature with what nature really is, what nature is is a philosophical question and doesn't have any isnight as to physics nor maths in general, well you can say that in order to revolutionise in maths and physics you need a good idea, which sometimes is also philosophical.
p.s, tegmark isn't the first physicist to argue this, look at wigner's article on the connections between maths and physics, i myself should give a look at it someday.

 

[Mike2]

perhpas I am ignorant but what does godels' incompleteness theorems has got to do with the theory of everything in physics?
it only deals with mathematical theories in first order logic.

Godel seemed to prove that mathematics is not complete - we can always find an equation which is true but not provable within mathematics. But then again this is true of any axiom of mathematics; we always just accept the axioms of mathematics without proof.

However, finding a TOE is not the same effort as finding every equation of math that is true. We don't expect that it will take ALL of math to describe all of physics. So the incompleteness of math tells us nothing about the completeness of physics.

 

[ccdantas]

Apparently, his philosophy is to equate the physical world with mathematics (yes, equate, not a sort of mapping between the two). He argues that this direct equality solves many problems. Actually, he seems to argue that such an equality solves the philosophical problem of whether there is an ultimate reality. Yes, there is one and it is pure mathematics. And everything is revealed! Isn't it obvious?

I may have misunderstood it all (I've only read his shorter paper - Shut up and calculate). In any case, I didn't find any of his arguments brilliant nor convincing. Looks like a very bad philosophy to me.

The fact that we can describe physical phenomena through mathematical reasoning is something much deeper to me and equating both is no solution (again, to me). It's like turning a difficult question into a trivial one as the best way to actually avoid it.

 

[garrett]

Mike2: Yep.

lqg: "what nature is is a philosophical question"
No, nature is certainly not a philosophical question. :D

And physics is not the answer, physics is the question... "yes" is the answer. (stolen from W.A.)

 

[Chronos]

That is both a hilarious and unsettling thought by Bee, marcus!

Tegmark is not shy by nature. His is a bold paper that could be very important, or a house of cards. It's sufficiently well constructed to be forgiveable, even if it turns out to be a dead end. It is. IMO, the right way to propose new ideas these days. Taking an occasional hit for going out on a limb is not necessarily fatal. 50 or more years ago a flawed paper was a problem, mainly because it took years to get one widely circulated. This is no longer an impediment. In the current Arxiv age, you can publish to your heart's content without fear of it taking a decade to refine, or cast aside your ideas. Intellectual integrity is still a necessary element, but, impeccability is a luxury most researchers cannot afford. The trade off is papers tend to be rushed to press nowadays. I can live with that.

 

[Demystifier]

The most weird thing with the mathematical universe is that, according to Tegmark, EVERY mathematical structure exists, and no mathematical structure is more real then other. Thus, not only quantum mechanics is real, but also classical mechanics is real, Ptolomei mechanics is real, a model in which the universe is a dodecahedron is real, anything. It seems that almost every paper on physics is correct, provided that a purely mathematical mistake has not been made. In fact, such papers with mathematical mistakes are also correct, because these papers themselves are also mathematical structures (because everything is a mathematical structure).

So, if Tegmark is right, what is the point in doing science?

 

[rewebster]

The most weird thing with the mathematical universe is that, according to Tegmark, EVERY mathematical structure exists, and no mathematical structure is more real then other. Thus, not only quantum mechanics is real, but also classical mechanics is real, Ptolomei mechanics is real, a model in which the universe is a dodecahedron is real, anything. It seems that almost every paper on physics is correct, provided that a purely mathematical mistake has not been made. In fact, such papers with mathematical mistakes are also correct, because these papers themselves are also mathematical structures (because everything is a mathematical structure).

So, if Tegmark is right, what is the point in doing science?

Old Tegmark wants to be a POPULAR guy --and make everyone happy and 'like' him for what his says.

 

[fleem]

Just some general responses to some of the comments I see in this thread:

1. Goedel used the rules of the universe to prove his incompleteness theorem. Therefore the truth in his theorem depends on the consistency of the universe. Therefore his theorem does not apply to the universe.

2. To say there are two separate sets of rules ("the universe" and "logic") is to say each must be describable using the other (otherwise we can claim there is a set of rules that never interacts with the universe--which is just plain silly), which is to say they are the same set of rules. Therefore there is only one set of rules and the "universelogic" is it. The universe is logic, incarnate. For this reason, that will be what we see whether there is a higher machinery or not. So noting it doesn't imply there is a higher machinery.

 

[fleem]

More general comments:

3. The universe allows us to make a false statement. So we should be careful to discriminate between false statements and statements that appear consistent with the universe (with apologies to Goedel).

4. Everything that happens in our brains, or in a computer, follows the rules of the universe because those things are part of the universe. For example, if I claim to be using "the square root of minus-one" in some calculation, I am lying (or mistaken). A close examination of the neural signals in my brain would prove the square root of minus-one never appears, nor anything implying that it has some reality to it.

 

[MathematicalPhysicist]

Just some general responses to some of the comments I see in this thread:

1. Goedel used the rules of the universe to prove his incompleteness theorem. Therefore the truth in his theorem depends on the consistency of the universe. Therefore his theorem does not apply to the universe.

I really wonder how many of you actually read the various proofs of godel's incompletness theorems, and know what axioms are being applied there.

what are the rules of the universe? and which of them godel actually used in his proof?

 

[Demystifier]

I really wonder how many of you actually read the various proofs of godel's incompletness theorems, and know what axioms are being applied there.

I have been reading the simplified versions given by Penrose in his semi-popular books, which seemed relatively easy to grasp and understand even intuitively. It seems to me that Godel's theorems do not have true practical implications, although I am not completely sure about that.

 

[Demystifier]

Old Tegmark wants to be a POPULAR guy --and make everyone happy and 'like' him for what his says.

Well, he certainly did not make ME happy. And according to the Bee's faces, it seems that it made her unhappy too.

 

[fleem]

I really wonder how many of you actually read the various proofs of godel's incompletness theorems, and know what axioms are being applied there.

what are the rules of the universe? and which of them godel actually used in his proof?

So in other words, Goedel used rules that are not of this universe. I must say that was quite an accomplishment, considering that the neurons in his brain most likely were, in fact, part of this universe.

 

[MathematicalPhysicist]

I have been reading the simplified versions given by Penrose in his semi-popular books, which seemed relatively easy to grasp and understand even intuitively. It seems to me that Godel's theorems do not have true practical implications, although I am not completely sure about that.

I don't say that's hard to grasp, but if you knew the details of the proofs and the lemmas and postualtes being used then you could have told me what rules of the universe are being used there if there are such rules.

look at smullyans' book on godel's incompletness theorems, gives his twist to the proofs.