Is the Game of Life a metaphor for the search for a Theory of Everything?

[microsansfil]

Hello,

How is it perceived the "Mathematical universe hypothesis" from Max Tegmark, in the scientific community ?

Thank
Patrick

 

[friend]

If you assert that everything mathematical is physical, then you run up against Godel's Incompleteness theorem, and physics becomes incomplete or inconsistent. Instead I prefer to think that we are only imposing a subset of math on physical concepts to produce the laws of physics. This would be something like math imposed on Euclidean geometry which is complete and consistent.

 

[MathematicalPhysicist]

Friend, why should we consider it to be complete and consistent?

Can we really know if the universe has an outside shape?

Can you really assure me that QFT is consistent, and not trickery math?

Anyway,we cannot prove either its consistency or its completeness, well if it includes Number theory as a subset of the mathematical theory of physical reality, then by Godel's theorem it's indeed incomplete.
I really need to find time to reread Smullyan's book on Godel's theorems.

 

[Demystifier]

Hello,

How is it perceived the "Mathematical universe hypothesis" from Max Tegmark, in the scientific community ?

Thank
Patrick

I think nobody really thinks that this hypothesis is true. Well, perhaps only Tegmark, but I suspect that not even him believes it.

 

[marcus]

Hello,
How is it perceived the "Mathematical universe hypothesis" from Max Tegmark, in the scientific community ?

Thank
Patrick

I think nobody really thinks that this hypothesis is true. Well, perhaps only Tegmark, but I suspect that not even him believes it.

Well put. I agree. Here's Hossenfelder's classic comment on it:
http://backreaction.blogspot.com/2007/09/imaginary-part.html

 

[microsansfil]

If you assert that everything mathematical is physical, then you run up against Godel's Incompleteness theorem, and physics becomes incomplete or inconsistent.

In other ontologically view point this would not be the case ? we can reach isomorphism between model and "realty" ?

Patrick

 

[microsansfil]

Friend, why should we consider it to be complete and consistent?

Maybe it's because there are two theorem of Gödel's incompleteness theorems ? This theorem are syntactic not semantic


Patrick

 

[friend]

Friend, why should we consider it to be complete and consistent?
...

Nothing exists outside the universe. The universe is by definition all that exists. Therefore, the universe as a whole is complete by definition of the word universe.

Nothing that exists in the universe contradicts anything else that exists in the universe. Therefore it is consistent.

Now all we need is a math that describes this consistency between things that exist.

 

[friend]

In other ontologically view point this would not be the case ? we can reach isomorphism between model and "realty" ?

Patrick

We may already have a model that is isomorphic to reality. Either something exists or is does not, and this can be mapped to true or false. So I believe logic can be seen as isomorphic with reality/existence.

 

[micromass]

Nothing exists outside the universe. The universe is by definition all that exists. Therefore, the universe as a whole is complete by definition of the word universe.

Nothing that exists in the universe contradicts anything else that exists in the universe. Therefore it is consistent.

Now all we need is a math that describes this consistency between things that exist.

You are using definitions of the word complete and consistent that are far removed from their mathematical meaning.

 

[micromass]

Anyway,we cannot prove either its consistency or its completeness, well if it includes Number theory as a subset of the mathematical theory of physical reality, then by Godel's theorem it's indeed incomplete.

Indeed, I see no reason at all to accept that Number Theory would be included in reality.

 

[microsansfil]

Well put. I agree. Here's Hossenfelder's classic comment on it:
http://backreaction.blogspot.com/2007/09/imaginary-part.html

Without language we can't build concept.

Galileos `Book of Nature : “ The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word."

Nevertheless I agree, map isn't the territory, even if the language concerned the map but the territory isn't the map. This is not a pipe.

Patrick

 

[friend]

You are using definitions of the word complete and consistent that are far removed from their mathematical meaning.

I'm not so sure. Complete and consistent have to do with axioms of a system being consistent and everything in the system being described by those axioms. That means all the axioms exist in logical conjunction with each other in that system, and no outside axioms are needed to proved anything about that system.

How is the validity of using the terms completeness and consistency undermined if I choose to use the word proposition instead of axiom? Certainly an axiom is also a type of proposition. Then the system consists of only those propositions in that system, and those propositions exist in conjunction so each of them materially implies any other? As I recall, propositional logic has been proved to be "complete and consistent". If this is valid language, then all one has to do is replace the word proposition with the word fact of reality so that reality is seen as complete and consistent.

 

[MathematicalPhysicist]

Indeed, I see no reason at all to accept that Number Theory would be included in reality.

Im not sure if you understood me well enough. In one of godels incompletness. It says that if our mathematical theory includes as a substheory robinson's weak arithmetics then this theory is incomplete. Now i don't see any reason to believe that the mathematical framework for physics doesn't include number theory and thus it should be incomplete. As for consisteny of this framework,well we cannot prove a consistency of mathematical theory within that theory. You need a meta theory that will tell you this, and then youll need another meta-meta ad infinitum.

 

[friend]

As I recall, propositional logic has been proved to be "complete and consistent". If this is valid language, then all one has to do is replace the word proposition with the word fact of reality so that reality is seen as complete and consistent.

Certainly we can say that the universe consists of all the facts in it, however you want to label them. But what is making them remain "consistent" with each other? Is the logic that holds them together part of that system? Or is that logic something other than the facts themselves?

 

[John G]

Im not sure if you understood me well enough. In one of godels incompletness. It says that if our mathematical theory includes as a substheory robinson's weak arithmetics then this theory is incomplete. Now i don't see any reason to believe that the mathematical framework for physics doesn't include number theory and thus it should be incomplete. As for consisteny of this framework,well we cannot prove a consistency of mathematical theory within that theory. You need a meta theory that will tell you this, and then youll need another meta-meta ad infinitum.

Via Gödel, a physics theory of course could still be a true theory that does correspond to the natural numbers even if you can't prove it.

 

[MathematicalPhysicist]

Via Gödel, a physics theory of course could still be a true theory that does correspond to the natural numbers even if you can't prove it.

Well first thing first, we have two theorems, one that states that a strong theory which includes number theory as a subtheory cannot prove its own consistency and the other theorem is that such a strong theory cannot be both consistent and complete.

You mean that they are true statements in the theory that aren't provable in that theory, well, then yes I agree, it does follow from Godel.

But then again we talked about completeness and consistency of a mathematical theory. (where the physical theory is modeled by sutiable mathematical theory which describes the observables).

 

[ftr]

I don't understand what Godel or any mathematical philosophy has anything to do with MUH. We are doing physics just fine with mathematics. The only issue is to find a theory that naturally computes the experimental inputs. That would be sufficient to declare reality being only mathematics. The truth of mathematic and the truth of reality correspond, no other truth exist.

 

[MathematicalPhysicist]

How do you know that there is no other truth? you have some background beliefs which are either believed without regrett as in faith or you are skeptical of.

 

[ftr]

How do you know that there is no other truth? you have some background beliefs which are either believed without regrett as in faith or you are skeptical of.

No, it is not based on faith it is based on 1000 years of doing science. Many phycisits conjectured such possibility based on evidence. We don't know any other truth in the same way we do science, we have no evidence for it.

 

[MathematicalPhysicist]

You do believe in stuff like causality, cause and effect etc; Just you probably aren't aware of it.

 

[John G]

Obviously something very different could happen at/above the Planck scale (where quantum field theory and relativity break down). Also something very different could happen if you add consciousness into your theory. I personally think math can still handle the Planck scale and consciousness but obviously you get quite far from where experiments can check things.

Future effects past causality can come via things like string theory wormholes or conformal gravity and I do think this occurs even at energy levels well below the Planck scale. Leads to block universe-like ideas.

 

[MathematicalPhysicist]

Well, i guess i have plenty of maths and physics to study.

 

[ftr]

You do believe in stuff like causality, cause and effect etc; Just you probably aren't aware of it.

The theory has to be consistent, logical and explains observation without experimental input, that is what is required. consistent in mathematical sense as well as conceptually as in unifying the picture of particles, forces, space, time in the whole energy spectrum without the sector problem. It should explain nonlocality. All in non ambigeous system. Causality, cause and effect status would naturally emerge from such theory. But I am not sure how your question is an objection to MUH.

 

[ftr]

Obviously something very different could happen at/above the Planck scale (where quantum field theory and relativity break down). Also something very different could happen if you add consciousness into your theory. I personally think math can still handle the Planck scale and consciousness but obviously you get quite far from where experiments can check things.

Future effects past causality can come via things like string theory wormholes or conformal gravity and I do think this occurs even at energy levels well below the Planck scale. Leads to block universe-like ideas.

We don't have to rap a string around Earth to know it is round we can check for only important facts that sufficiently confirms our theory.

 

[MathematicalPhysicist]

The theory has to be consistent, logical and explains observation without experimental input, that is what is required. consistent in mathematical sense as well as conceptually as in unifying the picture of particles, forces, space, time in the whole energy spectrum without the sector problem. It should explain nonlocality. All in non ambigeous system. Causality, cause and effect status would naturally emerge from such theory. But I am not sure how your question is an objection to MUH.

You said in your post that:"No, it is not based on faith it is based on 1000 years of doing science. Many phycisits conjectured such possibility based on evidence."

But surely the way you interpret your evidence depends on what do you believe, in QM we have endless interpratations for it. So my response was that it depends on your system of beliefs, in the era of Boltzmann's he was in the minority of people who believed that matter is constitued by corpsucles entities; if you heard of David Deustch's fantastic interview at the Edge website concerning his constructor theory then as he said there, physicists found some obstacles with the some physical theory which made them conjectured the existence of a new particle (such as the neutrino), they decided not to abandon the metaphysical law that was seem to be disobeyed there, but to conjecture a new particle.

But that's really depends on our interpratation, we could have also decided to change our metaphysical laws, to new ones, and still have a consistent physical theory.

I wish David would join our discussion.

 

[nikkkom]

Hello,

How is it perceived the "Mathematical universe hypothesis" from Max Tegmark, in the scientific community?

I bet you can find all kinds of opinions on it among scientists.

My own opinion is that since it is not falsifiable, it is not a "scientific theory" in a sense that it has no predictive power.

 

[microsansfil]

Hi nikkom,

My own opinion is that since it is not falsifiable, it is not a "scientific theory" in a sense that it has no predictive power.

I don't think that Max Tegmark claims to speak about a falsifiable scientific theory. It is his interpretation of his understanding of "scientific theory".

For Galilée "The Nature is a book written in mathematical language."
For Max Tegmark "The Nature IS (in itself) a mathematical structure"

Patrick

 

[ftr]

I bet you can find all kinds of opinions on it among scientists.

My own opinion is that since it is not falsifiable, it is not a "scientific theory" in a sense that it has no predictive power.

While it is true that Tegmark does not have the proof yet, however, it is clear(at least to me) that an ultimate TOE should be purely a reality which is designed with mathematics only. The theory should have everything calculable. FQXI has started a new contest around the concept, so I am sure you will hear many opinions that may change your mind.

 

[nikkkom]

Basically, it revolves around a question of what word "exists" really means.

For example, there exist solutions for the differential equation u'' = -u with two initial conditions u(0)=0 and u'(0)=0. They all have the form u(x) = a*sin(x)+b*cos(x).

If we'd take that equation and conditions as "laws of nature" of some universe, then each of these functions fully describe a possible universe under that law.

Every mathematician would agree that these solutions exist. So, these "universes" all "exist", in some sense of this word.

Maybe there are much more complex equations which perfectly describe laws of nature of our Universe, but by being just a set of equations, they have a multitude of valid solutions, and every of those solutions "exists" in mathematical sense of this word. One of them describes our Universe, other describe other possible Universes under the same laws of nature.

Maybe it's really so. This is all cool to think about, but it does not bring any new _predictions_ (the "universes" that "exist" in the above sense can't interact). It's not hard science theory. It's philosophy. I'm not a big fan of philosophy. As an old joke goes, philosophers, unlike mathematicians, do not need erasers.