Isn't a Cosmos Made from Nothing Self-Consistent?

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If the universe is mathematically based - which it looks increasingly like it is the case - than it would be self consistent to view what we believe are physical objects as actually made from a mathematical structure rather than 'indivisible matter'. That would apply to space itself.
Then the whole structure does not need any physical space to exist at all, because AFAIK mathematics does not require a spatial dimension in order to exist.
 

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  • #2
marcus
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If the universe is mathematically based - which it looks increasingly like it is the case - than it would be self consistent to view what we believe are physical objects as actually made from a mathematical structure rather than 'indivisible matter'. That would apply to space itself.
Then the whole structure does not need any physical space to exist at all, because AFAIK mathematics does not require a spatial dimension in order to exist.
I suspect you may be confused, wawenspop. I will try to help you.

The universe is not based on mathematics any more than it is based on the English language.

Mathematics, like English, is a naturally evolving human language. Its vocab and grammar rules change from century to century primarily by a process of natural selection governed by a self-defining semi-aristocratic community: the mathematicians. Ultimately they decide what problems are interesting and what concepts are most effective in dealing with them. Which symbols/ideas win out and are imitated.

The natural selection process in the mathematical physics branch involves comparing math models with experimental data and astrophysical observation. Ideas win out, gain prestige, are imitated etc if they work well to describe and predict, in the judgement of the community of physicists. They decide what works and what gets discarded.

There is no immutable essence you can say is "mathematics". What will be regarded as mathematics will be different in year 2100 and in year 2200. You cannot say what mathematics will be in year 2200. It is a pragmatic human artifact, like English. You cannot predict the future evolution of the English language either.

You could also say that English "does not require any spatial dimension to exist". And English can also be used to describe the universe (not very well, it is not as highly evolved as the math models).

Are you going to claim that "what we believe are physical objects as actually made from English sentences, i.e. from an English structure?"

There is a modern fad to attribute physical reality to any and all fantasies which can be described by currently popular mathematics. "M-theory describes 1000 different universes, therefore those 1000 universes must physically exist!" :biggrin: In 100 or 200 years M-theory may be completely forgotten as a math project, what will have happened to those 1000 "real" universes?

If you are the Pop of Wawen, you might encourage Wawen to think about something more sensible. :biggrin: Just my two cents. I may be in the minority on this issue.
 
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  • #3
qsa
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If the universe is mathematically based - which it looks increasingly like it is the case - than it would be self consistent to view what we believe are physical objects as actually made from a mathematical structure rather than 'indivisible matter'. That would apply to space itself.
Then the whole structure does not need any physical space to exist at all, because AFAIK mathematics does not require a spatial dimension in order to exist.
Are you familiar with the MUH Of DR. Tegmark.google
 
  • #4
marcus
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Here's Bee Hossenfelder's comment on Tegmark's Math Universe Hyp.
http://backreaction.blogspot.com/2007/09/imaginary-part.html
when Tegmark proposed it in 2007.

I haven't seen any serious followup. but the idea sure is floating around in the air :biggrin:

Tegmark also promoted some fashionable "multiverse" ideas in around 2006, with a Scientific american article.

Meanwhile some people keep on trying to pragmatically model and understand the real universe that we have, with models that can be observationally and experimentally tested.

Bee Hossenfelder works with that sort of people. Last year she organized and hosted an international conference on the Experimental Search for Quantum Gravity, at the institute in Stockholm where she works.

Strongly contrasting intellectual styles.
 
  • #5
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If the universe is mathematically based - which it looks increasingly like it is the case - than it would be self consistent to view what we believe are physical objects as actually made from a mathematical structure rather than 'indivisible matter'. That would apply to space itself.
Then the whole structure does not need any physical space to exist at all, because AFAIK mathematics does not require a spatial dimension in order to exist.
If we are part of that mathematical structure, then we would "perceive" our place in it as space and time.
 
  • #6
Chalnoth
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I suspect you may be confused, wawenspop. I will try to help you.

The universe is not based on mathematics any more than it is based on the English language.
I would disagree with that pretty strongly. There is a crucial difference between mathematics and natural language: mathematics is a set of structures which follow definite rules and never break them, while natural languages are cobbled together structures that often break what few rules they have.

Furthermore, we have to separate between the underlying mathematical structure and a representation of said structure. For instance, the typical representation of basic arithmetic makes use of the notions of addition, subtraction, multiplication, and division using a specific set of symbols. But this same mathematical structure could potentially be represented in any number of other possible ways. That representation is more analogous to the English language, in that it is arbitrary and human-specific. But the underlying structure could well be the basis for some sort of universe.

But I would have to say that whatever mathematical structure describes the nature of our universe must also describe our space-time within the same formalism that it describes matter. It would be nonsense to even have the word "exist" if you don't say this space-time exists.
 
  • #7
qsa
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Here's Bee Hossenfelder's comment on Tegmark's Math Universe Hyp.
http://backreaction.blogspot.com/2007/09/imaginary-part.html
when Tegmark proposed it in 2007.

I haven't seen any serious followup. but the idea sure is floating around in the air :biggrin:

Tegmark also promoted some fashionable "multiverse" ideas in around 2006, with a Scientific american article.

Meanwhile some people keep on trying to pragmatically model and understand the real universe that we have, with models that can be observationally and experimentally tested.

Bee Hossenfelder works with that sort of people. Last year she organized and hosted an international conference on the Experimental Search for Quantum Gravity, at the institute in Stockholm where she works.

Strongly contrasting intellectual styles.
I am well aware of all of that. Yes, there haven't been a serious followup, but I conjecture that there will be one soon:surprised. A fundamental theory should not have any experimental input or guessed parameters, it should do the opposite, validate experiments output.


What is the thing that all people can accept as true more than anything else? It is the only thing that exists on its own, no need to be justified. No conceivable entity can exist beside it, try as hard as you like, you could not believe it even if you wanted to.
 
  • #8
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Regarding the English language. What is it? Is it an object of the universe?
The English language has zero mass and zero spatial size. It is 0 inches big and has a mass of 0 grammes.
Same for beauty, knowledge, and thinking.
They are non spatial entities that rely on interpretation of states. At its lowest level 2 quantum states. At a higher abstraction writing or DVDs even.
 
  • #9
Chalnoth
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I am well aware of all of that. Yes, there haven't been a serious followup, but I conjecture that there will be one soon:surprised.
Don't hold your breath. This has been the dream of theoretical physicists pretty much since the beginning of physics. It has proved to be quite elusive.

A fundamental theory should not have any experimental input or guessed parameters, it should do the opposite, validate experiments output.
That's something that we can't guarantee either. Today we have one candidate fundamental theory: string theory. But there is as yet no indication that there is any way to obtain specific experimental predictions from it.

The best we can hope for, at the moment, is that if we can determine all potential mathematical structures that, in principle, could underly reality, that the correct one would be enough different from the others that it would be possible to distinguish them. But even that is far from certain.
 
  • #10
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Suggest changing Hilbert space / operator style of analysis with numerical solutions.
Computers could then do the donkey work on possible scenarios and tested against experiment. QFT would be better done that way.
 
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  • #11
Chalnoth
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Suggest changing Hilbert space / operator style of analysis with numerical solutions.
Computers could then do the donkey work on possible scenarios and tested against experiment. QFT would be better done that way.
Numerical solutions are always approximate, though.
 
  • #12
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Numerical solutions are always approximate, though.
Yes approximate. But that is ok, we just set the precision to almost what we want.
 
  • #13
Chalnoth
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Yes approximate. But that is ok, we just set the precision to almost what we want.
Huh? No, that won't cut it in this case. The problem is that we need to be sure that our conclusions aren't the artifacts of numerical errors.

But perhaps more to the point, we don't even have a way of classifying mathematical structures in a way that would be required to do this. Simply plugging stuff into a computer won't give us any sort of answer if we don't know how to ask it the right question. And even then, there is no guarantee that the computational requirements would be such that the calculation would finish in our lifetime.
 
  • #14
Chronos
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In other words, Chalnoth, if you are asserting Godel's incompleteness theorem is still in play - I agree. That Godel guy was pretty bright.
 
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  • #15
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In other words, Chalnoth,h if you are asserting Godel's incompleteness theorem is still in play - I agree. That Godel guy was pretty bright.
Godel's theorem is very beautiful but a Universe only needs enough mathematical rules to make it work. It does not need to 'know' all axioms.
It only needs to *use* a limited quite simple set of axioms.
A computer program works in this way.
We do not need to understand all mathematics to make a program run. A computer can only add numbers ultimately.
Its a practicle engineering issue to make a cosmos NOT an 'intelligent' knowledge of all things. Its just not necessary to know all the games numbers can play.
 
  • #16
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If we Tron-like got stuck in a computer game would we be able to work out using intelligence that we were in a program?
The answer is without doubt YES. Its an engineering problem NOT an ultimate knowledge of all numerical axioms that is needed. Look at Jürgen Schmidhuber (1997) work who argued that Gödel's theorems are irrelevant for computable physics

I believe that the way our Universe works is really quite simple. Why not? Must it be unknowable and impossibly obscure? Why? Are we supposed to be 'in awe' of it? Why?

Of course we could not calculate which way every wavefunction peturbation is going to turn out because its too big a computing problem. Why would the Universe need to do that? We could not easily compute which way a computer game would go either- too many changing states.

So, a mathematical universe is self consistent because it makes a Universe from nothing apart from differences between quantum states (spin for example) which is all it needs to create spatial dimensions. A Universe situated in no physical space and 'made' from mathematics is consistent. Even intelligence itself can be considered only a game in numbers and can never escape those numbers. But there is nothing to prevent an intelligence working out what it is. Why should there be?
 
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  • #17
Chalnoth
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We do not need to understand all mathematics to make a program run. A computer can only add numbers ultimately.
Its a practicle engineering issue to make a cosmos NOT an 'intelligent' knowledge of all things. Its just not necessary to know all the games numbers can play.
As I said, computers are not magic. Think, for a moment, about what would be required of such a program:

1. As input, you would need a list of potential axioms that a mathematical structure could have. So far as I am aware, we have no way currently of describing said list.
2. To show whether or not the theory which results from a specific set of actions is valid, you'd then need to go through and show that it is consistent. With some sets of axioms, this step would stop very quickly. But for most any mathematical structure of interest, Goedel's incompleteness theorem guarantees that the computer won't ever stop.

So the problem is we don't know the inputs for the program, and the program could never stop for interesting mathematical structures anyway. So I just don't see this as being possible.
 
  • #18
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Godel's theorem is very beautiful but a Universe only needs enough mathematical rules to make it work. It does not need to 'know' all axioms.
It only needs to *use* a limited quite simple set of axioms.QUOTE]

If the universe only needs to *use* a limited quite simple set of axioms, then that is the complete and entire set of axioms as far as the universe knows. Therefore it does need to 'know' all axioms, as these axioms are what it needs to exist. It doesn't need a knowledge of extraneous axioms that it simply ignores, and thus effectively reduces the number of mathematical rules it requires (as compared to the larger number of extra axioms). Whenever one talks about the universe; as we are part of it and made of the same elements as it, everything we are (including intelligence) is contained in the universe. It is self consistent.
Anway just my opinion.
Thanks
 
  • #19
Chalnoth
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If the universe only needs to *use* a limited quite simple set of axioms, then that is the complete and entire set of axioms as far as the universe knows. Therefore it does need to 'know' all axioms, as these axioms are what it needs to exist. It doesn't need a knowledge of extraneous axioms that it simply ignores, and thus effectively reduces the number of mathematical rules it requires (as compared to the larger number of extra axioms). Whenever one talks about the universe; as we are part of it and made of the same elements as it, everything we are (including intelligence) is contained in the universe. It is self consistent.
Anway just my opinion.
Thanks
I think what we have here is a misuse of language (not on your part). Goedel's theorem doesn't deal with the completeness of the axioms that form a mathematical structure, but instead of the resultant statements that exist within the system. From that perspective, what p764rds must have been talking about wasn't really axioms, but instead just statements within the structure.

And what Goedel's incompleteness theorem states is that if it is possible within the mathematical structure to write down a statement about the structure's own consistency, then either the structure is inconsistent, or there exist statements within it that are true but unprovable within the system.
 
  • #20
qsa
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If we Tron-like got stuck in a computer game would we be able to work out using intelligence that we were in a program?
The answer is without doubt YES. Its an engineering problem NOT an ultimate knowledge of all numerical axioms that is needed. Look at Jürgen Schmidhuber (1997) work who argued that Gödel's theorems are irrelevant for computable physics

I believe that the way our Universe works is really quite simple. Why not? Must it be unknowable and impossibly obscure? Why? Are we supposed to be 'in awe' of it? Why?

Of course we could not calculate which way every wavefunction peturbation is going to turn out because its too big a computing problem. Why would the Universe need to do that? We could not easily compute which way a computer game would go either- too many changing states.

So, a mathematical universe is self consistent because it makes a Universe from nothing apart from differences between quantum states (spin for example) which is all it needs to create spatial dimensions. A Universe situated in no physical space and 'made' from mathematics is consistent. Even intelligence itself can be considered only a game in numbers and can never escape those numbers. But there is nothing to prevent an intelligence working out what it is. Why should there be?
I have send you each a PM explaining the idea in detail.
 

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