LHC - the last chance for all theories of everything?

[tom.stoer]

... you have made the most beautiful statement so far in this discussion

“You can turn it the other way round and state that mathematics exists w/o any physical existence”

But if that is true, how this mathematical existence does manifest itself? It can not hang in thin of nothing and exist. Well then, I don’t need to repeat how its existence is manifested

It can. Or better: it need not manifest itself.

Let's make some simple examples:
Assume the twin prime conjecture is false; then there is a largest twin prime. Does this number EXIST even before anybody KNOWS its value?
Before the discovery of quantum mechanics and the work of Hilbert: Do you think that Hilbert spaces already existed 200 years ago?
Continuum hypothesis: as we now know both its proof and its disproof are impossible in ZFC. So there is the possibility that there exists sets S with cardinality |N| < |S| < |R|. Do you think that such a set EXISTS even if there is no construction?

I would say that modern mathematics provides some strong hints that its entities, theorems and other contents may exist w/o any physical manifestation. For me mathematics exists w/o physical representation (brain, paper, computer, ..., universe in the sense of MUH). But again: this is my belief and there's neither a proof nor a disproof.

 

[Dmitry67]

What if indirect arguments for MUH are true, say,

When TOE is discovered, it will be possible to write it without any word "baggage" and derive everything else from scratch;
Initial conditions are null

Would it help you to believe in MUH?

 

[tom.stoer]

It depends on the structure of that ToE.

If it is a "unique" framework containing axioms, theorems or something like that which indicate what I used to call "selection principle" then I would believe in the ToE but NOT in MUH.

If the ToE is a framework for producing theories together with a hint (I do not know how it can look like) that at least our universe (plus some others) can be derived, then I would start to believe in the existence of these other universes.

If the ToE is only the meta-framework and a statement that all consistent mathematical frameworks are physically existent "somewhere", then I would say (because the selection principle or hint is missing) the ToE (which is identical to MUH) is meaningless or empty and I would call it ToN.

=> I cannot answer your question unless I have an indication how that ToE would look like.

 

[friend]

Correct me if I'm wrong, but it seems all mathematical formulae are hypotheticals,... meaning, IF you have some input, THEN you have some output. And so mathematical descriptions apply just as easily to fictitious situations as to real situations. You can just as easily calculate the trajectory of unicorns as to cannon balls. Math makes no distinction between fact and fiction.

 

[Dmitry67]

IF you have some input, THEN you have some output. And so mathematical descriptions apply just as easily to fictitious situations as to real situations. You can just as easily calculate the trajectory of unicorns as to cannon balls. Math makes no distinction between fact and fiction.

No, no, and no!
friend, what input is used to develop a theory of natural numbers? If it uses some input then you probably can provide another theory of natural numbers, where number 19 is not prime?

your unicorns vs cannon balls is just a variation of an argument about the initial conditions I answered before.

 

[friend]

No, no, and no!
friend, what input is used to develop a theory of natural numbers? If it uses some input then you probably can provide another theory of natural numbers, where number 19 is not prime?

your unicorns vs cannon balls is just a variation of an argument about the initial conditions I answered before.

Dude, do you honestly think you're going to find a theory that tells you the position and momentum of every particle in the universe, even those behind the cosmological event horizon? Are we going to find a ToE that predicts the human form with the right number of fingers, toes, eyes, and even my individual hair color? Will it predict all of human history? I seriously doubt that. I think the best to be expected is to determine generalities that describe what kinds of things are possible. And by definition generalities give you results based on input that is not determined by that generality. It's even worse, we'll probably only get at best a range of probable outcomes given an input. That doesn't sound isomorphic to a reality which definitely IS.

 

[Dmitry67]

friend, are you aware how MWI deals with these issues? multihistory theories can be deterministic but look random for all observers

 

[friend]

friend, are you aware how MWI deals with these issues? multihistory theories can be deterministic but look random for all observers

I think the MWI is nonsense. If some other possible universe does not have any affect on us, then it does not exist as far as we are concerned.

This MWI came about to explain the alternative paths in Feynman's path integral. But the formulation predicts that it takes ALL possible paths to make a reality. That means none of them exist apart from each other.

 

[Dmitry67]

Yes, all these branches exist. Looks like your argument is just an emotional one, because you are aware that MWI is consistent with the observations.

So I will reply you on the emotional level. Do you see how elegant MWI is? Look at a list of QM interpretations asking a question about the initial conditions.

In our world symmetry is broken many times. Random interpretations (CI, TI) do not have any problems with it, they can start from null initial conditions, but they are hated for being non-deterministic.

Deterministic interpretations (BM) look weird because they mean that I, typing this text, was pre-coded in the positions of the particles in the Big bang.

MWI is *the only* deterministic theory which can start from the null initial conditions (and multihistory is the price you have to pay for they wonderful combination)

 

[qsa]

The universe is something we observe or measure. Mathematics is something we calculate. The mathematics would be a kind of language or description of the universe. And no equation we could write would account for every single particle or field at any time. We use math to figure out different configurations or general features that we are interested in. Math only tells us that given some input some output results. It doesn't tell us that a given input IS the case.

thanks

It can. Or better: it need not manifest itself.

Let's make some simple examples:
Assume the twin prime conjecture is false; then there is a largest twin prime. Does this number EXIST even before anybody KNOWS its value?
Before the discovery of quantum mechanics and the work of Hilbert: Do you think that Hilbert spaces already existed 200 years ago?
Continuum hypothesis: as we now know both its proof and its disproof are impossible in ZFC. So there is the possibility that there exists sets S with cardinality |N| < |S| < |R|. Do you think that such a set EXISTS even if there is no construction?

I would say that modern mathematics provides some strong hints that its entities, theorems and other contents may exist w/o any physical manifestation. For me mathematics exists w/o physical representation (brain, paper, computer, ..., universe in the sense of MUH). But again: this is my belief and there's neither a proof nor a disproof.

Tom, I can debate about the nature of math and what it means when and where, but I have a more usefull comment

Tom, if you say that math can exist without physical, but physical is there and we find math in it (even worse, it is the only language that describes it). Doesn’t that strike you as odd coincident? Einstein put it in this way “the only thing that is incomprehensible about reality it is that it’s comprehensible” .What I mean is that math could have existed without physical but it had to appear with physical, and then describe physical, hmm.

 

[tom.stoer]

I don't think it's coincidence.

I agree to some statements in this thread that reality must follow some basic rules of logic (perhaps more complex than classical logic, e.g. due to quantum mechanics).

I would say that if nature represents some rules of logic this implies that it must represent all fields of mathematics that emerge from logic. As logic (+ set theory) leads automatically to natural numbers, it is not too strange that we find natural numbers in physics

I do not know why nature has chosen to exist in some other (more complex) representations of certain fields of mathematics. Classically nature represents (in addition to natural numbers) certain manifolds etc. Quantum mechanically it represents Hilbert spaces. I do not know why Hilbert spaces and not some more general Banach spaces - or something totally different.

Perhaps these more complex structures are a hint that we must focus on the derivation of the complex physical structures from more simple ones; that would mean that nature encodes or represents something like the emergence of mathematical frameworks in certain limits, but that the basic laws are quite "simple".

In that sense some ideas of modern physics are definately going into the wrong direction. Strings are certainly not the building blocks as their fundamental laws seem to be quite complex (nobody knows them today). Loops are closer to this idea, but still too complex (the simplest framework seems to be a certain spin foam model, but still this requires complex reasoning). I am not an expert but causal sets could be a step into the right direction.

In the very beginning I said that MUH seems to be quite strange because it replaces the quest for a fundamental matehmatical principle with the statement that there is no such principle ("all mathematical frameworks do exist"). I guess that there must be a basic principle, a selection rule or something which - together with a rather simple mathematical framework - allows nature (description of nature) to emerge from these fundamental entities. This principle would be a physical principle in the sense that it appears as a mathematical axiom = something w/o proof = something you have to believe in.

I know thta this idea does not mean that you can get rid of all human baggage as we called it. In addition it does not explain why nature respects logic (or logic plus some entities, principles, ...). It does not explain why "this principle" and not "that one".

But I see this as a rather modest step towards a "ToE".

 

[Dmitry67]

I guess that there must be a basic principle, a selection rule or something which - together with a rather simple mathematical framework - allows nature (description of nature) to emerge from these fundamental entities. This principle would be a physical principle in the sense that it appears as a mathematical axiom = something w/o proof = something you have to believe in.

tom, can you imagine a different universe where intelligent observerse can evolve?

By the different universe I mean universe with different laws: say, 4 generations of quarks, or even more dramatic differences, like, more macroscopic dimensions, absolutely different laws?

I know that MOST of physical laws provide 'bad' universes. This is called a fine tuning problem. So 'good' universes are VERY RARE. But are you saying that our universe IS THE ONLY POSSIBLE ONE (mathematically) where intelligent observers can evolve?

P.S. I know you distingusih "EXISTS" and "CAN EXIST". My question is not about if alternative 'good' unvierses EXIST, but if you agree that they CAN EXIST.

 

[tom.stoer]

That again depends on the ToE and its ontological interpretation.

If the ToE provides a rather restrictive framework which e.g. fixes the charges, coupling constants and generations, then I would say that only our universe EXISTS.

If the ToE provides a less restrictive framework than we can still speculate that different universes CAN EXIST w/o the ability to prove or disprove if they REALLY EXIST.

If the ToE provides a hint how a multiverse with evolving or somehow different laws in different universes could look like and how these different universes can be spawned from the multiverse, then I am willing to accept that these universes DO EXIST. This spawning must happen in our universe, i.e. it should have (at least in principe) physical effects; if it takes place "outside" the universe = w/o any feedback I would still say these additional universes CAN EXIST.

But we are coming back to the discussion we had several weeks ago: I think that physically the lack of a fundamental principle (selection, uniqueness, ...) is a weakness, whereas in your opinion its a strength. Btw. - and to avoid a discussion regarding Ockham's razor: our positions are not differing regarding the number of principles we have, they are only differing regarding the type of principle:

My yet to be discovered PHYSICAL principle will select a ToE and therefore a (class of) EXISTING universe(s) from all possible mathematical frameworks.
Your ONTOLOGICAL principle says that everything which can be cast into a baggage-free mathematical framework DOES EXIST in reality.

Therefore we do not so much differ in the application of Ockhams razor but in the very nature of the principle itself.

 

[Dmitry67]

Yes, I was trying to avoid discussion about the EXISTS/VS CAN EXIST, but you replied on that. And I wanted to talk about the mysterious "selection principle"

Ok, my turn anyway.
Imagine that neutron decays instantly. It would be fatal for stars and life. It is an example of HARD selection princliple, some kind of no-go for lide. HARD selection principles limits the conditions and universes where the life can evolve. We both agree that such principles do exist

But I was asking if OTHER universes where life is possible can (mathematically) exist.

To be consistent, you have a choice:

1) You can say: NO, only OUR Universe favours life, in all possible axiomatic systems which define laws one can in principle imagine life can not evolve!
So saying 1 you can claim that the selection principle is a HARD one. Even I see that option as very unlikely this is verifiable, as the principle is HARD.

2) If you don't claim that, then you agree that some can invent a mathematical framework where some other intelligent beings can exist. Say, universe with intelligent snakes, built from Singularium - an element which consists of 23 arba and 17 kadabras. Now the question is, how any selection principle can favour US versus intelligent snakes?

Lets call that selection principle a 'SOFT' one because it does not exclude all possible unverses except the only one (ours), it just says that ours is better

What option do you chose? HARD or SOFT? If SOFT, then why our universe is better? Can soft principle be something better then 'God hates snakes and preferes ebings with 2 hands built from Carbon'?

 

[friend]

...I guess that there must be a basic principle, a selection rule or something which - together with a rather simple mathematical framework - allows nature (description of nature) to emerge from these fundamental entities. This principle would be a physical principle in the sense that it appears as a mathematical axiom = something w/o proof = something you have to believe in.

I know thta this idea does not mean that you can get rid of all human baggage as we called it. In addition it does not explain why nature respects logic (or logic plus some entities, principles, ...). It does not explain why "this principle" and not "that one".

Could it be that the physical principle that selects which logic physics can be derived from is this: a logical conjunction of facts. In other words, whatever there might be, if physical facts exist, then they must co-exist together, not one contradicts any other. They exist in conjucntion. That sounds like a physical requirement imposed on whatever logic determines reality. Or is there other kinds of math that require a set of elements which exist in conjunction?

 

[Fra]

I have a feeling that I have made my position clear enough already but...

Could it be that the physical principle that selects which logic physics can be derived from is this: a logical conjunction of facts. In other words, whatever there might be, if physical facts exist, then they must co-exist together, not one contradicts any other. They exist in conjucntion. That sounds like a physical requirement imposed on whatever logic determines reality. Or is there other kinds of math that require a set of elements which exist in conjunction?

It sounds almost like a physical version of Hilbert's vision?

Gödel should suggest that you can't be both complete and consistent, suggesting something is wrong with your vision?

Unless, you consider (like I do) that that selection of logic, and the inferences of laws are themselves processes that are one-2-one with physical processes that do occur in nature, at non-human generic system level.

This way, the problem is not how to find a complete set of consistent axioms, but rather to describe how a set of axioms actually are constrained to EVOLVE, BECAUSE of the fact that it's either inconsistent or incomplete, or both.

This is how I see it. If I am to project my thinking onto what you guys are doing, I would say that I am looking not for an axiom system, but to understand how and why certain axiom systems are selected, and how they rationally respond to inconsistencies and evolve into others.

I ponder question like, how to make sense out of a conjuction of two inconsistent facts, in a way that the end result is again in some sense "consistent".

If you see this in what I think is the wrong way then it makes no sense. A conjuction of two inconsistent things simply result in a halt.

However, if you look at a inductive inference model, then it can be that the prior and the new evidence really signal different things. The result is a rational revision which results in a new posterior.

Let me take another intuitive example, if a human makes inferences that repeatadly proves to be at variance with observations, then any rational human would start to doubt his own inferences, and revise the inference system itself.

There are different kinds of "logic". Why does the deductive and axiomatic type of hard logic seem so obvious and unique? For me, the crispness and apparent decidability of that logic is easily deceptive; something of which Gödel's theorem gives some good hints. I think Tom already considered this problem - the question is; what is the resolution?

More general inference systems such as inductive and fuzzy logic are IMO more powerful, and renders the deductive logic as a special case of more general forms of logic.

I think you are stuck in insisting on a particular form of reasoning. I can't see another way out of there but to start to see that "logic" is not necesarily unique. I think that's a deception :)

/Fredrik

 

[friend]

I think you are stuck in insisting on a particular form of reasoning. I can't see another way out of there but to start to see that "logic" is not necesarily unique. I think that's a deception :)

/Fredrik

I don't think it is a tenable premise to start by assuming there is no system of logic or reason that you can trust in. I don't see how any results can be derived from that. You seem to be suggesting that science advances by proving contradictions in our logic. Honestly, I think you're going to drive yourself crazy if you keep asserting that there is no reasoning process that can be trusted. (And I mean "you" in the general sense of anybody)

 

[Fra]

Honestly, I think you're going to drive yourself crazy if you keep asserting that there is no reasoning process that can be trusted.

First of all I'm willing to take that risk :) Second, what I suggest about evolving logic system doesn't mean there is nothing to trust at all, it just says there is no 100% trust. But you do not need 100% confidence to play this game of life, neither do I think nature needs.

As you see, even in my strange reasoning there IS a kind of logic right? It's just that it's DIFFERENT from yours. So I do not really say there is "no logic", I just doubt your version; the hard deductive logic as the only one.

/Fredrik

 

[moniker2]

tom, can you imagine a different universe where intelligent observerse can evolve?

By the different universe I mean universe with different laws: say, 4 generations of quarks, or even more dramatic differences, like, more macroscopic dimensions, absolutely different laws?

I know that MOST of physical laws provide 'bad' universes. This is called a fine tuning problem. So 'good' universes are VERY RARE. But are you saying that our universe IS THE ONLY POSSIBLE ONE (mathematically) where intelligent observers can evolve?

P.S. I know you distingusih "EXISTS" and "CAN EXIST". My question is not about if alternative 'good' unvierses EXIST, but if you agree that they CAN EXIST.

in a single worldline why can't you have a model of initial frames?
and if they can, why wouldn't they bunch together?

 

[Dmitry67]

sorry, I don't understand if it is YES or NO :)