LHC - the last chance for all theories of everything?

[tom.stoer]

ConradDJ,

thanks for mentioning Heidegger. I studied Sein und Zeit (I am German therefore I need no translation :-) - but I think I only scratched the surface (which means that even in German it's not easy to understand him :-(.

A final remark before turning back to physics: I admire the fathers of QM not only because they were able to figure out how to calculate atomic spectra etc., but because they were able to initiate a paradigm shift. Perhaps something like this is required today as well (we were happy with the standard model for some decades, therefore we still try to solve physical problems with the toolbox of the standard model ...). Reading Heisenberg or Schrödinger I heave the impression that they were educated and able to understand both - science and philosophy; the latter ability is missing today, at least partially (I do not know were it comes from; I have some ideas but it does not make sense to discuss in this thread).

Unfortunately I did not state my reasoning regarding Goedel carefully enough. Consistency is not the (core) issue, you are right. What I wanted to say is that during this discussion we try to develop a better understanding of what a ToE is and means and what the requirements, restriction etc. should be. I have the feeling that this is like a video game were you can enter the next stage but are immediately confronted with similar tasks, alien space ships etc. It's not really a new quality, is the same task with nastier enemies only. But you are never forced to leave the entire video game and cope with something totally new. So looking for physical theories is quite similar. You start with Newtonian mechanics, then Maxwell theory, then relativity, then quantum mechanics, etc. Even strings, holography etc. are no paradigm shift. If you are happy with this next stage everything is fine. This is like science works, it is successfull (for centuries!) - but we will never be able to leave the video game.

So this is my alternative 2) - we will never manage it; we will enter the next stage and after some decades ask ourselves "why green spacecraft s?" we will complete shooting all green alien spacecraft s, enter the next stage and find - red spacecraft s - ****!

Alternative 1) is to leave the entire game and find something totally different (a new game, all games at once, understand how video games are programmed, programm a video game generator, program a winning strategy generator, ...) Once we are able to specify what this means and how we can escape from the endless "next stage dilemma" the hole platonic world becomes directly visible to us, not only indirectly as in Platon's famous allegory of the cave. But this hole platonic world is rather closed to the idea of the MUH (mathematical universe hypothesis) discussed a couple of days or weeks ago.

99.9% percent of all scientists are working according to the "next stage model" - something we want to overcome - at least here in this thread :-). I do not have any idea how this could work (!) but alternative 1) seems to be as far-reaching as possible - even if I reasoned some time ago that I don't believe in it.

Don't get me wrong - a successful description of evolving physical laws, inference etc. is certainly more than just red spacecraft s. It's comparable to the revolution of quantum physics! So even if we see no hope in succeeding with 1) there is much sense in working on 2)

 

[tom.stoer]

that's funny; I tried to post "s..." and it get's replaced ... works with "f..." as well :-)

 

[RUTA]

Alternative 1) is to leave the entire game and find something totally different (a new game, all games at once, understand how video games are programmed, programm a video game generator, program a winning strategy generator, ...) Once we are able to specify what this means and how we can escape from the endless "next stage dilemma" the hole platonic world becomes directly visible to us, not only indirectly as in Platon's famous allegory of the cave. But this hole platonic world is rather closed to the idea of the MUH (mathematical universe hypothesis) discussed a couple of days or weeks ago.

99.9% percent of all scientists are working according to the "next stage model" - something we want to overcome - at least here in this thread :-). I do not have any idea how this could work (!) but alternative 1) seems to be as far-reaching as possible - even if I reasoned some time ago that I don't believe in it.

We avoid the dilemma of "the next stage model" because we admit a priori that the entire enterprise is one of self-consistency rather than fundamental laws governing the motion of fundamental entities in space as a function of time. Thus, the ultimate expression is not something “at the bottom,” begging for justification from something yet “deeper,” but a mathematical articulation of the self-consistency criterion for the process as a whole. It's a very different way of viewing the game itself, even though it's not a departure from the formalism per se (discrete path integrals a la quantum Regge calculus). Once you view the game differently, you begin to ask different questions of your formalism. Is that what you're talking about? If not, just ignore this post

 

[friend]

We avoid the dilemma of "the next stage model" because we admit a priori that the entire enterprise is one of self-consistency rather than fundamental laws governing the motion of fundamental entities in space as a function of time.
...
but a mathematical articulation of the self-consistency criterion for the process as a whole...

The trouble we encounter is which set of consistent math describes physical properties. It seems we need to start with some physical properties and then try to discover a consistent math that describes it. This is the normal curve fitting techiques that science is acustomed to.

The only alternative is to trust with blind faith in consistency itself and see where it leads us. Then the question is how to translate this logical consistency between all facts into mathematical expressions. That seems like a tall order. I don't think we'd have much faith in such an effort until we could derive some familiar physical principles, like Fyenman's path integral or something. But once we started to get something that looks like physics, it would be hard to accept that it would not derive all of physics. Maybe it's worth a Google search to see if anyone has ever found "Physics derived from logic alone". I wonder if it's on the arXiv yet?

 

[RUTA]

The trouble we encounter is which set of consistent math describes physical properties. It seems we need to start with some physical properties and then try to discover a consistent math that describe it. This is the normal curve fitting techiques that science is acustomed to.

The only alternative is to trust with blind faith in consistency itself and see where it leads us. Then the question is how to translate this logical consistency between all facts into mathematical expressions. That seems like a tall order. I don't think we'd have much faith in such an effort until we could derive some familiar physical principles, like Fyenman's path integral or something. But once we started to get something that looks like physics, it would hard to accept that it would not derive all of physics. Maybe it's worth a Google search to see if anyone has ever found "Physics derived from logic alone". I wonder if it's on the arXiv yet?

The self-consistency criterion (SCC) we propose is nothing so grand. Our SCC is just the discrete counterpart to the boundary of a boundary principle as used to construct the action for the transition amplitude. The form of the SCC survives the statistical limit and is responsible for classical field theory by construction. Roughly, we stick "boundary of a boundary is zero" in the bottom (so that it rules fundamental physics) in such a way that it is guaranteed to come out on top (survive the statistical limit and rule classical physics). Thus, on our view, the entire process of physics is one of self-consistency in this very specific (mathematically articulated) sense. See arXiv 0908.4348 for details. We shouldn't discuss this further here, but I would appreciate any comments, just send them to me directly via my PF profile.

 

[tom.stoer]

I still do not understand the role of (self) consistency.

Let's assume a ToE is a mathematical framework, that means it consists of
1) basic rules (alphabet, ...) to define expressions
2) definitions, axioms
3) (derived) theorems = proofs according to 1+2)

This framework will (I guess) rich enough to contain at least logic and natural numbers, that means it will certainly have the Peano axoims as a subset. But then we know by Goedels theorem that it is
- either incomplete = not all true theorems are provable (*)
- or inconsistent = all theorems (true and false ones) are provable;
(*) one central theorem which is not provable is the consistency of the framework;
this last sentence has been proved by Goedel.

What does that mean when it is applied to a physical theory?

 

[friend]

This framework will (I guess) rich enough to contain at least logic and natural numbers, that means it will certainly have the Peano axoims as a subset. But then we know by Goedels theorem that it is
- either incomplete = not all true theorems are provable (*)
- or inconsistent = all theorems (true and false ones) are provable;

What does that mean when it is applied to a physical theory?

Physics is not the attempt to prove the completeness of math. No one expects to need every possible math statement to describe physics. In fact we are looking for a minimum set of equations that describe physics. We are looking for the overall, underlying principle from which all of physics is implied. This principle, by definitinon, would have to include all possible facts in the universe so that it would be impossible to find exceptions. This suggests one underlying principle that all facts exist in conjunction, which means every fact is consistent with every other fact in the universe, so that every fact proves every other. The question is can you derive physical law from this principle?

 

[RUTA]

I still do not understand the role of (self) consistency.

Let's assume a ToE is a mathematical framework, that means it consists of
1) basic rules (alphabet, ...) to define expressions
2) definitions, axioms
3) (derived) theorems = proofs according to 1+2)

This framework will (I guess) rich enough to contain at least logic and natural numbers, that means it will certainly have the Peano axoims as a subset. But then we know by Goedels theorem that it is
- either incomplete = not all true theorems are provable (*)
- or inconsistent = all theorems (true and false ones) are provable;
(*) one central theorem which is not provable is the consistency of the framework;
this last sentence has been proved by Goedel.

What does that mean when it is applied to a physical theory?

As friend said, physics isn't responsible for the self consistency of logic and math. The kind of self consistency we habor in physics is much less complicated. Einstein’s equations of general relativity (GR) provide an example. Momentum, force and energy all depend on spatiotemporal measurements (tacit or explicit), so the stress-energy tensor cannot be constructed without tacit or explicit knowledge of the spacetime metric (technically, the stress-energy tensor can be written as the functional derivative of the matter-energy Lagrangian with respect to the metric). But, if one wants a ‘dynamic’ spacetime in the parlance of GR, the spacetime metric must depend on the matter-energy distribution in spacetime. GR solves this dilemma by demanding the stress-energy tensor be ‘consistent’ with the spacetime metric per Einstein’s equations.

 

[tom.stoer]

We avoid the dilemma of "the next stage model" because we admit a priori that the entire enterprise is one of self-consistency rather than ...

The trouble we encounter is which set of consistent math describes physical properties. ...

The only alternative is to trust with blind faith in consistency itself and see where it leads us. ...

Physics is not the attempt to prove the completeness of math.

I only wanted to stress that we cannot trust in consistency of theorems or math systems. Constructing a math system as a candidate-ToE automatically excludes the proof of its consistency.

That's why I am a bit more willing now to think about the idea that the ToE is not one single math system but the collection of all consistent systems.

 

[RUTA]

I only wanted to stress that we cannot trust in consistency of theorems or math systems. Constructing a math system as a candidate-ToE automatically excludes the proof of its consistency.

That's why I am a bit more willing now to think about the idea that the ToE is not one single math system but the collection of all consistent systems.

That may be true for a Theory of Everything. Do you think physics alone can produce such a theory? It seems to be ruled out by virture of the fact that physics is concerned with the objective, not the subjective, so by its very nature any theory of physics cannot explain "everything."

 

[friend]

That's why I am a bit more willing now to think about the idea that the ToE is not one single math system but the collection of all consistent systems.

A collection of consistent systems that are each consistent with every other should be regarded as one consistent system.

so by its very nature any theory of physics cannot explain "everything."

Are you suggesting that there are somethings that cannot be explained, that are illogical and deny all reason itself?

 

[RUTA]

Are you suggesting that there are somethings that cannot be explained, that are illogical and deny all reason itself?

It may be true that some phenomena defy logic, but even if all phenomena are logical, I don't think physics can explain everything. As I argued previously, physics, as a system to explain the objective, cannot explain the subjective. Perhaps, you can appreciate my claim per the hard problem of consciousness.

Suppose we were able to explain all brain activity via physics (neurology and neurochemisty explained via physics). Using this you construct an explanation of what happens in the brain when a person sees the color red. You give this explanation to Alice who has never seen the color red, but she is very bright so she understands the explanation. You then show her something red. Does she have new knowledge after actually seeing red that she didn't possesses prior thereto, even though she had and totally comprehended a complete physical explanation of seeing red? If you answer affirmatively, then you share my belief that physics cannot explain the subjective.

Similarly, Penrose claimed we cannot create a mathematical description of everything because part of everything is the recognition of the truth of a mathematical proof, which is itself beyond mathematics.

 

[tom.stoer]

That may be true for a Theory of Everything. Do you think physics alone can produce such a theory? It seems to be ruled out by virture of the fact that physics is concerned with the objective, not the subjective, so by its very nature any theory of physics cannot explain "everything."

I don't think that physics alone (as it is understood today) is able. The question is what a ToE really IS. If you give me a set of equations and claim that this is the ToE, then what are good reasons for me to believe you?
That the theory makes physically correct predictions? The standard model would do the job!
That it explains some (all) free parameters? OK, let's assume string theory eventually provides a selection principle which essentially predicts U(1)*SU(2)*SU(3) + three generations; Of course my next question would be: why strings?
That it is consistent (whatever that means)? We believe that the standard model plus gravity is somehow inconsistent, but as I said we will never be able (for no complex mathematical framework) toprove its consistency.

What we are talking about is more than a ToE with a set of equations, rules etc. which is (as Marcus said) predictive up to arbitrary high energies. It is a kind of meta-theory that provides in some sense a good reasoning why it is the way it is. And I think it's exactly this question we are not able to answer.

 

[tom.stoer]

A collection of consistent systems that are each consistent with every other should be regarded as one consistent system.

Of course it only makes sense to distinguish between two systems if they are either independet from each other or inconsistent with one another

Is [set theory with continuum hypothesis] and [set theory with the negation of the continuum hypothesis] one system? I do not know if a ToE requires a specific choice for the continuum hypothesis; but if it does, we have to ask what about a different ToE were "somebody" made a different choice.

The continuum hypothesis may be artifical, but homeomorphic, non-diffeomorphic manifolds may very well be physically interesting!

 

[tom.stoer]

... I don't think physics can explain everything.

Similarly, Penrose claimed we cannot create a mathematical description of everything because part of everything is the recognition of the truth of a mathematical proof, which is itself beyond mathematics.

This seems to be very reasonable and indicates that physics is limited in its explanatory ability.

But - isn't it possible to transcend this reasoning? Let's assume that the only requirement for a ToE in a mathematical multiverse is that the ToE must be consistent. Of course one cannot proof consistency of the theory, but one can claim (in a platonic sense) that one specific theory either IS consistent or it is NOT (just like any natural number either IS prime or it is NOT prime, regardless if we already checked it). If we do that we reduce all theories to a subset, namely the consistent theories.

 

[RUTA]

This seems to be very reasonable and indicates that physics is limited in its explanatory ability.

But - isn't it possible to transcend this reasoning? Let's assume that the only requirement for a ToE in a mathematical multiverse is that the ToE must be consistent. Of course one cannot proof consistency of the theory, but one can claim (in a platonic sense) that one specific theory either IS consistent or it is NOT (just like any natural number either IS prime or it is NOT prime, regardless if we already checked it). If we do that we reduce all theories to a subset, namely the consistent theories.

Of course, if what you mean by "everything" is restricted to a small enough domain of discourse, you can get a ToE in any context! I'm a physicist working on the unification of physics, so mine is purely self criticism here. It's ridiculous to think physics is the be-all end-all of knowledge and reason.

 

[BigFairy]

Of course, if what you mean by "everything" is restricted to a small enough domain of discourse, you can get a ToE in any context! I'm a physicist working on the unification of physics, so mine is purely self criticism here. It's ridiculous to think physics is the be-all end-all of knowledge and reason.

Oh? i would beg otherwise..

 

[moniker2]

Of course it only makes sense to distinguish between two systems if they are either independet from each other or inconsistent with one another

Is [set theory with continuum hypothesis] and [set theory with the negation of the continuum hypothesis] one system? I do not know if a ToE requires a specific choice for the continuum hypothesis; but if it does, we have to ask what about a different ToE were "somebody" made a different choice.

The continuum hypothesis may be artifical, but homeomorphic, non-diffeomorphic manifolds may very well be physically interesting!

I have seen something like that before, around two years ago. I posted here and was called a crackpot and banned.

 

[Fra]

FWIW - here is some more fuel on the fire.

About this discussions about deductive systems of inference and consistency and how it relates to physics, I think there are different ways to view the relation between physics and logic, but I'll just trow in these reflections.

From my point of view of physical law, and physical action as pretty much one to one with an inference system, I see some analogies that I can related to, but I think in terms of inductive inference and actions beein constrained by the inference system, and feedback from the environment to change the inference system.

This Gödel stuff is quite different in that it applies to deductive systems of inference, which from my point of view makes no sense in physics for the very reason that I think that if you take the inference seriously, then even the inference system itself must be inferred, which effectively measn that even for the special case of deductive systems, the axioms are not chosen at will, they are the result of an inference process. But not a deductive one.

The consistency I would personally usually make sense of in physics, is just that if we see the laws of physics as a system of inference (whereby initial conditions implies the future) then consistency would normally mean that different observers should arrive at the "same future", or alternatively that different observers making an inference/abduction of laws from experience they would end up with the same laws of physics.

However, for various reasons I do not think that there is any meaning in that because such consistency is not inferrable from the point of view of an inside observer. To me this is largely intuitive, but there are also some other arguments. This is maybe vaguely similar to gödels incompleteness theorem, but still not quite of course.

Anway, Instead, my view is that inconsistencies in the above sense might actually occur, but observation of those inconsistencies is exactly what causes evolution or defomration of the inference system as represented by a physical observer.

So instead of thinking that physics is a system of consistent "inference systems", I personally think of it as systems of *interacting* inference systems, and interaction terms can sort of be traced to partial inconsistencies between the actions/inference systems of the interacting observers.

Because I do not think in terms of deductive inference, but rather inductive inference, the "inconsistencies" are not truly the kind of thing that crashes the logical system, instead the inconsistency produces a "negative" feedback that will decrease the confidence in the inconsisntent inference system, which will instead evolving to something MORE consisntent, but not necessarily perfectly so.

/Fredrik

 

[Fra]

then consistency would normally mean that different observers should arrive at the "same future", or alternatively that different observers making an inference/abduction of laws from experience they would end up with the same laws of physics.

the trick I envison to make sense out of this: Almost needless to say, the futures we are talking about here are not actual futures, it's only the INFERRED future, based on whatever incomplete premises and imperfect inference system at hand, and the only FUNCTION of this inferred future is that it impacts the ACTION of the inference system itsef.

Just like the behaviour of the human, depends on what expectations of the future the brain has; the action is clearly invariant with regards to the ACTUAL future. In reality, the inferece systems itself is update during the evolution; not just jumping from initial to final state.

Thus, in this view I think it's crystal clear that this is not a true contradiction - it is rather the basis for an interaction.

One might ask why can't this defined by the class of "disagreements", is well defined and can be treated like we usually do on physics with gauge symmetries and gauge interactions and thus this transformation IS then the REAL law that is invariant, and thus restores consistency.

I think the problem with this "resolution" is that it isn't realisable, when you acknolwedge that the information required to actuall infere the symmetry, is not localised to ONE observer, it's an entire local population of observers. But this is also why this scheme DOES make sense when you study a confined subsystem; like is the case in particle experiments. but this is not equally obvious when you consider how a particle experiences it's own environment, or how things behave very very far from equilibrium. Such as the big band or other hypotetical scenarios. This scheme is also (IMHO at least) quote doubtful for cosmological thinking.

/Fredrik

 

[ConradDJ]

The question is what a ToE really IS. If you give me a set of equations and claim that this is the ToE, then what are good reasons for me to believe you?
That the theory makes physically correct predictions? The standard model would do the job!

What we are talking about is more than a ToE with a set of equations, rules etc. which is (as Marcus said) predictive up to arbitrary high energies. It is a kind of meta-theory that provides in some sense a good reasoning why it is the way it is. And I think it's exactly this question we are not able to answer.

Physics has never been concerned to answer "why it is the way it is." But I agree it's become important to ask this question now. It's certainly possible that the LHC will uncover phenomena that once again point theorists in a new direction. And it's possible that technical developments in quantum gravity will come up with something that seems compelling. But to me it's amazing how much is known about fundamental physics, and how little we've been able to learn from that vast body of knowledge, about what's going on here.

In biology, the question "why things are the way they are" has a remarkably clear answer, that provides a foundation for the entire field. It's not unreasonable to expect something similar in physics.

My own sense is that whatever's going on in physics is not just mathematical. If we just regard the world as a pattern of given facts, we can try to model it mathematically -- and this has essentially been accomplished, with the Standard Model. We can push on in the direction of Unification... but is there really any deep basis for our belief that the world must be built on a single structure? Once we get beneath the atomic level, is there really any empirical support for this? For every step toward unification, we've opened up new kinds of differences between fundamental structures.

But the thing is, our world is much more than a body of fact. Among other things, it's a system that makes its facts physically meaningful -- i.e. observable and definable in terms of other facts, that are also physically observable and definable.

Mathematical systems seem to work very differently -- they're logical structures built on undefined basic elements / operations. These basic elements are meaningful to us, because we live in a physical world that has analogues to them. But there seem to be very basic features of the physical world that we haven't yet tried to account for in our theoretical models.

 

[tom.stoer]

I have seen something like that before, around two years ago. I posted here and was called a crackpot and banned.

Dear friend,

let's wait and see what will happen to me :-)

btw - a few days ago a got a hint to read the following paper:

http://arxiv.org/abs/gr-qc/0404088
Quantum general relativity and the classification of smooth manifolds
Hendryk Pfeiffer
(Submitted on 21 Apr 2004 (v1), last revised 17 May 2004 (this version, v2))
Abstract: The gauge symmetry of classical general relativity under space-time diffeomorphisms implies that any path integral quantization which can be interpreted as a sum over space-time geometries, gives rise to a formal invariant of smooth manifolds. This is an opportunity to review results on the classification of smooth, piecewise-linear and topological manifolds. It turns out that differential topology distinguishes the space-time dimension d=3+1 from any other lower or higher dimension and relates the sought-after path integral quantization of general relativity in d=3+1 with an open problem in topology, namely to construct non-trivial invariants of smooth manifolds using their piecewise-linear structure. In any dimension d<=5+1, the classification results provide us with triangulations of space-time which are not merely approximations nor introduce any physical cut-off, but which rather capture the full information about smooth manifolds up to diffeomorphism. Conditions on refinements of these triangulations reveal what replaces block-spin renormalization group transformations in theories with dynamical geometry. The classification results finally suggest that it is space-time dimension rather than absence of gravitons that renders pure gravity in d=2+1 a `topological' theory.

Tom
(on behalf of all crackpots)

 

[MTd2]

Hey Tom, I didn't you also liked exotic smoothness. Right?

 

[tom.stoer]

FWIW - here is some more fuel on the fire.

... the "inconsistencies" are not truly the kind of thing that crashes the logical system, instead the inconsistency produces a "negative" feedback that will decrease the confidence in the inconsisntent inference system, which will instead evolving to something MORE consisntent, but not necessarily perfectly so.

Honestly speaking I expected something like that!

I came to the conclusion that insisting on inference and at the same time relying on axiomatic methods would cause big trouble for you approach. It would rely on consistency w/o being able to prove or disprove it. Every question for consistency or completeness would force you to enter the next stage where you eventually face the same kind of problems.

So it seems like a clearance to change the perspective and let the hole thing become subject to evolution w/o ever referring to "something" fixed. I was thinking about consistency being the only selection criterion, but I couldn't make sense out of it because in any axiomatic approach inconsistency is not something you can deal with - you must simply throw it away.

I still see problems with that approach:
1) I still have the feeling that there is "something" in your approach that is NOT subject to evolution and that is NOT immune regarding the following argument:
2) I think that you can change perspective again and map your approach into a kind of axiomatic system or a member of a family of axiomatic systems.
3) Then you are trapped again because now you have to deal with inconsistent axiomatic systems - not a very nice idea.

But I should stress that this is perhaps not the problem of your approach but only my problem in understanding it (or being able to attack my own prejudices).

 

[tom.stoer]

Physics has never been concerned to answer "why it is the way it is."

I disagree. I think these kind of questions are the very driving force for the progress of science over centuries! I think latest since the early days of quantum mechanics every day physics is concerned with questions regarding measurements and predictions, but every revolution in science has its roots in questions like "why is ...". Nobody was able to present a full answer, only approximations to some deeper truth, so perhaps that's why we are not used to ask and analyze these questions.
In addition certain philosophers claimed that those questions are meaningless and must be avoided in all sound systems - which is a reasoning we know from "The Fox and the Grapes".

But to me it's amazing how much is known about fundamental physics, and how little we've been able to learn from that vast body of knowledge, about what's going on here.

Good point! I think Smolin was pointing out that for a further development of quantum gravity, unification etc. we do not necessarily have to wait for new experimental results. Let me explain why: Progress in physics was always a step-wise approach. First there were experimental results w/o a theoretical explanation. Then there was a theory able to post-dict these phenomena - and to predict new ones. Today we are confronted with a couple of phenomena (4-dim. spacetime, dark energy, U(1)*SU(2)*SU(3), three generations, ...) we do not understand and we cannot explain (why spacetime is four-dimensional is a very good question even w/o referring to string theory). So the very first step for a candidate ToE need not be to predict new phenomena but to post-dict the known ones!

But there seem to be very basic features of the physical world that we haven't yet tried to account for in our theoretical models.

Can you give me examples?

 

[tom.stoer]

Hey Tom, I didn't you also liked exotic smoothness. Right?

What do you mean exactly?

 

[MTd2]

What do you mean exactly?

You said "The continuum hypothesis may be artifical, but homeomorphic, non-diffeomorphic manifolds may very well be physically interesting!"

In 4 dimensions, that is exotic smoothness. Google for it! :) This is the topic that I like the most, and I think it is at the very core of every 4 dimensional theory with fractal dimensions, like Horava gravity, LQG, Loll's universe, Asymptotic Safety, and the likes.

This is also closely relateted to the classificantion of smooth 4-dimensional manifolds. The simple connected case has not classification, and it is also related to the question if the generalized poincare conjecture is true or not in 4 dimensions. That is, about the existence of exotic smooth sphere. Hendryk Pfeiffer paper above is related to all this.

 

[RUTA]

To repeat Dicke's famous response, "Well boys, we've been scooped." The search for the unified force is over:

http://www.theonion.com/content/node/39512

Damn, I had my money on LQG.

 

[Fra]

Honestly speaking I expected something like that!

I came to the conclusion that insisting on inference and at the same time relying on axiomatic methods would cause big trouble for you approach. It would rely on consistency w/o being able to prove or disprove it.

I think you are starting to see the logic I tried to convey.

I still see problems with that approach:
1) I still have the feeling that there is "something" in your approach that is NOT subject to evolution and that is NOT immune regarding the following argument:
2) I think that you can change perspective again and map your approach into a kind of axiomatic system or a member of a family of axiomatic systems.
3) Then you are trapped again because now you have to deal with inconsistent axiomatic systems - not a very nice idea.

I guess it is possible to try to map this into a kind of sujbective axiomatic approach, but then to keep the spirit, the set of subjective axioms would sort of constitute the DNA of the inference system, and those actual systems encoding in their actions a particular inference system, would still be subject to challange/selection, and one could say that the inference system implicit in a set of axioms, can have varying degrees of "success" of actually making inferences that MATCH the actual future, and here there is a selection for the axioms, so that axioms can be lost, like genes can be lost, and new axioms can come.

So if we insiste on a axiomatic approach, and still insist on keeping the spirit of reasoning here, then the axioms are still subject to evolution. One one is faced with the problem of understand the logic behind going from axiomatic system to another.

That might make sense to me, but it doesn't make the problem easier, it's just putting it in different words. IT's still very different from the ordinary axiomatic approach, which is more like an accumulative buildup of an axiomatic system. This does not match what I envision because the "choice of axioms actually contains information" about what's fit and what's not. And the axiomatic system are still bounded in complexity in my view, since it's encoded by a finite inside observer.

So the really ordinary axiomatic method (without this evolving stuff I talk about) does not as I see it match this.

/Fredrik

 

[tom.stoer]

In 4 dimensions, that is exotic smoothness. Google for it! :) This is the topic that I like the most, and I think it is at the very core of every 4 dimensional theory with fractal dimensions, like Horava gravity, LQG, Loll's universe, Asymptotic Safety, and the likes.

This is also closely relateted to the classificantion of smooth 4-dimensional manifolds. The simple connected case has not classification, and it is also related to the question if the generalized poincare conjecture is true or not in 4 dimensions. That is, about the existence of exotic smooth sphere. Hendryk Pfeiffer paper above is related to all this.

Yes, you are right, this is exactly what I am talking about. The paper provides a fresh view on PL manifolds which could be used as "diffeomorphims-invariant triangulation". This is a very interesting idea.

I am not so sure if exotic smoothness for R^4 is the very core of 4 dim. physics. Pfeiffer explicitly excludes topologogically inequivalent manifolds, but I would expect that different topologies will matter as well. (I've seen some statements in this regard in the CDT context, but I can't remember the details ...)

 

[tom.stoer]

I guess it is possible to try to map this into a kind of sujbective axiomatic approach, ... ... and here there is a selection for the axioms, so that axioms can be lost, like genes can be lost, and new axioms can come.

So if we insiste on a axiomatic approach, and still insist on keeping the spirit of reasoning here, then the axioms are still subject to evolution. One one is faced with the problem of understand the logic behind going from axiomatic system to another.

That might make sense to me, but it doesn't make the problem easier, it's just putting it in different words. ...

No, it's not just putting it in different words.

1) If you succeed with this reformulation you will have an axiomatic approach which describes how axiomatic systems can evolve. It describes (sets the rules) how axioms can be lost and how one can go from one axiomatic system to another. It will be very interesting to learn if this meta-level is again an axiomatic system, if it is subject to evolution, if it can be constructed explicitly or if you can only prove existence, what about my "next stage ..." reasoning etc.

2) If you fail you will hopefully learn from failing if your approach is richer than the purely axiomatic one; perhaps failing with the construction will be a success for your approach ...

So you will learn if your approach is immune to my criticism - and if this is a feature or a weakness (weakness in the sense that self-immunization may be non-scientific; refer to arguments against the anthropic principle).

 

[Fra]

No, it's not just putting it in different words.

1) If you succeed with this reformulation you will have an axiomatic approach which describes how axiomatic systems can evolve. It describes (sets the rules) how axioms can be lost and how one can go from one axiomatic system to another. It will be very interesting to learn if this meta-level is again an axiomatic system, if it is subject to evolution, if it can be constructed explicitly or if you can only prove existence, what about my "next stage ..." reasoning etc.

2) If you fail you will hopefully learn from failing if your approach is richer than the purely axiomatic one; perhaps failing with the construction will be a success for your approach ...

So you will learn if your approach is immune to my criticism - and if this is a feature or a weakness (weakness in the sense that self-immunization may be non-scientific; refer to arguments against the anthropic principle).

I thikn I see what you mean.

Do you mean wether it's possible to describe what I propose - the evolving axiom system - again as a *fixed* objective larger axiom system?

I think that is not possible - it would in fact not be very conceptually consistent with the spirit of the idea. What I think is possible OTOH, which also part of the idea here, is that it IS possible to describe the evolution of axiom systems, RELATIVE to another axiomsystem. But there is no objective universal axiomsystem which we can see in a realist view.

I figure you also think it's weird that if there are no objective, or non evolving structure, how can this possibly get predictive? The idea is that I view this as a game, and all we can do is play.

One might compare this again to Gödel stuff in that the consistency of one system could be provable from another axiom system (normally larger), and the correspondence of this in my view would be how one observer inferes the action of parts of it's environment.

But there is as far as I have analyzed this, always more questions that you CAN NOT answer, but you can insist on asking them - this is in my mind related to evolution and also at a different level in the hierarcy time.


/Fredrik

 

[Fra]

It will be very interesting to learn if this meta-level is again an axiomatic system, if it is subject to evolution, if it can be constructed explicitly or if you can only prove existence, what about my "next stage ..." reasoning etc.

I'm not sure my response made sense to you but what I mean to say, is that to predict one axiomatic system or inference system, you need another inference system. (observer2 observes observer1) This could I think probably we realized at least effectively if we consider the inference system we discuss when we do particle physics. Because then we can make inferences of this inference system, relative to the environment which in a way is a much larger inference system.

This is I think possible, but the larger context is itself evolving, and there simply is no external axiom system, much like there is no external space which the universe is expanding INTO. Neither do I think there is an objective configuration space for the universe which describes multiverses.

That's quite analogous to the problem of inference systems.

I THINK you are wondering if what I suggest can be phrased in terms of a possible larger fixed axiomatic system that plays the rold of meta law. If so, I do not think that so, and neither do I at least see it as a problem. It's probably the natural way you'd want to see it, when coming from the traditional view: To try to axiomatise, the axiom evolution, or to describe the evolution by law by a meta law. This is not how I see it. But like I tried to convey, there ONE correspondence to "meta law" I do see, is still constrained to an inside view which is usually bounded (the size of the genome is bounded), there is no external context where it can be, unless you do take on a structural realist view, THEN it makes sense, but I don't. And it also introduces an enourmous ambiouity - massive landscape of possible "master inference systems". And I think others have made that mistake before, and I don't intend to repeat it :)

/Fredrik

 

[tom.stoer]

Do you mean wether it's possible to describe what I propose - the evolving axiom system - again as a *fixed* objective larger axiom system?

I think that is not possible - it would in fact not be very conceptually consistent with the spirit of the idea.

Yes. I am not convinced that your approach is right, but IF it is right, this must be true, of course.

What I think is possible OTOH, which also part of the idea here, is that it IS possible to describe the evolution of axiom systems, RELATIVE to another axiomsystem. But there is no objective universal axiomsystem which we can see in a realist view.

Again my question is how these laws of evolution become subject to evolution.

Let me present you one argumentation which demonstrates why and how your approach will fail - or at least why you fail in explaining it to us:

Assume for a moment that you were able to figure out how it works, that you were able to explain in detail and that finally we all agree. Wouldn't that mean that your approach became a somehow fixed system of rules and statements? Wouldn't that mean that it is no longer subject to evolution? Wouldn't that mean that your meta-program became an "axiomatic system"?

If you have to admit that the answer is "yes", there are two possible conclusions:
If you accept this reasoning, you have to admit that your approach has failed.
If you insist on the success of your program the only way out is to accept that you will never be able to figure it out completely and explain it to us.

If you say that the answer to the above raised questions is "no" there is only one conclusion, namely that the approach is somehow inconsistent or incomplete as we agreed to accept it,but at the same time we concluded (right now!) that it is not fixed but subject to change and therefore we have to withdraw our acceptance unless you have finished your work.

A last way out would of course be to abandon the theory (at least partially) and admit that the theory itself is immune to this discussion - or that these self-referential constructions must be excluded due to consistency. But that of course means that it's no longer a ToE but that its domain of application is in some sense limited.

 

[Fra]

I see and acknowledge your question. I've certainly thought about this but I need to think a bit on how to phrase it to be more clear. Part of the ambigouity is that this is my own reasoning ie. it's subjective. So this is indeed only as per my own inference system and "educated guess".

Am I CERTAIN that this program will succed? Of couse not! But - here is my subjective basis - I see NO better option. It's the most plausible idea I have. If you have a better one and are able to convince me, I am open.

Similarly, I fully understand that it's not trivial to convey and abstract idea to anyone else. I do not expect you to easily get it. This is why like I said before, the ultimatey argument will be if and when I succeed. But most probably the first publication will not be on here :)

But for sure the argument I present now and here are not meant to be definitive arguments at all for my approach. It is only plausible arguments as part of a sound discussion.

I'll see how I can make this clearer, but I apparently need a different way to putting.

More later

/Fredrik

 

[ConradDJ]

But the thing is, our world is much more than a body of fact. Among other things, it's a system that makes its facts physically meaningful -- i.e. observable and definable in terms of other facts, that are also physically observable and definable.

Mathematical systems seem to work very differently -- they're logical structures built on undefined basic elements / operations. These basic elements are meaningful to us, because we live in a physical world that has analogues to them. But there seem to be very basic features of the physical world that we haven't yet tried to account for in our theoretical models.

Can you give me examples?

Yes... the key example is just this business of measurement. If you have a physical fact -- say the mass of a particle -- there is also a physical context of interaction that allows its measurement. This context involves other kinds of physical facts -- to observe the mass of a particle, you need to be able to measure space/time intervals, etc. Another way to describe this: the world is not only a set of facts, but is also a system that physically communicates those facts... by means of other kinds of facts, that are observable in the context of other facts. Our current theories aim to be mathematical models of the fact-structure, but I don’t know of anything that models the structure of the communications system.

I tried to describe this kind of functionality in another thread –
https://www.physicsforums.com/showthread.php?t=332292"

But there are other “basic features of the physical world” that – so far as I know – haven’t been modeled mathematically. Our laws of physics obviously support more or less stable structures – atoms and molecules, crystals, all kinds of material objects. How does this work? It all depends on the functionality of the basic “building-blocks” – but atomic structure is very complicated, dependent on several apparently unrelated principles, e.g. electromagnetism, the exclusion principle, and whatever the laws are that keep nuclear particles stable.

So our world clearly provides highly functional “building-blocks” – but is there a theory that tries to explain what kinds of physical principles are required to do this?

Then too there’s the “calculation problem”. Obviously, in our world, physical systems obey dynamic laws, to a remarkable degree of precision. Yet we know that even in such a simple case as Newtonian gravitational dynamics among three point-particles, the equations have no analytic solution. Very clearly, physical systems do not have to compute their dynamics... so how does this thing of “obeying laws of physics” actually work? How does the physical world constantly create precise real-time “solutions” to problems that are mathematically intractable?

Basically I’m responding to your idea that we need a radical new paradigm, by saying – there are basic things we take for granted about the physical world, that haven’t yet been addressed in physical theory. If you’re taking seriously the question – why are things the way they are? – maybe these other aspects of “how things are” need to be considered, to get the complete picture.

 

[MTd2]

I am not so sure if exotic smoothness for R^4 is the very core of 4 dim. physics. Pfeiffer explicitly excludes topologogically inequivalent manifolds, but I would expect that different topologies will matter as well. (I've seen some statements in this regard in the CDT context, but I can't remember the details ...)

Exotic smoothness exists for an infinite type of different topologies! What I said about exotic sphere it is that it is the most difficult one is the the one case in which there is homomorphism to a sphere, thus, an exotic sphere. There are exotic spheres in several dimensions, but in 4 dimensions it is unkown. But if there is, it will be one that has infinite non-diffeomorphic kinds. In other dimensions, the number is merely finite.

 

[tom.stoer]

Exotic smoothness exists for an infinite type of different topologies!

All I wanted to say is that before different differential structures for one fixed topology become interesting, different topologies will be important. Look at strings: there you do not have several differential structures but its the basic topology of the world sheet that matters.

But I agree, exotic smoothness is a fascinating discovery.

 

[tom.stoer]

I see NO better option. ... If you have a better one and are able to convince me, I am open.

I certainly do not have a better one :-)

I am still thinking about the (ontological) relation between mathematical structures and physical entities. I am thinking about criteria for a candidate-ToE. I would say that a rather direct relation between mathematics and physics is obvious - otherwise it's magic why mathematics describes our world in a very accurate way. But I am not willing to accept that mathematics IS reality = IS physics.

Mathematics cannot answer questions regarding existence. THINKING about new axioms for set theory in order to overcome the axiom of choice and the riddle regarding the continuum hypothesis is neither equivalent to CREATING corresponding universes nor is it equivalent to DISCOVERING these (already existing) universes. Therefore there is a missing link between physical existence and mathematical truth.

I am still more conservative in the sense that I believe in rather fixed physical laws which do not change in time or which emerge from a deeper structure. If the latter would be true I would immediately try to get hands on this deeper (but then again fixed) structure and take this as a more fundamental law. And I am conservatice in the sense that I do not like anthropic reasoning as it seems to me to be a collection of excuses only.

Later I will try to explain in more detail how my proposal could look like. Unfortunately currently I am only able to tell you how it does NOT look like.

 

[MTd2]

Look at strings: there you do not have several differential structures but its the basic topology of the world sheet that matters.

You do have exotic structures in string theory. Actualy, Witten was the first one to write about exotic structures, although in 8 dimensions.

http://math.ucr.edu/home/baez//week141.html

Edward Witten, Global gravitational anomalies, Commun. Math. Phys. 100 (1985), 197-229.

http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1103943444

But I rather study the most complex ones, infinitely more, which are in 4 dimensions, and it also happens to be the dimension we live in.

 

[Fra]

Wouldn't that mean that your approach became a somehow fixed system of rules and statements? Wouldn't that mean that it is no longer subject to evolution? Wouldn't that mean that your meta-program became an "axiomatic system"?
...
If you say that the answer to the above raised questions is "no" there is only one conclusion, namely that the approach is somehow inconsistent or incomplete as we agreed to accept it,but at the same time we concluded (right now!) that it is not fixed but subject to change and therefore we have to withdraw our acceptance unless you have finished your work.

My answer to the above would be the no option.

I follow your reasoning but I think your expected logic is too rigid to be fit for the quest we face, and I think the explanation might be a difference in focus here. I used to think like that - I didn't always like the concept of evolving law - but I changed my mind. I think your rigid thinking is connected to your "traditional view" of fixed laws, that's how it was for me. But the more I thought about this the more did I see that this really isn't what I see, it was just what I expected to see.

So what is the problem at hand? To find and capture the TOE? No, not in my mind. The problem is that we want to increase our understanding as much as possible as fast as possible as rational as possible. the point is that even if a TOE is a goal, the ROAD to the TOE is the more immediate goal. Thus the goal is to infere the immediate future, not the end of time. And by construction then the inference system is present "now", is different from the one present in a definite future.

At no point in this process, must the fact that we are still on a journey, or the fact that our inference system can improve, inhibit us from actually doing so. I have a feeling thta your quest for "perfection" or ultimate consistency, ambitious as it may be, is actually inhibiting. You almost run into a halt. Nature don't do that. I'm just projecting here my own path from where I was to where I am. But my hat would go off if you can capture the perfect eternal consistency between the palms of your hans, but I couldn't do it, and I don't see how it would even make sense. My attempt of TRYING, lead to my my current strategy. So I did consider the rigid inference system, but I can't make sense out of it. Thereof my position.

I'm repeating myself here but I think your resistance against accepting evolving inference systems as an actual best descriptio nof nature (rather than a fixed on) is similar to Einsteins original resistance against the evolving/expanding universe. At first he tried to make it static, because he didn't first know that the universe ISN'T static.

Look around, does the inference systems we can distinguish in nature seem fixed? Not as far as I can see.

/Fredrik

 

[friend]

Mathematics cannot answer questions regarding existence. ...Therefore there is a missing link between physical existence and mathematical truth.

The only representation we have of the states of existence or non-existence is binary logic with its algebric manipulation of true and false. Here true represents what exists, and false represents what does not exist. We always consider true those statements that describe what really is, and visa versa. So any ToE that proports to determine what is, as opposed to what is not, would have to be based in logic. Can you imagine a theory of physics which does not comply with logic? I think logic is a ToE since we assume it applies to everything physical. The question is how do we extract laws of physics from this.

It may not be that hard. Whatever the tiniest constituents of reality are, it's fair to assume they can be describe with statements or propositions. And it's fair to assume that every little part co-exists with every other little part. That means reality is described as a logical conjuntion of all the propositions for every little part. I would assume that there is an infinite number of porposition required to describe all of reality. And in order to distinguish each little part, every proposition would have to be assigned numbers, or coordinates to keep track of them.

Any mathematical law of physics by definition has to describe how things go from one state to the next, how one set of propositions necessarily implies the next. These laws, like any function, describe how given one state what the next state will be, and given that what the next state will be, and given that what the next will be, etc. We could use a variable, say, t, to parameterize which step along the path you're at. And since all the facts co-exist together, there is no preferred path in the way one proposition implies the next, and every path would have to be considered. So maybe this conjunction of propositions can be manipulated into a combination of paths of implication and somehow integrated using the assigned coordinates to give us something that looks like a physical law, say something like Feynman's path integral or something.

 

[tom.stoer]

My answer to the above would be the no option.

At no point in this process, must the fact that we are still on a journey, or the fact that our inference system can improve, inhibit us from actually doing so.

OK, now you position is clear. You include in the process not only nature's evolution of laws but also our quest for these laws. My feeling as that it becomes al little too subjective, but that's my position - and I don't want to repeat it here.

I have a feeling thta your quest for "perfection" or ultimate consistency, ambitious as it may be, is actually inhibiting. You almost run into a halt. Nature don't do that. ... My attempt of TRYING, lead to my my current strategy. So I did consider the rigid inference system, but I can't make sense out of it. Thereof my position.

Yes, you are right. As I just said I can only tell you how it does NOT work (what a pitty). If it is this what you mean by "halting" then I agree.

Looking at the dilemma we face, there are two very different options.

You have chosen to search for evolving laws - and you somehow adapt your search strategy accordingly. You are like Achilles running after the turtle. You never overtake the turtle, but you are coming closer and closer - and perhaps this is the best you can do.

I have chosen (together with other traditionalists) to look for deeper levels of understanding and laws. It's a layer model, where uncovering the next layer immediately raises new questions. Here it doesn't matter if the layers are fixed and static or if they are evolving, because in this picture the laws for evolution would somehow be located at the next layer, so it fits into the picture.

If we focus in your picture more on the process of science, then we more or less agree; it's just a special description of philosophy of science. My new layers are paradigm shifts or revolutions (I think Kuhn wrote something like that).

If we focus on the nature and existence (or emerence) of laws then we disagree - but that's the interesting point here :-)

 

[tom.stoer]

The only representation we have of the states of existence or non-existence is binary logic with its algebric manipulation of true and false. Here true represents what exists, and false represents what does not exist. We always consider true those statements that describe what really is, and visa versa.

I agree to one part of the statement: 1) Everything that EXISTS must respect some laws of (binary?) logic and therefore correpsonds to some consistent mathematical system. But the other way round it's deep philosopophical statemet which I cannot accept w/o further discussion: 2) EVERY sound mathematical (logical) system EXISTS.
(I hope that is the meaning of your "vice versa")

So any ToE that proports to determine what is, as opposed to what is not, would have to be based in logic. Can you imagine a theory of physics which does not comply with logic? I think logic is a ToE since we assume it applies to everything physical. The question is how do we extract laws of physics from this.[/QUOTE

Very good starting point.

... every proposition would have to be assigned numbers, or coordinates to keep track of them.[/QUOTE

Then you face the usual trouble with natural numbers, Gödel etc. Binary logic alone seems to not powerfull enough to do the job; using natural numbers may lead to inconsistent or incomplete systems w/o any chance to prove or disprove it.

Let me ask some questions to get a better understanding of your second statement:

Do you believe that natural numbers exist?

Do you believe that this is not only a platonic existence, but that there is a level of mathematics (say the natural numbers) that IS physically EXISTING = fundamental physical entities (which we haven't discovered so far).

Do you believe that you can somehow construct physical laws (which rely on more than logic) from logic itself? That means do you think that natural numbers, real numbers etc. emergy somehow from logic alone?

Or do you think that if we uncover the ultimate laws of science those concepts fade away as purely approximate descriptions and we are faced with a system of logical automata interacting with each other?

 

[ConradDJ]

The only representation we have of the states of existence or non-existence is binary logic with its algebric manipulation of true and false. Here true represents what exists, and false represents what does not exist... So any ToE that proports to determine what is, as opposed to what is not, would have to be based in logic... I think logic is a ToE since we assume it applies to everything physical. The question is how do we extract laws of physics from this.

It may not be that hard. Whatever the tiniest constituents of reality are, it's fair to assume they can be describe with statements or propositions...

Friend -- The point I was trying to make above (#149, 186) is that this binary representation of physical existence isn’t adequate. For a proposition “A exists” to have any meaning, it must be possible for something to determine something about A through interaction, within some particular frame of reference.

The very essence of classical physics is the assumption that these conditions under which something can be meaningfully determined have nothing to do with the nature of physical existence itself – a thing “just is” what it is, regardless of the conditions under which it can make a difference to anything else in the world. The essence of QM is the discovery that this is not the case.

Likewise the logical proposition “A=A” is fine, but has meaning only insofar as you can actually identify a determinate “A” and distinguish it from and compare it with other things. Because our physical universe gives us many, many ways of doing this, logic seems to apply to everything, as you say, a priori.

But again, the classical assumption is being made that the functionality that let's the existence of things be physically meaningful to each other, is irrelevant... that is, the complex conditions under which things can make a definite difference to each other, and under which propositions can be meaningfully true or false.

I'm not arguing against the use of logic, of course. I'm arguing that there are other aspects of physical existence that need to be considered. To reduce physics to logic is much the same as reducing human language to logic, assuming all the conditions of meaningful communication are irrelevant.

Logic and mathematics are abstractions supported by the complex functionality of language. I think the logical and mathematical aspects of physics are likewise abstractions from "physical existence" -- a complex functionality that we generally take for granted.

 

[friend]

Let me ask some questions to get a better understanding of your second statement:

Do you believe that natural numbers exist?

Do you believe that this is not only a platonic existence, but that there is a level of mathematics (say the natural numbers) that IS physically EXISTING = fundamental physical entities (which we haven't discovered so far).

Do you believe that you can somehow construct physical laws (which rely on more than logic) from logic itself? That means do you think that natural numbers, real numbers etc. emergy somehow from logic alone?

Or do you think that if we uncover the ultimate laws of science those concepts fade away as purely approximate descriptions and we are faced with a system of logical automata interacting with each other?

No, at this time I don't believe numbers in and of themselves have any physical meaning. Propositional logic and numbers and math are only a human contrivance of language to help us better describe reality. There are no fundamental particles that have a "1" or a "2" written on them. We can just as easily count them in a different order.

I don't know how numbers can be derived from logic alone. I understand Whitehead and Russel wrote a book doing just that. They also attempted to proved the completeness of math, but failed.

However, I do believe that the laws of physics can be derived from principle alone, without the need for measurement. Although, we might need measurements in order to check the math. For example, I've seen derivations of the path integral from logic alone. It's not on the arXiv yet, so I'm not allowed to publish here. PM me if you are interested in seeing it.

 

[friend]

Friend -- The point I was trying to make above (#149, 186) is that this binary representation of physical existence isn’t adequate. For a proposition “A exists” to have any meaning, it must be possible for something to determine something about A through interaction, within some particular frame of reference.

Yes, binary logic may not be sufficient, we do end up using numbers to quantify things.

But when you say, "it must be possible for something to determine something about A through interaction", I'm understanding material implication from that; we need some sort of B to prove A. Yet this is part of binary logic as well.

 

[Fra]

I think we're starting to reach a mutual understanding of positions.

OK, now you position is clear. You include in the process not only nature's evolution of laws but also our quest for these laws. My feeling as that it becomes al little too subjective, but that's my position - and I don't want to repeat it here.

Yes. I also understand why you think my position is a subjective - it is. The question where we differ, if it's avoidable or not - does the real world fit into a static description?

Yes, you are right. As I just said I can only tell you how it does NOT work (what a pitty). If it is this what you mean by "halting" then I agree.

Yes something like that is what I mean.

You have chosen to search for evolving laws - and you somehow adapt your search strategy accordingly. You are like Achilles running after the turtle. You never overtake the turtle, but you are coming closer and closer - and perhaps this is the best you can do.

That analogy seems a bit odd :) but it's true that I think the point is the quest for best performance. The perfect performance might be impossible.

Implicit in my reasoning is indeed a special view also of the philosophy of science. I use the very same abstraction to describe the scientific method & process, as I use to describe physical law and physical processes.

If we focus on the nature and existence (or emerence) of laws then we disagree - but that's the interesting point here :-)

Yes, I think this is where from my point of view, I would classify you as a kind of structural realist, enough though you currently seems to be in a process of finding out the problems of this approach and it seems, like you say yourself that you've at least partially found out what does not make sense.

I'm curious to see what your understanding eventually evolve into :)

/Fredrik

 

[moniker2]

does the real world fit into a static description? I think so...if you look at the world in terms of frames of time.

friends, I would like to bring up a theory I read two years ago. It's starts with the idea that LHC will not find any Higgs Boson particle, and it looks at the idea of quantum inertia. I think it's seven equations in total, but I'm not sure.

 

[tom.stoer]

I don't know how numbers can be derived from logic alone. I understand Whitehead and Russel wrote a book doing just that. They also attempted to proved the completeness of math, but failed.

I think set theory was required as well.