LHC - the last chance for all theories of everything?

[Fra]

Fra, do all observers share the same verson of mathematics? Is it possible that for some observers 2+2=5?

I am not sure what you mean here, you probably need to provide an example so I can interpret this.

A fundamental thing in my view is that in a certain sense all observers share what I call a natural or rational action. There is a way of "counting evidence", and from each inside view this framework is in a certain same the same. The reason for this expectation is that any observer not implementing a rational action (the meaning of this is a different discussion so I'll leave that) will be exposed to forces that selects for a particular change.

My view would contain a reconstruction of a kind a new probabilistic framework, where the "probability" rather than frequentists intrepretation is a sort of "inside count" of evidence. Then from such a picture, there is a "natural action" which is closely relate to the principle of minimum information divergence, also related to max ent principles and principle of least action.

I'm basically looking for a deeper way to infere a transition amplitude a la path intergral, where the action itself is defined through a recursive flow. So the action S is not hardcoded, it's itself evolving.

In there, my basic conjecture is that there is a rational and natural way to count evidence, and the so constructed "information state" contains a natural action! No need to postulate wicked string actions, the action is a natural action in the inference system.

This of statistical mechanics, where the microstructure defines a natural measure of missing information (entropy). Now picture this idea much more genralised, where the microstructure is not a baggage but rather is a result of evolution, and also the microstructure is more complex, like a system of related structures, defined by transformations, like a complex memory system. Then such a complex microstructure-system implies a much more complex "natural action" also for changes. This is what I'm trying to work out.

A space of differential changs are defined, and on that space a natural information divergence measure is defined. That defines a transition amplitued for each possibility. But as the microstructure is not one simple space, but an evolved system of spaces, and the microstructure is not based on continuous probabilit but on "counting evidence" (basically a combinatorical approach) interesting new logic emerges. Quantum logic superposition are expected gets natural explanation here. quantum logic is simlpy (at times) more FIT than classical logic.

When I have worked this out, I will produce some papers for sure. Until then I constrain my reasoning here to general IMO sound arguments.

When I get to the point of publishing something concrete one can talk about "theory", and it will be more readily subject to critics. To me it's simple, either this will produce new insights or it will not. If not, it's a failure.

/Fredrik

 

[Dmitry67]

But what value your "theory" might have if we don't agree that all observers share the same logic? Then your theory can be valid for observer Fra but not be me

 

[Fra]

But what value your "theory" might have if we don't agree that all observers share the same logic? Then your theory can be valid for observer Fra but not be me

Of course, the theory will be the same for me and you, and all scientists on earth. This is explained by the emergent objectivity. The basis for our expectations are massive enough, and we are well equilibrated enough to be exactly in consistenct _for all practical purposes_.

I never said that everything is totally subjective in an uncontrolled way, that would make little sense. This makes sense only if complemented with a mechanism for emergent objectivity. This emergence, is a physical process, but if we are talking about the laws of subatomic physics for example, not doubt all of us will be in agreement.

The supposed value of this approach, is that it will explain the choice of the emergent physical laws. In particular interesting is this to me when you consider the case where the observers are not you and me, bu say a proton an a neutron for example. I think this scheme will constrain the possible mutual actions of these systems.

The predictive power here, is that the insight of the "inside perspecitve" will allow us humans from an external perspecitve defined by a laboratory frame to constrain how the actions of microphysics is like, what symmetries we have etc. So this should eventually (when it's mature) give clear predictions.

The idea is to use the zero end of the complexity scale, to constrain the possible actions. And then see what happens as the complexity scale grows. This complexity scaling is also given a physical interpretation as generation of mass.

This is why the laws of physics emerge along with massive observers(matter).

Sure, maybe I will fail in this vision, but that's my loss, I'm not eating anyones elses investments :) Unfortunately the same can not be said about some other approaches.

/Fredrik

 

[ConradDJ]

I think many people agree that mathematics can perfectly describe the reality. But (they think) the formulas are dead until you "incarnate" them into something, until you fill them with some substance. But for TOE, there should be no magical substances, because TOE by definition must describe everything.

TOE is different from any theories we had because TOE ends the reduction: "bodies-molecules-atoms-hadrons-quarks-strings.." so the most fundamental entities can not be "made of something". If they are not "made of something" they are just "described by formulas". I don't see any possible void where the difference between the ultimate description of reality and reality can hide.

Hi Dmitry --

The difference between a “reality” and a “description” of that reality is that a reality is assumed to exist and to be well-defined “in itself”, while a description requires a context in which what is described has meaning, in some sense – i.e. makes a definable difference to something else.

To me, the fundamental point of both Relativity and QM is that we don’t have a base-level “reality” that’s well-defined in itself, without requiring any frame of reference or any context of interaction to define it. What’s physical about the physical world is not that it’s “made of something”, but that it’s observable – that it provides reference-frames and interaction-contexts that make everything in it physically meaningful.

Of course both Relativity and QM are mathematical theories. And in both cases, we can certainly ignore the questions about what makes things observable and why observing something makes a difference to the ways in which its description is determinate.

If we look only at the mathematics, lo and behold, everything looks well-defined – because it’s easy for us to convince ourselves that logic and mathematical structures “exist” in some absolute sense. We live in a physical environment that gives us lots of distinct identifiable objects, so counting makes sense, “A=A” makes sense. The physical world has a very clear and simple geometry, so the concept of a point or an interval or a vector makes sense. Even something as paradoxical as a “continuum” of points makes intuitive sense to us, because of the way our world is physically structured. We can hardly imagine a world in which these ideas don’t make sense.

However, we’ve learned that in the early stages of our universe, the physical conditions did not exist that would make any of these basic concepts meaningful. We tend to assume that this doesn’t matter – that the basic structure of the world will turn out to be well-defined mathematically, and that the mathematical structure is all physics cares about anyway.

That’s a reasonable point of view, but not necessarily correct. The other point of view is that the context of relationships that let's things be defined and observed, that let them make a definite difference to each other, is important and can’t be neglected. As Fredrik says, this is not necessarily “subjective” – we’re not talking about “conscious” observers. We’re talking about the aspects of physical structure that provide a context of meaningful definition for other aspects of physical structure.

Ultimately, as you know, mathematics is based on undefined elements – points and lines, for example – and logical operations like “=”, also undefined except for their formal properties. Physics is different – everything in physics has physical meaning because there’s a context of other physically observable regularities to which it can make an observable difference.

Even if each of these regularities is describable mathematically – and I assume that’s the case – the functionality of such a system of mutually-defining types of structure is something entirely different from the formal self-consistency of a mathematical system.

I don’t think Tegmark’s point of view has any real merit – except that it demonstrates the difficulty we have in conceptualizing the difference between “physical” and “mathematical” -- as obvious that difference is to us in ordinary life. The world he describes is the world of all possible mathematical structures... and so? By claiming this is the physical world, all he’s doing is making explicit the common assumption that we can safely ignore the aspects of physical structure that make things observable.

 

[ConradDJ]

Also for this [consistency] to even have meaning in my view, the observers must be interacting.

In this respect I think Rovelli phrased it well in his RQM paper that the only way for two observers to relate their measurements is to communicate - ie. to interact.

So given that requirement, then a certain form of consistency or consensus between the observer is emergent, as a result of the interaction.

This means that in my view

- observers that aren't interacting, does not even have the notion of mutual consistency defined since it is only defined through the interaction.

- even observers that are communicating, can be inconsistent transiently, but mutual inconsistency always means off-equilibrium and thus interaction forces.

The main difference from the standard notion of consistency as defined by say a symmetry transformation, is that in my view this transformation itself is not given, it's emergent, and without interactions the transformation itself is undefined.

I'm not much into MWI, but certainly if the observers are in different non-interacting branches the notion of consistency has no meaning...

Fredrik – I just want to underline this point, with which I completely agree.

Rovelli points to this “emergent” agreement among observers as what’s most remarkable about the structure of the world as described by QM. But as I’ve said before, he doesn’t go further to tell us what’s involved here – what the structures are that make this work.

I think you’re right that there’s a parallel between what scientists do in observing things and developing a coherent picture of the world, and what happens in the world itself at a basic level. What’s “physical” about our world, I argued in the post above, is precisely that it develops a coherent “picture” of itself through physical communications among all its participants.

It seems reasonable to me that your quest for an internal inference-logic would play a role here – just because the “picture” intercommunicated among things is not precisely well-focused to begin with, being limited by the discrete quantum nature of interaction.

But it seems to me the most basic issue has to do with the existence of observation-contexts (“measurement situations”) in which any information at all can be conveyed – since without some sort of primitive information-exchange, inference has no data to work with.

 

[Dmitry67]

Ultimately, as you know, mathematics is based on undefined elements – points and lines, for example – and logical operations like “=”, also undefined except for their formal properties. Physics is different – everything in physics has physical meaning because there’s a context of other physically observable regularities to which it can make an observable difference.

Mathematical entities are abstract. They are not reducted to the simpler entities; but it is wrong to say that they are undefined! They are defined using the relationships between them.

This is exactly what we expect from TOE. If some theory would say that time consists of timions, and strings constist of vibrions, then by definition it would not be TOE - it would be just a another step towards the understanding the structure vibrions and timions.

In TOE the ultimate entities MUST (it is not a justified hope - there is just no alternatives) be abstract, defined (exactly like in mathematics) based on the relationship with them.

 

[ConradDJ]

Mathematical entities are abstract. They are not reducted to the simpler entities; but it is wrong to say that they are undefined! They are defined using the relationships between them...

In TOE the ultimate entities MUST (it is not a justified hope - there is just no alternatives) be abstract, defined (exactly like in mathematics) based on the relationship with them.

I get your first point... my old geometry teacher gave us points and lines as undefined elements, but it probably does make more sense to think of them as inter-defined, in terms of each other. However what makes them "abstract" is that there is no requirement that anything actually be observed by anything else -- i.e. that any information about anything be communicated. We are happy to stay in the realm of abstract definitions, where an interaction is just an instance of an equation -- nothing actually "happens" and no information is exchanged.

In a mathematical system, what counts as a "point of view"? Surely it's true that in the physical world that there are points of view, and information in fact gets exchanged between them. To quote Rovelli, "Physics is about the descriptions systems give of other physical systems."

So my point is just that the kind of inter-definition you're talking about is something quite different from the mutually-defining observation-contexts that we know exist in the physical world. You don't have to be in a mathematical system to "see" it -- in fact there's no meaning to being in it, and the "seeing" is a purely mental activity.

This is not to say that observation-contexts may not someday be modeled in some sort of mathematical system. But envisioning them abstractly, "from the outside", will still be something purely mental, derived from an actual experience of physically being-there, participating with things.

Again, I don't mean to deny the rationality of a viewpoint that says -- whether things are observable has nothing to do with the basic physics. But QM has clearly called this into question, at least. So it's also reasonable to try to understand physical observation-contexts and how they differ from mathematical contexts of definition.

 

[Dmitry67]

ConradDJ, so what you are saying is that mathematical structure is different from reality, because it is 'dead'. In order for any mathematical structure to become reality, there must be some magic process used, a process, which 'incarnates' the formulas into reality (or how hawking called it "breathing fire into formulas"). I just wanted to confirm that my version of your vision is correct before I answer.

 

[qsa]

ConardDJ, I don't know what Dmitry has in store for you, but you can look at it this way. We can write this equation x^2+y^2=r^2 and then draw a circle that represents it, wow! We have already breathed life into our equation. Now complicate your equation and as its solution complicated structure resembling particles interacting gravity doing its job and you start plotting them. as your model is so sophisticated (a 22nd century physics) early life begins to appear...and so on. When you look at your 3D computer screen(probably made by sony-just trying to be funny-!) you see people are doing their thing( not unlike how nurbs mathematics generate one hell of a realistic scene. Do they feel alive and real? You bet. for us are in a computer or we exist because of the imperativeness of the existence of math, that is a secondary question and I think with our power of science at that time the question should answered relatively easy.

 

[friend]

What I suggest is not all that different to what you say. The difference is wether the logic system is fixed and eternal, or if it's emergent?

But the problem even in Your approach, from a scientific point of view is, when a given "logic system" or say "theory" is proving WRONG, it when it's falsified - HOW do you find a new theory without starting from scratch? - This is where my main point is, here my view contains a rational scheme for howto infere the new inference system from the old system given detection of slight inconsistency.

Fredrik

dude, either something exists or it does not. For what observer is that ever going to change? If things exist, then you can count them. For what observer is that ever going to change?

The trouble here is that abstractly, we can consider the possibility that something does not exist. Our logic has both true and false values. But in reality there is no state of non-existence. There is no physical entity that does not exist. What we are left with is a logical conjunction of all the little pieces that do exist. If anyone of them did not exist, then that would make the whole thing a false description.

The question is how do you manipulate a conjunction of propositions you can count into mathematical formulas that describe physics? Every mathematical formula asserts that given some input a particular outcome results. And this is exactly what the logical operation of "material implication" does, if a premise is true (or given) then a conclusion results. So the trick is to somehow represent a conjunction in terms of implication and to describe implication in mathematical terms to see if you get something that looks like physics.

I've seen this done. But it is not on the arXiv yet. If you want to see the math, just PM me.

 

[Dmitry67]

Rereading your post...

Ultimately, as you know, mathematics is based on undefined elements – points and lines, for example – and logical operations like “=”, also undefined except for their formal properties. Physics is different – everything in physics has physical meaning because there’s a context of other physically observable regularities to which it can make an observable difference.

So, physical structures are different from the purely mathematical ones, because they are physical? :)

So my question, as you could probably quess, how you can tell a physical system from a purely mathematical one? (this question is not so easy as it sounds)

 

[qsa]

When a complex molecule is simulated on a computer with mathematical modeling, you can see how it vibrates and responds to environment, it looks alive. The algorithms that produced those molecules (however crude) are mathematical containing line, points, vectors, surfaces, probabilities, you name it. What we conjecture, that by a similar process we the “physical” become alive because of computation. The only difference is we can see the simulation of ourselves by ourselves without a computer screen. And this simulation is real because math is the only thing that is real = fact, what else could be? It will always exist regardless. Everything else is considered to be subjective by definition because of not being “scientific”. In another word, I can tell you what math is but can you tell me what physical is really, hay, and don’t explain it using mathematics ok, I’ll be really mad!

 

[qsa]

When a complex molecule is simulated on a computer with mathematical modeling, you can see how it vibrates and responds to environment, it looks alive. The algorithms that produced those molecules (however crude) are mathematical containing line, points, vectors, surfaces, probabilities, you name it. What we conjecture, that by a similar process we the “physical” become alive because of computation. The only difference is we can see the simulation of ourselves by ourselves without a computer screen. And this simulation is real because math is the only thing that is real = fact, what else could be? It will always exist regardless. Everything else is considered to be subjective by definition because of not being “scientific”. In another word, I can tell you what math is but can you tell me what physical is really, hay, and don’t explain it using mathematics ok, I’ll be really mad!

 

[Fra]

I think I've tried to convey and motivate the ideas behind evolving INDUCTIVE inference system and law, as constrast to fixed, external realist type of DEDUCTIVE inference. There is no point for me in repeating more or less the same arguments over and over again. If what I already said doesn't make sense, I'm afraid just echoing it again probably won't help, so I'll try to fade out my voice of this discussion for now at least :)

/Fredrik

 

[member 11137]

A very interesting discussion indeed : what is the physical reality of a mathematical object? And what is its ability to represent the reality? The strange point here is that any mathematical tool or object has at least one real representation : ink on the paper. And why should mathematical tools not also have a 3D representation? (e. g. the cubes of my theory).
Other point since the discussion here seems to be very general: do we really know what a mass is? It is usualy unserstood as a synonym of energy. But do we know what energy is? I mean we do not really progress in labeling things of which we in fact ignore the signification. I mean we have to propose a personal and courageaus representation of the nature if we want to progress. E. g.: Could it be that a mass is not describing the property of an object but is in reality just a natural tool to avoid discontinuity of the topologic background of our universe? a kind of propagating surgery kit? Who knows?
Best regards.

 

[tom.stoer]

So, the laws are identical, but initial conditions are different? If Universe is infinite, all combinations must happen. ...

Hi, I stepped out for a while, but I would like to come back now.

My question was if I can create a universe with a tenth planet simply by writing down the general equations for the solar system and introducing a tenth planet in theory. You replied that this is a problem regarding initial conditions in an (infinite) universe.

Let's assume that within the MU you have several mathematical structures describing more or less our universe. As far as I understand you the different universes with - say - nine or ten planets - would belong to the SAME mathematical mutliverse but would live in different "areas" of the "many world" multiverse. If string theory is rigth then all its solutions would still belong to the same mathematical universe but live in different branches of the "many world" multiverse. But If I introduce another system like "game of life", then I would have to refer to the mathematical multiverse (I guess game of life is not a vacuum of string theory :-)

Looking at the "game of life" it serves as a toy model. It can either be described by a (completely Goedelized) mathematical structure and it would therefore be an own universe. Or it can be simulated by computer programs within our universe, therefore it can be seen as a substructure of the mathematical structure being our universe. Therefore within MUH we have the situation that mathematical structures can be own universes, or they can be substructures of universes.

Now we can look at the "game of live" from a third perspective. It can serve as a model for a universal Turing machine. Now having said that we remember that a universal Turing machine is able to simulate all other Turing machines. Therfeore game of life is able to simulate a large class of universes.

That means that a universe can exist on its own or it can be simulated by another universe. Within the universe everything looks identical (the structure is the same), but from the outside it looks different. Whereas the abstract structure can exit w/o any context, the simulated structure lives in a certain context. That means that we can construct an infinite tower of universes containing (simulating) each other.

But as any mathematical framework shall be free of any baggage, we must identify all structures with a certain kind of "algebraic isomorphism". So we must identify the Turing machine universe with the "game of life" universe.

Now let's assume for a moment that our universe is computable. Then we could (must!) identify it with a certain Turing machine or with a universal Turing machine + certain input. But then you have to explain why our universe looks so different from a Turing machine - or "game of life"! Of course I can easily escape this reasoning by giving up the idea that our universe is computable. So the other conclusion would be that our universe is not computable. Having concluded that our universe is not computable we immediately know that our universe is either (Goedel-)incomplete or inconsistent. As our universe exists and should therefore be consistent it must be incomplete. That means there are true statements which cannot be proven within our universe.

Now what does it mean for a mathematical structure to exists? Do we need a proof? What are these structures that exist within our universe w/o having the ability to be justified by our universe?

 

[member 11137]

Hi, I stepped out for a while, but I would like to come back now.

Now what does it mean for a mathematical structure to exists? Do we need a proof? What are these structures that exist within our universe w/o having the ability to be justified by our universe?

Let us assume that our universe exists (only because we can state it) and that it is a computer then there are some mathematical motors or structures existing to give it its internal coherence even if it is not complete (of course it is in creation) ! A self evoluting machine...

 

[ConradDJ]

So my question, as you could probably guess, how you can tell a physical system from a purely mathematical one? (this question is not so easy as it sounds)

Dmitry, you are right on the money with this parenthetical remark. I think there is a fundamental – and very obvious – difference between physical systems and mathematical ones... but it is not at all easy to be clear about this difference. When I say obvious – well look, you can bang into something physical, but not something mathematical. That would presumably convince anyone but a physicist!...

But I don’t expect it to get anywhere with you or qsa, who understand physics (including banging into things) to be mathematical. If I understand you, you would say the above-mentioned difference is between mathematics that’s in your mind or in a textbook, and mathematics that really exists “out there” in Platonic eternality – one small part of which is what we experience as our physical world.

So how do we tell if the world around us is “just mathematics” or something more – and in what sense could it be “more”?

If we assume the physical world is a set of given, well-defined facts, I would say you are essentially right – or at least, right enough that there’s no point in arguing about it. Some of the facts would fall into mathematical patterns; others might just be random data, that can be located / defined in a mathematical framework. In that case I’d be happy to assume that someday we’ll have appropriate mathematics to describe all the facts... and if you want to say the facts are mathematics, fine... we’re down to semantics. In any case we would have something like a one-to-one mapping between the physical and its mathematics.

So is the physical world more than a set of describable facts? Yes – for one thing, it ’s a system that does its own describing. It’s a network of data-channels that communicates information about every part of itself to other parts. And a set of contexts that make incoming data meaningful for setting up other contexts.

There is a spacetime structure to this network, such that at any given point, information about certain other parts of the world (past light-cone) is accessible, while information about other parts is not. And there is an interactional structure such that in any given situation, certain information is measurable, while other information is not. And at any given point, the accessible / measurable information sets up a structure of possibilities (wave-function), out of which certain new information becomes “fact”, that gets communicated out as part of the base-information for other situations that create other facts.

So maybe your metaphor of “dead” mathematics and “living” physics is apt, in a certain way – though there’s nothing “magic” in this picture, this is just well-established physics. But it looks like physics is doing something that we don’t expect mathematics to do.

What we expect mathematics to do is give us coherent, more or less consistent descriptions of given structure. If we assume physics is just “a given structure”, then it’s not essentially different from mathematics. But we don’t expect a mathematical structure to create partial descriptions of itself and send them to other parts as a basis for new partial descriptions, or create measurement-contexts in which new information can be defined.

As I said above, I’m happy to stipulate that each component in this physical system will someday have a good mathematical description. My point is that there’s a functionality involved in how these components work together that amounts to “being physically real” – and that goes beyond what we think of as mathematical structure. But I admit that this functionality is very difficult to be clear about. And if anyone wants to take this as a sign that the whole idea is nonsense, I can’t very well blame them!

But here’s my question for you – if you take the physical world to be mathematical, then what in this mathematical system corresponds to a measurement? Or to the communication of information? In what way does this system provide descriptions of itself, and in what way are these descriptions made accessible only to certain parts of the system and not others?

In other words, can you really describe a mathematical system that looks anything like the world we live in, and does the kinds of things we see happening all the time? Or is it just a matter of faith that physics “must be” a mathematical structure “and nothing more,” based on our success in modeling many separate aspects of the world in equations?

 

[Dmitry67]

ConradDJ, that you for your detailed answer, even I did not understand it completely. You claim that physics is something more, then mathematics, but you fail naming that mystical "more", admitting that it is "very difficult to be clear about"

Can we agree on a simpler statements:

1. If there is a difference between mathematical and physical, that difference can't be tested experimantally by the frogs inside the universe.

2. If universe is perfectly emulated, then frogs can't detect if it is real or perfectly emulated

3. Perfectly emulated system is isomorfic to a real one.

4. Hence it is absolutely irrelevant if we are emulated or not. In fact, the emulation is an argument for MUH: if there are universes which can emulate others, then all sorts of universes MUST exist

If we agree the theory of natural numbers is the same no matter if it is written by ink, or in PDF, or scratched on a stone, so mathematics is independent from the substance, then we must agree that it is irrelevant if it is emulated or not.

(Q: ha, but what if emulator glitches or I destroy the Turung Machine?
A: We are talking about the PERFECT emulation. If you can't atop it it is not)

This is also an answer to tom.stoer (1,2,3,4)

 

[Dmitry67]

1 But here’s my question for you – if you take the physical world to be mathematical, then what in this mathematical system corresponds to a measurement? Or to the communication of information? In what way does this system provide descriptions of itself, and in what way are these descriptions made accessible only to certain parts of the system and not others?

2 In other words, can you really describe a mathematical system that looks anything like the world we live in, and does the kinds of things we see happening all the time? Or is it just a matter of faith that physics “must be” a mathematical structure “and nothing more,” based on our success in modeling many separate aspects of the world in equations?

1 Measurement is described by the physical laws of the Universe. As I said before, for the frogs inside Universe is real and measurable. It is like in MWI, narrow-minded observer in every branch would cry "only my branch is real!". The same in MUH - for any forg only "his" Universe is real.

2 You are asking for the ultimate TOE equations? Just a minute... where did I put them? ok, let me find a piece of paper where I wrote them... hope it is not in the bin...

 

[Dmitry67]

But do we know what energy is? I mean we do not really progress in labeling things of which we in fact ignore the signification.

All fundamental notions are just mere labels. They don't have any properties per se, all their properties describe their relationships with the other entities.

So the question "what is a true meaning of the Energy" either suggests just another step of an infinite reduction (like energy is made of energions, but in that case energy is not fundamental, so we have the same story again with the "energions") or is meaningless, like asking, "what numbers are made of".

 

[Fra]

I couldn't resist adding a comment on one more thing here.

So my question, as you could probably quess, how you can tell a physical system from a purely mathematical one? (this question is not so easy as it sounds)

It seems Dmitry is somewhat into Tegemarks idea of mathematical universe?

In a certain sense I can remotely connect to this, but I still see it different so I could at least comment what I mean with physical and non-physical inferece/math from my point of view because to me it has a special meaning:

Mathematics is the natural language of making quantiative predictions and calculations. So it is even more me of course. However mathematics has also evolved, just like physics. So in principle, there is no major difference. The quantiative framework is often more or less one-2-one to physics. I think Dmitry called it labels? I fully agree so far. I have no problem to imagine the class of all isomorphic constructs here.

One can even think of mathematical calculations as at least supposedly one-2-one with physical actions and processes (or inferences like I like to think of it). so far, that's fine.

So what I mean with non-physical inference, is when one observer; a human in most examples, uses some of his PHYSICAL mathematics, and try to impose it as one-2-one to a much more constrained system with very low complexity.

To me one basic conjecture is that regardless of the CHOICE of represenation or lables, there is an information theoretic abstraction where the COMPLEXITY is the same wether it's mathematics or a physical object, and this complexity constraints what are the POSSIBLE represenations.

What I for example mean is that, it does not make sense to picture a very simple low end computer to actually be able to run a a gigantic algorithem designe for a supercomputer. This is a decent analogy, since I can also accept if we choose mathematics as representation, that physical interactions are like computations. But then the question is which computations are going on in certain processes, and how does the "computers" look like?

This is again just different words for my "inference system". The reason I call in uncertain inference is that the computers themselves EVOLVE _in time_ therefore they change unpredicatably (but controlled) during actualy computations!

THIS is why I don't think it's as simple as deductions. One premise giving one output for example, since during the physical process of producing the output, the calculational machinery responsds to feedback and changes.

So when *I* talk about mathematics, of course all of that is physical for me, as someone noted, at least it's represented in papers, litterature etc. However, if we are trying to impose that very complex logical system into often ARBITRARY small systems, or even points! then we are abusing the complexity constraints.

Fwiw, I supect this is not going to make any sense, but it's my differentiation. It's exactly this I mean when I object to physical redundance of mathematics, in particular a lot of the continuum mathematics.

A final note: What do You think the common say UV infinities are a symptom of?

/Fredrik

 

[Dmitry67]

UV infinities are the symptom that distances can not be infinitely small, of course, what else?

Fra, what is more complex: TOE or Standard Model? Or SR/GR? In some sense, TOE is the most fundamental (does it mean that it is more complex?) So, Standard Model emerge from TOE on low energies, like Newtonian physics emerge on our daily life limit.

We are moving from Classical physics to TOE, in opposite direction. But during the history of our Universe the 'laws' 'evolved' from TOE to Standard Model, then even heavy quarks dissapered, then classical physics... I mean, as it cooled down, the laws evolved from TOE to Classical physic.

BUT: if TOE is the most complext one, then laws did not evolve, they had actually simplified!

 

[Fra]

UV infinities are the symptom that distances can not be infinitely small, of course, what else?

It was a bit of a rhetorical question, but I meant to link the divergence calcuations with our failuer to see that the inference system - beeing the "calculations" - must scale along with the complexity of the inference systems. So I think it's more than just distance. It can also be interpreted as an "information overflow".

But let's skip this, it was pretty much a rethorical question.

Fra, what is more complex: TOE or Standard Model? Or SR/GR? In some sense, TOE is the most fundamental (does it mean that it is more complex?) So, Standard Model emerge from TOE on low energies, like Newtonian physics emerge on our daily life limit.

We are moving from Classical physics to TOE, in opposite direction. But during the history of our Universe the 'laws' 'evolved' from TOE to Standard Model, then even heavy quarks dissapered, then classical physics... I mean, as it cooled down, the laws evolved from TOE to Classical physic.

BUT: if TOE is the most complext one, then laws did not evolve, they had actually simplified!

I see your reasoning, and it illustrates also the problems you face.

Your "TOE" are necessarily pretty much infinitely complex, from which the observed simplicity follows deductively? You are faced with an enourmous initial value problem, which basically is an infinite improbable initial state. I predict that the tuning problem you are faced with is overwhealming, like the landscape problem in string theory.

The amount of information needed to represent this infinite configuration space and the computing power/time needed to make computations on in would I think stall your progress.

Ie. I do not see how your vision can lead to improved predictive power, because it seems to me you are inflating the COMPLEXITY of your inference system to the point where it violates your own complexity. I thikn only something like a god could make use of your master plan.

BUT: if TOE is the most complext one, then laws did not evolve, they had actually simplified!

I have the requirement of beeing able to make computable predictions. A theory that isn't mangable in the complexity and computability sense simply isn't viable to me. I am taking his seriously in my view.

So in this view, there were no coherent very complex inference systems during this supposed big bang, this is why the complexity you envision (from which simplicity emerged) is not a proper inside view. It's to me an imaginary external view that lacks physical meaning.

So A TOE as seen relative to a human today would be complex, but a TOE seem from the emergent inference systems during say the big bang, would have been very simlpe. Simple mathematics and therefore also simple laws.

The question is instead not how an improbable initial conditions in an infinite configuration space evolves to the probable present, it's how during this process an ARBITRARY initial condition, constrained by a very limited configuration space, INFLATED the configurations space and while doing that evolved new interactions that was originalkly indistinguishable from each other.

/Fredrik

 

[Dmitry67]

Regarding the "improbable initial state" - this is a problem for Bohmians. As you probably remember, I am fanatical MWIer, so for me this problem doesn't exist - Universe started at very simple initial state (probably with null or very simple initial conditions) and the total amount of information in the Universe is probably 0

"but a TOE seem from the emergent inference systems during say the big bang" - wait, do you deny the existence of heavy quarks soon after the BB? If not, do you think that the laws they obeyed were simpler then the Quantum Chromodynamics they obey now?

 

[Fra]

Regarding the "improbable initial state" - this is a problem for Bohmians. As you probably remember, I am fanatical MWIer, so for me this problem doesn't exist - Universe started at very simple initial state (probably with null or very simple initial conditions) and the total amount of information in the Universe is probably 0

I have to admit that since I find a lot of the MWI reasoning a bit weird, I do not in detail follow the supposed logic there.

But in a certain sense, the "zero information" starting point is not too unlike my view.

However, in my view information can be created and destroyed, if you ackonwledge the intrinsic view, it's just that no observer EXPECTS it, and therefor all stable laws does conserve information. But information conservation doesn't apply to the case where the inference systems is either loosing or gaining complexity.

The zero information in my view, simply means that there are not yet any coherent observers. There is no information because there are no "memory devices" to put it crudely.

"but a TOE seem from the emergent inference systems during say the big bang" - wait, do you deny the existence of heavy quarks soon after the BB? If not, do you think that the laws they obeyed were simpler then the Quantum Chromodynamics they obey now?

This is a difficult question and for sure my ideas are not yet developed enough to explain quark interactions :)

But as a generic "prediction" of my vision, I certainly expext a unification of QCD, electroweak AND gravity. And the inside view of this must be simpler, at least in the sense of explaining a lot of the paramters parameters.

At the point where spacetime is emergent, there is unavoidably also emergent inference systsm that I associate with matter or "confined energy" systems. If this is new particles, or some of the existing standard model particles is way too early to see. But if my vision is to make sense, then there must be a level of a simple inference system from which QCD gravity and electroweak follows as the scaling of the inference system complexity/mass grows.

It's just prematute for me to have any expectations on this. But given the formulation of the standard model, as based on QFT, I think the explanation must start already at the emergent of the continuum and dimensions. And to assume that some non-trivial massive stuff like heavy quarks appear in the first part of reconstruction I find quite unlikely, unless they are the FIRST non-trivial systems to emergen as spacetime is formed. But I really can not comment on that at this point.

But it is definitely things that should be answered from a theoretical point of view..

/Fredrik

 

[Dmitry67]

The zero information in my view, simply means that there are not yet any coherent observers. There is no information because there are no "memory devices" to put it crudely.

No, system can be infinitely complex - and yet - contains no information!

Take an empty chessboard. It has only 1 possible state, so it contains no information.
Put 1 figure on any of 64 squares. Now you have 64 possible states and it contains some information.
Put 2nd figure - you have 64*63 possible states.
Adding more and more figures, you add more and more information, until.. until you start to approach the UNIVERSUM (in our case it is a full board)
There are only 64*63 configurations with 62 figures, 64 with 63 figures, and only 1 - with 64 figures.

'Something' is equivalent (on information level) to UNIVERSUM minus something.
Empty set is equivalent to the UNIVERSUM and contains no information.

In MWI Universe contains zero information not because it is void, but because it contains all possible states. Interestingly enough, for any frog the amount of information in the universe is huge.

P.S.
It would be interesting to develop a theory of relativity of information. For example, for observer who is aware that 2 particles are entangled, the amount information in such system is less than for an observer who is not aware of it.

 

[ConradDJ]

When a complex molecule is simulated on a computer with mathematical modeling, you can see how it vibrates and responds to environment, it looks alive... What we conjecture, that by a similar process we the “physical” become alive because of computation. The only difference is we can see the simulation of ourselves by ourselves without a computer screen.

Can we agree on a simpler statements:

1. If there is a difference between mathematical and physical, that difference can't be tested experimentally by the frogs inside the universe.

2. If universe is perfectly emulated, then frogs can't detect if it is real or perfectly emulated.

3. Perfectly emulated system is isomorfic to a real one.

4. Hence it is absolutely irrelevant if we are emulated or not.

Thanks for the lovely argument! But talking of “simulation” or “emulation” raises an issue that’s much easier to argue than what I was being incomprehensible about above.

There is no analytic solution to a problem as simple as the Newtonian 3-body problem. In other words, if I understand correctly, in a classical universe even very simple physical systems would constantly be finding exact solutions to problems that a computer can solve only approximately – and would be doing so in real time, with no expenditure of energy.

We don’t live in a classical universe, and it’s not clear how that affects the computation problem. On the one hand, the properties of systems don’t have to be specified by an infinite amount of information, and on the other hand the equations are a lot harder to compute.

But I think we can agree that any system capable of emulating the behavior of 3 particles is going to be a lot more complex than the 3 particles themselves, and it has to behave in much more complex ways. And of course, the computation problem becomes vastly more difficult if we have 4 or 5 particles – not to mention the number involved in any realistic physical situation.

The existence of computer simulations makes it easy for us to imagine that we also inhabit a simulation. But it’s easy to see this is really just a fantasy, if you think about the magnitude of the problem involved in, say, computing the paths of individual molecules in 1cc of air over the course of a second. This is something the physical world handles just fine, but no computer ever will.

I think your original idea was not about one system simulating another one, though... it was more like, the world does not need to be “simulated” or “computed” because it already is a mathematical pattern.

 

[ConradDJ]

Measurement is described by the physical laws of the Universe.

I would say this is a statement of faith, not fact.

Our closest approximation to a description of measurement is given in quantum “wave-functions” – which are mathematical entities, but rather vague ones. They refer to physical situations in which certain outcomes are possible – but the mathematics doesn’t actually say very much about those situations, it just assumes they are there, and that they can distinguish the various outcomes.

You certainly could not “emulate” a physical measurement-situation in any level of detail, by manipulating the wave-function used in connection with it. The math of QM is a very useful tool for predicting measurement-outcomes, but it doesn’t actually tell us much about what’s physically involved in a measurement.

And of course... the wave–function gives us only a set of probable outcomes, whereas in the physical world we get a random selection of an actual outcome. Yes I know, from an MWI perspective there is no “selection” and all the outcomes are equally “there”. In other words, in the big picture measurements don’t actually happen, and the wave-function is the complete picture. But this doesn’t get us closer to mathematics and physical laws describing what happens in a measurement.

From the perspective of any observer in any universe, the world is constantly offering up new facts that could not in principle be predicted on the basis of prior facts, and which often have profound consequences for what can be observed in the future.

So I think mathematics gives us wonderfully effective partial representations of many different (highly simplified) aspects of the physical world. If we take any small part of a measurement-situation, a photon or an electron, say, we can give a good mathematical description of it. But that doesn't mean we've described the structure of the situation as a whole, or described how it does what it does.

I don’t doubt that our ability to model more and more of the world mathematically will continue to improve. But the leap to the idea that mathematical structure per se explains what’s going on in the world is a long leap of faith... or maybe, a default position based on the difficulty of imagining alternatives.

It’s not clear what’s going on in quantum measurement-processes... but to me, MWI just offers a nice way to avoid dealing with the problem. That’s a sensible choice to make based on a faith that the world is mathematical, and that issues we don’t know how to frame mathematically can’t be really important. But I don’t believe there’s a strong argument there.

 

[Fra]

No, system can be infinitely complex - and yet - contains no information!

I know what you mean, but then your certain information measure and state space is a baggage. This baggage carried background information in my view. So your information measure is "relative to" the context, which is fixed in your view.

I don't think there is an innocent background, in my view the context is evolving. Therefore there exists a feedback between information, and information carrier.

I know you can define microstructure of infinite size, and an information measure. Then zero information is simply the equipartitioning.

But the ergodic hypothesis is not unique, this choice does carry background information. In my view I am trying to account for this.

This is why I also talked about a reconstruction of information theory, which is pretty much on the same table as the reconstruction of probabiltity theory.

The ambition is exactly a theory of relativity of information (and inference) that you mention! So if you like that, then there might be some grains in here that you can like as well. Now, I think a theory of relativit for information necessarily evolves, because there exists no static fixed solutions. The inference processes resulting from this relativity, are physical ones, that possesses things like inertia etc in my view. This is how I intend to extract physics from the actual inference process, and the evolution of matter (and distinguishable law) from the evolution of infernefce system, by the requirement of preservation. "Consistenctly inconsistent" systems are not present in the equilibrium "population", however "transient inconsistency" is unavoidalbe and part of the evolution/development.

Edit(with regards to post 331): The connection to the holographic principle is an interesting lead, there is actually some interesting connections to that and to my abstraction of inference system, but currently I'll be away for some days and it's unclear wether I will have any internet access. There is actually a mathematical abstraction of an inference system, and in there there is something you can call a communication channel, and this has as size measured by the distinguishable states. This "size" or area, together with some other stuff, like the information capacity on one side of the "screen" limits the inferrable information of the other side. But this is a pure abstraction so far, the screen is not interpreted as a space-area. OTOH, this would clearly turn into something interesting as spacetime emerges. This is one of the things I'm working on and it's not yet finished. But there are at least potentially very interesting links.

In particular am I interested in finding information theoretical interpretations to several constants.

About overestimating information, that is also an interesting direction of discussion.

/Fredrik