Exploring the Universe: Describing it Through Logical Axioms

[Phred101.2]

After reading about someone who has attempted to describe the world without mathematics, and after looking at some of the projects around on the web that are trying to construct "model universes", I have thought about this and about the best way to describe the "data structures" an informatic model might need, and a question I have is:
How far is it possible to describe the universe using logical axioms? We know that there are symmetries in the universe and here in our immediate locale. The most obvious is the one Einstein uncovered.
Can the equivalence of mass/energy be viewed (and I know this is getting straight into math concepts) as a 2-d plane, where either side is "visible" to the universe, like a reflection that can only be viewed "one of two" ways? So there is no "degree-of-freedom" for mass-energy to "become" or reflect any other "image" at the universe (the mirror has no thickness)?
Could this kind of axiom be extended to other symmetries? Or has it been tried and abandoned because a reference (for us humans) is always needed, rather than an indefinite number of points on some plane?
Sorry if this doesn't make much sense, but I've been trying to think about the universe and what it was (like) before observers came along. Also about how matter "communicates" -via photons, and charge and gravity, and of course superposition.
If you consider a universe that is something like ours was meant to be, say, after inflation but before the condensation, sometime during the first 0.3b yrs, so no atomic hydrogen or deuterons, just lots of vibrating matter and energy, along with the other "interactions":
How could this be treated (successfully or otherwise) as a "network" or connected graph of some kind, where connections are the interactions? Or does this all sound completely impractical and obviously some mathematical model is where to start first?

 

[OOO]

The extent to which nature can be described by algorithms that follow from some axioms or other prescriptions is an open question, and, this is what physics is all about. Even if the answer was known today, it certainly couldn't be given in the context of this thread.

Keep on thinking about reality, but your above comments make me remember you of one thing: for every single fact in physics there are usually several different representations. One representation being clear and graphic to you (or even to the majority of physicists) must not be confused with reality itself.

 

[Chronos]

Reality is like looking into a mirror. At some point, logic collapses and you face a singularity. All modeling approaches collapse as you approach t=0.

 

[Phred101.2]

OK thanks for your comment(s). I don't want to do much more though, than look at building some model and seeing if it can do anything interesting. To that end, I thought about how 'simple' a model needs to be -to start, and how the universe, at least before matter condensed and there was a bit more "wiggle" room, so to speak, was in a fairly 'homogenous' state.
So its a bit like trying to see what the minimum "genome" is for a universe, in some sense. Also a look at what we do know, and how we came to know, or how we initially noticed that change could be recorded and used. The information we started to "remember" became more and more useful, but it started somewhere, and we must have made basic observations at the first (which presumably a lot of other mammals do too), before we started keeping track of days and moons, say, by maintaining oral and symbolic (written or painted) 'memories'.

 

[OOO]

Using intuition can be very satisfying. But from my experience I tend to say that intuition is shaped by experience. As to physics, intuition is shaped by experiment and theoretical discourse.

I don't believe there is any a-priori intuition you can use for understanding nature without using math or experimental investigation. Of course, you always have your mental creativity and this probably leads you to some new insights, if carefully applied to experience or math. But there is no assurance of such a benefit.

Would you expect that a Cro-Magnon should have been able to intuitively grasp the laws of electromagnetism (which is proven to be a highly accurate description of almost everything in our daily lives) ?

 

[Fra]

Fred, from some of your other posts, I personally think your thinking is developing in a good direction. You seem to be doing philosophical reflections of some important but yet unanswered questions from the information perspective. Keep up the thinking. I think reflecting upon the strange questions is a first good step in refining and finally answering them.

How could this be treated (successfully or otherwise) as a "network" or connected graph of some kind, where connections are the interactions? Or does this all sound completely impractical and obviously some mathematical model is where to start first?

In line with Chronos post, it seems the challange is howto construct the universe from nothing. This to me seems to suggest that it makes little sense to consider a background structure, because how can this structure be motivated?

What kind of model can self-destruct and the again self-assemble and still be somewhat consistent? The main option I currently see is a sort of learning/self-organisation model. And it does not make sense to think of a computer doing this learning, because the "computer" would clearly constitute a background structure, which is not acceptable. So the computer must be self-assembled! And the "computing devices" are probably nothing but matter and physical systems themselves. An atom could easily be "pictured" as a computing devices. What kind of formalism do we need for this? That's my question, and it's probably not easy to answer. But it's my personal conviction that the laws of physics is best understood in terms of generic self-organisation, just like biology is. This is my personal expectations on the "next generation of fundamental models", and I have a little hard to see how this can be done without a somewhat improved formalism. And I have even harder to see how we can insist on fundamental unitarity in such new formalism, but that's just me.

/Fredrik

 

[Phred101.2]

Could the argument be made that modelling it in any practical sense is ultimately impossible, therefore? We can only ever consider such a thing, but never build it (a model universe that "works" in a representative way)? Ultimately an axiomatic approach defeats itself (because we can't include the things in the model that are fundamental axioms, type of thing...)?

 

[Phred101.2]

There's the big question of superposition, the newest surprise in the universal bag of tricks. Because our concept of entanglement is a "unknowable state", that resolves into a single (from some infinite) value. The "entanglement info" or projection, is indeterminate (uncountable), but when we 'count' it, it becomes a real mass/energy in the world. Nonetheless this uncountability it seems, is a useable resource, even when it doesn't "exist".

 

[Phred101.2]

Also not to forget that this mysterious property seems to "require" an observer so it can "contribute" its information, otherwise this presumably remains "unknown" (to any part of the external world). So we need a model that contains observers of some kind (when you think about it, nothing else that is "known" can really "exist" except for the observer of it -which argument seems to get stuck in the same black logic hole...)

 

[Fra]

Could the argument be made that modelling it in any practical sense is ultimately impossible, therefore? We can only ever consider such a thing, but never build it (a model universe that "works" in a representative way)? Ultimately an axiomatic approach defeats itself (because we can't include the things in the model that are fundamental axioms, type of thing...)?

I don't think I understand this question. "axiomatic approach" to me is sort of synonymous to the pillars that is responsible for the supposed mapping between "reality" and our mathematical model, and then working from the mathematical formulation of the axioms, the model is easier to give mathematical rigour.

I think the critical part is howto choose axioms that make our description as simple as possible. For example, I am not very fond of the axioms/postulates of QM. From a mathematical point of view I see no issues, the real issue is if that axiom system is the best way to describe reality or not, which I don't see as a mathematical question.

I think the difficult thing that is sometimes confusing is to try to think beyond ourselves. We are humans and everything we think live inside our brains, so what does it mean when we are trynig to project our models on say elementary particles? How does an atom perceive the world? What does my ideas mean, in terms of something that lack a human brain? It means we need to find a more fundamental level of communication and relations. I tried to get some experience in this some time ago, by trying to imagine myself beeing a cell. What would I do if I were a yeast cell? Meaning also what could I do? I would have no brain, so my reflective as well as handling power would be strongly constraining. What are the universal principles that applies to all complexity scales, and that can provide a cross-complexity communication?

/Fredrik

 

[Fra]

There's the big question of superposition, the newest surprise in the universal bag of tricks. Because our concept of entanglement is a "unknowable state", that resolves into a single (from some infinite) value. The "entanglement info" or projection, is indeterminate (uncountable), but when we 'count' it, it becomes a real mass/energy in the world. Nonetheless this uncountability it seems, is a useable resource, even when it doesn't "exist".

This is philosophical reflections...

If my thinking, the "superposition" is realized/encoded in the microstate of the observer and is therefore subjectively real. Since this is encoded in the observers microstate, the _superposition itself_ (not the individual options) is what influences the observers next change/move, the actual result after interaction will not have an impact until _after_ the interaction. I don't see any obvious logical problem with this.

A particle doesn't "calculate" probabilities of course but I think that there is still sort of a discrete representation of an "effective probability" in terms of the microstates and microstructure, because due to intertial phenomena some changes are simply more "likely" than others.

/Fredrik

 

[Phred101.2]

Perhaps the "hiddenness" of superposition information is just a facet of our observation. So it always exists as a single "potential" quantum value, rather than any potentially infinite value (of some quantum), this resolves into one of an infinitely possible values. But this leaves the question of how it achieves this "infinitely possible" state, or where it "borrows" the ability or means to do this from.

Despite a 'particle' or a superposition (of properties which are wave-like) being indifferent to calculation, this is what some research groups appear to be getting closer to doing in a non-trivial way. To them, I guess the question of observers being a requirement is moot if it works. We still don't know what makes gravity work either, but this hasn't been a big deal (except to the thinkers).

 

[Fra]

Perhaps the "hiddenness" of superposition information is just a facet of our observation. So it always exists as a single "potential" quantum value, rather than any potentially infinite value (of some quantum), this resolves into one of an infinitely possible values. But this leaves the question of how it achieves this "infinitely possible" state, or where it "borrows" the ability or means to do this from.

I don't completely understand your wordings.

But to guess, my personal vision of this microstructure of the observer is that this is relative as well. Another observer may describe the microstructure differently, and in particular the degrees of freedom. I imagine the "saving grace" that keeps the world from completely falling apart is that the ongoing interactions (communications) is what keeps the parts together, and yields the apparent stability. I expect intertial phenomena and also gravity to somehow be a consequence in this not yet identified formalism.

The microstructure of the environment, is in my thinking, mirrored or "projected" onto the microstructure of the observer, but the "projection" itself, IS realized by the interactions. I think this is philosophically very plausible once you think about it and is somewhat intuitive, but still it is hard to nail the formalism that would give this a solid representation. My only attemtps so far involves probabilities defined in terms of distinguishable combinations of microstrucutre states, but the complication factor is thta the microstructure isn't given, this is is also described probabilistically. One fundamental problem IMO is to find a fixed point to relate the structure too. It would be possible to invent some background space and then let the model live in there, and by choosing the background space (manually) it should be possible to find an effective model that works. But that wouldn't be a fundamental model IMO, and thus philosophically unsatisfactory, at least for me.

This is why the most interesting idea to me, is to find a formalism where the probability spaces (indirectly the microstructures) themselves are dynamical, and thus subject to uncertainties just like the states of the microstructures are. The challange seems to find the consistent principles that yields stability and a non-trivial structure formation (effective elementary particles). And all this without introducing ad hoc structures. This is why I think a sort of self-stabilisation seems like the only acceptable idea. Certainly once we have the concept of intertia, and inertia in information updates, even "asymptotically" unstable systems will enjoy a transient effective stability that is simply due to intertia.

/Fredrik

 

[Phred101.2]

Fredrik:
You appear to imply that reality is an evolving, or telic, process. The universe 'stabilises'; perhaps matter "tells itself" to behave, to change or do something useful... I think this fits ok with other, somewhat whimsical explanations. The question would then be: "why does it do this?". We are definitely at the point of explaining superposition in epistemic terms (as gravity is understood, say). We might also, because of the 'peculiar' nature of this property of matter, find out about why it does what it does (or appears to). This will, I believe, involve a revolution of some kind in scientific thinking about the nature of reality, and this seems to be the expectation I come across reading papers on the subject.
Observer and observed appear to be the 'concept" we have of "available" information, and there has been discussion about what we need to do to change our 'expectation', perhaps. The philosophical conundrum with observation of quantum states is being analysed from various angles. I for one am quite interested in this, and what the researchers have to say -because they, if you like, are doing much of the observing...

 

[Chronos]

I can't add much substance to what Fra already said, other than agree. Science is hard, especially cosmology. Small steps are necessary.

 

[Fra]

You appear to imply that reality is an evolving, or telic, process. The universe 'stabilises'; perhaps matter "tells itself" to behave, to change or do something useful... I think this fits ok with other, somewhat whimsical explanations. The question would then be: "why does it do this?".

Since I am trying to find a satisfactory answer myself, I do not have any good answer yet, but to comment at least in line with the previously elaborated philosophy of science and vision:

> The question would then be: "why does it do this?"

I own my questions. I currently think (who knows what I will think tomorrow) the only acceptable answer is that "it does this" because there is no other viable choice :)

What does this mean? The stabilisation must is not put in by hand by some "magic mechanism" in the theories, the whole idea is that the uncertainty analysis in this formalism should show that there exists in effect a "natural selection" that can be explained in terms of (albeit floating/dynamical/adaptive) probability framework.

So the answer should be that nature does this because it's the most probable way of doing it, and this is our best answer.

That's is the idea IMO, but it remains to find a formalism, and really work out the connections here and prove that the framework has these formal properties. Note the similarity here between a general learning model. A self-sustaining adaptive model has two choices, adapt and survive, or fail to adapt and die. The idea is simple and can be sort of stated as a communication problem where each observer is a transciever, but they have no prior agreed upon protocol or even communicatio channel! The transcievers have to FIND THIS OUT themselves, and work towards a mutual agreement and so to speak "learn to" communicate. And in this process the transcievers are evolving. Clearly there will be some kind of selection of transcievers here. Those who never learn to make sense out of anything will remain marginal. I see potential to identify strucutres and forces in such a picture, but it's hard. And the problem is that there is no obvious starting point. We have to build our starting point, and then be prepared to adapt it.

But this certainly tangents the philosophy of science. I can only argue for my own personal standpoint. And I judgde the relevance of all this by it's success in bringing me forward, in line with the above.

/Fredrik

 

[Phred101.2]

Life appears to be something that is and does because it simply is that way (perhaps it's an inevitable part of everything).
It has to change (or it dies). This change necessarily is an 'observation' of change (both of itself and the world). Observation is itself change (or it needs change). What does that 'make' a memory (become)? We believe memory to be our 'advantage' against the inevitable changes, like a record we can keep to remind ourselves that we're here...

 

[Fra]

What does that 'make' a memory (become)?

This is an interesting question. If we take memory to be part of some ontological construct and then considers evolvment of the contents of memory and memory itself as epistemology, then we are facing a self-feedback. It seems intuitive that one without the other makes no sense, so somehow this seems to be different view of something fundamental.

Since there is not obvious fix-point starting point, my current focus is to try to formalise the self-feeback mechanism that explains the duality between ontological constructs and epistemological constructs, and hopefully one can unite these. And if my intuition is right, this will sort of prove to be impossible to do in a fixed model, an instead one leads to apparent circular reasning, but this circular reasonig is not circular when you look closer - it is evolutionary! This is what I imagine is responsible for the "forming time". The essence of nature is a "differential questions", and each answer transforms the question into a new question.

I don't remember the link but there are some philosophical papers trying to formalise the concept of "what is a question", and some ideas were to identify a question with a subjective probability distribution. It defines both the question and the estimated possible answers. And the answer (new information) will revise the question, and a New question will form, and this just goes on...

I think we are closing in on a reasonably close idea of what the questions are. I like your perspective.

The task for me now, is howto find the mathematical formalism that implements these ideas into something quantitatively computable. My emphasis on all this philosophy is that it defines to me what i am looking for and a guide in the search.

/Fredrik