Is Information Theory Driving Astrophysics in the 21st Century?

[Fra]

I want to find an induction principle (like Ariel Caticha) that by construction works by the minimum speculation principle, that generates a guide for betting. This togther with the unavoidable element of uncertainty I want to use to infere the laws of physics and probably also to guess the most likely simplest possible AND distinguishable mictrostructure.

An addiotnal thing that may or many not clarify what I tried to convey:

The obvious approach I've found is bayesian reasoning and bayes rule or the "analog of bayes approach" in any non-probabilistic approach but there is still some unsatisfactory things there... The choice of initial prior and howto infer the probability space it self, this leads to inductive principles to the probability space itself / alternatively the microstructure... so we get like an induction principle, not only for the "probability distribution" or state of the microstructure (am speaking loosely here), but also for the probabilti pace / microstructure itself. Giving a non-linear and quite complex feedback.

Chris, do you have any direct pointers for such specific application, assuming I made myself understood in the first place :)

I have initiated a construct on my own, but progress is slow.

The idea is that the simplest answer to the question what is the microstructure of reality is that we don't know. Then I question that answer, and want a better one. It seems an arbitrary guess is better than no guess - so someone may exlaim STRINGS (better than no answer). Then again, I question that answer and want a motivation for the guess. How can we formalise an inductive reasoning when the underlying mictrostructure is part of the unknown? Not only is the state of the mictrostructure unknown, the mictrostructure itself is unknown!

That is my problem, made short.

Any ideas relating to that, would be highly appreciated.

/Fredrik

 

[Fra]

Addition to answer the estimated comments.

This induction suggest a nonlinear thing or an algorithm that can be approximated one level at a time by wildly assuming a mictrostructure of the landscape of the world of misctrostructures at the desired level. But what kind of memory capacity in natur eis needed to reflect this degree of sophistication? This is where I see an exploit to rule out overly complex things, by trying to assign information also to the framework, effectively giving also the framework "mass"/"info capacity".

This kind of reasoning seems to naturally lead to at least gravity like phenomena. This is why I figured this "problem" should be dead on to someone like you, except that perhaps it's too much potty philosophy for your taste? Comment?

/Fredrik

 

[Chris Hillman]

I guess I might ask, extract the pure math of what? :) Perhaps this explains in a nutshell my angle. I see many ways of coming up with mathematics, unless I know what how it relates to reality.

I'm sort of trying to apply this to what I percept as reality, I am trying to find a relation between reality and a mathematical formalism.

Define "reality".

From my point of view, "an energy partition" is quite fuzzy to start with, since what is energy? Unless the notion of energy is defined, the entire construct is compromised

Maybe you misunderstood something?

Boltzmann entropies are a property of finite partitions; since any function induces a partition into preimages, we can associated a Boltzmann entropy with any function on a finite set. Neither the set nor the function need have any physical interpretation.

Meaning that the part of history that has not dissipated from the observer memory is at hand.

Assuming that you are indeed responding to what I wrote, none of what I said involves any notion of an "observer".

Also I think that if I were to define my application in your preferred language, I would have to quite some time to refresh my group theory skills

The undergraduate text by Neumann et al. and the undergraduate text by Cameron are more than enough background.

it's hard to convey something that is not mature...I offer my apologees in advance in case this is message appears scrambled.

None of your posts #35-37 make sense to me, so allowing your ideas to mature while you do some reading seems advisable.

 

[Fra]

Hmmm Interesting, I guess this settles it for now at least.

I appreciate your feedback. It was interesting to see how remarkably poor my communication performed.

But thanks for the responses and your time! Even a misunderstood communication is feedback, I obviously need to work out my ideas in more detail. I guess I was completely mistaken that the problem I consider would be easily conveyed to someone with your background. But that wasn't so.

/Fredrik

 

[Chris Hillman]

I suspect that you need to acquire much more background to refine your thinking, and also to understand how to explain your refined thinking to others. Your posts also seemed rather "manic" to me.

 

[Fra]

To the others interested in this thread, please keep up the discussions. Don't let my communiciation to Chris halt this thread! I'd personally like to see more reflections on this topic in relation to physics.

It would be interesting to hear the views/thinking of everyone else, fuzzy or not. Just spit it out and see what happens :)

/Fredrik

 

[Chronos]

It might be interesting to analyze radio communications using information theory. A simple ping [morse code] model would probably be manageable.

 

[Chris Hillman]

Been there, done that

It might be interesting to analyze radio communications using information theory. A simple ping [morse code] model would probably be manageable.

Sigh.. I refer you to Shannon 1948 (see link in second paragraph of http://www.math.uni-hamburg.de/home/gunesch/Entropy/infcode.html). Isn't anyone out there planning to follow my advice and read this paper, which is by common consent one of the greatest scientific papers of all time? And also one of the funniest? I mean, what's not to love?

 

[Fra]

I don't know what Chronos application is but if we are talking about say ordinary communication like TV, radio etc... Shannon indeed seems like a good and right thing to start with. This is not quite what I was into that's why I didn't comment.

I got a feeling that people dare not say anything in this thread now out of fear to seem like fools relative to Chris massive expertise :)

Shannons paper http://plan9.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf is 55 pages, and in the introduction it says...

The recent development of various methods of modulation such as PCM and PPM which exchange bandwidth for signal-to-noise ratio has intensified the interest in a general theory of communication. A basis for such a theory is contained in the important papers of Nyquist1 and Hartley2 on this subject.

...

The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point. Frequently the messages have meaning; that is they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem.

As far as I see it, this problem description seems to take for granted that the logical problem of defining the comparasion of the message sent by the sender and the message received by the receiver is solved. How would you make this comparasion, without communication in the first place, and where do you get that trusted communication channel from, and how is that selected?

The way I see it, this is a bit analogous to the problem of
1) how two different observers in different frames can compare vectors? There is obviously need for some kind of communication? And starting from no prior common references, how can this be done?
2) how does two different observers - starting out with no common references - in general compare their observations? they need to communicate indeed. But I think a secure communication is something emergent. From what I can see, this is not a problem Shannon is treating.

So it seems Shannon mainly has in mind what he calls the engineering problem, like TV, radio and the likes, in which case the trusted channels are easily selected.

/Fredrik

 

[Chronos]

There is a certain amount of fear, and respect for Chris. I was hoping for a pedagogical review. The 'ping' model I proposed has already been done - as I am sure Chris knows. The links Chris gave, unfortunately, were mostly broken and the 'Shannon' link is in PS format - which is unfortunate for me. I read Shannon's paper about 20 years ago, but would not object to reading it again.

 

[Fra]

The last link I supplied is a pdf, and it's the very same paper as the postscript file.

Here is also a simple quick&dirty online postscript to pdf converter:
http://www.ps2pdf.com/convert/convert.htm

/Fredrik