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Inductive inference

  1. Sep 15, 2010 #1
    thank to Marcus for finding this paper

    This paper handles subjective inference from an informational theory viewpoint, if i understand him wright he keeps objectif reality out the door.

    http://arxiv.org/abs/1009.2423
    Quantum theory as inductive inference
    Authors: Ryszard Paweł Kostecki
    (Submitted on 10 Sep 2010 (v1), last revised 14 Sep 2010 (this version, v2))
    Abstract: We present the elements of a new approach to the foundations of quantum theory and information theory which is based on the algebraic approach to integration, information geometry, and maximum relative entropy methods. It enables us to deal with conceptual and mathematical problems of quantum theory without any appeal to Hilbert space framework and without frequentist or subjective interpretation of probability.
     
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  3. Sep 15, 2010 #2

    Fra

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    Thanks for the link, I'll look into that later. The general domaiin of reasoning is in my taste, but there are still quite different approaches within that general domain. i'll get back when I've had tim to skim it.

    /Fredrik
     
  4. Sep 17, 2010 #3

    Fra

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    I haven't had the time to analyze the paper in depth. Also are are almost no arxiv references which makes it timeconsuming to locate references. Even though the paper is not so many pages, as it's a lineout of a series or more in depth reasoning (yet to come as I understand) it's very compact and I didn't get a proper handle on their thinking from the first skimming.

    The way I usually approach ideas when I read papers is to first try to understand, what question they are asking, and then the general way of reasoning in order to arrive at a solution and then judge if it's worth more time; only then does details become relevant.

    The general idea that quantum theory, is best understood as an inference. IE. the EXPECTATIONS of quantum theory are simply inductive style inferences, conditional on the observers prior info. And that the EXPECTED dynamics INBETWEEN observers (as seen by a third one) is also just ruled by a negotiated/evolved inter-observer inferences, is something that's exactly what I think is correct as well.

    This seems to be loosely in their spirit too. I just need to analyse their details to understand the specific constructions.

    The use the word intersubjective inference, which normally refers to something in between objective and completely subjective inference. Of course this is exactly what you get from subjective inferences that are negotiating end evolving. ie. the "intersubjective inference rules" does correspond to equilibrium points. Certainly we expect OUR universe to sit on such an equilibrium point.

    You can call emergent "social laws" also as intersubjective laws. It's somehow an emergent intersubjective agreement based on a population of subjects.

    The real quest here, is to try to see, what possible such intersubjective "equilibrium-measures" that would be expected. Ie. can the analysis of the inference systems, and how they INTERACT be used to somehow produce a "prediction" on the expected negotiated intersubjective inferences?

    I think so, and I think this paper somehow has a suggestion on this. But they seems to refer to "unique" constructions which worries me; but it could be just a "truncation" of an otherwise good reasoning. They seem to make use of many mathematical assumptions and pretend it has not physical significance. But I need to spend time on this paper and try to if possible locate some of their references to be able to judge it.

    The general idea to use deviations and information diveregences to define information geometry is also prefectly in line with my personal thinking.

    The one suspicion I have is wether they acknowledge thta the "intersubjective" rules of inference must in fact be seen as evolving, and therefor statements such as finding a unique rule sounds ba dto me. But it could be due to my first impression only.

    Does anyone know who Ryszard Pawel Kostecki is?

    /Fredrik
     
  5. Sep 17, 2010 #4

    marcus

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    http://www.fuw.edu.pl/~kostecki/school.html

    I guess he is a Physics PhD student at the Uni Warsaw. One of the local organizing committee of the highly successful QGQG school March 2007 at Zakopane. Two PF members (fh and francesca) went to the school--they would know him in real life. His interests are listed at his Warsaw U page.

    http://www.fuw.edu.pl/~kostecki/

    Again Richard was one of the committee of 4 local organizers of the March 2008 QG workshop at Zakopane:
    http://www.fuw.edu.pl/~kostecki/zakopane08/index.html
    I gather that was very successful as well.
     
    Last edited: Sep 17, 2010
  6. Sep 20, 2010 #5

    Fra

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    Thanks Marcus.

    There is one general vision where I fully agree with the spirit of the paper, and it is the idea that - just like framework of thermodynamics and stat mech essentially follows inference models. Ie. predictions of thermodynamics are rational expectations based on inference. This applies even to the dynamics, as entropic dissipation is nothing but expected dynamics from inference models based on commutative microstructurs of probability theory - quantum mechanics and in particular things like the uncertaint relations etc, are nothing but expectations from inference models, but based on non-commutative microstructures.

    So in this sense, what they suggesting is a "generalisation" of probability theory to incorporate non-commutative structures. Then it's not longer a propert probability theory, but it still inference. This is a generalisation that is needed I agree, simply because the inference models we need can't be based on probability theory, because of several reasons. The continuum but also the fact that real life information aren't stored in commutative structures. This is why bayesian inference is a special case. I think this should be standard though, not controversial.

    I'm convinced that this is going in the right direction. The question what the exact generalisation is and how to connect the abstractions to physics, and then not only QM, but also full QG context.

    But when we look at the details I'm not sure I appreciate the specifics. They mention something like replacing ontological things with abstract languages (that thus need not be motivated) and this is structural realism. It strikes me as similar to Rovelli, although he doesn't speak of inference at all.

    I would like a version of this, where information capacty connects to complexity of matter (association mass/energy) at a quite basic level. They also escape too much in the mathematical realm, and then the problme is that even if a possible solution comes out, it's relevance to physical inference is unclear.

    One of my points is that I'm convinced that one of the main constraints of physical inference, is the complexity of the inference machiner and the encoding. IF this isn't acknowledge I somehow loose contact with things.

    But I think it would be interesting to folllow up the work of Kostecki and his future papers. I think this direction of thinking is needed and should be encouraged. Even i I may not undersstand his detailed idea, I like the overall inference perspective and this is in my eyes at least orders of magnitues better than the spin network and "string" pictures :)

    /Fredrik
     
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