Re: [Fis] QI-session: concluding remarks
Dear Andrei and colleagues, Thanks a lot for your re-capping of the session. It is a very thoughtful perspective on information from the quantum side. My only comments would relate to your (partial) identification of models, reality, and mathematics. It sounds too strong to my hears. We have cut science from its human origins, and then we resort to very curious reification myths. How does the practice of science relate to our human nature? The tentative new branch of neuromathematics (it has already surfaced in past discussions) could throw interesting new light on the several fascinating topics around the necessarily social construction of human knowledge... I join your concerns when you state: I am trying to sell the idea that the whole quantum enterprise is about simplification of description of extremely complex physical phenomena. I developed models in that the quantum probabilistic model appears as a projection of more complex classical statistical model. Then I proceed: Wau! In such a case it seems that quantum probability theory and quantum information could be used everywhere where we could not provide the complete description of phenomena and we just try to create a simplified representation in complex Hilbert space. So one can apply quantum information theory everywhere, from financial mathematics to genetics. Months ago, when discussing on biomolecular networks, I argued that rather than a classical state the central info construct of the living cell should be the cycle, then implying the advancement of a phase (recapitulating and somehow making continuous the classical biomolecular views of Start, Gap1, Mitosis, Gap2 as discrete phases of the cell cycle) maintaining at the same time a continuous adaptation of the inner molecular population to the environmental demands. These biological sentences may sound very different from quantum statements, but I do not think so. My opinion is that the the living cell and other genuine informational entities share a fundamental adaptability problem, having to fit with with limited processing resources to an open ended environment, and then having to tune their production-degradation engines to cope with both their own phase in the cycle and their external happenstance. Michael Conrad produced great stuff on formal quantum-inspired approaches to ecological adaptability (see Kevin Kirby in this list too). And it could be done for aspects of nervous systems and economic life too... Unfortunately a Gordian knot of themes appears: sensibility, robustness, networking, fitness-value-meaning, adaptability, evolvability (to mention but a few). The future will tell whether we are able to trascend formal analogies between realms and achieve a new, more catholic approach to information --none of the current approaches has achieved a breakthrough yet, so the need for our exchange of views! I also think that recent developments in string theory are a good help --and quite inspiring-- for our problems. See Leonard Suskind, with his Landscape approach (The Cosmic Landscape, 2005). Breaking the continuous at the Planck scale means also a new hint on where we can situate fundamental laws of nature physically --a question not responded yet in the discussion, for my taste. Thanking your inspiring comments, Pedro ___ fis mailing list fis@listas.unizar.es http://webmail.unizar.es/mailman/listinfo/fis
[Fis] QI-session: concluding remarks
Dear Collegues! During summer holidays we were involved in interesting debates on Quantum and Classical Information Theories (which were tarnsformed finally into a deep discussion on meaning of informartion and its reality). I would like to present some concluding remarks. After this I propose that everybody who is interested can send his own concluding remarks and after that (may be in one--two weeks) session will be closed. I recall my viewpoint: We all work with models of reality. We cannot understand reality, but only describe it by using this or that model. The most advanced way of modeling of reality is mathematical modeling. Sometimes reality is even identified with a mathematical model. This happened with the modern picture of space-time reality which is based on using of real continuum. I pointed out that there were attempts to propose alternative models of reality even for space-time, e.g., p-adic models. There are two main mathematical models of information: a). Classical thermodynamical model in that information is defined from entropy and the latter is based on the Kolmogorov measure-theoretic definition of probability. b). Quantum information model in that information is defined by using linear algebra (operator theory). Mathematical structures of models are different. In particular, QI is noncommutative theory. The natural question arises: Is it just difference in mathematical models, in mathematical descriptions, so just different mathematical representations of the same kind of reality or one should consider two extremely different types of physical phenomena, classical and quantum? The conventional point of view is that there are two extremely different domains of physics, quantum and classical. The first one is about microworld and the second is about macroworld. This is the Copenhagen viewpoint: there are microscopic systems and macroscopic observers. It induces many problems and paradoxes, but nevertheless it is convenient in applications and it dominates in physics. One of the main problems is the boundary between the quantum and classical domains. In the quantum domain a system can be in a superposition of a few different states. This is precisely why quantum computers should work quicker than classical ones. In classical it could not. For example, as was pointed by Roger Penrose, a single neuron could not be at the same time in the superposition of two states: firing and nonfiring. The famous Schrodinger cat was created by Schrrodinger to show absurdness of Copenhagen interpretation. This example was proposed in his letter to Einstein and it was a modification of an example from one of Einsteins letters about pistolet and bomb. The main idea was that if one assumes superposition of states for microscopic systems one would be always able to lift this superposition to macroscopic systems. My point was that two information theories are based on two probability theories: classical Kolmogorov measure-theoretic probability and quantum von Neumann Hilbert space probability. In the second case we operate not directly with probabilities but with complex probability amplitudes. Some people think that quantum probability is more complicated than the classical one. I do not think so. Theory of Lebesgues integral is essentially deeper and more complicated from the mathematical viewpoint than linear algebra, especially in finite dimensional spaces which are used in quantum information theory. I am trying to sell the idea that the whole quantum enterprise is about simplification of description of extremely complex physical phenomena. I developed models in that the quantum probabilistic model appears as a projection of more complex classical statistical model. Then I proceed: Wau! In such a case it seems that quantum probability theory and quantum information could be used everywhere where we could not provide the complete description of phenomena and we just try to create a simplified representation in complex Hilbert space. So one can apply quantum information theory everywhere, from financial mathematics to genetics. Finally, about the last part of discussion about reality of information. I understood that my rather restricted philosophic basis was not sufficient to debate this problem on the same level as opponents of non--reality of information. But I stay on my position: information is not less real than mass or charge. I agree with Søren Brier that the main problem is that in modern science information is always reduced to probability: Thus information as a basic quality in the world is something entirely different from the present information theory that is based on thermodynamics ensemble theory. That information concept is then more basic than quantum theory. There should be done something cardinally new... I would like to thank all participants of out discussion. References: Khrennikov A.Yu. ,p-adic valued distributions and their
