Dear Harrison,

thanks so much for your kind comments. I could not agree more with your sentence: "Determinism is not empirically necessary, and indeterminism is a far more reasonable, and objective, explanation of time asymmetry and causality."

I will study more in detail your DCM, and comment in your page, if I can.

Best wishes,

Flavio

Dear Lorraine,

The entropy is the average information per datum. It's perfectly well-defined. If the datum's states are all equiprobable, then the entropy simplifies down to log(num states)/log(2) = num bits.

- Shawn

Flavio and Shawn,

"Information entropy" is not "information" in the same sense that "car speed" is not a "car".

"Shannon information" is about the probability or surprisal value of information: it is not the actual information.

Symbolic representations of information are not information: they are symbols.

It is important to refrain from muddying the waters when it comes to the subject of information: words which mean one thing should not be redefined to mean another thing.

    Dear Shawn,

    I'm questioning definitions of information; I'm not questioning your knowledge of these definitions. I have (accidentally) replied below.

    Lorraine

    Dear Lorraine,

    It's a physics essay. We are talking about information theory, not the lay, dictionary definition of information.

    Basically, I say data, metadata. You say information, 'metainformation'. Where do data fit into your model? Or are data and information the same thing?

    - Shawn

    Flavio and Shawn,

    I'm questioning accepted definitions of information; and I'm questioning your logical abilities.

    If you do physics or anything else, you need logic. This is the logic of it:

    "Information entropy" is not "information" in the same sense that "car speed" is not a "car".

    "Shannon information" is about the probability or surprisal value of information: it is not the actual information.

    Symbolic representations of information are not information: they are symbols.

    Is it any wonder that people are confused about information when both of you blindly and unthinkingly accept illogical definitions of information that muddy the waters for everybody?

    Dear Flavio and Shawn,

    I'm questioning the accepted definitions of information; and I'm wondering if you have ever questioned the logic of these definitions. I would think that it is abundantly clear that the accepted definitions of information are completely illogical:

    "Information entropy" is not "information" in the same sense that "car speed" is not a "car".

    "Shannon information" is about the probability or surprisal value of information: it is not the actual information.

    Symbolic representations of information are not information: they are symbols.

    Is it any wonder that people are confused about what information is, when the above illogical definitions of information are guaranteed to muddy the waters for everybody? The problem is that the label "information" is illogical: other words need to be found to describe these categories of information. Physics needs clear and logical concepts, or it will continue to confuse itself about the issue of information.

    Dear Lorraine,

    Don't get too upset... you're part of the majority.

    - Shawn

    Dear Flavio and Shawn,

    As I am trying to explain, the issue is NOT me or "the majority". I doubt "the majority" is even slightly interested in this issue. But I have been interested in this issue, ever since I studied Information Science at university.

    The issue is that, in both physics and computing, "information" is not a clear, unambiguous or logical concept. And one cannot solve this problem by imposing a mathematical concept or mathematical definition onto the issue. The mathematical concept/ definition does NOT solve the "information" problem.

    So Shawn,

    I would say that information is a general term, where all information is representable as category names and associated numbers, or representable as category names and associated TRUE/ FALSE values. "Shannon information" is just one such category of information. "Shannon information" does not define what information is.

    Information is information because it always exists in context/ relationship to other categories of information. If it has no context, it is not information.

    And symbols only represent information from the point of view of those who know what the symbols are meant to represent.

    - Lorraine :-)

    I enjoyed your arguments that classical mechanics was sometimes views as indeterministic. I think that is correct, and determinism is not really the big difference between classical and quantum mechanics.

    A couple of very minor nits: "its nineteenth decimal digit is a 4."

    I think you meant the 19th decimal digit after the decimal point. I would say the 20th decimal digit is 4, because the 1st decimal digit is 3.

    "a theory id said to be causal" -- You mean "is".

      Hello Dr Del Santo,

      I liked a lot your essay, one of my favorites. You describe so well this uncertainty compared with our classical physics to predict thus future.

      I wish you all the best in this Contest.

      Regards

        Dear Flavio, Very interesting and groundbreaking essay, well informed by history, philosophy, physics, and mathematics (in the Newtonian tradition criticized here for other reasons!). It seems to me that we are only at the beginning of dealing with the drawbacks of the use of the real numbers in physics, and similar idealizations which have led to the conclusion that determinism itself is an idealization, even or especially in classical physics (which is what I take to be the main message of this essay). My own hunch is that intuitionistic and constructive mathematics may provide a way out, although, as Hilbert feared, this means we are driven out of Cantor's Paradise and we have to start all over again. In view of the tremendous success of even classical physics (think of putting men on the moon) this might be too much to ask, so there should be some result to the effect that physics based on the real numbers gives valid results with high probability (from the point of view of the new physics based on finite approximations), or so. Alternatively, think of results (due to Gödel and others) that theorems of classical mathematics are valid even intuitionistically if they are replaced by versions that are classically equivalent but intuitionistically different (typically by adding a double negation). In this spirit, results of classical physics based on the real numbers should be replaced by results that are empirically equivalent but logically different in your system, and provable in that system.

        Best wishes, Klaas

          Dear Roger,

          thanks for reading my essay and pointing out the small inaccuracy and the typo.

          Best,

          Flavio

          Dear Steve (if I may),

          very many thanks for your kind words!

          best wishes,

          Flavio

          Yes of course, you are welcome also , I loved your essay, it is one of my favorites.

          best regards

          Dear Klaas,

          thanks, I really appreciate your kind comments. I totally agree that we are just now scratching the surface of problems that have been either not recognized, or deliberately ignored, putting them under the carpet for ages. I think that we will soon reach a critical mass, though, of people that recognize this issues in a non trivial way. I believe we should rediscover the eneasyness of some eminent scholars of the past, as I try to do in my essay by pointing out some historical arguments. Fore instance, only today I found a very interesting document; Thomas Kuhn interviewed a student of Boltzmann, who reported: " there was in Boltzmann's ideas some anticipation of quantum theory [...]. He had from the beginning the idea that the space of phases must be fundamentally quantized".

          Moreover, you are completely right that we should seek new mathematical ways to model our physics. And constructive mathematics, perhaps intuitivism, seems most promising.

          All the best,

          Flavio

          I really enjoyed this essay. The insight into the importance of infinite precision to classical physics is a really valuable one and I'm very interested in your work on an indeterministic formulation of classical physics.

          I did have some questions about the overall motivation for this work. As I understand it, your argument is that real numbers cannot be physically meaningful because they contain an infinite amount of information. This is supposed to be a problem because it would violate the Bekinstein bound; but the Bekinstein bound comes from GR and/or quantum physics, so is there any reason to think it should hold in classical physics?

          Alternatively, it supposed to be a problem because 'physical systems have finite size' and this implies a limit on density of information - but do physical systems have finite size in classical physics? Perhaps there is a coherent interpretation of classical physics where the world is constituted of pointlike particles?

          These questions are linked to a larger questions about what an 'interpretation' of classical physics is supposed to do. When we try to `interpret' quantum mechanics, I take it that we are making hypotheses about what the actual reality underlying quantum mechanics might be like. But we don't need to do this in the case of classical mechanics, since the reality underlying classical mechanics is understood to be quantum mechanics. So when we ask whether classical mechanics is deterministic, we're not asking about whether reality is deterministic, rather I guess we're asking whether the view that classical physics is deterministic was a coherent one - but in that case it seems unfair to make an argument based on facts that are not inherent in classical physics? Does it make sense to try to 'interpret' classical physics from the point of view of a modern physicist?