Dear Inés,

thanks for the careful reading and for the comments. You write By all means, don't take this as a critique. Wouldn't it be rather boring if we all already agreed on every tiny little detail? ;-)

@2: I should have phrased that more carefully - this was mainly about my lack of knowledge. For instance, when reading Erik Hoel's essay and scanning the references I got the impression that there might be interesting models which I should learn about. I essentially agree with all you say here.

@1: You say Bolzmann derived irreversibility assuming particles had independent positions and velocities after each collision, which is ultimately not true. He thereby introduced irreversibility.

There is no such assumption in Boltzmann's derivation of irreversibilty, it doesn't even require the notion of collisions. I think I've retold the relevant parts almost completely in my essay. If you'd like more details I really recommend this article by Lebowitz.

Maybe you had some calculation from the kinetic theory of gases in mind?

There is only one way, in which you could claim that Boltzmann already introduced irreversibility through a backdoor, in order to then derive it: On a cosmic scale you have to assume that the universe started in a very special highly ordered state. However, Boltzmann was well aware of that. I recently had a nice discussion about this point with a friend back over at facebook.

@3: I agree. I only gave examples concerning the required rigidity and flexibility. I didn't define these concepts in a general and precise way. I'd love to, but so far I don't know how. And I'd also expect that one can frame those conditions in a substrate-independent fashion.

Thanks again for the stimulating comments!

Cheers, Stefan

Dear Dale, thanks for the kind remarks. I replied over at your essay's thread. Cheers, Stefan

4 days later

Stefan,

Clear and sensible connection between micro and macro worlds, a conclusion that "if the macroscopic entities under question are sufficiently flexible and sufficiently rigid,mindless mathematical laws can give rise to aims and intention"

In my essay I feature the mindless physical law of entropy operating at many levels in the universe with an interesting theory built on the second law of dynamics by Jeremy England. Without making your clear micro-macro connection I try to show that human decisions sometimes speculate theories putting together complex arrangements of life's elements.

Hope you can provide your ideas on my essay.

Regards,

Jim Hoover

    I liked the discussion of rigidity, it is an interesting observation. Buckminster Fuller would say that you need both tension and integrity. In my essay I hinted at interactions between solidity and liquidity.

      Dear Jim, thanks for reading and pointing to the ideas of Jeremy England, which might eventually lead us to a better understanding of origin and characteristics of life and possibly other life-like phenomena. I also commented over at your page. Cheers, Stefan

      Stefan,

      Did you read my essay and give it a rating? During this contest, there are more partisan strikes piggy-backing on comments or providing no comments.

      Jim

      Hi Dear Stefan,

      I have opened your essay and start read it. My first impression is that your approach is surprisingly logic. After reading of you, everybody can think that is very simple to understand that all beautiful buildings are constructed from bricks. OK, it is, but there are many people, who do not like to start from such simplest truth, and they move to complications and making trouble for themselves! I am writing on this subject mainly in my essay, calling them to go on the comprehensible path ... I think we can find comprehension with each other on this. Hope you will look my work and we will continue talk in my page.

      Best Regards

        No, I didn't. And I didn't give you a particularly bad rating either, if that's what you want to imply. Not everybody rates at the very same time they post, and I have also noticed a couple of strange movements in my rating, which I don't think were correlated with how the discussion here evolved. The rating system is somewhat strange, but the winners will be picked by expert judges and prizes are not all. However, I don't think that this is the kind of discussion we should be having here. The contest is fun with lots of good ideas coming up. I already learned some nice things.

        Dear Miles, thanks for reading and commenting. I have to admit that my definitions of rigidity and flexibility are rather vague -- essentially, I just discuss examples. Therefore, I wouldn't want to make strong claims about how these notions relate to solidity or fluidity -- although this is a valid suggestion of yours! As Inés pointed out above, it should be possible to frame those conditions in a substrate-independent fashion. Cheers, Stefan

        Dear George, thanks for the praise. As you suggest, I'll comment on the topics of your essay at your page. Cheers, Stefan

        Many thanks Stefan for your kindly comment (in my page.)

        Unfortunately I cannot promise to read recommended books, I am not so well with english to read such serious works. But I am very thankful to you that you pointed on de Broglie - Bohm theory that is one most respected for me work in theoretic physics. Let me just say one remark on this. If we are agree with rightness and significance of this theory then we must to reject the accepted present interpretation of QM. Then you can imagine where we can reach by this way. I think this understand not only you and me, but our advanced leaders also. However they cannot say and do this because they will forced to recognise that more than 100 years we was on the wrong path! Particularly, for this now you and me are forced rethinking again on what is the purpose of natural science, of math. Or, on what purpose God or math (meaningless!) had made all things and on other such "actual" questions to got the prizes! That is why we going by different ways! (Because now there is not seen any reasonable direction at all!)

        Whatever, let to wish successes each to other!

        Best Regards

        Dear Stefan,

        You phrase the problem very well: goals characterize macroscopic systems [virus, bacteria, ...humans] but are absent from microscopic [atoms, molecules]. You use Boltzman's explanation of irreversibility to link macrostates to ensembles of microstates with varying distributions, the basis of the Partition function. You ask "could the explanation for emergent goal-oriented dynamics in the world which is, microscopically, governed by 'mindless mathematical laws' be similar to Boltzman's explanation of irreversibility?"

        Your discussion of microstates of an arm was quite interesting, leading to the desirability of including new descriptive terms like goals and intentions, and this is "not automatically at variance with goal-free microscopic laws." I thought your examples of rigidity and flexibility were insightful and appropriate.

        You've produced a well reasoned essay in which you conclude that "mindless mathematical laws can give rise to aims and intentions." But I believe this is because of the way in which you framed the argument. I believe rather than such 'emerging' from mindless math, you have instead 'imposed' such on mindless math.

        Thanks for an interesting read, and thanks for reading and commenting on my essay.

        My best regards,

        Edwin Eugene Klingman

          Dear Edwin,

          thank you for reading and commenting. I agree that my conclusion that "mindless mathematical laws can give rise to aims and intentions" heavily depends on how I interpreted FQXi's question. Many contributions fall into two categories corresponding to two different interpretations of the question "How can mindless mathematical laws give rise to aims and intention?"

          Some essays interpret the "mindless mathematical laws" as elements of our theories about the world. Then the question gets the following meaning: (i) We use the notions of goals, aims or intention in some of our theories about the world. (ii) We do not use these notions in what we call our "fundamental" theories. (iii) How can that be? Can (i) even be consistent with (ii)? If yes, what happens somewhere on the way from (ii) to (i). My essay falls in this category.

          Other essays interpret the "mindless mathematical laws" in an ontological way. Then the question presupposes that mathematics itself is the foundation of the world, not only as an element of a theory but as an element of the world itself. The task would then be to explain how the material world together with goals, aims or intentions arises from mathematics. Some essays embrace this idea and develop some kind of Platonism. Others reject it. Yours is of the latter kind.

          Your conclusion "math is a formal byproduct, having nothing to do with giving rise to awareness, volition, or purpose" and my conclusion cited above sound mutually exclusive. But given that we answer different questions, I think that our conclusions do not even contradict each other.

          Cheers, Stefan

          Dear Stefan,

          With great interest I read your essay, which of course is worthy of the highest praise.

          You are absolutely right that «macroscopic theories are necessary in order to describe the world on a larger scale, and that these theories, even when they display qualitatively new features, are fully compatible with microscopic descriptions from which the very same features are absent.»

          I believe that it is provisions of yours that are the key to the answer about the self-organization of matter and to the question set by this contest.

          In addition, I show that «The assertion of the existence of quantum phenomena only in the microcosm is not sufficiently substantiated the phenomenological generalizations.»

          You might also like reading my essay .

          I wish you success in the contest.

          Kind regards,

          Vladimir

            Dear Vladimir, thank you for the kind words. I'll have to read your essay carefully before I can reply to your comment. Cheers, Stefan