Dear Alexey and Lev

Thanks for commenting on my essay and the interest in it.

As to your question: Mathematics define the relations that exists in the physical system, and the effectiveness of mathematics "is probable that there is some secret here which remains to be discovered" as you well quoted Wigner work. In my view the subjectivity is embedded in the uniqueness and singularity of every movement-phenomenon. This uniqueness is embedded in the qualities of its attributes. In every movement there are attributes like behavior, character, matter, form, communication-language, memory, aims (purposes) etc. As such the physical occurrence of the phenomena is not based on causality principle but rather on the process of selecting the subjective action that exits to the phenomenon in its relation to others.Causality is special case in the occurrence of a phenomenon. A mathematical model can and should be developed for such activity.

Ethics are not a higher level, or "above" ontological occurrence of the phenomenon, and it is embedded in the perception of reality by the subject.

Love is a degree of quality in the attribute of "character" of each movement or the assembly of movements.

It is all ontological and the beauty in reality stem from the eminent subjectivity and uniqueness of each movement which gives us the transcendental glory effect within reality. In the essay, I explained that reality is being continuously ratified itself as being a unique self organization though we continuously changing. "alexey" is ratifying "lev" and so on. There wasn't like you in the past nor in the future, you are unique and singular.

With great ratification and appreciation

Have a great weekend

yehuda atai

    Dear Yehuda,

    Your essay shows the value of individual things, while most of others concentrate on the universal aspects of reality. Mathematics tells about latter, arts focus on the former, and each is ratified through its special beauty.

    Thank you,

    Alexey.

    Dear Alexey and Lev,

    I was inspired and impressed by your beautiful argument in the first part of your essay. It is very important to repeat this argument often e.g. "the hypothesis of aleatory or mechanical emergence of thought from matter should be rejected, and not even due to the significant hurdles of its scientific weakness and unfalsifiability but because of its Epimenidic character, its entailment of cognitive suicide."

    But I hope you don't mind if I criticise the ideas in the second part of your essay. You asked me to be "as critical as you like"!

    From my point of view, the main issue is: do the things of the universe have the power, or does the power lie outside the universe in a Platonic realm? By "the power" I mean: the ability to generate/create rules, to know rules, to implement rules. By "the things of the universe" I mean: particles, atoms, molecules and living things.

    I assume a self-sufficient universe, which has very different implications for the nature of reality than a universe plus Platonic realm combination. Rather than abstract beauty (Kallone) "always deciding the fate" (Moira), I see the things of the universe as having the power to create new initial-value rules (e.g. the outcomes of "quantum randomness" can be seen as re-initialising one or more variables), within the limits of existing earlier-created law-of-nature rules. I.e. the things of the universe are free within limits.

    Re "in its idea, mathematics is entirely detached from all that is specific to humanity and even to nature. It is a composition of pure, abstract, timeless reason, reason per se.":

    I see mathematics differently. To me, mathematics is a purely human-derived study that creates representations of possible relationships and investigates their properties. So mathematics is about categories and relationships that together form new categories; and the conclusions that logically derive from such relationships; and the conclusions that logically derive from all possible types of relationships; and numbers. To me, what we call "logic" is like a property of relationships and assumptions: logic does not have a separate existence.

    We human beings can understand representations of mathematical relationships/ rules because relationships/ rules represent the essence of the structure of physical reality. So to me: 1) the content of human (and animal and cellular) consciousness is reducible to categories and relationships, where categories are just transposed relationships, and categories are concepts i.e. they are subjective experience; and 2) law-of-nature rules are reducible to categories and relationships, where mass and charge are examples of categories, and where numbers (initial values, i, and even the non-algebraic number pi) found in nature must ultimately derive from real relationships where the numerator and denominator categories cancel out, forming a number, i.e. a thing without a category. I.e. reality has more underlying infrastructure than expected.

    So, I see similarities, not differences, between consciousness, laws-of-nature and mathematics. Mathematics is "beautiful" because it mirrors something about reality, about 'Who are we?' (Schrodinger).

    Regards,

    Lorraine

      Alexey and Lev -

      You have given us a lovely essay, one which draws together physics, philosophy, literature and aesthetics. I like the point you make that trying to explain thought from the material is self-contradictory. Of course, I happen to agree.

      The interposition of the three spheres of physical, mental and mathematical (a la Penrose) also makes sense, although this model leave us in a "tri-ality". Penrose highlights the mystery by which these three are unified. The triune conceptualization may be a more accurate description of reality than Cartesian dualism, but still leaves us searching for unity.

      I'm not convinced beauty is the integrating solution. If, as you point out, the compelling attraction to beauty is simply a subjective reflection of the inevitability of cognitive and therefore evolutionary success, then beauty could be epiphenomenal rather than fundamental. Love, on the other hand (as I argue), is the defining feature of intention and integrates the "tri-ality" into a whole.

      In your reply comment on my essay (The How and the Why of Emergence and Intention), you asked me about my response to your initial comment --- I said "Ah, yes, the Demiurge strikes again." This was my attempt at humor. In your comment you referenced the "Demiurge" (Descartes' evil demon) as a theme in your current and previous essays --- my comment was a pun on "Demi" (meaning half part) and "urge" (meaning desire or intention), and "strikes again" (since it was a theme in both your essays).

      I also said "I'll be most interested in seeing how you can sail the empirical arguments through the treacherous shoals between the rocks of Godel and QP" This is a reference to Scylla and Charybdis (in Greek myth) - and my argument that empirical evidence and mathematical reasoning cannot overcome the paradoxes of quantum indeterminacy / complementary or Godellian incompleteness.

      My reference to "how the Upper Mind conceives of intentionality." is also a humorous play on words (you used the term "Upper Mind"). To the extent one believes in an Upper Mind (as I do - although in my essay I avoided extending the concept of cosmic intentionality to cosmic agency), one would, I think, agree that the conceptions of such a mind would constitute intentions in our world.

      Thanks again for your thoughtful comments on my essay, and for the excellent essay you have contributed. Good luck!

      -George Gantz

        Dear Lorraine,

        We are pleased to see you in our space; many thanks for coming and speaking!

        Both your compliments and criticism are very valuable for us, because of the independence, courage and will to the deepest truth we see in your thinking. Our responses to your objections follow.

        1.

        "From my point of view, the main issue is: do the things of the universe have the power, or does the power lie outside the universe in a Platonic realm? By "the power" I mean: the ability to generate/create rules, to know rules, to implement rules. By "the things of the universe" I mean: particles, atoms, molecules and living things"

        Let's accept this as the main question, Lorraine. The answer seems obvious: the material objects do not have any ability to change fundamental laws of nature. It is unthinkable for the electrons to decide and agree about values of their spin and charge, photons cannot change Maxwell equations, galaxies cannot change the laws of gravity; neither animals nor humans can do any of that. However, one may try to express your question in a bit different way, as a question about thinking entity, existing within the universe and permeating it, sort of immanent Soul. Although I would not debate in favor of this hypothesis, but I have a sympathy to it, and it seems sufficiently reasonable to me. Let's assume it is true, that the World Soul does exist. I could assume then, as a reasonable follow-up, that the Soul is responsible for the origin of life, its evolution, and appearance of thinking beings on our planet and maybe not only. All these constitutes a worldview called panpsychism. The main problem of the panpsychism is addressed in the next item.

        2.

        "I assume a self-sufficient universe"

        In your essay, you also use a word "closed" for that. Here is the main problem of the panpsychism, which assumes, as you do, that the universe is self-sufficient. If the Soul is a part of the universe, how It can be responsible for the fundamental physical laws? To choose and hold them firm through the Big Bang until now, the Soul must be more than a part of the universe, It must be the Author, which authority cannot be shaken by whatever happening with the material world. Thus, the Soul must be either a part or an agent of the transcendental Creator. This constitutes the main argument against panpsychism with its closed self-sufficient animated universe.

        3.

        "I see mathematics differently. To me, mathematics is a purely human-derived study"

        That is clear from your essay and the special 'anti-Platonist' comment on your page. The question is if your anti-Platonic belief is true? I do not see on your page any reflection on the pro-Platonic arguments, so your denial of Platonism looks unjustified to me.

        One argument for the mathematical Platonism is historical: in the long history of mathematics, from the Pythagorean schools and up to now, none of high level mathematicians denied Platonism, as far as I know. The latest confirmation of that fact I saw right at this contest, on a page of George Ellis; he noted, "I talked with Andrew Wiles last year about the Platonic nature of Mathematics, and he strongly believes that good working mathematicians all agree they are exploring mathematical structures rather than inventing them." This argument should be already sufficient, I think, to accept Platonism, keeping in mind a sharp rationalism of the high-rank mathematicians, with huge variety of their cultural backgrounds and personal qualities, for all epochs. This historical argument can be complemented by a logical one. J. Dieudonne wrote in his last book, that Mathematics was formed by two core ideas of Greeks: the idea of proof and the idea of the World of Forms. The latter gave mathematicians the power of pure mathematical thinking, free from any care about possible loadings of the ideas by external contents of matter, nature or humanity. That is why Platonism was and is so important and inseparable from the pure mathematics, wherefrom all mathematical discoveries came. That is why the beauty of Mathematics, according to the top mathematicians, has nothing to do with specific features of our biology or even natural world, as we stressed in our essay.

        At the end, I'd like to thank you again for your interest to our text, your compliments and clear objections. I hope you will find useful this exchange of ideas. And yes, special thanks for your rating of our essay!

        All the best,

        Alexey Burov.

        Dear Lorraine,

        After Alexey and I have discussed his answer to you, we realized that you do, in fact, provide a reason against the Platonic world, whose consideration is missing in his post. In bringing that up, I also wanted to ask for a clarification on your essay and your other posts as regards a certain difficulty I'm having with them. I cannot seem to get away from a confusion between what you call the universe, a synonym of "all there is", and that which traditionally is viewed as only a part of "all there is," usually called material reality, determined (sans quantum chaos) by laws of nature. In the former sense, there can only be one universe, but in the latter we can envision many different worlds in different relationships with each other, not all of them material or even temporal, such as the Platonic world providing laws to the rest.

        In my conversations with "anti-Platonists," I seem to consistently come up to an underlying protest against realism's perceived overbearing perfection and determinism. Yet your objection seems to be different (although I cannot seem to find it now, so please correct me if I'm misinterpreting). You say that in postulating the Platonic world we express distrust to the universe to be self-sufficient. I'm not quite sure how to understand that. In light of the two definitions of "universe" above, would you say that the following quote from C.S. Lewis' Miracles is a criticism to your idea?

        "You must go a little away from her, and then turn round, and look back. Then at last the true landscape will become visible. You must have tasted, however briefly, the pure water from beyond the world before you can be distinctly conscious of the hot, salty tang of Nature's current. To treat her as God, or as Everything, is to lose the whole pith and pleasure of her. Come out, look back, and then you will see ... this astonishing cataract of bears, babies, and bananas: this immoderate deluge of atoms, orchids, oranges, cancers, canaries, fleas, gases, tornadoes and toads. How could you ever have thought this was the ultimate reality? How could you ever have thought that it was merely a stage-set for the moral drama of men and women? She is herself. Offer her neither worship nor contempt. Meet her and know her. If we are immortal, and if she is doomed (as the scientists tell us) to run down and die, we shall miss this half-shy and half-flamboyant creature, this ogress, this hoyden, this incorrigible fairy, this dumb witch. But the theologians tell us that she, like ourselves, is to be redeemed. The 'vanity' to which she was subjected was her disease, not her essence. She will be cured in character: not tamed (Heaven forbid) nor sterilised. We shall still be able to recognise our old enemy, friend, playfellow and foster-mother, so perfected as to be not less, but more, herself. And that will be a merry meeting."

        Lev

        Dear Alexey and Lev,

        To clarify, I contend that there is only one universe. It is self-sufficient and "all there is".

        I don't like C. S. Lewis's attitude towards "Nature". He doesn't believe that he is a part of Nature. He doesn't actually love Nature: it is merely an interesting object to him, he believes he is above it. He doesn't see that he himself is what Nature is, and that he is not more than what Nature is.

        Re "do the things of the universe have the power...?":

        I'm contending that reality is not Fate; I'm contending that living things genuinely have free will to navigate towards a goal. So what is free will? Free will is the ability of things to move themselves relative to the block universe. Moving "relative to the block" merely requires that one or more outcome variables are initialised to a new number, such as what clearly occurs in the outcomes of "quantum randomness". I'm contending that the outcome of "quantum randomness" is lawful because it is representable as a one-off local initial-value rule or equation having been injected into to the local system. So I'm saying that free will exists, and that it is all about generating a new local initial-value rule/law in order to move relative to the block universe. I'm claiming that we live in a different type of universe than what is commonly imagined.

        Re panpsychism, "the Soul", "the Author":

        Perhaps in the beginning, when law-of-nature rules were generated, the universe was one thing; and subsequent to that, the universe became many things.

        Re Platonism:

        The Platonic realm concept has a number of flaws. One is the sheer extravagance of a realm containing every possible number and rule. Another is the issue of what interconnects this Platonic realm with the universe: seemingly it would be a Law, representable as a mathematical equation that doesn't live in the Platonic realm. But I would question that a Platonic realm is necessary, if the universe is such that it generates its own rules.

        Regards,

        Lorraine

        Dear George,

        Thanks for your compliments and careful reading. Contemplating Being as a tri-ality of spheres, as thinks Penrose, or a tree-ality of systems, as you express in your essay, there hides a unifying mystery. Shall we argue whether the mystery is at the center or at the top? Love or Beauty, which unifies reality? Perhaps they are aspects of the same. But then again, how could the center be also the top?

        One common objection to Platonism is that relations have no meaning without the relata, that there have to be things before there can be relations between things, forms of reason being relations. So, if we defend Platonism, wouldn't we contradict ourselves if we question primacy of love on account of it being a relation? It seems Plato himself didn't see it along those lines, and to me also love seems to be of different kind.

        Perhaps it is a question to you more than to us, though, since you have made a stronger claim, it seems. Your essay concludes by stating that it "provided evidence that cosmic intentionality is a reasonable, consistent and complete inference about why the universe is the way it is," and that it is such through the cosmic principle of love. But, is it really that consistent and reasonable? Mathematics, even if conceived as consisting purely of relations, is quite thinkable as a standalone world; the word "abstract" seems to mean just that. But can you really claim that love is also abstract and would exist without conscious beings, whom it connects? Where was this cosmic principle before the second conscious being was born (for there to be at least two)? Or do you imply that multiple conscious beings have existed always, that there wasn't a "second"? If always, and assuming they are temporal, then time extends back into infinity, an idea apparently fraught with contradiction. On the other hand, if temporality is an illusion, so is free will and with it our existence as individuals, in which case, there no longer is a multiplicity of subjects to relate with love, thus no love itself. It seems that either you have to take back the cosmic principle you propose or its reasonableness and consistency. Or do you have something in mind for which I haven't accounted here? Have you changed your mind about the "ineluctable paradoxes" since your previous fqxi essay, "The Hole at the Center of Creation"?

        From this perspective, were we to claim, like Plato, that beauty is ultimately fully atemporal, the picture would appear to be quite consistent and reasonable. We do not. We don't say that "compelling attraction to beauty is simply a subjective reflection of the inevitability of cognitive and therefore evolutionary success." We point out an interplay between beauty that is objective and eternal and our subjective and temporal attraction and response to it. We say that "beauty breathes freedom" and "a belief that we are marionettes, even in God's hands, is incompatible with inspiration for a worthy response." In either case, however, while for evolutionary success beauty could be considered epiphenomenal, Epimenides forbids it be so for the cognitive success in mathematics.

        If beauty and love are more fundamental than reason itself, can we use the terms of reason, such as the term "fundamental", to show which one is more fundamental?

        I'll leave the hard questions for Alexey to answer. Thanks again and good luck to you as well!

        Lev

        Dear Lorraine,

        I feel that some more comments from my side might be useful.

        Re panpsychism, "the Soul", "the Author":

        I do not see your attention to the the fundamental laws of nature. They are very specific, as we stress in our essay, they are mathematically elegant, they are universal and anthropic. Altogether, they are discoverable. Panpsychism may stay only by means of disregarding this.

        Re Platonism:

        "what interconnects this Platonic realm with the universe" was never thought as one more equation or law. Traditionally this connection was attributed to the God's will, or its synonym, Mystery. The necessity of Platonic World is shown in my previous post on the ground of unanimous agreement of great mathematicians and the logic behind it.

        We agree that reality is not pre-determined, we believe in free will of humans, and even, in a reduced sense, of animals. The world is unpredictable even for its Creator.

        Cheers,

        Alexey.

        Dear George,

        Apparently Lev has left for me the easiest of your questions,

        "I'll be most interested in seeing how you can sail the empirical arguments through the treacherous shoals between the rocks of Godel and QP."

        Well, I do not think that our arguments are empirical; rather they take into account the achievements of physics, reflecting on them to get something new for philosophy. Godel's theorems and QP are not rocks for us; I would call them good news. The former rids mathematics from a nightmare to be exhausted, suggesting infinity of different interesting problems; the latter opens the door for free will, saving the physical law at the same time. Ontologically, the freedom of will is above reason, so its paradoxes can be accepted as soon as its primacy is realized.

        Many thanks for your generous compliments and deep questions!

        Alexey.

        Dear Lev

        I understand your reasoning but let me explain mine in more detail because there are more things to consider. Possibly I will be somewhat boring in this attempt to clarify the subject as much as possible.

        First, let me clarify that I did not say that physical laws are as simple as possible; the assumption that I considered is that the Universe is as simple as possible. This does not imply that physical laws are as simple as possible; truly, such a statement is meaningless - at least I can't understand it. Physical laws are a consequence of the nature of the universe.

        What allows one to assume that the universe might be "as simple as possible" as a working hypothesis? The fact that we cannot assume anything else. If we consider the possibility of assuming differently, then whatever conclusion becomes possible - therefore meaningless.

        Physics is always searching for a conception of the nature of the universe as simple as possible; that has led to the discover of the atom, then of particles, then of quarks; an endless quest towards simplicity.

        In spite of all this, I agree with you that the assumption of the simplicity of the universe is acceptable as a working hypothesis but not to support conclusions. Furthermore, we cannot conclude from this argument of simplicity that a model of the universe has to be "understandable". I have a quite different reason to consider so but I did not want to mention it because it can be interpreted as arrogance, which it is not. That reason is that I succeed to "take the magic out" of the Cosmological model, of Relativity theory and of a considerable number of phenomena; therefore I think that "non-understandable" models are the result of their assumptions and not evidence that the universe is non-understandable. You can verify whether I am correct or not by seeing one draft paper I have on vixra (vixra.org/abs/1107.0016 ) and another one on the arxiv (arxiv.org/abs/physics/0205033 ). In both cases, the cause of the peculiar properties we have been attributing to the universe is the dependence of standard length units with motion, field and time. We can always model data considering that standard units are invariant, provided that we can add ad hoc parameters, like dark matter and dark energy, or we can consider peculiar properties, like spacetime properties, and to consider that there is no "objective reality.

        I think that "non-understandable" mathematical models of data are an essential step in the discovery process, allowing collecting and organizing data; then we must start the second phase of the discovery process, which is to put theory aside and to deduce a new paradigm from data - the deductive-empiricist phase of the process. The fact that a model is non-understandable is a proof that it is based in wrong assumptions, not that the universe is non-understandable. Of course that this is just a personal opinion, based on my personal experience, but also is the opposite one. Note that by considering that the universe we know by now is still understandable does not mean that it can be explained by some simpleton reasoning - on the contrary, it is amazingly subtle.

        I apologize for only now answer you but I had not seen your reply. I took a quick look to your paper. What I can say by now is that nothing of what I say contradicts your beliefs, just your line of reasoning and arguments, namely in what concerns the tuning to a goal. Maybe the universe is fine tuned to a goal, but I think that is not as you think, that things are much more sophisticated. I put a commentary in my blog addressed to "all" but written thinking in all the persons that follow a certain line of reasoning; maybe you can understand me better after reading it. To clarify all the differences between our lines of reasoning requires a long discussion but I am at your disposal if you are interested in it - my email: alf.g.oliveira@gmail.com.

        I want to thank you this discussion; my goal in this contest is the exchange and discussion of different points of view, which requires that we assume our differences openly - as you did.

        Best regards,

        Alfredo

        Alexey -

        Yes, I had made that remark before reading your essay. My apologies. Your arguments extend well into the philosophical. I agree that Godel and QP are ultimately good news for physics - they confront the serous thinker with paradoxes that force new thinking, to those who are willing to grasp the challenge.

        Lev -

        I quite agree that there is no meaning without relata. Indeed, as discussed in The Hole at the Center of Creation, there is nothing before the beginning. (Ah - it is so hard to talk about nothing!) Creation starts with a distinction - something from nothing - one separated from the void - the infinite partitioning into the finite. The act of distinction (in my metaphysic) creates the form/math in which substance/energy flows. This is an intentional act of love - manifest in the relationship of creator with creation. We can speak of this love abstractly, but it is not an abstraction - it is an actual flowing intention.

        Beauty in my view is a response, a perception, a reaction by sentient beings to that which is created. Beauty is thus contingent on sentient intention and a consequence of love.

        As to what is reasonable, I quite agree that it is a paradox to attempt a justification of love with reason. But my reasoning is also supplemented with experience - the sense of beauty in the flight of birds - the exquisite joy of a child at play.

        It would be a delight to discuss our two essays in a coffee shop somewhere. The FQXi comment process is a poor substitute for conversation!

        Deep regards - George

        Dear Alexey and Lev,

        Your essay is very nicely written, I like your prose and poetry. If I had one criticism to make, it would be that you ask to many questions and some of them seem to be left unanswered, but maybe I should read your essay again.

        All the best,

        Patrick

          Dear Alexey and Lev,

          To the dithyrambs which have sounded into your address, I need to add my voice only. Your work is really good, clever and poetical. But however, I will afford some speculations concerning the topic.

          I suppose that the Mathematics is a contour map of that beautiful landscape which is named as the Laws of Nature which Beauty is a image (reflection) of Harmony. Harmony is the ideal of mind motivating it (mind) to evolution, i.e. to perpetually tendency to Harmony.

          My very best regards,

          Vladimir A. Rodin

          http://fqxi.org/community/forum/topic/2752

          Many thanks, George!

          To increase our chances for that coffee shop discussion, I've just sent you a LinkedIn connection request. In case you will happen to be in the Chicago area, please do not hesitate to let us know.

          Yours, Alexey.

          Dear Patrick,

          Your compliments have a special weight for us. Thanks!

          Could it really happen that some of our questions are left unanswered? :^)

          Cheers,

          Alexey.

          Dear Vladimir,

          Many thanks for your encouraging voice. Apparently, your speculations above are in full harmony with ours, aren't they?

          I just started reading your essay, so you may expect some comments on your page.

          Cheers,

          Alexey.

            Dear, George, I agree. Here seems little more than a good place to outline basic positions. My Gmail is just a catenation of my first and last name. Now I have one more amazing conversation to look forward to. If you happen to travel past Chicago, Cafe Descartes is on me!

            Dear Alexey & Lev,

            I've just returned to your essay. Very well written but I struggled with it the first time so didn't comment or score it. ..But as you don't mine quibbles!: You seemed to dismiss any possibility of a 'thought & matter' relationship before moving away to eulogize mathematics. I'd hoped you may see the architecture described in mine and other similar and excellent essays. You haven't commented on mine, but have you looked and considered them?

            From philosophy I find Dennett's view the most coherent; that there really is no longer a problem. Are you familiar with that? He describes looking at a laptop at screen & mouse scale and saying "We can't possibly understand how that really works"! Do you refute his views?

            From AI we now produce learning, decision making and consequential decisions drawn from memories serving the first via neural feedback loops which then becomes what we call an 'aim'. Any input can trigger some response. The models here show similar if far more complex mechanisms from multi trillion particle systems. Can you identify what more fundamental effect is required to replicate most mental processes?

            And is Haldane's supposed 'self contradiction' not logically meaningless?

            I do agree and embrace other parts, particularly the geometers. I hadn't seen Hardy on Euclid's and Pythagoras' theorems; "...there is a very high degree of unexpectedness, combined with inevitability and economy." Thanks for that. Interestingly I extend Pythagoras to 3D dynamics to identify a classical derivation of QM. Certainly 'unexpected' (except by John Bell!) not to mention shocking, but falsifiable and self evident none the less, for any not too scared to look!

            I've found some from Fermilab have old doctrine fermly embedded! but I do hope you'll get to read mine carefully, do some rationalisation and comment.

            Many thanks for your patience, and well done. Very best.

            Peter

              Dear Vladimir,

              I have to admit that mostly I am puzzled by your composition, so that I do not even see how it does relate to the topic of this contest. One thing though attracted my attention in a special way:

              "Eternity in our Universe is just a moment for the next level Universe, which our one is nested in, as a spatial pixel."

              This image reminded me the butterfly parable of Chuang Chou (Zhuangzi), leading to his famous question, repeated much later by Descartes: what if all wanderings toward goals are totally misleading and futile, as dreams? Apparently, the Chinese sage left this problem unresolved, while the French father of science gave his circular solution. I guess this problem belongs to the core of the contest's topic.

              Cheers,

              Alexey Burov.