Dear Jim Stanfield,

interesting essay, although with some leaps of faith in it in my opinion. I like your description of the rubber sheet, which shows that spacetime, if continous, must be very twisted at the lower scales because all that has mass contributes to its shape.

I am not entirely sure whether you take mathematics as a platonic realm or as something that was created (surely before physical things were created) along a certain process.

By taking the empty set as some kind of first cause, you tacitly have inserted what you want to show: the duality of an empty set does enable a self-creation process. But this seems to me to be only true (if at all) under the assumption that maths and moreover logics is somewhat already there. Furthermore you make a twist to arrive at your polarity: the abstract existence of nonbeing. It seems to me that this is just an a posteriori view from the point of view of an observer who operates logically due to what he has observed. An empty set at the beginning 'of it all' does not differentiate between the abstract existence of nonbeing and being (the latter you obviously have identified with the empty set as the abstract being-part).

So, we have to 'nothingnesses', one is the empty set (the abstract being), the other is all that is not included within the empty set (means outside of it, the abstract nonbeing). I think these two nothingnesses are only differentiated linguistically. If in the empty set there would be some property that this set leads to being and outside this set there is the lack of this property, then the 'empty set' cannot anymore considered to be empty. It has some additional property (besides the fact that it abstractly exists).

What you need is some kind of pre-existing logic which discriminates between what is possible (what can exist) and what can't exist. Because your empty set is devoid of logic, it equals what has been termed 'nothingness' and traditionally understood by it. True nothingness not even contains an empty set, it is devoid of any meaning, logics, rules and potentiality. This is the reason why you can't comment on what qualifies mathematics to generate physical substances other than assuming it by taking it for guaranteed that mathematics (abstract relationships) have the fire within them to instantiate themselves somehow. Your empty set, even though tought of as a kind of polarity, cannot create anything further because it is devoid of any transcendental meaning. For modeling such a creation process, you need an 'empty set' which is only defined as empty relative to our experience of 'something' *and* relative to our logic which operates mostly in dual terms (means, in the modus of antivalent logic).

The phase transition from the abstract to the physical is unclear to me. You make your case with some kind of string theory, but i think with that you slowly loose the path and take speculations as realities due to the presupposed firepower of mathematics (the latter having been inserted into maths by you some lines of reasoning before).

The square root of -1, in my opinion, is an expression of taking a non-mathematical statement into the equations to proceed with a mathematical description of reality. Insofar it is an inconsistence to take the square root of -1 as a mathematical entity. It is just an expression of the fact that logics can transcend its limits of deducability such that it must induce that its origins must be located out of itself. Logics cannot have logically produced itself, and neither can mathematics via an empty set. Either these abstract structures are an accident in a lawless, unknown nothingness, or they are necessary due to some higher purpose (higher logic in the sense of an intelligent being which intentionally has created the landscape of mathematics and our world [both by a process of separation]). I think the square root of -1 speaks for the latter case. This higher logic could be in my opinion a synthetical a priori. Its existence is further obvious to me when pondering about logics itself. I think there are good reasons to assume that logics is consistent, but incomplete (in the sense that there must be a higher logics).

Best wishes,

Stefan Weckbach

    I now begin to rate the essays i read so far. Since yours is - in my opinion - underrated, i will give it a more realistic rating, compared to the other contributions. Although i think that my critizism holds, i should give you something like a 6. I do not compensate the zinger you received, if Jonathan is right with his comment above, because this would confuse the whole ranking system and obscure the comparison to other essays. So with a 6 you should arrive at something like 4.3 according to 4 votings. Anyways, your attempt is sensible, but i think not sufficient to prove some teleological bias.

    Hi Jim,

    I read your interesting submission and if I had excepted its premise (math predates universe) I would give it high marks. But I don't except its premise because I was working on the very same idea years ago and I found out where the idea fails. If you disagree on my conclusion, please tell me where I went wrong.

    The stumbling block for me concerning the idea that math predates the universe was how is this communicated to the universe. Math is no small subject in terms of quantity of information in contains. While I was trying to figure this out, I had also decided to read a book that had been on my shelf for many years "Adventures In Group Theory" by David Joyner. the book explains group theory through the puzzle of Rubik's Cube, which I learned to solve independent of books teaching how to solve. I figured my knowledge of Rubik's Cube would help me in understanding group theory. So I learned some group theory and it impressed on me the the consequences of numbers and their relationship to other numbers of the same quantity. So then I asked the very simple question; the universe started out as one object and went on to many objects, between that time it passed through six objects, those six objects instantly possessed the rules of group theory for six objects, where did it get them? My current answer is that it didn't get them from anywhere, the rules for six objects in group theory are there only if we asked them. I am not pioneering a new thing in math here. You, yourself already know that spacetime is only considered Euclidean if the rules of Euclidean geometry apply, otherwise it is non-euclidean. All I am saying is that the rules of any particular topic of math when applied to this universe only apply when asked and give an answer in the positive or the negative. To exaggerate my statement. Do the rules of topology apply to the color of my grass in my backyard? No. Do the rules of topology apply to the surface of the donut I eat this morning? Yes. Euclidean geometry only shows up where the rules of Euclidean geometry are valid. Topology only shows up where the rules of topology are valid. Group theory only shows up where the rules of group theory are valid. Set theory only shows up where the rules of set theory are valid. I could go on all day like this.

    The strangest thing about writing this post is that FQXi spell checker has flagged donut as misspelled. If I can't spell donut what good am I.

    Jim Akerlund

      Dear James Gordon Stanfield,

      Please excuse me for I have no intention of disparaging in any way any part of your essay.

      I merely wish to point out that "Everything should be made as simple as possible, but not simpler." Albert Einstein (1879 - 1955) Physicist & Nobel Laureate.

      Only nature could produce a reality so simple, a single cell amoeba could deal with it.

      The real Universe must consist only of one unified visible infinite physical surface occurring in one infinite dimension, that am always illuminated by infinite non-surface light.

      A more detailed explanation of natural reality can be found in my essay, SCORE ONE FOR SIMPLICITY. I do hope that you will read my essay and perhaps comment on its merit.

      Joe Fisher, Realist

      Nice essay Stanfield,

      Your ideas and thinking are excellent like...

      The effectiveness of math is reasonable only to the extent that the assumption that math is taken to be a discovery is reasonable. Starting with the metaphysical assumption that the Abstract Realm of Mathematics (ARM) 'predates' the beginning of the physical universe

      You are considering expanding Universe with a beginning, that means 40 % of Galaxies in the Universe only you are considering, which are red shifted, Why don't you consider remaining 60 % which are blue shifted and quasars ? Quasars are blue shifted. I hope you are not angry with those other Galaxies ? There are many places like Dark matter and Dark energy the expanding universe model fails

      ..................... At this point I want you to ask you to please have a look at my essay, where ...............reproduction of Galaxies in the Universe is described. Dynamic Universe Model is another mathematical model for Universe. Its mathematics show that the movement of masses will be having a purpose or goal, Different Galaxies will be born and die (quench) etc...just have a look at my essay... "Distances, Locations, Ages and Reproduction of Galaxies in our Dynamic Universe" where UGF (Universal Gravitational force) acting on each and every mass, will create a direction and purpose of movement.....

      I think intension (some form of consciousness) is inherited from Universe itself to all Biological systems

      For your information Dynamic Universe model is totally based on experimental results. Here in Dynamic Universe Model Space is Space and time is time in cosmology level or in any level. In the classical general relativity, space and time are convertible in to each other.

      Many papers and books on Dynamic Universe Model were published by the author on unsolved problems of present day Physics, for example 'Absolute Rest frame of reference is not necessary' (1994) , 'Multiple bending of light ray can create many images for one Galaxy: in our dynamic universe', About "SITA" simulations, 'Missing mass in Galaxy is NOT required', "New mathematics tensors without Differential and Integral equations", "Information, Reality and Relics of Cosmic Microwave Background", "Dynamic Universe Model explains the Discrepancies of Very-Long-Baseline Interferometry Observations.", in 2015 'Explaining Formation of Astronomical Jets Using Dynamic Universe Model, 'Explaining Pioneer anomaly', 'Explaining Near luminal velocities in Astronomical jets', 'Observation of super luminal neutrinos', 'Process of quenching in Galaxies due to formation of hole at the center of Galaxy, as its central densemass dries up', "Dynamic Universe Model Predicts the Trajectory of New Horizons Satellite Going to Pluto" etc., are some more papers from the Dynamic Universe model. Four Books also were published. Book1 shows Dynamic Universe Model is singularity free and body to collision free, Book 2, and Book 3 are explanation of equations of Dynamic Universe model. Book 4 deals about prediction and finding of Blue shifted Galaxies in the universe.

      With axioms like... No Isotropy; No Homogeneity; No Space-time continuum; Non-uniform density of matter(Universe is lumpy); No singularities; No collisions between bodies; No Blackholes; No warm holes; No Bigbang; No repulsion between distant Galaxies; Non-empty Universe; No imaginary or negative time axis; No imaginary X, Y, Z axes; No differential and Integral Equations mathematically; No General Relativity and Model does not reduce to General Relativity on any condition; No Creation of matter like Bigbang or steady-state models; No many mini Bigbangs; No Missing Mass; No Dark matter; No Dark energy; No Bigbang generated CMB detected; No Multi-verses etc.

      Many predictions of Dynamic Universe Model came true, like Blue shifted Galaxies and no dark matter. Dynamic Universe Model gave many results otherwise difficult to explain

      Have a look at my essay on Dynamic Universe Model and its blog also where all my books and papers are available for free downloading...

      http://vaksdynamicuniversemodel.blogspot.in/

      Best wishes to your essay.

      For your blessings please................

      =snp. gupta

      9 days later

      Jonathan,

      Thank you so much for your constructively critical review and apologize for the length of time it took me to get back to you. I was also unaware of the "zinger" technique of discrediting essays and now fear that my resultant low score will discourage readership. Thank you for pointing that out. Otherwise I would have been even more discouraged by it.

      You make good points about my usurpation of Yau's name (and feel bad about not using Calabi's as well) in the renaming of this imaginary construct, and my misspelling of orbifold compounds the offense. I was hoping to project some measure of poetic resonance on the idea.

      Also, I should have stressed in the essay that all these ideas are my attempts at coming up with visualizations for all these things. Some of them, as you rightfully point out, are wildly conjectural and fall way out of the mainstream of scientific discourse. I am hoping that each construct might be taken independently and will afford at least some explanatory traction to the issues at hand.

      I read your fine essay and will rate it highly. Your inclusion of this quote: "non commutative measure spaces evolve with time!" (exclamation point) is my feeling exactly when it comes to the unfolding fractal processes of nature. Also you mentioned the Leech Lattice, a particularly elegant mathematical structure which most likely has no physical implementation. But yet it can be used in a visualization which, absent length constraints on our essays, I would have liked to explore in terms of neighbor types for my MYO construct: Newton-neighbors in the open dimensions and Huygens-neighbors on the complex, compactified dimensions somehow explaining entanglement and spooky action at a distance. These are even more outlandish conjectures but I love the mathematical paths they lead me down. If course, I could never have become a mathematician because my favorite prime number is sixteen;-)

      I would be happy to communicate with you further.

      Jim

      5 days later

      Thanks for your thoughtful reply Jim..

      You have some cool ideas, and maybe there are more links to mainstream authors than you imagine. I have seen folks make presentations at conferences, citing only their prior work, later to be told they duplicated something once explored by Dirac or Bohr, then it's off to the races again - with a new twist.

      On the one hand, it gives you a sense that your work is more credible, to discover prior work in that vein, and on the other hand it gives you an incentive to distinguish what you are doing from older work. Sometimes; Physics people have developed a new formalism, only to find it was already discovered by the Math dept. folks. I think part of the reason Einstein's Relativity theory has the flavor it does is that Tensors had become popular, as a tool, during the time he was working on it.

      So keep working, but be aware of how some of what you are working on could have already been done by someone somewhere before.

      All the Best,

      Jonathan

      For what it's worth..

      I admire your being able to encapsulate so nicely the intended idea, to use the term Abstract Realm of Mathematics. You have a great clarity in your thinking and presentation Jim, and you only lack familiarity with some of what's out there. That is what contests like this one are good for! Perhaps leaving thoughtful comments about the essays of others will get them to check back on yours. There are thoughtful ways you could ask people to assess their work in light of the ARM hypothesis, which is similar to but different from Tegmark's MUH or Platonism.

      All the Best,

      Jonathan

      7 days later

      Thank you for your lovely comment..

      I am touched by your comments on my essay page, Jim. I appreciate the understanding of what it is I am trying to say on a root level. There is a more extensive reply on my page which I have appended below.

      Warm Regards, JJD

      Thank you very much Jim!

      As I recall; I am preaching to the choir for you, because your essay strongly espoused a view that the universe is mathematical at its roots. But your detailed comments indicate that you read the essay top to bottom, which means I kept your attention throughout. Some of the complication introduced by hyper-complex terms that arise in Physics were there to start with, only not acknowledged on their own terms (pun intended). The fact remains that nature is often more complex than we imagined, so it is not such a stretch that hyper-complex numbers are required to model its evolving grace of form.

      For what it's worth; Paul Kainen endorses the way I used his work in my essay, and was flattered to be mentioned in connection with statements by Connes. Those were his comments to me in correspondence after seeing the essay. But a lot of people stop short of the answers that are right in front of them, because their knowledge of the Maths that would let them take the next step is lacking. So they imagine no answers exist, because a lot of the experts (save Connes and a few radical figures) are failing to see the potential or the need for non-commutative and non-associative geometry and algebra, for Physics at all.

      It appears that you grasp some parts of my essay that others would have missed, so I am leaving the full comment visible for now. A good friend of mine uses the words "if they only did the Math right" frequently, when referring to the fact that most Physics folks take the easy way out, while other folks are not afraid to follow the arc of analytic continuation out to its completion - taking the next step until there are none. My friend is rather smart, though. Another contest participant, Andy Beckwith, is a 999 (99.9th percentile) and he just returned from Rencontres de Moriond, but we both agree he is much smarter.

      However we all agree some of this stuff should be basic training for serious Physics folks, that most will only learn if they go for a second or third doctoral degree. This is no priority for American scholars, unfortunately, so there are a lot of folks with an incomplete education in the Mathematics which would allow them to invent next-generation Physics. People like Ed Witten (whom I have met) have a big enough mathematical toolbox and a broad enough perspective to explore many paths and be less attached to something like String Theory (though he is its guru). But not all are accorded the freedom to look where the answers actually are.

      More later,

      Jonathan

      Jim -

      I enjoyed your far ranging and discursive essay, but I have a few questions for you. The first is in regards to your term "teleological bias". Are you saying that sentient beings are biased to see aims and goals wherever they look, even if there are none? Or are you saying that the sentient being is able to see and understand aims and goals - and to act on their own aims and goals?

      Second, you make the statement "Now we jump from particles to living things. The science between these two ranges of phenomena is well explored territory." I'd love to hear a little more explanation about how you see this jump working. It seems to me that man of the essays are struggling with this jump. A few (myself included) do not see this jump as discontinuous, but as part of the same dynamic process. For example, galaxies form spirals - just as living things (e.g. the head of the sunflower) form spirals.

      May your essay continue to rise in the scoring - George Gantz (The How and The Why of Emergence and Intention)

        James Akerlund,

        Thank you so much for leaving a comment on my essay thread. It brought to light a distinction between mathematics and information I had not fully communicated. I take them as separate entities. Certainly the number of abstract objects and their relationships are extensive and indeed infinite. However I consider information as something physical; contained within the negentropy of the universe. I agree with you that the physical evolution of the universe proceeds through numbered states. However, the number six might not be an eigenstate. The Universe may have jumped from 4 to 8. But that does not rule out six as a valid abstract object. I believe the abstract objects are there whether we look for them or not. Our concept of Euclidian geometry, which can be derived by logic from an underlying subset of relationships in the ARM, represents an excellent first-order mapping of our physical reality. Space time is non-Euclidean, not because we ask it to be but because it more closely maps to abstract mathematical structures of higher complexity. Does the color of your grass map to topology? Yes it does, but not completely. At the most fundamental level, the topology of the causal lattice determines the nature of electromagnetic vibrations that impinge upon the objects that we subjectively experience as the qualia of color. Color is an emergent phenomenon that occurs within the consciousness of any sentient being with color receptors. But that qualia owes its attributes (hue, saturation and brightness) to their supervenience on a long chain of emergent physical structures which owe their commanding form to the abstract relationships in the underlying emergent structures in the ARM. We certainly cannot explain color by topology alone but we cannot fully explain color without it. As all of mathematics seems to be based on set theory, it would be hard to give an example anywhere in nature were set theory does not apply.

        Best regards,

        Jim Stanfield

        Dear Sirs!

        Physics of Descartes, which existed prior to the physics of Newton returned as the New Cartesian Physic and promises to be a theory of everything. To tell you this good news I use «spam».

        New Cartesian Physic based on the identity of space and matter. It showed that the formula of mass-energy equivalence comes from the pressure of the Universe, the flow of force which on the corpuscle is equal to the product of Planck's constant to the speed of light.

        New Cartesian Physic has great potential for understanding the world. To show it, I ventured to give "materialistic explanations of the paranormal and supernatural" is the title of my essay.

        Visit my essay, you will find there the New Cartesian Physic and make a short entry: "I believe that space is a matter" I will answer you in return. Can put me 1.

        Sincerely,

        Dizhechko Boris

        George Gantz,

        Thank you for reading and commenting on my essay, and I would particularly like to thank you for the question about teleological bias (T-bias). This is a term that I am not altogether satisfied with. First off, the word teleological carries a certain amount of religious or spiritual baggage I wish to avoid. In its most basic definition, I intend it to convey the subjective feeling or goal within a sentient being, no matter how primitive, to survive and flourish.

        In reading your well-written essay, I noticed my own internal definitions of many of the T-biased words we both use have substantially different meanings to the way you use them. I think I would need to construct a George-Jim Rosetta Stone to translate between them. I find it useful to slightly redefine several of the most common words used in these discussions. These are phenomenal definitions. A sentient being is nothing more than an individuated organism, which is connected to and reacts to the variations in its environment by way of receptor and proprioceptor nerve endings. By this definition a worm can be sentient. Intelligence is the quantitative and qualitative capacity to process and organize information. By this definition, the computer Watson is highly intelligent. Consciousness is the subjective phenomenal experience of the qualia of sentience as a first-person observation of the present moment. An agenda somehow comes out of this and presents itself directly to the subject.

        It would occur to us in retrospect that the veracity, completeness and therefore the predictive power of this internalized observation of reality would serve an organism well. But this would beg the question: how, on the evolutionary trail, did an organism's acquisition of an agenda to extract meaningful and relevant information for survival arise? Somehow, it must be connected to existential threat. But how does the organism come to sense that existential threat? My simplistic answer is that an organism's nerve endings, no matter how primitive, provide the initial feedback. All sentient beings have skin in the game. But there still remains the problem of how that feedback might be converted into consciousness and the sensation of jeopardy.

        {Insert hand waving here}

        Once the sense of jeopardy has been detected, the obvious back reaction would be a teleological bias to fulfill the dual agendas: stay in the energy flux and avoid destruction. This would require the organism to choose a path through phase space that would provide the requisite energy flux or reservoir needed to maintain the dissipative state of the organism in order to be able to selectively navigate this evolutionary landscape. Adaptive response to the environment occurs over a temporal spectrum from real-time to the life of the species. This would go for the tubeworms living near a steam vent or, as more neural circuitry is thrown at the problem in service of this agenda, an investment banker competing for her share of the billions in bonuses available to maintain herself far from equilibrium.

        I generally try to avoid the use of the word 'intentional' as it can be confused with the less descriptive philosophical term of art denoting the content or object of consciousness. This definition is unfortunate. Here, I will attempt to provide you with a more complete picture of what I'm trying to get at with the term T-bias as it applies to sentient beings with intelligence and consciousness but it does not apply to any systems or processes that do not have these attributes. It is exclusively a property of life.

        Which is to say, I agree with your essay up to the point where you introduce cosmic intention. When you assume the existence of that which is to be explained, then all further explanation stops. Indeed consciousness is mysterious. They don't call it the hard problem for nothing.

        Self-identity and self-interest progress in stages. Right after I am born, with my first inklings of self-awareness my identity and my self-interest stop at my skin. Then as I discriminate myself from my immediate surroundings and the active agents within it I soon come to the awareness of my dependence upon these other active agents for my well-being: my family, my friends and my community. I develop a feeling of what is good for these extensions of myself are good for me. And as I extend my self-definition outwards to my school, the company I work for, my country and finally, if all goes well, the entire globe with its social, economic and political connectivity, and with its ecology and environment, it is in my enlightened self-interest to become one with everything. The greatest good for the greatest number might become the end of this outward self-definition, but this is only half the story. This final step is too easily perverted. Utilitarianism has been used for human sacrifice. The final step of enlightened self-interest is to bring back a balance to what I call the I-thou symmetry. If I do not value and protect my own being as an individual then the whole point of my being is lost. This concept is beautifully contained in the Golden rule and in Kant's contrapositive formulation of the categorical imperative: "do not do to anyone else what you would not have done to you."

        As you noted, we have the standard model of particle physics. Just think, if the sciences had been properly funded we could have had the deluxe model!

        Best regards,

        Jim Stanfield

        Stefan Weckback,

        I greatly enjoyed your well-written article. You make so many solid points for arguments in favor of free will. I will happily fold them into my own advocacy of its existence. Right from the beginning of your essay you see the problem of the objectification of science. Reductionistic science concentrates solely on the object of study without regard for the necessity of a sentient observer and the curiosity that motivates it; little lone avoiding the teleological pitfalls built into our descriptive language (and the way we think). Math affords a neutral ground for this description but in doing so avoids any pretense of agenda other than following its own internal logic; and even here in this sentence I was unable to avoid that trap. I start from phenomenology: cogito ergo sum. That we are mud that got to sit up and look around is wondrous to me. To modernize Kant's lingo a bit, the nominal can only be known through the phenomenal. To paraphrase Stanfield's (named after my father Arthur Stanfield) three rules of perception: 1) It is a reconstruction. 2) Remember it is a reconstruction. 3) Don't forget it's a reconstruction. The need for these three rules flows from the extreme transparency of the process which would naïvely lead us to believe that we are seeing objective reality directly. It is always filtered through the teleological biases of the individuated, subjective sentient observer. As I say in my essay: we have skin in the game.

        From my remarks to John Ellis on his essay:

        Purpose is something we see within ourselves and see in others. As embodied minds, we take its existence for granted as part of the requirement for the evolution of life. And like consciousness, it seems to resist a reductionistic explanation. Existence, sentience, consciousness and the nature and mechanism behind the collapse of the wavefunction remain elusive mysterious.

        A sentient being is an individuated organism which is connected to and reacts to the variations in its environment by way of receptor and proprioceptor nerve endings. By this definition a worm can be sentient. Consciousness is the subjective phenomenal experience of the qualia of sentience as a first-person observation of the present moment in interaction with an external environment. An agenda somehow comes out of this and presents itself directly to the subject. It would occur to us in retrospect that the veracity, completeness and therefore the predictive power of this internalized observation of reality would serve an organism well. But this would beg the question: how, on the evolutionary trail, did an organism's acquisition of an agenda to extract meaningful and relevant information for survival arise? Somehow, it must be connected to existential threat. But how does the organism come to sense that existential threat? My simplistic answer is that an organism's nerve endings, no matter how primitive, provide the initial feedback. All sentient beings have skin in the game. But there still remains the problem of how that feedback might be converted into consciousness and the sensation of jeopardy. {Insert hand waving here} Once the sense of jeopardy has been detected, the obvious back reaction would be a teleological bias to fulfill the dual agendas: stay in the energy flux and avoid destruction. This would go for the tubeworms living near a steam vent or, as more neural circuitry is thrown at the problem in service of this agenda, an investment banker competing for her share of the billions in bonuses available to maintain herself far from equilibrium.

        To answer the question you posed on my essay thread, I make the distinction between the existence of the Abstract Realm of Mathematics (ARM) as a discovery and the Platonic realm of mathematics, also as a discovery, but existing in the form of ideas which then would seem to require a consciousness as the medium of existence. On this score I am an agnostic. I jokingly say about myself that I used to be an Orthodox Platonist but now I am a reformed Pythagorean. I love to guess at metaphysical questions but I have a great aversion to taking as the starting axiom, that which is to be explained. The perennial philosophy of taking consciousness as the ground of all being is very comfortable. Perhaps I will be able to arrive at a conclusion eventually, but in the meantime I have the feeling that when I do, all further explanation cease. As the fundamentalists said to his son, do you want to study your biology homework or just say God did it and go out and play.

        Whenever I came upon your phrase, 'simply not fully formalizable,' I had to stop and think what you meant by it. Then I realized that I didn't have a clue. My intuitive guess was that you meant that all of nature cannot be described in terms of an equation (with an underlying set of mathematical relationships) that is deterministic. If that is what you were getting at then I agree. There is an underlying mathematical structure there but it opens into a phase space that renders it indeterminate. Math is open-ended. Then later in your essay I came upon your mention of Gödel's incompleteness theorem and figured we were thinking along the same lines.

        Reductionism works well with inanimate objects such as physics and chemistry but it loses explanatory traction at biology. Trying to explain evolution without purpose or volition, just by the principles of random chance becomes problematic.

        Also from the standpoint of duality, which I have found to be the most powerful tool in the philosopher's toolkit, whenever I perceive an attribute in nature I must always realize that in order to see that attribute it must be seen against the background of its conjugate attribute. The conjugate attribute pair, CAP [objective/ subjective] is one of the more basic ones. The most basic CAP is [being/ nonbeing]. Love is the opposite of hate but the conjugate attribute of them both his indifference. All three of these seem to go with sentience. The universe partitions into the observer, the object or attribute and the rest. I would say that the CAP of sentience is non-sentience but that would be ridiculous;-) I now realize that I do not have a good word for the CAP of sentience but I do believe the universe needs both ends of the continuum in order to manifest either one. In conclusion I would say, if the ARM 'am' (first-person singular) totally suffused with consciousness then what is the motivation for physical being.

        Best regards,

        Jim Stanfield

        Hi Jim.

        Yee of little imagination. I quote part of your last sentence in your reply. "it would be hard to give an example anywhere in nature were set theory does not apply."

        I suggest you look up in the sky and try applying set theory to the clouds. Good luck in counting them. If you can do this, I would very much like to read the math paper that results in your research.

        Jim Akerlund

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