Art, Philosophy, Science: Joy Of Knowledge

As Ludwig Van said: “O Freunde, nicht diese Toene! Sondern lasst uns angenehmere anstimmen und freundenvollere!” (“Oh friends! Not these tunes! Instead let’s strike more pleasant and friendly sounds”)  [My translation of Beethoven’s 9th lyrics introduction.]

Oh friends, not this Germanoid Greek Euro tragi-comedy! Enough of those critters so unworthy, they can’t conceive of themselves, independently of America!

Considered abstractly, and in essence, philosophy, art, science, and even engineering are extreme aspects of general cognition.

This Is Not Just Art, But Discovery. Grotte Chauvet.

This Is Not Just Art, But Discovery. Grotte Chauvet.

[Chauvet cave is up to 32,400 years old, according to Carbon 14 studies; some of the paintings are 12 meters wide, more than 3 meters tall; the cave was discovered just 20 years ago. Picasso once said after exiting the Lascaux cave back in 1940 that “we have discovered nothing”.]

When intellectual property lawyers describe inventions, they use the term “art”. Was the art innovative?

Each of philosophy, art, science, engineering is both knowledge and method. They are tied together, and go together being the opposite poles of cognition. Science as a body of knowledge, is what is known, for sure. Philosophy, as a body of knowledge, is what ought to be true.

Science as a method is the category (Aristotle!) of all ways to ascertain what is absolutely true.

Science, as a category of established facts, enables a plane to successfully take off, more than once a second, worldwide.

Philosophy, as a method, determines not just what “ought” to be true morally, but what “ought” to be true, as an educated guess. Thus, all and any application of the scientific method, requires the philosophical method. The philosophical method is the first approach, always.

An obvious, and state-of-the-art example, is the notion of infinity, where the debate is not just still on-going, after 25 centuries. Progress is made, in the sense that logical subtleties, which lay uncovered for millennia, were recently revealed. Uncovered for the first time, just as those Chauvet lions. Looking differently at Archimedes’ axiom, 23 centuries old, Model theorists discovered something new about numbers. (Model Theory is a part of pure logic which interface strongly with mathematics; actually I just found, as per Archimedes himself, that it should be called Eudoxus Axiom.) I have proposed to go much further with a different philosophical insight in Number Theory (in still another direction Archimedes could not have imagined).

And what of art in all this? Well, it’s the third pole of cognition, where emotion finds truth, before philosophy and, a fortiori, science, ever can. More than the logos, it depicts, or resounds with, the logics of emotion.

Both art and philosophy need just one fact, one intuition, to make a world. Science finds, painstakingly and patiently, what this world is really made of. Just as patiently and painstakingly, mathematics imagine, what this world is really made of. And then philosophy and art lash back further far out.

Cognition is one, approaches to it, and possibilities, are many. There are many possible worlds in our future minds than we can imagine, and they will blossom, as long we take joy in doing what we do best: “Plus Oultre” (“Plus Ultra”)!

Patrice Ayme’


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34 Responses to “Art, Philosophy, Science: Joy Of Knowledge”

  1. gmax Says:

    Didn’t you write somewhere that “all and any worthy mathematics can only be proven finitely?”

    • Patrice Ayme Says:

      Indeed. There are two proofs. The simplest is that any math proof contains only a finite set of symbols.(So infinity is an illusion, if there ever was one!)

      • gmax Says:

        That answer is beyond smart!

        • Patrice Ayme Says:

          The other proof is more subtle and in a completely different category. It’s about having strict upper and lower bounds on energy, hence only a finite number of symbols. So infinity is impossible: can’t write it down, or define it.

          • brodix Says:

            Doesn’t that make it a closed set and therefore subject to entropy?
            In an open or infinite network, any particular frame will lose energy to surrounding frames, but also gain energy from them.
            So if we are simply projecting linearly to infinity, it does pose conceptual problems, but in a truly infinite system, given nature abhors a vacuum, there is consequent feedback from any such projection, which creates inherent horizon lines of accessibility. So an overall infinite system creates the stable frames we would otherwise impose arbitrarily.

          • brodix Says:

            Stable, yet still dynamic…

          • Patrice Ayme Says:

            As I abstracted for GMax and detailed in “Largest Number” etc, the fact we have only a finite energy at hand (within the event horizon).
            Entropy is not a Quantum concept. YET.
            I do believe there is a thermodynamics of the isolated particle. However, that’s still science-fiction.
            This way I generate Dark Matter and maybe Dark Energy

  2. brodix Says:

    Science is reductionistic, while art is wholistic.
    Science is the information extracted and art is touching something too large to isolate.
    Science is conquering nature and art is nature’s laughter.

    • Patrice Ayme Says:

      Nicely said.

      However, the Quantum is HOLISTIC too. So it would seem to me scientific reductionism is having a problem. Moreover, all together, science has been mind expansionary, not reductive. Prehistoric paintings, like cooking, rested on science. Chimpanzees prefer their food cooked! Cooking food is science, chimps don’t have it, and the science of cooking, besides being an art, is expansionary, not reductive.

      • brodix Says:


        It is that cycle of expansion and consolidation running through everything. Our thought processes collect lots of information carrying energy and extract the signals of our perception from it.
        Science and society are constantly absorbing, creating, editing arranging information.
        So yes, it does expand out, by consolidating from a much bigger supply of potential input.
        The problem is there is no objective perspective, so it becomes a kaleidoscope of changing impressions and forms, that once we settle on a particular sense of order, it becomes subject to entropy, because it is, by definition, a closed set.
        Order is like ice. It needs a proper context to be stable.

      • EugenR Says:

        Cooking is rather technology than science. There should be clear differentiation between these two. Science is about understanding the existence perceivable by senses, while technology is about creating tools to manipulate or better perceive the perceivable existence. So the Habel telescope is technology, while understanding that the universe is expanding is science. Em2 is science, while atomic bomb is technology. Etc.

        • Patrice Ayme Says:

          Hubble was a lawyer who decided to figure out for sure whether the universe expanded or not.
          Techno-logy (GREEK) means a specialized logos. Science (LATIN) means what we know (for sure). Lots of science progresses only because of better tech. The heliocentric theory got sort of philosophically proven for millennia (the small Earth ought to go around the big sun). But the definitive proof came from the phases of Venus in mid 17th Century (thanks to telescopes, when they got powerful enough).

          So I disagree to a “SHARP” difference between science and tech. No science, no tech, no tech, no science.

          Actually, if you look at HUBBLE’s data, you see his linear law of expansion of the universe was (interpretative) ART. Yes A R T…With lots of imagination.

          Atom bomb came from Irene Curie’s discovery of the chain reaction, plus very fast electronic and explosive, hypersonic lenses.

  3. pshakkottai Says:

    Hi Patrice:
    These cave paintings look beautiful. Not stick drawings one might expect but real art drawn realistically with correct proportion and choice of limited mineral color. I guess the French had the aptitude for art starting 33,000 years ago! Other cave drawings also use three dimensionality of bulges in rocks for realism.

  4. brodix Says:

    It occurs to me that gravity acts like a vacuum and can only be modeled geometrically, which only describes it, but doesn’t clarify how it functions.
    As well as dark energy is an explanation for the parabolic outward curvature of intergalactic space.
    So basically they are opposite effects; The inward curvature of space in galaxies and the outward curvature of the space between them, which apparently balance, as Einstein suggested with his original Cosmological Constant.
    I think we apply too many of our linear, definitional conceptual needs, often for reasons of professional ego, to a dynamic that would come together much more neatly without them.
    Unfortunately it is a Catch 22. Those most involved are the most committed to supporting a model that has 100 years of patches, rather than being able to start a fresh operating system.

    • Patrice Ayme Says:

      My own theory of truth is local, modelled as it is, on fiber space theory. So definitions are local (as the definitions of curvature and torque are local in differentiable manifold theory).

      So modern geometry is made of patches.

      • brodix Says:

        So wouldn’t saying that infinity is an illusion also be a patch, necessitated by all definition being local??

        • Patrice Ayme Says:

          To use the type of reasoning you dwell in, let me say:

          Infinity is an abstraction from a finitude. Abs-tract: drawn out. Of a finitude, thus finite.
          Even David Hilbert would be pleased.

          • brodix Says:


            That is an interesting way to see it.

            Doesn’t “abstract,” mean drawn out, in terms of extracted from? Such that an abstract would be brief or smaller set describing the larger? Like a map is an abstract of the territory.

            If we abstract infinity from the finite, wouldn’t that make infinity a subset of the finite?

            Let me extend that reasoning;
            Does that mean the unknown is abstracted from the known?
            That noise is abstracted from the signal?

            I would see it the other way around, that the finite is the defined set and infinite is the open network, in which any number of such frames could exist.

          • brodix Says:


            Also, wouldn’t it be the monolithic logical basis for monotheism; That there is an ultimate universal frame which contains all? The proverbial “God’s eye view.”

            It would seem to me to be a supreme presumption, to assume there isn’t an infinite unknown, because we presume to know that definition and the eventual, if not currently theistic/deterministic knowledge thereof is the absolute state. As unless we make those assumptions, there is no argument for universal finitude.

          • Patrice Ayme Says:

            I understand what you are saying. It’s my reason for not being a formal, absolute atheist: in a sense to be a full atheist, one needs to be god, a contradiction.

            My argument for finitude is that we are bound within the local patch… Determined in General Relativity by the event horizon. (Funny thing is that I have a Non-Local subquantic theory, which would have to be considered, but I am presently travelling, heavily jet lagged, and, well, another time…)

  5. brodix Says:

    I very much agree we are bound within the local patch, but as a consequence of horizon lines and feedback to any linear projection.

    Also I have a strong objection to reducing space to an effect of measurement and geometry. For instance, infinite(?) numbers of dimensionless points can’t add up to anything, as even infinity multiplied by zero is still zero.

    As I keep arguing with the cosmologists and none of them have shown me where I’m wrong, that saying ‘space expands” overlooks the fact that the theory still assumes a stable speed of light, as the denominator against which to judge this expansion and that assumes a stable dimension of space, in which that expansion is effectively only increasing distance.

    Now given the sun is 8 minutes away, at lightspeed and the nearest star is 4.3 lightyears away, it seems dismissing space is the supreme hubris.

    Good luck on your trip!

    • Patrice Ayme Says:

      Trip is not happening at the speed of light. Where is my SST?

      Cosmologists know mathematics often more by rote, than really under-standing it.

      In General Relativity, the speed of light is not constant. It can get arbitrarily slow. Not locally, but globally. That’s the whole problem of Black Holes, and related endless discussions (which I am happy to have launched, way back, in Stanford at a seminar I led).

      A 4 dimensional Lorentzian differentiable manifold can be embedded in a high dimensional space with flat geometry. An n dimensional reasonable manifold can be viewed as expanding in an appropriate 2n +1 flat space. one does not need the internal geometry to define expansion.

      • brodix Says:


        Yes and if space is a non-physical state of infinite equilibrium, it would be the basis of all geometric frames, not a creation of them. The Michelson Morley experiment only showed there is no aether, not that space is a creation of its contents.
        Logically if a clock slows in a moving frame, then the frame with the fastest clock would be closest to this equilibrium of the vacuum, through which light travels at C. Otherwise what would be the basis of C? Why wouldn’t two frames pass each other, with internal activity in one exceeding the speed of light in the other, even if it were only apparent as massive blueshift on entering the other?
        So it would be as a property of space that what might happen in a Euclidian frame would be distorted in a non-Euclidian frame and multiple frames can interact, within only the non-physical parameters of infinity and equilibrium.
        As neither equilibrium or infinity(0, oo) are physical properties, they don’t need physical cause, such as a big bang.
        So space is the blank paper on which geometry is written.

        It may not need the internal geometry, but it has it. Those distant galaxies are presumed to recede, such that the light will take longer to cross from them. In GR, when space contracts, time dilates and so the speed of light remains constant to the distance. Which is not what is being proposed here.

    • Patrice Ayme Says:

      Yes, but how far in Quantum Time? ;-0

      • brodix Says:

        I keep making the argument that time is an effect of activity, specifically the relationship of energy to its form.
        So since energy is conserved, it only exists as the present, while the form is constantly changing, thus reading into the past.
        Now consider this in terms of the issues with the quanta;
        We don’t know what form the energy will adopt, until it has formulated it. Fo instance, we don’t know the amplitude of a wave, until it has peaked. We can’t measure the location of a particle without interfering with it. When a wave collapses, it is releasing the energy which created it. Etc.
        In all these, we only “know” at the point the form has peaked and is therefore receding. Measurement is an act of confining energy.
        Any way there is to know is to create definition, yet that only creates a transition for the energy, as it is interfered by the measuring energy.
        So the energy goes to other forms, dissipating from the old forms and the order we thought we had, only starts to recede, like the wave that has peaked, leaving us with just a hollow measurement.

        • brodix Says:

          thus receding into the past

        • Patrice Ayme Says:

          Many ways to measure time, they all concur.
          Aside from celestial mechanics, we have return force oscillations (springs, pendulum, etc.), light clocks, atomic/elementary particle decay.

          A measurement is a measurement, I don’t know what makes it “hollow”.

          “Amplitude” is not part of Quantum Theory now, except in a trivial way. It has to with number of particles (that causes endless confusions). In QFT, energy of the Quantum Fields is not locally fixed… And this is what really happens (measurements! Hollow or not…).

          • brodix Says:

            They concur because they all occur in the present, but there is no universal measure because there is no universal action.

            Measures occur in the present and the present is hollowed out as it becomes past.

            I was only pointing out that quantum theory seems to be trying to nail down measurements that are seemingly endlessly slippery. Maybe it isn’t because quanta are so very small, but because this seeming reality, that only exists as a transient present, is so very slippery.
            Even a moving car doesn’t have an exact location.

          • Patrice Ayme Says:

            It’s because reality is made of waves: non-local, not that compressible. OK, getting on a plane, off WIFI for next few days…

          • brodix Says:


            “non-local, not that compressible.”

            Very true. So why do we seem to favor these point particles?

            Is it because our primary intellectual tool is focus and concentration and when your favorite tool is a hammer, everything becomes a nail?

            Is the absolute, the universal state, the point at the center of the graph, or is it the paper on which the graph is drawn?

            When the old orders were obsessing over ever more convoluted and corrupted strictures, it was said of the French and Russian Revolutions that “power was left lying in the streets.”

            The absolute is the essence from which we rise, not an ideal from which we fell.

            Good luck on the trip!

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