Essay Abstract

The question of whether reality is necessarily continuous or discrete (i.e., analog or digital) is investigated by examining the nature of physics. It is argued that the view of physics as describing substance--common since ancient Greece--is today obsolete, and that modern physics is better understood as a way of describing reality as mathematical order. The question of whether reality is discrete or continuous is then reframed as a question of the nature of theories and the mathematics that they use. Because both measurement and theory are fundamentally grounded in discrete mathematical concepts based on distinctions, it is concluded that any description of reality by physics is necessarily discrete at its foundations. This conclusion points to a more fundamental insight into the nature of reality beyond the scope of physics.

Author Bio

After graduating with distinction from Stanford University in physics, Thomas McFarlane earned a graduate degree in mathematics from the University of Washington, specializing in algebraic invariants of knots. He is currently a patent agent and partner at a Silicon Valley patent firm and an independent scholar with interests in the philosophy of physics. In addition to his background in science, he also has a graduate degree in philosophy and religion, and is author of Einstein and Buddha: The Parallel Sayings.

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  • Post #2

Excellent paper. And of course, Bohr:

"...[In] our description of nature the purpose is not to disclose the real essence of the phenomena but only to track down, so far as it is possible, relations between the manifold aspects of our experience."

and:

"Strictly speaking, the mathematical formalism of quantum mechanics and electrodynamics merely offers rules of calculation for the deduction of expectations about observations obtained under well defined experimental conditions specified by classical physical concepts."

Which some people still don't get.

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  • Post #3

Knew your coda was reminiscent of something:

6.41 The sense of the world must lie outside the world. In the world everything is as it is and happens as it does happen. In it there is no value -- and if there were, it would be of no value.

If there is a value which is of value, it must lie outside all happening and being-so. For all happening and being-so is accidental.

What makes it non-accidental cannot lie in the world, for otherwise this would again be accidental.

It must lie outside the world.

    4 days later

    Thomas,

    I don't know if you've had a chance to check out Joy Christian's article here. It claims that all of the so-called violations of Bell's inequality are based on an erroneous calculation. If so, the current interpretations of non-locality and non-reality are incorrect. I believe this to be the case, but only time will tell.

    You quote Weyl to the effect that: "objectivity means invariance with respect to a group of automorphisms."

    I would see this world as a perpetual motion machine, 'auto-morphing' endlessly into itself in meaningless fashion. Definitely compatible with nikman's "In it there is no value...". There clearly would be no room for either free will or randomness, but I see that you covered this at the end with "chaos", although it's unclear how order and chaos are coupled into one reality.

    It is also unclear to me how 'scale' plays into a purely mathematical world, but perhaps it can.

    I also wonder, from a theoretical viewpoint how one can reconcile such a reality with different coordinate systems. I have worked in Cartesian, spherical, cylindrical and other systems, but one of my physics books describes eleven different coordinate systems used in physics. Let us consider any problem, say the hydrogen atom, solved in each of these coordinate systems. Surely we will not obtain the exact same answer for all of these systems, so which one is "right"? If the universe is only mathematical, one of them must surely describe "reality".

    There seem to me to be other problems in this perspective, but I'm curious as to your response to the above.

    Finally, you state:

    "Reality in its totality, then, encompasses both the cosmos(order) and its complement(chaos)."

    This dualism appears to me schizophrenic, with an unbridgeable gap between the order and chaos of our universe. At this point it becomes meta-physics, not physics.

    No one has any special authority to criticize anothers meta-physics, but we do have a right to our own preferences, and my preference for decades has been a unitary metaphysics that I believe is best represented by an objective substantial reality that connects order and chaos into one whole universe.

    My brief introduction to this approach is here.

    Edwin Eugene Klingman

      Thanks for your feedback. Those quotes from Bohr and Wittgenstein are good ones!

      Edwin,

      I have not studied Joy Christian's article. However, while my essay mentions violations of Bell's inequality, its argument does not hinge on them.

      Your point about different coordinate systems is not clear to me. Solving the Schrödinger equation for the hydrogen atom will give the same orbitals, irrespective of whether one uses rectangular or spherical coordinates to describe them. It's just that the latter has a simpler expression due to the spherical symmetry of the problem.

      The way physics is defined in the essay, the complement of the cosmos is indeed outside of physics. However, the distinction between the cosmos and its complement is not necessarily "an unbridgeable gap." On the contrary, insofar as they are aspects of a single reality, there is not an absolute distinction between them.

      Regards,

      Tom

      Tom,

      Thanks for reply. I'm confused by your idea of a single reality and how order and chaos are connected, but that's a difficult problem for anyone to answer.

      I sincerely doubt that solving the hydrogen atom in eleven different coordinate systems will provide exactly the same orbitals. Eons ago I had to solve such a problem by expanding an analytic integral as a series expansion. Being young and gung-ho, and faced with three indices, I expanded the series in all eight possible ways. To my surprise I found that seven of these expressions were 'infinite' but one of the expressions truncated with a finite number of terms, implying, I suppose, an exact answer.

      I am not convinced that all coordinate systems will produce exactly the same answers, and if they do not, then the issue arises of 'which' math is real, whereas in a substantial universe there *is* a reality, and the fact that some mathematical maps get only so close to reality is not a problem.

      If you are correct, that all math solutions in all possible frameworks give the exact same answer, then this supports your theory.

      Good luck in the essay contest,

      Edwin Eugene Klingman

      5 days later

      Edwin,

      The notion of a single reality is simple. Perhaps what is confusing is the relationship between its two aspects: 1) cosmos or order and 2) its complement, which could be called chaos or formlessness. The connection between these two inheres in their nature as complementary aspects of the one reality. In other words, they exist in mutual interdependence and therefore are not absolutely independent or separable from each other. Or, to explain it in terms of a graphical metaphor, the distinction between them joins them as much as divides them. Rather than being separated by an unbridgeable gap, they are connected by an infinitesimally thin distinction.

      I hope this helps clarify it.

      Regards,

      Tom

      Thomas,

      Interesting essay. Your write, "The cosmos described by physics, however, is a characterization of only that aspect of reality which is revealed when we look through the lens of discrete mathematical concepts which are all traced back to the primordial act of making a distinction." This resonates fairly well with my own conclusion, except that I'm more of an empiricist and, while I argue for the discreteness of our knowledge of the universe, I am opposed to equating the universe itself with its mathematical model(s).

      As Dean Rickles noted when discussing his own essay, you might enjoy Eddington. I wrote my PhD thesis on Eddington's Fundamental Theory (which was wrong in many ways, but still quite enlightening). I dusted it off recently (actually after Dean and his co-authors cited it in the book he mentioned in that same discussion) and have been talking to CUP about turning it into a book, but haven't gotten around to it. It's on the arXiv, but the first few chapters (which are just background material anyway) aren't that great.

        Tom,

        I note your second degrees in philosophy and religion, so I assume this influences your perspective. [I considered such a switch from physics, but didn't.]

        My essay in the previous fqxi contest was Fundamental Physics of Consciousness wherein I propose that the essence of one reality is 'awareness and volition' [=consciousness].

        To interact with itself, a distributed field must somehow 'be aware of' itself, and any 'action' can imply 'volition'. We can of course ignore these aspects of reality and simply formulate 'potentials' and 'forces', but that doesn't change the facts.

        From this perspective 'volition' is 'free will' and the implication is that consciousness has been here 'from the beginning'. Since over half a century of experiencing and thinking about awareness has convinced me that it could never arise locally from simply arranging the Lego blocks in the 'proper' order, this is compatible with my theory.

        I mention this because you seem to want to break the world into 'Order' and 'Chaos', where chaos implies random to me. I prefer the concept of free will, and distinguish free will from random as follows:

        free will = action by reason of awareness,

        random = action for no reason at all.

        This may or may not fit into your scheme of thinking, but it works well for me.

        Edwin Eugene Klingman

        Ian,

        Thanks for the reference to your dissertation on Eddington. I've just downloaded it from the arxiv and look forward to studying it.

        Regarding the relationship of reality to the manner in which it is empirically known, I agree that they are distinct (see the conclusion of my essay). Perhaps your definition of 'universe' has a different meaning, though.

        Regards,

        Tom

        Dear Tom,

        i read your essay and enjoyed it very much. Very clearly and consequently argued lines of reasoning.

        "Insofar as the distinctions we use to describe order are free imaginative constructs, they are not so much properties inherent in reality itself, but the basic elements that make it possible to characterize and describe a cosmos at all. We may then redefine objectivity in purely mathematical terms, without any implication of an independently existing substance."

        Yes, that's my line of thinking too. George Spencer-Brown has outlined the universal basement of distinctions in his famous book "laws of form".

        All physical processes, be them human beings or just physical facts, must obey these laws of distinction as long as they are coupled to "duality". A fact is a provable distinction, means a 1 bit decision. If one cannot decide a thing, there's no information and hence there are no "facts".

        There may be a metaphysical realm where the duality of mutually exclusive alternatives is transcendental, and i think QM is a hint in that direction.

        "Because the cosmos is discrete, this suggests that its complement is a continuum--not the mathematical continuum which has definite structure, but an indefinite continuum, a formless void (i.e., the original meaning of the Greek word chaos) that lacks any order and is thus beyond comprehension in terms of concepts or distinction."

        Yes again. One can think about "infinity" as "undefined" - it has no borders that could make a distinction. Hence it is "un-definite", "undefined".

        My standpoint is that maths can never capture the whole ultimate reality. denumerability and non-denumerability are concepts intimately related to determinism. But no exclusively mathematical and therefore deterministic proof can prove the exclusiveness of determinism/mathematics. This does not necessarily mean that ultimate reality couldn't be exclusively deterministic/mathematic, but i strongly assume that it underlines that mathematics is limited for the same reasons why distinctions are possible in this world: namely because limits (distinctions) are the operational basement to produce facts and hence information in a dualistic world.

        Thanks for visiting my site,

        all the best

        Stefan

          Thomas,

          I found your essay to be insightful and very well written. Until I got to the last two paragraphs, I thought that the essay was intended to make a case for the discrete nature of reality, and it argues this rather effectively.

          The last two paragraphs confused me a bit. Was the intent to suggest that reality may be both discrete and continuous, after all? Or that this question is unanswerable? If so, it did not balance the first part at all in terms of depth of treatment given to defend that position. In fact, the concept of the 'complement of the cosmos', based on the sparse description offered, strikes me as a bit mystical. Does it have a place in science? It seems to me that you take the position that it doesn't ('beyond the scope of mathematics, physics ...'). There clearly are subjects which are outside the scope of these fields, but how can the boundaries of physics and mathematics with these subjects be mapped onto the boundary between the discrete and continuous aspects of reality? I wished that this argument would have been fleshed out a bit more.

          Nonetheless, I did enjoy reading your essay and wish you the best.

          Armin

            4 days later

            Stefan,

            Thanks for your comments, with which I'm in agreement. I'm familiar with Laws of Form. Lou Kauffman has done some interesting related work.

            Best regards,

            Tom

            Armin,

            Thanks for your comments. I'm glad you enjoyed the essay.

            Regarding the last couple paragraphs of the essay, you are correct that they touch upon a topic that is outside the scope of the fields of mathematics and physics. That was the primary reason why I did not develop those ideas further in the essay, despite the fact that fleshing them out more (as you suggest) could be interesting.

            The kind of 'continuity' associated with the complement to the cosmos is perhaps more appropriately termed 'formlessness' in order to avoid confusion with the continuity associated with the mathematical continuum, which actually has a definite structure to it. So the mathematical continuum would then be a kind of order that is comprehensible using our discrete concepts, while the formlessness that is the complement to what is comprehensible by discrete concepts would be ineffable.

            Physics and mathematics, as particular ways of viewing reality, would not have boundaries that correspond to the limit of comprehensibility per se since there are various other possible ways of viewing reality.

            I hope this addresses your questions.

            Regards,

            Tom

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            • Post #16

            Hi,

            Christian is right TH, really ! But your are strong, we know your skillings, that said ,the formless is without real sense...if we take the chaos and disorders as justy foto of our motions.It's important you know that....

            Steve

            Tom,

            I think we agree, actually. I gave your essay a more in-depth study and it has the same basic fundamental idea behind it as mine does. It's actually an excellent essay, the more I think about it.

            Ian

            6 days later

            Hi Tom,

            Finally got around to reading your essay properly. It's very impressive. You, Ian, and I have somehow developed a very similar worldview: it's uncanny. My guess is a love of Symmetry and Kant (Weyl and Eddington shared this too, of course!). Hopefully my rating will boost you up the rankings, as is deserved.

            Best,

            Dean

              Hi Dean,

              Thank you for your feedback. I appreciate it! I've also been very impressed by your essays and look forward to following your work (and Ian's) since your perspective resonates with mine.

              Cheers,

              Tom