Essay Abstract

Physical theories are expected to explain the phenomena around us. Algorithmically, this means that a computer program simulating the dynamics of a certain physical system must be able to predict experimental results. Fundamental theories, in addition, are also expected to help us understand the ultimate nature of reality. I here propose that a theory is fundamental if it is conceptual and general. A conceptual theory is one that can be instantiated by a short computer program, whereas a general one is applicable to a large variety of situations. This algorithmic view of the construction of physical theories may be paralleled with the development of formal systems in mathematics. The parallelism between the two disciplines may even be stretched as far as to question the realism of the most basic ontological entities in the phenomena accessible to us.

Author Bio

Ines Samengo has a PhD in Physics, after which she switched to computational neuroscience, with a HFSP postoc with Prof. Alessandro Treves (Trieste), and then an Alexander von Humboldt fellowship with Prof. Andreas Herz (Berlin). She presently works in Bariloche, Argentina, as a researcher of CONICET, applying information-theoretical tools and dynamical-systems theory to the analysis of neural activity in behaving animals, aiming at disclosing the relevant features in the encoding and transmission of sensory information. She is also a professor in Instituto Balseiro, in charge of "Probability and Stochastic Processes" and "Information Theory" in Engineering in Telecommunications.

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Wonderful essay, my favorite so far. Crystal clear as it keeps away from the troubled waters of ontology. Great, really.

    Dear Dr Ines Samengo,

    Reliable evidence exists that proves that the surface of the earth was formed millions of years before man and his utterly complex finite informational systems ever appeared on that surface. It logically follows that Nature must have permanently devised the only single physical construct of earth allowable.

    Joe Fisher, Realist

    Dear Ines;

    Your essay is a struggle. Not only axioms and rules are the basis of the inference game, but also the definition of the "Basic elements" for which the axioms are enunciated and the rules of combinations proposed. That's why in the end you had to renounce your inference program; the basic concepts and variables used in classical physics are biased by the senses (see my essay for clarification). Your program implies proposing a set of axioms and rules of inference that would fit the observed patterns of the chosen variables; having these observations as the departing premises. This will confine your theory to the set of theories that era expressed in terms of the observed variables, i.e., sense derived variable and sense dependent basic objects and concepts.

    I think that "Frege [2], Hilbert [3], and Whitehead and Russel [4]" were right when they, "not only encouraged mathematical derivations dissociated from any corporeal instantiation, but also, detached the act of deducing theorems (the bare use of mathematical logic) from any justification based on self evidence". That would allow to apply the logical and mathematical formalism to any set of basic concepts, elements and variables, not only those of classical and neoclassical physics.

    In 1931, when Kurt Godel demonstrated his Incompleteness Theorem, He destroyed the deterministic dogma and with it the TOE program.

    It is good to see how you "tend to believe that the theoretical entities that enable the calculations performed by the program have a fundamental ontological status" and Quantum Mechanics destroyed that perception. And forced on physicists an ontological shift.

    What Godel tells us is that the origin of the observable universe cannot be explained with theories based on the observed; but the other way around is not negated: Having a Essential Stuff with a minimum set of properties that allow it to generate basic structures and entities, that in turn generate the underlying phenomena that make possible the interactions that make up the fundamental observable properties of the universe. Please check my essay for the details of a program like that.

    Humility exists when we recognize that with the road taken we got to a dead end; but it does not mean we have to stop there, we can start with a new program.

    Yours;

    Diogenes

      Hi, Diogenes, thanks for your thoughtful and interesting comment.

      As I conceive it, the "basic elements" you mention are the material used to construct the formation rules. I did not necessarily meant them to be quantities obtained (or easily derived) from the senses. I would take any quantity as valid, as long as it may serve to predict what we observe. The latter, yes, obtained or derived from the senses. From my senses, in this single life I live, or have the illusion to live.

      My disappointment is not so much due to the fact that classical mechanics could not do the job, but rather, because (if I undestand the theory well) quantum mechanics claims that there is no such thing as "a single reality" to be explained. If we insist on trying to predict single measurements, we are bound to fail.

      I do take your message, though. Having reached a dead end does not mean we need to stop, we can start anew. I guess my essay was my personal obituary to the dream to believe my senses and my reason can define what is real. If I relinquish this dream, maybe other solutions are possible. Those solutions, however, will be able to predict stuff - but not the stuff I want to predict. I will predict the stuff that logic and evidence claim that can be predicted. But I still need my obituary, because in my arrogance, I do not find easy to swallow that logic and evidence should prevail over my single and first-person perspective of my history and my life. A private cry, if you wish ...

      Thanks for giving me notice of your essay, I will read it carefully as soon as I have time, and give you my feedback.

      best!

      ineś.

      Dear Ines,

      thank you for your essay, that I appreciated very much - I wish you all the best for the contest, it's a very interesting point of view.

      You write that

      > Quantum mechanics does not model what happens, but rather, whatever could have happened, including the interferences between the alternative possibilities. In the derived ontology, reality becomes an attribute of collections of entangled histories, and not of individual experiences.

      and

      > there is no absolute way an observer living inside the universe can assign universal truth values to histories, nor to states.

      The ontology that you derive from your analysis has many points in common with the one I state in my essay about absolute relativism, derived from Nagarjuna's philosophy. Of course with some differences, since my perspective is more a philosophical one.

      All the best!

      Francesco D'Isa

        Hi Ines, I enjoyed reading your essay; it was interesting. Page 4, you indicate that the most fundamental theory is the one that produces the shortest programs and can be applied to the largest number of equation. Based on this view of fundamentalness, simple logic seems the most fundamental theory. What is your opinion on this statement?

        Kind regards, Christophe

          Hi Francesco, thanks for commenting. I will read your essay some time soon, and also provide some feedback. I am very fond of philosophy, even if I have no training in the subject.

          Thanks!

          inés.

          Interesting! As I conceived the programs in my essay, they must always be able to reproduce experimental data. So in that respect, I would say that logic alone does not qualify, because in the absence of a context (fundamental constants, initial conditions, etc.) logic does not manage to reproduce the data. However, the experiments performed at the smallest scales provide evidence that not all data can be reproduced with short programs. So in a way, not all experimental data (not all formation rules, we could say) qualify as "apt to be reproduced". Only ensembles of data can be modeled, or equivalently, we cannot model what *does* happen, we can only model what *can* happen. In a way, this conclusion (which interestingly, is based on evidence) pushes us away from the so-called real world, towards a more ideal world. The theory is less attached to reality, and more do formality. I do not think today we can go as far as to claim that logic is the most fundamental physical theory, but we do seem to be moving in that direction, who knows how far we shall get...

          Thanks for this interesting perspective!

          inés.

          Dear Ines,

          Thank you for wonderful essay. You write that:

          ... "it is natural to believe that time and space exist. Simply because by postulating their existence we may reproduce a lot of the observed data..." It is classical concept of space and time.

          May be the difficulties with QM are related to the misunderstanding concepts of space and time. The new concepts of space and time resolves EPR paradox (see my essay "Fundamental entities in Physics").

          Best regards,

          Ilgaitis

            I sure will! These are my favourite topics. More soon, in your entry!

            inés.

            Dear Inés,

            First, I love the clarity of your writing and thinking. The argument is so coherent I could follow it easily, even though every sentence adds something new to consider. The historical background sets the stage very nicely, and the analogy between math and physics seemed to make perfect sense - though I would never have imagined a connection between axioms and initial conditions, or between theorems and evidence. Interesting! Treating theories as computer programs gets to the heart of the matter - matching experimental results - and makes clear the two essential criteria for theories to be more or less fundamental. And by pointing out that generality and conceptual depth (algorithmic simplicity) don't necessarily go hand-in-hand, you directly address the question of this contest.

            The key issue in your essay seems to be - to what extent is what happens in the world determined by rules? Since ancient times, it's the rule-determined aspect of things that's been taken as basic (and even divine), since it corresponds to how we've learned to think. To the extent the data is not predictable, in quantum theory, it can seem alien to our understanding, like undecidable propositions in mathematics. You say, "The experiences we collect throughout our (single) life do not form a valid string, nor a target for a theory."

            This reminds me of the Medieval definition of truth - adaequatio intellectus et res. It implies not only that our minds are made to understand the world, but also that the world is made to fulfill our potential for understanding. But now it seems as though this mutual adequacy might be broken. If I may, I'll try to sketch how I think it might be restored.

            The world of classical physics is strictly deterministic - in simple situations like the sphere falling from the tower, our algorithms reproduce the measured data as closely as we like. Yet even a situation as simple as three bodies moving in space, per Newton's law of gravity, can only be approximated, reiterating the algorithm for two bodies over and over. We can prove there's a unique solution to the three-body problem, but it's not directly computable. So even before we get to quantum mechanics, there's a gap between what our algorithms can do and what the physical world can do.

            QM formalizes this gap. Its algorithms give the statistics, very accurately, but leave the measured results up to chance. We can see this as a failure we have to live with. But maybe the algorithms and measurement-contexts are two distinct aspects of the system, both needed to make it work. One determines the regularities that support classical physics, the other determines the unique events that constitute our world of experiences. Maybe these two kinds of determining, lawful and random, are what enables the world to do what the algorithms alone could not.

            In any case, in today's physics, the evidence is well-explained, but the theories themselves are not. They're so far from being simple or self-evident that physicists refuse to consider them fundamental, despite the lack of any empirical evidence pointing beyond them. What's missing is not generality but conceptual depth. What I've tried to show in my current essay is that the structural requirements for a system of measurement-contexts might provide this.

            Thanks for an excellent and highly relevant essay. And, congratulations on your well-deserved prize in last year's contest!

            Best wishes, Conrad

              Dear Ines,

              I think your choice of analyzing 'Fundamentality' in such an ontologically light manner is very astute. I myself have also given more importance to theories, language and meaning over physics, and have spoken similarly on the economization of theories (although in a more language-heavy context; I was reluctant to use the word 'algorithm' due to potential issues brought up by the Halting Problem)-I think, in light of your essay, that I can say that my own essay will be of quite significant interest to you-; your similarly subjective approach is, I believe, the right way to go.

              Regards,

              Aditya

                Dear Conrad, so nice to meet you again! Once again, you make me think...

                > The key issue in your essay seems to be - to what extent is what happens in the world determined by rules?

                Yes and no, I only partially agree. Your question, as well as the initial part of my essay, seem to imply that there is one such thing as "what happens", and that it makes sense to ask whether that thing, whatever it be, is governed by rules. But we know for a fact that only some of the things that happen are determined by rules: the things (the systems) that we describe within the language of the rules. If we choose the wrong variables in physics we cannot predict anything. So the ability to predict goes hand in hand with the ability to choose the right variables (and this is closely connected to your essay, by the way!). As a consequence, we tend to think that the variables that can be predicted (the variables that follow the rules) are the "right" variables, they are the ones that truly capture the essence of what exists, the ones with prominent ontological status. But then comes quantum mechanics, to tell us that we, our experiences and our histories do not qualify. If the essence of the universe is that that can be predicted, we (individually) do not belong to the essential set. The essence is all what we could have been, all what we could have lived, all that could have happened. Moreover, there are different versions of all these ensembles, depending on who is the observer and how they observe. (?)

                > So even before we get to quantum mechanics, there's a gap between what our algorithms can do and what the physical world can do.

                Yes, this is absolutely true. But I have not focused on this aspect, because if we have the right equations, our algorithms can get better and better, progressively approaching the "right" solution (assuming there is one such thing) just by increasing computational power (decreasing the integration time step, increasing the precision of all the numbers involved, etc). We shall never manage it, we may always be far away from the solution, but at least we can establish a methodology for progressively approach the solution. It may be exponentially hard to get actual improvements, we may need unlimited resources, ok. But different is the quantum indeterminacy, which we cannot even approach...

                By the way, did you read the "Three body problem"? Is that where you got your example from? I have read the first volume, and am waiting to receive the other two, so please don't give me spoilers. I very much enjoyed it, also because I used to work in the three body problem long long ago (no kidding!).

                I very much like the Escher's Drawing Hands images that often come to my mind when I read what you say. In my entry, in your essay, in last year's essay. And those images trigger a whole lot of thoughts in me, which I will try to condense and share with you at your entry some time soon. I read your essay, and really liked it. Also, because I see the connection with last year, and by now, I am also more familiar with the context of your thoughts :-)

                More soon!

                Inés.

                Dear Aditya, thanks for reading and commenting. I am somewhat behind with the reading in this context, but I'll make sure to read and comment on (at least) all the essays that have a computational flavour.

                more soon!

                inés.

                Hello Ines,

                it looks that we developed in parallel the same concept. namely algorithmic approach. I believe that this is a consequence of the fact that algorithmic information theory is a well established science which empowered computer science as well as mathematics and physics. Its use to assess the concept of "being fundamental" looks straightforward to those coming from that field, so it is natural that more Essays were based on this common ground. I think we may consider this as the most obvious and conservative, but at the same time solid, output of the Essay Contest. In my case I adopt such principle to assess the real level of understanding achieved through deep learning, which to me required an assessment from an epistemic perspective after the huge development and the expectations around it, but I agree that such principle is general.

                I strongly agree with you that "Simply because by postulating their existence we may reproduce a lot of the observed data. The same holds for mass, energy, momentum, and for all the intermediate entities that we do not necessarily observe, but that are generated by the program as a means to interpolate between the events we do observe"

                A bit less when you say: "In quantum mechanics, when an observer makes a measurement, different versions of him or her become entangled with the different possible outcomes of the experiment [18, 19]." To my knowledge there is no C*-algebra which accounts for both a quantum (non commutative algebra without identity) and a classical (commutative algebra with identity) object in the same time, so it is difficult to follow you unless you declare what is the space you are using to describe your system and you show that is it mathematically consistent.

                Overall, very nice work.

                My best regards

                E.

                  dear Ines,

                  I think my essay is the most relevant to yours. I derive QM, QFT, gravity from the same system through a mathematical structure using computer simulation. The programs are available in JavaScript and are modifiable.

                  https://fqxi.org/community/forum/topic/3127

                    Inés - such a pleasure to hear from you again!

                    I haven't yet read the 3-body novels, though they're on my list. But how interesting that you worked on this problem. At one point it was a revelation to me to discover it, and realize that physics is in a sense far more powerful than mathematics. One can of course create quite complex worlds through computer algorithms... but you don't do it the way our physical world does, operating everything through one-on-one relationships between individuals, because that becomes computationally intractable very fast.

                    You're right that this isn't a practical issue, since we have computers already that can model interactions between millions of stars. But what it means to me is that "the essence of the universe" is not only the algorithmic part, which constantly generates possibilities. The other part is that whenever there's a context of given facts in which some new fact becomes measurable, the possibilities "collapse" into some particular subset, which then contributes "initial conditions" for generating new possibilities. As an analogy, the genome of a species contains the possibility of creating countless genetically distinct organisms, but only a small subset of these are born and reproduce their DNA, recreating the species genome.

                    This kind of dual dynamics - generating possibilities for random selection that generates more specific possibilities - is apparently far more powerful than any deterministic algorithm. And if this is essentially what's going on in the world, then you and I are definitely part of it.

                    Nonetheless, your essay expresses a deep personal attachment to the old idea of the world as governed by reasons. That's the feeling at the heart of Western thought all along, and I was lucky enough to inherit it from both my parents. Happily, the world is such that our ways of conceiving the reasons keep on needing to evolve.

                    Looking forward to your comments on my essay, and on Marc's etc. But no rush!

                    Conrad