Dear Jochen --

Thank you for your kind remarks. I certainly agree that it's possible to say silly things about Gödel's Theorem--perhaps you'll agree even that it tends to attract them.

A few years ago, I spent some time with philosophers associated with the University of New Mexico, an hour's drive (at high-speed across the desert) from Santa Fe. They were constantly employing diagonalization, and importing a huge amount of that mathematics into philosophical arguments. And I spent a lot of time hammering back in a skeptical mode, asking whether the substance of their arguments required this machinery. You can take a look at our reading list here: http://tuvalu.santafe.edu/~simon/undecidables.txt

In the end I was convinced that many of these arguments actually did matter, despite their unfamiliarity and their often strange patterns. And that it was often not too hard to adapt them to problems apparently outside their scope.

For example, consider the vagueness problem you mention. If I get you to attribute probabilities to whether or not a book is meaningful under some sufficiently self-referential criterion of meaningfulness, then I'm already off to the undecidability races. It doesn't matter if I get it wrong from time to time, or if people disagree--as long as there is some content to the notion of "meaning", something above-null and beyond triviality, that I can get at or approximate through debate and discussion, then it's pretty simple to show how all of the disastrous logical machinery still kicks into gear.

Just because a debate exists, in other words, does not imply that there's nothing there to debate--indeed, one can quite easily make the opposite case: that they very persistence of that debate shows that there is some substance there.

By the way, I was just visiting some folks at MIRI in Berkeley yesterday, and (again) I found myself playing the skeptic on these kinds of arguments. One of the things I took away from them, Jessica Taylor in particular, was that these arguments can also provide new kinds of upper (or lower) bounds. The MIRI style seems to be to assume oracles and other forms of hypercomputation and to show that even then, one can't get what one wants.

For that reason, I like your account of incompressibility. Of course, the underlying idea is Komolgorov Complexity, which is itself uncomputable (an earlier draft of the essay had this material, but I was over word-count). So by assuming the existence of a way to compute it, you're actually beginning a MIRI-style argument there. I'm not sure if I want to go the direction you're going. Indeed, there are often meaningful statements that are meaningful just because they can be rephrased or made more succinct--think about how mathematicians find shorter and shorter proofs of a theorem. But perhaps I don't grok it yet.

Finally: I'd agree that this gap is an epistemic one, not an ontological one. That doesn't make it any less real, of course! And because we're epistemic, knowledge-seeking creatures, it has lots of effects in the material world: like causing me to type too long and almost miss my flight, aaa!

Yours,

Simon

Hi Simon

I had a gap and my comment. It was erased when went back to see your essay again. Well it was unexpected.

To your essay: I agree with you that there is a gap that is responsible to the unexpected action that a phenomenon A or "existat A, relate to another phenomenon B or more. i.e. each existent is choosing a concrete subjective action (or non-action) out of the potential actions it has in the relation.

It seems to me that the "freedom of choice selection mode" for each unique phenomenon (and each phenomenon is unique' from a sub particle to a galaxy) is the sub-strata language of nature. The natural language of Movements, which is elaborated in my 25000 philosophical characters : "we are Together, therefore I am", here, in the contest.

thanks for your unique approach.

Yehuda Atai

Sorry to be a fly in the ointment Simon..

This essay is well-written, and your point is logically argued given your premises, but I can easily take some of them apart.

A lecture at the 10th Frontiers of Fundamental Physics conference (in '09 at UWA near Perth) by Mikhail Kovalyov stated that the Physics including the higher-order terms IS what's fundamental, so jerk is in no way a departure from fundamental Physics. He explained that non-linear terms are hard to deal with, and often lead to unsolvable equations, so people make limiting assumptions to have solvable equations, plug in numbers, and test their basic assumptions. It is unwise to equate basic with fundamental, though, especially in a topic like Physics. So I see your doing so as a big logical flaw.

Some of your statements about transient phenomena still make sense, and I love the discussion about fine-grained vs coarse-graining of phenomena, but it is a critical error to put an elevator jerk on a par with something like what Brian Greene talks about in Elegant Universe, where rips in spacetime are self-healing because catastrophic flop transitions are forbidden. As you say "You'll be reminded of the limits of your knowledge, but the universe will not catch fire" because transient phenomena are not an existential threat. However there are limits to your analogy.

I've been researching exceptions to your generalizations for more than 30 years, starting with a discovery involving the Mandelbrot Set, and a few phone conversations with Ben Mandelbrot back in the 80s. My essay this year focuses on the Octonions, and addresses some of the issue you raise. But the Mandelbrot Set is a wonderful example of a self-referential action in pure Math. Start with a (complex number) value, multiply it by itself, add back the starting value, then repeat. Each time the point of origin is referenced again, but that is the whole formula in a nutshell. But you end up with something that spawns endless copies of itself in miniature.

I have been filling in the gaps you describe as a student of many of the origin mysteries you describe, for some time now. I assure you some of the problems you talk about are solved, if you don't want to re-invent the wheel. But I'll sign off for now. It was a good read and a good try, Simon, but you simply get a few things wrong. I'll be happy to take as much time as needed to explain. Mind you; it gets kind of deep probing the ultimate origins, but that's why I attended almost all of the quantum gravity lectures at GR21.

All the Best,

Jonathan

    On a lighter note..

    Given the topic of your research; I assume you are aware of the great little book The Hidden Dimension, by Edward T. Hall, but if not it's worth checking out..

    All the Best,

    Jonathan

    Some things show up as mathematical proofs..

    Arved Huebler has an elegant result on page 3 obtained by mathematical induction showing the nature of origins. In my comments for his essay, I talk about parallels with the Chinese philosophy of Wu Ji and Tai Ji. Wu Ji is the primal state beyond and before the grand ultimate of separated forms Tai Ji. Analogies can also be made with non-commutative geometry. But my perspective is very different from yours, since I look for parallels across disciplines rather than staying with the views in one field.

    Regards,

    Jonathan

    In regards to Borges' library...

    I think the example is too simplistic to produce meaningful works, like the Sonnets of Shakespeare or the like. One would need randomness along with some rule that enforces directionality to achieve meaning or congruency in any one room. This does appear to arise naturally in the context of non-associative geometry. I got to talk a bit with Tevian Dray about this at GR21 (in the context of quantum gravity), and that forms the basis of my essay. But I have written several pages of octonion poetry, and here's one of my favorite examples.

    One open, as multiplicity and formless nothingness, finds peace in true relation and knows all as self.

    But the curious thing is that when one follows the rules of progression dictated by the octonion framework, it is a hierarchy of levels of abstraction. In this way; each possible outcome is a span from most abstract to most specific conceptually. So this notion shows more promise, in being able to crank out meaningful works, than the schema of Borges.

    However; it would seem the analogy with Borges holds at a level closer to the origin. There is evidence that human language is a paring down of the glossolalia metalanguage of young children, such that the tonal elements of a specific language of one's family or nation of origin - instead of the prior notion that syntax is hard wired. So at that hierarchical level, the example might make more sense. I look forward to seeing your response.

    All the Best,

    Jonathan

    Dear Jonathan --

    The difficulty with higher-derivative theories is not that they lead to "unsolvable" equations that then must be approximated, but rather that they contain negative energy states, violate probability conservation, and generally lead to non-physical results. One needs to re-interpret them as effective theories for something else in order to handle these problems. It's important to distinguish higher-order (e.g., polynomial functions of fields and their derivatives) with higher-derivative (e.g., a Lagrangian with a fourth derivative) theories. There's a large and complex literature on this (you can dig into the references from the papers with Alan and Dimitrios, including Jonathan Simon's).

    I don't buy the idea that the Mandelbrot set is the kind of self-reference that matters, though it's a nice suggestion. It is indeed a set whose boundary is defined by the fixed point of a function, so there's a recursive feel to it. But not all fixed point questions trigger Gödelian concerns. I can find the Nash equilibrium of a finite game (for example) and it's usually not the most mindblowing thing of all time; indeed, finding the Nash Equilibrium of an arbitrary game is somewhere between P and NP-complete.

    I'll have to take a look at Edward Hall's book, and your "octonions" essay, to get a better sense of the things you're after.

    Yours,

    Simon

    Quite impressive, Simon.

    You've taken us on somewhat of a metaphorical journey into ontological meaning.

    "the universe runs in assembly code, the coarse-grained version runs in LISP, and its from that the world of aim and intention grows." I have used FORTRAN, an older language but not LISP, a perfect language to simulate and characterize life, thus used for AI robotics and function humans perform. Assembly Language, ones and zeros basic.

    Math, physics and learning gaps and the eloquent leaps of vivid comparisons: non-life to life, chemical reaction to mind, one thing to everything.

    I think that you wax eloquent with vivid comparisons to supercharge your argument.

    Hope you get a chance to comment on my essay.

    Jim Hoover

      Thanks for the thoughtful reply Simon..

      I think you'll appreciate Hall's book on proxemics, and perhaps your views will grow on me, but I feel that your essay reveals a blind spot to me, which your comments above acknowledge but do not deal with entirely. I'll return to this thread later, and I'll be open to further discussion even when things wrap up.

      I've still got a lot of essays to digest!

      All the Best,

      Jonathan

      Dear Simon DeDeo,

      Thank you for your delightful essay. It was a real pleasure to read and I agree that the counterintuitive nature of specifying scale is very real indeed. In another large-scale example, Hubble's Classification scheme of spiral galaxies was at first deemed too simple because of its simplicity, but it has turned out to stand the test of time precisely because of that, and is still in use today. I also enjoyed your intriguing conclusion that there may be more stages/levels (accelerations) to come in our quest for understanding intelligence and ultimately us.

      I have in the meantime rated your essay and wish you good luck in the contest.

      Regards,

      Robert

      Dear Simon,

      thanks for the reading list---there's certainly some interesting stuff on there I'm going to check out!

      And I should reiterate that I did not wish to imply you abused Gödelian reasoning; however, it has been so often abused that it nowadays almost seems to invite a knee-jerk rejection of certain kinds of arguments. If you've never read it, Torkel Franzén's Gödel's Theorem: An Incomplete Guide to Its Use and Abuse indeed provides what its subtitle proclaims.

      Also, I didn't mean to suggest that Kolmogorov complexity is computable, and I don't think the argument needs it---rather, that meaning is incomputable would be a reduction to the incomputability of Kolmogorov complexity, if it's indeed the case that no program/description exists that picks out all the 'meaningful' books which is itself significantly shorter than the collection of these books.

      And I agree with your last paragraph: epistemic does not mean unimportant; but it does mean that we don't have to either accept ontological dualism or eliminativism, which to me are both rather unpalatable options whose individual problems are perhaps even more severe than those they seek to overcome.

      Hope you caught your flight!

      Cheers,

      Jochen

      Dear Jim --

      Thank you for your kind remarks.

      There's an old joke, due to Philip Greenspun--perhaps you know it. Any sufficiently complicated C or Fortran program contains an ad-hoc, informally-specified, bug-ridden, slow implementation of half of Common Lisp. https://en.wikipedia.org/wiki/Greenspun%27s_tenth_rule

      Yours,

      Simon

      Dear Wilhelmus --

      The flow of time is a lovely problem. I draw from your remarks here that it is indeed connected to memory. What I remember, how long I remember it for, what persists and how, is presumably what is dictating the feeling of the passage of time, rapid or slow, for the organism or process in question.

      The old question--what is it like to ride on the back of a photon? The whole history of the world, in zero proper time...

      Yours,

      Simon

      Dear Jochen --

      Ah, yes! I like what you say about KC here. I remember a similar argument by Stu Kaufmann (I believe he might have referenced it back to others as well)--that when we ask for laws, we are really asking for "compressible" descriptions. KC of course applies only to the notion of a "shortest" law, so if we did believe we had an optimal law-making system, we'd be in trouble.

      I wonder if weaker notions also cause problems, though--e.g., a function that always either compresses something or leaves the same length. It's easy to do a diagonalization argument to show that some things must be missed by this (if you make some things shorter, but nothing longer, then the map is no longer one-to-one for a few things).

      I agree with your remark about dualism. Both ontological dualism and eliminativism really do feel like a hold-over from a previous theology. Perhaps one day they really will seem to be debates about "angels on the head of a pin".

      Yours,

      Simon

      PS: I made it home.

      Simon, I see you will be one of the winers of this first essay contest... congratulations, I already read your essay and rated it.

      Please, consider to have into account my essay which main proposal is:

      "A essay that could revolutionize the future of Cosmological Physics: Aristotle, Newton, Einstein,..."

      The Dynamic Laws of Physics (and Universal Gravitation) have varied over time, and even Einstein had already proposed that they still has to evolve:

      ARISTOTLE: F = m.v

      NEWTON: F = m.a

      EINSTEIN. E = m.c2 (*)

      MOND: F = m.a.(A/A0)

      FRACTAL RAINBOW: F = f (scale) = m.a.(scale factor)

      Or better G (Gravity Constant) vary with the scale/distance due to fractal space-time: G = f ( Scale/distance factor)

      (*) This equation does not correspond to the same dynamic concept but has many similarities.

      Dear Simon DeDeo

      You gave an interesting hypothesis about jerk. I also thought about how third derivation by time can be physically important. According to symmetries it can be strange that it does not exist. Maybe some hidden physics exists where all time derivations are important.

      But, I think that our feeling for jerk can be explained differently. Human beings needed feeling for forces and acceleration in his evolution, he used it at walking, riding, fighting, etc. Therefore, she/he recognizes not only forces, but also changes of forces. Besides, a phenomenon retroactive inhibition is known from physiology. It means, for instance, that if we smell some odour some time, we do not sense it anymore after some time. Similarly it is with forces: if some constant force acts on us, consciousness forgets on this force, but change of force reminds us again.

      Anyway, it is interesting that sense of jerk is informatics, but sense of force is physics. At this, I claim that real physics does not exist, everything is only informatics or mathematics. Namely, I wrote also about dimensionless constants. Thus, 200 years ago, it was understood that one meter is a pure physical quantity. Today one meter is, the most probably, dimensionless quantity, which can be expressed as multiple of Planck's distance. Therefore, it can be operater only as mathematical quantity, and probably it is only mathematical quantity. The same is true for one second and for one kilogram.

      My essay

      Best regards, Janko Kokošar

      Dear Simon,

      This is a wonderful essay and found great interest reading it.

      I enjoyed your thoughts on the 2nd derivatives in nature yet we nonetheless are able to sense higher derivatives. I think it's profound that the fundamental laws of nature are typically unstable in some way if formulated with higher derivatives. I'm aware of many higher derivative theories of gravity, some of which have interesting ways to get around pathologies that I'm not completely familiar with.

      I definitely agree with your ideas on effective field theories. Even in my field of particle physics, people are often too cavalier to dismiss non-renormalisable theories as broken, despite being perfectly predictive effective theories. It is definitely interesting to consider renormlisation at once with emergent phenomena such as social dynamics even. You link coarse-graining with memory, and it is intriguing that coarse graining is actually a loss of (microscopic) information, yet it allows new structures like the brain or silicon chips to store richer information.

      Self-reference and renormalisation are themes we also touch on in what I wrote with my coauthor.

      Thank you again for a really enjoyable read.

      Best,

      Jesse

      Simon - Thank you for a delightful and imaginative essay. I was reminded of the old "God of the Gaps" trope - your essay hints at a "physics of the gaps" that stems from logical limits in self-referential systems (my favorite topic in the 2015 contest - see The Hole at the Center of Creation). However, I do not find the appeal to renormalization convincing - for the same reasons you allude to in discussing the difficulty or origins.

      Our essays have some interesting parallels - although I think your treatment of Borges library is a more interesting narrative than my appeal to the 100 monkeys theorem, we both end up with all of the works of Shakespeare.

      I hope you have a chance to read and score my essay if you have not already - The How and The Why of Emergence and Intention.

      Regards - George Gantz

      Simon,

      Interesting approach. Do you think it's wrong to consider higher orders in terms of perturbation theory? I've not heard the word 'jerk' before but have considered 'change in rates of change, such as accelerations, as always implemented THROUGH the 'next order up'. i.e. If a pendulum 'feels and shows' acceleration (brains and accelerometers don't require you to video a pendulum!) does it not equally and simply show all ('higher order') CHANGES IN RATE of that acceleration?

      I agree much of your content, and don't mind the word 'jerk' (I suspect English has less than half the words science really needs!) But do you think what you describe may be just a glimpse of a far more universal truth about nature and logic; from the quanta upwards through relativity to universes, that a scale hierarchy with consistent unseen relationship laws may be a fundamental structure?

      My essay last year identified the rules of brackets in arithmetic and 'layered' ('modal' or 'quantum') propositional dynamic logic (DL) as consistent with that. (No part of a compound proposition can relate another outside it's local 'frame' in the hierarchy, yet it's product directly relates). Is that consistent with your schema?

      I agree with your comment above about the; "crazy arguments about quantum mechanics and free will which I think are both wrong ("quantum" randomness is not special, and the wavefunction evolves deterministically)" This year I link memory with hierarchies & 'feedback loops' to produce decisions as aims & intents, and identify a momentum 'missed' at the finest scale (QM) allowing a casual derivation of it's predictions. Most find that hard to conceive but your excellent work suggest an ability to overcome the cognitive dissonance produced. I hope you can read it and respond.

      Very well done and thank you for yours which I feel is certainly a top 10 candidate.

      Peter