Dear Marc,

Thank you for taking the time to read my essay and for your kind words!

I'm not sure I can say I have an optimistic attitude or hold hope. Should there be a theory of everything, I realize it's not even granted that we will ever find it. Unlike winning the lottery (where someone has to win at some point), a TOE is not a guaranteed miracle. It's more that I am somewhat pointing to the possibilities of living in an open universe, with an infinite future, vastly larger than its past. Trapped in finite lives, it's easy for us to forget that others will follow us and that it's nearly impossible to predict the future of mankind (although it looks bleak at this point with ecological problems and whatnot).

I don't think there is a way to show that a proton must exist, unless one takes quite a zen approach, eg. protons happened when time started, so in a sense they always existed and therefore must exist. This obviously doesn't produce a lot of helpful insight. But there is a way to create an infinite number of universes just like this one by keeping the ratios constant, as you said, the 1860 proton to electron mass. Thus the masses of the particles would be equivalent between universes, modulo something, along with all the other constants; all these universes would look the same. Take that something from modulo and replace it with all the real numbers, one at a time; suddenly the chance for our universe to be looks strangely different (the chance for this universe to be among an infinite number of universes made by varying the cosmological constant is 0; 0*aleph1, the cardinality of the set of reals, what's that? Should we multiply zero with the cardinality or with the value of the cardinality, and if we multiply with the value what do we get?). To make a toy model just for fun to explain this bizarre ratio, I'll choose the idea behind technicolor theory, where fundamental particles are made from a single type of constituent that's held together in bunches by a superstrong force; it's the only example I can find right now and I find it intuitive. Say this even more fundamental constituent is duplicated and configured inside each particle, so for an electron we have 10 pcs of it and for a proton we have 30 pcs, 10 for each quark. Then we take these configurations and plug them in some perturbation theory, the first few loops raising the difference in mass up to a factor of one thousand and then the next loops converging to some masses that share that ratio. Of course I'm not saying that there even is such a theory; I'm saying that we can't rule out the possibility that it exists or the possibility that we could one day find it. Even if the values that we have look weird.

About the hidden logical rules. Our universe, the one that insists to make sense is also the one that influences our thinking. If we were to live in a level V universe, out math may have looked different; it would have been the math of the infinitely intelligent mathematician. He can understand ours, but we can't understand his (or maybe we can with proper training, but we're not inclined to use it from our own initiative). Our universe does have regularities and we were all born here, so our thinking seeks patterns. If we were to live in a universe with time swirls, we'd even have problems defining the number 4 in the way we do here. Natural numbers were born from the need to count so say that a prehistoric being is trying to count food urns, 4 of them, but when he finishes counting, a time swirl takes the 4th urn. Not just that only 3 urns remain, but only 3 urns were ever there because of the problem of the local direction of time. But the time swirl that took the urn left its memory unaffected so the notion of 4 will from now on be associated with 3 objects, in a superposition where you mean 4 and see 3. Of course this may not be a very good example but there's only so much one can do to make a definition have a meaning and the opposite. Depending on how that universe is constrained, it's maybe even possible to live in it (to keep it simple, say it has all our constants, but some small scale thermodynamic oddities), but the way that the inhabitants interpret the world should be different from ours. Perhaps they have a real-world number system that helps them count these awful disappearing objects and a second ideal number system that works like ours and is used only in philosophy classrooms, having no application to their world. A universe where the time direction is locally not constant would certainly generate minds that would seem odd to us. Our universe came with built-in math with conservation laws; why? Well that's a hidden rule, for now.

I enjoyed your questions, by the way. Wish you all the best!

Warm regards,

Alma

Dear Mr. Fisher,

Thank you for reading my essay and for your comments! I appreciate your realistic view of the world.

Wish you best of luck in the contest!

Warm regards,

Alma

Thank you, Gary! Your kind words are much appreciated.

Yes indeed, the one that went blind would be Euler. He tried to learn to write without looking while he still retained some sight, but after losing his sight his writing was too unclear to serve any purpose. I used that trick to encourage the readers' feeling of participation, because I thought you would recognize every case. I'm also glad you liked the man-years approximation.

I downloaded your essay and took a look. It's certainly quite dense so it will take me a while to digest it, but it looks appetizing and I will certainly comment on it once I manage to understand it.

Warm regards and best wishes,

Alma

Dear Alma,

Fun speculations! I like the idea that beings living in a universe based on math that does not support conservation laws would have an appropriate mathematics that would work in their world, and also mathematics that resembles ours, but is only used in philosophy classrooms! It looks like something out of a Borges story, or something that could exist in some remote corner of Terry Pratchett's Discworld...

Keep Maxiversing!

Marc

Dear Marc,

Right, I forgot to say something; you first mentioned that my writing style is enjoyable. I think I can say I mostly learned English from Terry Pratchett's books, so even if I can't compare my writing to his, I think I retain some of the formulation quirks and comparisons he used to make.

Cheers,

Alma

Dear Alma:

A very nice and well written essay, I really like it! I agree that math can't work on it's own --- that's the biggest problem my "pragmatic physicist" has with Tegmark's mathematical universe. It isn't of much use knowing we live in a mathematical universe if we don't know where we live. We'd still have to go out and figure that out. It didn't really become clear to me though whether you are arguing for or against reductionism, or maybe the middle way in which reductionism works 'in principle' but not 'in practice'?

-- Sophia

    Dear Sophia,

    Very nice to hear from you!

    Actually that's a very good question because I didn't consider reductionism when I wrote the essay. My thoughts on the topic are not as clear as they should be considering the difficulty of the topic - but to answer your question, I think that maybe I can say that reductionism can work in practice but not in principle. What I mean is that finding descriptions for emergent phenomena may be possible and they would probably come in handy, however it may not be completely satisfactory. To give the best example that can illustrate my case - some day we may find a great description of the human brain and it will have life-saving applications in medicine; that description however may not include qualia and even if it does and we can rationally argue that it's complete, I very much doubt that it can feel complete.

    Warm regards,

    Alma

    12 days later

    Alma,

    Interesting read. I like your chatty, almost poetic style, like a narrative we want to continue, and I like your Socratic inquisitions.

    When you say "We seem to come to a halt momentarily ..", do you mean nothing stunning has occurred, like finding the Higgs through LHC was expected -- but they now expect a larger-mass Higgs is being hidden as they increase energy.

    I think scientific approaches can be more directly looking for solutions to mysteries in the classical world like looking into the almost 100% efficiency of photosynthesis and tying it to superposition in the quantum world and quantum biology's look into the European robin's navigation N to S. The math follows.

    Enjoyed your essay.

    Jim

      Dear Jim,

      Thank you for reading my essay and for your kind words!

      I said that we seem to have come to a halt at the present time because some long sought after principles have failed to show, like SUSY or Higgs' brothers, dark matter signatures in LUX or any other number of different things we were hoping to find, but my main idea was to plead for patience. That we didn't find something in the last years does not mean much because we haven't been searching for long enough to despair.

      The examples that you give, new unexpected puzzles that may lead to new conceptions about the world or new valuable applications, are wonderful and help make my point.

      Warm regards,

      Alma

      Dear Alma,

      I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

      All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

      Joe Fisher

        6 days later

        Alma,

        I revisited your essay and am thankful you checked out mine. I find that I did not rate yours, something I usually do to those I enjoy, so I am rectifying that. I like the bounciness, the hopefulness and the openness of your essay.

        Jim

        Dear Alma,

        thanks for reading my essay and your words. I want to make the unification of science using math very clear.

        But I gave the complement back. I also read your essay and it is really great. Much easier to read then my essay (and maybe also easier to uderstand for any reader). I'm glad that the conclusion of our essay are (in principle) the same.

        I wish you also the best luck for the contest (for that I gave a high rate).

        Torsten

          Dear Alma,

          Excellent analysis in the spirit of Cartesian doubt. Deep, all-encompassing questions on fundamental questions of Mathematics and Physics and the direction of finding the answers to them:

          "That our knowledge manifests gaps around emergent phenomena seems to be an indication that we lack some insight of the mathematical description itself, not just of what happens physically. It may very well be a gap in our total knowledge of the world, not of the physical, or biological or mathematical fields in isolation. Are we just lacking the right mathematics to treat other fields with similar power and rigor as physics? You know you're missing something when there's just too much you can't explain. "

          "Our math does not make sense in a million ways, 7 but always choses a certain correct path and discards everything else. We woke up in a place where so many things might have headed in a different direction, yet our universe is very well constrained.

          The constants are not changing and reality seems sturdy, like it will last forever. Everything insists to make perfect sense. "

          Indeed: "But there's still time. Just wait to see our children."... My high appreciation.

          It's time we start the path...

          I am sure that current problems of Mathematics and Physics - a problems with the ontology. Dialectics too, do not be afraid, it is a good helper for a deeper vision of the dialogic Nature. Dialectics and ontology help to see Universum as a whole, understand the nature of the information, time, consciousness. The Information age requires revision and updating of the basic concepts of fundamental science. The new paradigm and a new vision of the world, including the Foundations of Mathematics and Physics, filling them with the sense of "life-world" is possible only on the basis of the broadest synthesis, taking into account all accumulated knowledge, teamwork «ratio», «intuition», «emotion».

          Good luck in the contest,

          Kind regards,

          Vladimir

            Dear Alma,

            Don't know for what reason your essay had not caught my eye. Probably because of the number of essays. Better late than never. Certainly a brilliant contribution and will reflect in my rating.

            Under the section, Simplicity and What Follows, you wrote, "My room and everything in it is made from one type of lepton and two types of quarks... The universe takes a bunch of matchsticks, assembles them in the shape of various Rube Goldberg machines and obtains an overwhelming level of diversity". This is an area of great interest to me and I discuss this as well in my essay.

            If we assume the matchsticks to be indivisible lengths, if you break down the various Rube Goldberg machines, the lepton and quarks into their matchsticks, what will distinguish one matchstick from another? Or framed another way, what can distinguish one fundamental length from another assuming space either of distance or of matter is not infinitely divisible? Certainly, what will separate the matchsticks into discreteness cannot be of same nature as the matchstick or can it?

            The other issue I have to ask here, is whether these matchsticks are eternally existing? Whether they have the same date of manufacture? Whether they have the same expiration date? If your answer is no, can "time" distinguish the universe's matchsticks?

            All the best in the competition. Well done.

            Regards,

            Akinbo

            *If you don't mind could you leave me a note on my forum that you have responded so I can be alerted.

              Alma,

              You mention the Langlands program, which is pretty close to what I am looking into. The generalization of the Tanyama-Shimura conjecture into algebraic varieties and categories is one reason why I have been looking into this homotopy approach to the foundations of mathematics.

              Your essay was interesting and was free of obvious problems or errors. Mathematics has qualities as you say with the complex plane and fractals that make it appear less of an invention and more as something discovered.

              Cheers LC

                Dear Alma,

                It was a pleasure reading your well-written and enjoyable essay, with many points to take home, and commonalities with the ideas in our essay. Especially the emphasis that mathematical physics is as good as the physical insight preceding it [what we called conceptual unification].

                A noteworthy remark you make concerns thinking of mathematics as an emergent process. Very interesting. Now on the one hand of course elegant theorems follow from axioms. Can one think of this as emergence in the same sense as emergence in physical and biological systems? Does a theorem possess emergent properties which the axioms do not have, and which could not have been anticipated just by staring at the axioms. We suppose yes, as for instance features we see in number theory - properties possessed by a collection of numbers which simply cannot be guessed by looking at individual numbers. Perhaps you make a very important point here. Can emergence in physical systems be in any way linked to the corresponding emergence in the maths used to describe them? We will appreciate any thoughts you might have on this.

                Kind regards,

                Anshu, Tejinder

                  Dear gentlemen,

                  Thank you for this greatly engaging comment! I like your formulation of conceptual unification and with your permission I will keep it.

                  I too think that theorems have emergent properties. One thing that seems to confirm this conjecture is that we have theorems that are very hard to prove. If all the properties were contained in the number theory we have so far, demonstrating or disproving the Riemann hypothesis should be a walk in the park. What leads to proofs is usually a little extra insight, a moment of intuition not unlike a critical point that acts a bit like a phase transition.

                  You're posing a difficult question with regards to emergence to which I'm inclined to answer yes. Emergence seems to be happening in both physical and mathematical systems, however it's difficult to ascertain at this point if this has a significance beyond philosophical considerations. Ideally such a link should help us determine more things about the world and have applications. For what I recall, there has been a recent breakthrough in modelling a sand pile avalanche, which is known to happen as a phase transition from complete stability to a state where sand flows down the slope much like a liquid. The breakthrough was achieved because the shape of the sand grains (somewhat like a quarter moon) was taken into consideration. I'm afraid I can't find the reference on self organized criticality right now, but my point is that - for me at least - there are hints that this direction of chaos and emergence is very promising. I think it is also very appetizing that the concept of chaotic attractors is seemingly so close to the perturbations used nowadays in QFT. Hopefully soon the answer to this question will be definitely affirmative.

                  Thank you again for your most thought provoking comments!

                  Warm regards,

                  Alma

                  Dear Alma,

                  Thank you for your comments. It will be great if someone took to investigating common emergence in physical phenomena and the in the mathematics used to describe it. For instance, there are concrete studies which derive quantum theory as an emergent phenomenon, and gravity as an emergent phenomenon, and they use precise mathematics at all levels. It will be interesting to explore if the corresponding mathematics can be described as emergent.

                  Just one small correction Alma ...one of us (Anshu) is female :-) We understand of course that it is not always easy to deduce gender from foreign names.

                  Kind regards,

                  Anshu, Tejinder

                  I don't know to what extent theorems have emergent properties as it might be the things theorem refer to. I have been working on how spacetime is a coarse grained manifestation of large N entanglements, which have a period 8 structure. In this way the basic SLOCC structure is 4-bit or 8-bit even if there are 2^n = N large number of quantum bits. The geometry of spacetime time then comes about from event horizons that are measures of these entanglements. This in part goes in favor of those who say that time is a sort of illusion, but as I think space is a bit of an illusion also.

                  On this basis we could say that distance measures, say the Pythagorean theorem, is not emergent so much as the underlying constructions of points, lines, planes and so forth. Given that those elements exist, even if they are emergent, then Pythagoras was right as is so much of other mathematics. Of course we are talking about physical emergence, not so much mathematical. Mathematics as an idealized system of models does not seem to my mind emerge as such, but rather the underlying natural system the mathematics models is emergent.

                  LC

                  Dear Torsten,

                  Thank you for taking the time to read my essay! I am very glad that you found our ideas similar. Actually after submitting, by reading other essays, I realized that I must have underestimated the level that was acceptable. I hope that the lightness of the style doesn't take much off the weight of the argument.

                  Warm regards,

                  Alma