Dear Akinbo,

Thank you for writing such an interesting essay.

What I get from it is that the real numbers are not a good model for physical space and physics in general. This leads to an interesting question: why does physics work so well with a bad model of it? Because of all the discrepancies you bring up between R and physics, why is it that R nevertheless works so well?

Another question. Much of physics can be rewritten with finite approximations. Is there some result in physics which demands the real numbers and would not work with a finite approximation?

Thank you again for a great essay.

All the best,

Noson

    Thanks for your comments Marc. Ultimately, what I have argued and tried put across is that whatever is given the attribute of existence must have the capability of the opposite, i.e. non-existence. If our universe perishes, nothing whether physical or mathematical will outlive it and the ball is in the court who propose the opposite to show the place and the manner how such timeless existence is exhibited.

    Regards,

    Akinbo

    Dear Noson,

    Thanks for finding the time to comment on my essay.

    As regards, your first query why the real number system works so well in spite of all the discrepancies highlighted in my essay. My initial answer would be that most models would work well, if adhoc entities are invented to fill the loop holes in the modelling, even though paradoxes, counter-intuitive notions and inconsistencies may result in many cases. An example of this is the use of Calculus using the real number system to model motion. The adhoc entity in this instance is the infinitesimal, dx. For the real number system to work, dx must be capable of being both zero and not zero, i.e.

    dx = 0 and dx тЙа 0

    So if such contradictions are permissible, the real number system can work so well, but may be masking an aspect of reality, which if apprehended will do away with the adhoc improvisations used to cover the loopholes.

    Regarding the second question, as I noted in my essay, physical space must exhibit a duality. It must be be capable of exhibiting discreteness and finite approximations being not infinitely divisible, BUT, physical space, the great separator of things into discreteness can itself not play this role which it plays for other entities on itself, hence it also exhibits a continuous nature. Hence my use of 'syrupy' to describe it. However, despite this parts of space are not eternally existing or so to speak, all parts of this syrup do not have the same expiry dates. It is the expiry dates that confers discreteness on the continuous syrup call space.

    Finally, I love this quote from Roger Penrose, your fellow FQXi member. In his book, The Emperor's New Mind, p.113... "The system of real numbers has the property for example, that between any two of them, no matter how close, there lies a third. It is not at all clear that physical distances or times can realistically be said to have this property. If we continue to divide up the physical distance between two points, we should eventually reach scales so small that the very concept of distance, in the ordinary sense, could cease to have meaning. It is anticipated that at the 'quantum gravity' scale (...10-35m), this would indeed be the case", then further on,

    "We should at least be a little suspicious that (despite the logical elegance, consistency, and mathematical power of the real number system) there might be a difficulty of fundamental principle on the tiniest scales", and "This confidence - perhaps misplaced-..."

    It is the possibility that this confidence is misplaced that my essay tries to explore. I would have wanted your own opinion on how to divide a real number line, if there is always a third element between two elements and going by geometrical considerations these elements are uncuttable into parts, i.e. there is a point or number at each incidence of cutting and points cannot have parts or a part of it.

    Thanks for sharing.

    Regards,

    Akinbo

    *I will copy this reply on your forum as a notice.

    Akinbo,

    To answer your question about points there are discrete concepts of distance. A meter stick has discrete set of centimeter marks, and a discrete set of millimeter marks and so forth. We have no particular problem with integer distances or rational numbers that are distances. The subtle issue is with irranional numbers. An isosceles triangle with two lengths 1 and 45 degree angles has hypotenuse of sqrt{2}. You will not find this in a rational way. This gets one into the question of the continuum and how there are an uncountably infinite number of points between any two points. Dedekind made a point that one can find this point with an infinitely sharp "knife" that cuts perfectly.

    The problem is that we are dealing with infinities and are not directly computable. To compute something means one can run this on a machine and find a numeric expression. However, numbers such as sqrt{2} have no such representation. We can only at best express them numerically with a numerical approximation.

    This gets into my idea of mathematics having a body and soul, where the body involves things that can be physically computed, while the soul involves abstractions that can be infinite or infinitesimal. I am not committed to any existential properties of the "soul," but the body of mathematics is what is transduced into physical quantities. There are some funny elements to this, such as whether the fine structure constant really has this property, or is it after so many decimal points uncertain.

    LC

      Akinbo,

      A good well presented essay on an important topic where poor or limited understanding has always prevailed. I think this situation did need 'flagging up' to help remove creeping complacency. You well identify those present limits of descriptive powers and identify the flaws.

      I second your postulate, but with the proviso we are not ruling out 'disappear' from the Electromagnetic (EM) 'scale' regime as possibly still allowing some higher order quantum 'foam' or dark energy state smaller and not harmonically interactive with EM. i.e. if an EM particle is a cyclone, then the air molecules exist even when it disappears. or if an air molecule disappears; it's constituate fundamental particles remain. So I suggest we should consider 'dimensional orders', so 'disappear' to us may not necessarily be synonomous with 'cease to exist in any way.' How do you feel about that?

      My last question relates to the helix, much analysed in my previous essays. Do you agree we can 'identify' each cycle without 'cutting' anything? If two helical entities approach us directly we see two distinct orbits, yet if we observe from the side we see a continuous sine/cos wave form. The orbiting 'charge' of each may itself be a 'fractal' of that same dynamic, which is consistent with what optical science and neutron interferometry are finding (see my citations last year) with spin-orbit coupling and 'hyperfine' spin states.

      On the surface of the ocean are tiny wavelets on waves on ever bigger waves, through swells and tides. Do you agree the human experience may only see a small 'window' of that sequence, in the same way our eyes can only detect a tiny slice of the EM spectrum? Does that modify your analysis?

      Anyway, a great essay within reasonable non speculative limits. Good rating well earned.

      I hope and am sure you'll also like mine, revealing a few tricks and their implications, also important for improved understanding. I have a short video expanding on the implications (perhaps for after all the essay reading!)

      Well done and very best of luck in the contest.

      Peter

        Thanks for looking in Lawrence. I left some questions on your forum, which you have answered in part here.

        When you say here that "A meter stick has discrete set of 10-2m marks, and a discrete set of 10-3m marks and so forth..."

        Thus this and so forth extend beyond the 10-35m (Planck length limit)?

        In our universe, we know from experience that there can be a line AB, along which for example Newton's first law tells us an object can move if not subjected to force. We also know that a sharp knife can be swung and cut through this line despite not being infinitely sharp and despite Calculus suggesting that the line contains an infinite number of points. Following from these, i.e. the observation that cutting of a line can take place in our universe without an infinitely sharp knife, and in spite of the supposed presence of an infinite number of points between A and B, would it be unreasonable to look at other ways that this cutting can be logically achieved without the sort of absurdities that Dedekind tried to avoid?

        On the question of the continuum, would the fact that there can be no other point between two points not be sufficient to establish the continuum? I suggest if the points are "discrete concepts of distance" as you said, but there can be no other distance between two of these discrete concepts, then the continuum is established without appealing to an infinity of points. The remaining piece of the puzzle is, if distance cannot separate points, what can? It is here that we need to question whether points are eternally existing entities, and if not whether they have the same lifespan.

        Best regards,

        Akinbo

        Hi Peter,

        Thanks for looking in. I appreciate your comments and consider them. When you talk of 'disappearing' possibly being implemented by 'dimensional orders', this is possible for a universe or for physicists who believe that there can be any number of dimensions ranging from 0 to even 10 in our universe. I for now believe that ALL that exists does so in 3 dimensions. A line with length, but without breadth or depth cannot exist in my model. Likewise, a surface, which is usually referred to as 2-dimensional for ease of analysis, but in reality if its thickness is zero, that surface cannot exist. You may want to show me one such surface which has no thickness yet exists :-)

        I will check your essay this weekend. I had browsed through before but all this Bell's stuff getting me dizzy so I have left it to others. I however asked Gordon Watson to have a look at your essay and that of Edwin Klingmann because he seems to have a good grasp of what is involved. However, it appears you two have been in touch before and each has decided to stick only with his own model without compromise. Will look at your essay as I said and will rate appropriately.

        Best regards,

        Akinbo

        Akinbo,

        You seem to infer my hypothesis of 'smaller' states of motion than the limit for electromagnetic harmonic coupling may mean something other than "ALL that exists does so in 3 dimensions." Far from it. THAT is the big difference, and so consistent with just about all findings with no mysteries (i.e. the 'hyperfine' spin found in neutron interferometry).

        It just needs thinking beyond current doctrinal assumptions; So called 'quantum spin' is then just the rotation of the charge which orbits in the 'spin-orbit coupling' of light. In a way it's perhaps rather arrogant of us to assume we can 'detect' all that can exist, so I say you're right with "disappear", but that may not imply other things 'beyond' that! In the same way can't assume the current observable limits of the universe are all there is. We know well that's untrue!

        I must read Gordon's essay. We were in very close agreement about 'QM' previously. I suggest there's no mystery, it's all 3D and OAM, and show the it's the 'sock-switch' maths 'con trick' that confounds current doctrine.

        Have you seen the video? Do you have 9 mins to spare yet?

        Peter

        Akinbo,

        As time grows short, I am revisiting those I have read to see if I have rated yet. Yours I have not so I am doing so today.

        Thank you for reading mine.

        Jim

        Hi Akinbo,

        I enjoyed your thought provoking essay. Your proposed physics without conservation laws is I believe even more of an extreme revolution than the Instantaneous Action At A Distance principle that I am advocating. However it is indeed worthy of further thought.

        My feeling that the measurable fundamental quantities (mass and charge) that we can detect and measure with Newtonian mutual interaction force laws are real and are conserved. The historical problem came with the development of the concept of Energy. I believe that energy is not fundamental but is rather a human engineering invention which acts a very convenient book keeping method of accounting for force and motion. It also displays a property which implies conservation of this quantity and this tool undoubtedly hastened the industrial revolution and got physicists interested in this industrial quantity. However even by the time of Einstein and Dirac, energy became conflated with mass and required an interpretation of what was meant by negative and disappearing energy. While retaining the dimensions of energy, new concepts entered into the conservation of what was always a man made quantity. Now logically you seem to make a case that if we continue to use the current definitions of all of the supposedly conserved quantities we run into contradictions implying the failure of current theories.

        I have not had time to really study your argument, but would it be true that if energy conservation was not as fundamental as the conservation of Newtonian mass and charge (ie no Special and General Relativity) then maybe we could retain conservation as a bedrock of physics?

        Your essay demonstrates that there is much to discuss further in this area where physics meets philosophy. Well Done.

        Regards

        Neal Graneau

          Thanks Neal for your comments. Actually, there is obedience to the most fundamental conservation in what I describe. Perhaps, you will agree that displacement as an entity is more fundamental than energy, momentum, mass, charge, etc or you may not agree. But in motion and in Action at a distance, displacement is conserved. That is, in attraction or repulsion between bodies, the amount of displacement created or destroyed between bodies for repulsion or attraction respectively IS EQUAL TO the amount of displacement destroyed or created respectively outside the bodies in the line of interaction.

          From my cosmological perspective, nothing is ultimately conserved or stated in an alternative way, the sum of all being sought to be conserved is zero. That is why the universe can emerge from Nothing and expand, which Universe, when you add all the plus and minus side still sums to zero. Trying not to digress outside the topic here but can give a link to my tentative model, if you are interested. If the Universe starts from zero, is currently zero and will end up zero, then no mathematical laws are broken. In my model, Mass is and Radius is -, both summing to zero. As the universe starts from zero mass and zero radius, both M and R increase in tandem. The thermal history of the Big bang model of the Universe bears this out. Mass increases with radius. No point containing all the mass now in the universe from Day one - an absurdity, if I may call it so.

          Regards,

          Akinbo

          Dear Akinbo,

          This is true:

          "The non-zero dimensional point does not have an eternal existence, but can

          appear and disappear spontaneously, or when induced to do so "

          Previously produced many questions, such as:

          What is the distribution of the duration of the non-zero-dimensional points (particles)?

          Why proton has a very long duration?

          Why there are fermions and bosons?

          What kind of divisions is allowed in physics? ...

          You explained it, to a large extent, and you'll get a high rating. I invite you to comment my essay.

          Regards,

          Branko

          Dear Akinbo,

          After reading your essay for me there is one key take away, namely that to quantize something (in this case space) it would make sense to have something acting like a separator. In my opinion, the experiments showing that the spacetime is smooth and not discrete are very convincing, but it is a completely different matter to see this principle formulated in terms of sufficient reason. It is very surprising and nice to understand it from this point of view. I hope you do carry on with your research, for which I am rating your essay accordingly.

          Warm regards,

          Alma

          Dear Akinbo,

          thanks for reading my essay and the comment. In principle, I agree with you that there is no real infinity. As you I see it as a concept to an value which can be arbitrarily large (but not fixed).

          Certainly, if there is a conflict between physics and math I would prefer physics (if it is experimentally confirmed). But I think it is unlikely.

          I also read your essay and rate them higher (8 points) but with no real effect on the number.

          Good look for the contest

          Torsten

          Akinbo,

          You referred to Gordon Watson's essay in discussing mine. I did indeed find it consistent, if the maths slightly too complex for me! Gordon has also now made very generous comments supporting mine and we're discussing others.

          I see I have my 'minute of fame' at the top, which is far too early for the tape and last minute bun fight so all scores welcomed! I still think yours is under rated and see it's near the cusp. (I checked and yes I did rate it).

          Very best of luck in the run in.

          Peter

          Dear Akinbo,

          Contests FQXi - is primarily a competition for new ideas. You give such ideas. Your ideas are close to me in spirit, to overcome the split basis of fundamental science and the the "LifeWorld" (E.Husserl). My high score. It is always interesting to discuss with you on the forum.

          I invite you to see my analysis of the philosophical foundations of mathematics and physics, the method of ontological constructing of the primordial generating structure, "La Structure mère" as the ontological framework, carcass and foundation of knowledge, the core of which - the ontological (structural, cosmic) memory. I believe that the scientific picture of the world should be the same rich senses of the "LifeWorld", as a picture of the world poets and philosophers. Today, more than ever, are relevant philosophical covenants of A. Einstein and J. Wheeler:

          "Presently the physicist is compelled to deal with philosophical problems in much bigger degree, than it had to be done to physics of the previous generations. To it physicists are compelled by difficulties of their own science." "Philosophy is too important to be left to the philosophers."

          Kind regards,

          Vladimir

          Hi Akinbo,

          Thanks for kindly commenting in my forum, and for voting me up. The bottom line on our disagreement about mathematics and philosophy is also the bottom line of your essay: "I ... move the motion that we exorcise the lingering millennia old Parmenidean spell on our mathematics and physics and allow that what exists can perish. Nothing is ultimately conserved."

          I draw the line at "existence exists" as the necessary and sufficient foundation of logic -- I'll concede Aristotle and even Parmenides that much. :-)

          Even though I regard your philosophy as nihilistic, I'll give you as much credit as I give Aristotle for being entertaining as well as provocative!

          Best,

          Tom

          Dear Akinbo,

          I finally got to read your essay. Since it deals with a subject matter on which I am not expert, I can not make definitive assertions, but I may be able to help direct you towards potentially fruitful directions.

          1) I have the impression that subject matter of your essay is most directly covered by measure theory. Indeed there are "pathological" measures which may be useful in considering these sorts of problems. One is the Cantor set, which has measure zero but contains an uncountable number of points. There are others, and they may inform your view on this matter.

          2) Until I took set theory I had no appreciation (and I think this is also true for almost everyone else, including physicists) that any real number, say, 1, is a completely different animal from its natural number counterpart. Learning how to represent these numbers by sets teaches one to appreciate the difference. In short while each natural number can be considered as a single object, each real number is an infinity unto itself. Our notation helps bring about the failure to appreciate this: if we wanted to properly notate, say, the real number 1, we would have to write 1.0000000000000000000000000000000000000000000000000... stretching over an infinite distance. I think this distinction may have some bearing on your arguments.

          3) Your example involving Lagos and New York reminded me of the Alcubierre metric.

          4) You may also want to consider how your arguments turn out in other kinds of geometries, like the projective geometry, for example.

          Again, I regret that I could not say anything definitive about your ideas, but I hope that you found my pointers useful.

          Best wishes,

          Armin

          Dear Akinbo,

          You have presented a very interesting essay. I like how you take special care in distinguish the context of mathematics and physics in order to discuss your ideas. Moreover, you are able to analyse this different context and arrive to the conclusion that the meaning in both areas is different. I think that is a very good philosophical work.

          As a matter of speculation, is your essay supporting the idea that space and time must be discrete?

          Kind Regards,

          Yafet

          An enjoyable read Akinbo..

          I thought your reasoning was very tight, until some point near the end where an unwarranted conclusion or two slip in. But I'd have to read again for detail, to point out any error or false claim, and I must instead move on to a few more essays.

          All the Best,

          Jonathan