Dear Sir,

Mathematics is the science of numbers that describes quantitative aspects of Nature. Nature is what exists, is intelligible (knowable) and communicable (describable). Numbers are properties of all substances by which we differentiate between similars. If there are no similars, it is one; otherwise it is many, which is successive perceptions of 'one's at high speed. Below Planck scale, you cannot perceive anything. Thus, number stops there.

Separation of points by space would not be points, as space is the interval between objects that exist. Point has existence, though no dimensions. Thus, space is the interval between points also.

Since everything is three dimensional only, there cannot be a multitude of discrete points at the same point, as point has no extended dimension, but the intersection of three of its components.

The distance between Atlanta and his destination is neither infinite nor changing, whereas his own position has been replaced by momentum, which is ever approaching destination covering fixed positions. The paradox would have been valid, had the space also expanded or his velocity reduced proportionately.

Regarding whether one can perish, please read in our other comment.

Regards,

basudeba

Hi Akinbo,

I still don't quite get the "two points, one relating to matter and the other to 'empty space', occupying the same point." I see points as conceptual overlays on reality. The coordinate system is defined to consist of these conceptual points, which identify location. What is actually at that location, whether matter or 'empty space' is irrelevant. I don't see the "two points" as colliding or in any way interfering with each other. They aren't "real" in my view.

The question of whether the universe could start to exist is tougher. It's hard for me to understand this, but it's impossible for me to understand the universe that "always" existed, and the 'known' facts don't seem to support this. But now that it's here, I don't see it going away entirely. Nor do I have much faith in a 'cyclical' universe and none at all in the multiverse. One unitary universe does it for me.

And no, I don't believe that virtual particles pop in and out of existence. If there is highly concentrated energy, as at the LHC, it can 'spawn' particles, but they don't pop in and out of empty space. It's more like the energy 'condenses' into relatively stable local configurations. Feynman's pictures represent perturbation terms in an expansion, and are not necessarily to be taken literally.

I experience and am aware of continuity, and I do not believe that, other than through limiting processes of calculus, math has much to do with the physical continuity of reality, as it is a symbol system of truths, so I don't try too hard to formulate an accurate conceptual narrative to tell you how to "cut a 'continuous' line, ... consist[ing] of an infinite number of uncuttable points". But I very much enjoy reading your attempts to do so.

And I'm happy with your wine analogy.

I thank you for reading my essay and for your comments. John Cox left me a little note after my response to you to "lighten up". I'll try to do so. Going against the flow of current beliefs is tiring and frustrating, but as John points out, selling my ideas is probably not best accomplished by attacking others ideas disrespectfully.

Edwin Eugene Klingman

Akinbo,

A pretty good read. Thank you.

I will say that there is another way to think about division. That is as the inverse operation of multiplication. This effectively sidesteps many of your concerns since the act of division simply returns the thing that is divided to its pre-multiplication state.

Obviously, that ignores situations such as those that are the subject of your essay ... namely things that cannot clearly divided, or whose division is ambiguous.

Something that I have never understood regarding the concept of a Planck length ... I understand that it is intended to introduce a certain graininess to the universe, but the electron is considered to be a point particle in the truest sense. Therefore, why does the universe need to be grainy? Surely the electron is part of the universe.

Oddly enough, I have thought of the possibility of motion being a creator and destroyer of space. I have also thought of the possibility that a particle is created in the direction in which it is moving and destroyed in the direction from which it moves. The two general ideas seem to be pretty complimentary.

Best Regards,

Gary Simpson

    Gary,

    Thanks for offering me this fresh insight and new way to think about division. From this perspective, it would appear clear that that which is to be divided or multiplied must therefore have some finite NON-ZERO value. If that is the case, are you then of the opinion that there is no limit to division?

    The Planck length is suggested to be in some sense that limit to division, a fundamental sort of length.

    What do you understand by point particle? Is it a particle that has mass and is of zero dimension and thus infinite density? Or does your point have a dimension? Many mathematicians postulate that the point is of zero dimension. In my 2013 essay I discussed the history behind this idea.

    I am happy you have yourself contemplated these ideas about motion. The two ideas are complimentary as you said. Indeed, the second is the way motion is depicted on a computer and TV screen. I similarly thought about the possibility before opting for what I discuss in my essay, which also resolves the other Arrow paradox by Zeno, which you can view here and here.

    Regards,

    Akinbo

    Akinbo,

    To me, it is possible in mathematical abstraction to divide something as many times as desired. In practice, this is not true. So, it seems that you have identified a difference between mathematics and physics. Namely the concept of divisibility (or non-divisibility).

    So perhaps the Planck Length has meaning for empty space but not for particles such as protons or neutrons.

    It is easier to multiply numbers than it is to divide them. I was taught multiplication before I was taught division. So, division is thought of as the inverse operation of multiplication. That makes it easy to divide something if that something is the result of a multiplication. This is perhaps not useful if something can not easily be divided ... for example half of a proton. Of course, a distance could be half of the diameter of a proton.

    Best Regards,

    Gary Simpson

    Regarding the electron, my understanding is that it has no physical dimension and that it has mass. Therefore, it has infinite density. My inference from this is that we do not have a correct understanding of the electron. I have presented some speculation regarding the electron in two papers that are posted to viXra.org. In the first post in my forum, I list the web address of those papers.

    Thank you for reading my essay.

    I am thinking - now - that many physical laws, describing a mathematical world, does not have access to the real world (if describing material objects); there is ever a minimum dimension where the divisibility ad infinitum is not applicable. So that a mathematical object (the physical law) have a limit of applicability in the real world.

    Depends on how you have defined the operation and what you mean with the question. Provided that you mean the normal addition law in the natural numbers, it's a certainty, if you ask for mathematical proof. If you ask for the physical/observational truth, you will ever only get a high probability.

    Sophia,

    Thanks for your comment. In other words, I get from your comment that Mathematical truth is not necessarily the same as Physical/Experimental truth, even though they may be close.

    As I mention in y essay, even for Mathematical truth there is an unstated, underlying assumption that things that are being added cannot perish during the addition process. Is this a certainty even for mathematical truth?

    As I commented elsewhere, I speculate that it is not a certainty that 2 3 = 5 but a very, very, very high probability, with the probability increasing with the size of the object being counted and reducing with the size of the object. In other words, 2 house 3 houses = 5 houses is more likely to be correct than 2 electron 3 electrons = 5 electrons. Not necessarily because of the experimental difficulty in identifying an electron but as I discuss in my essay, it is more likely for an electron to perish than for a whole house during the process of counting to determine the sum total.

    Regards,

    Akinbo

    Dear Akinbo,

    Thank you for the comment you made about my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL My essay explains how the real Universe is occurring. Reality does not have an abstract uncommon, but abstract interesting perspective. I did not mistake an abstract image of an abstract object for the abstract object itself. You did that. Abstract images may be abstractly conveyed by abstract traveling abstract light, however, real light can only appear provided it is seen as adhering to a real surface that is traveling at the constant speed of surface.

    Only an abstract universe could come from an abstract nothing.

    Regards,

    Joe Fisher

      Dear Akinbo Ojo,

      Wow. You obviously put a lot of thought into this essay and I congratulate you on your effort. I found it very challenging to read partly because I couldn't see the "point" (no disrespect, but pun intended). I realize that it is typical of philosophers to pick a detail such as you did and obsess over it until they have pulled every possible string to its limit, but as an applied physicist, it is hard for me to follow without a clear end in sight.

      However, in regards to your hypothesis about time, you said, "Of course, not everybody accepts the cosmological theory, so we are assuming its correctness." Well, in fact, I disagree with the big-bang theory as well as interpretations of singularities as being black holes in spacetime. As I explained in my essay (Doctors of the Ring...) these are mis-perceptions of unified concepts (metaphorically represented by the "golden ring"). If you look at a circle from its side (or as a shadow on Plato's cave) you will see a line. And if there is a particle moving continuously on the ring, the shadow would make it look like an oscillation from one end to the other and back. If you believe that perspective, you will be trapped (under the spell) and won't rise above the plane of opposites to see their unity.

      Because the whole cosmological theory is based upon the notion that space is 3D and time is 1D, which is a lop-sided expansion of s = ct, correct mathematics has led to a lop-sided interpretation. It's a foregone conclusion.

      I have been working on a model of space-time-motion (which I am about to submit for publication) that represents space and time as conformal projections of motion onto a two-dimensional S-T plane.

      *Motion is what is real; it gives matter form. The word motion represents a complementary (unified) concept, i.e. "motion" is a single word used to express complementary antonyms (moving and not moving or at rest); yet the moving state can be expressed in terms of gradable parameters (displacement (s) and clock-time (t)),

      *The gradable parameters, s and t numerate (i.e. quantize) and denominate (i.e. reference to standard time scale) the moving state to provide a gradable spectrum by the ratio, v=s/t;

      *The speed of light in natural units is simply the state at which the ratio is 1:1

      Although I don't follow your logic, I think I agree with your statement that "time is the separator and conferor of discreteness on space". My reason has more to do with the fact that time is the scale that denominates motion, thus giving it a unit magnitude of change. The "curse of Zeno" may be resolved simply by shifting the reference from zero to unity. Any unit of measurement is defined by the "unit", i.e. one unit, not zero. "Zero" represents nothingness so any physically measurable model that includes zero length or displacement, is subject to Zeno's paradox. The concept of time is also subject to the "curse". A unit of time is "measured", although it is not a physical observable, by the motion of a clock (or grains of sand etc). So setting t=0 for analysis of a moving particle means zero relative motion, which is the rest state, so the moving model does not apply.

      I hope I made some sense, but it is very difficult to explain. If you are interested, you should read my first draft of the Space-time-motion diagram at http://vixra.org/abs/1402.0045. I have made some changes, mainly to cut down on the philosophy and background material, so check back in a few days to get the latest version.

      Oh yes, as for Parmenides philosophy: clearly I disagree with his view that change is impossible, but I agree that existence is timeless because time is nothing more than a scale for eternal (timeless - no beginning and no end) change.

      Best regards,

      Ted

        Your work convincingly relates that mathematics and physics are more artful.

        Sincerely,

        Miss. Sujatha Jagannathan

          Hello Akinbo,

          I was thinking about your idea of minimum physical length and whether probabilities of 2+3=5 exist depending of the length of the object. It could be useful to put objects into perspective to see if there is consistency.

          Maybe you can create a single log scale going from the maximum size object we know (universe) to the minimum size object we known. On this scale, you can highlight from what size we are starting to have issues with standard mathematics. Maybe it has already been done?

          Regards,

          Christophe

          Ted,

          Thanks for your comments. We seem not to be in the same boat on a number of issues, viz. eternally existing universe vs. my finitely existing universe; preference for space-time vs. my space; timeless existence vs. my finite duration of existence. But no matter.

          I rushed superficially through your paper, 'The space-time-motion diagram: a relational model'. I can see that you are like me interested in knowing what "continuum" means. It is a frequently used but in my opinion a poorly defined term. Your ideas make use of Lorentz transformation and you like other 'relational' physicists consider space a 'non-entity', unlike some of us who like Newton consider space an 'entity'. But before concluding about whether space or space-time is a non-entity ponder what entity vibrates as gravitational waves travelling at c, i.e. if GR is correct, and also check what entity is compressed or extended in the Alcubierre drive, a model based on space-time like yours.

          I will request more clarification on your thread how you resolve Zeno's paradox with your model.

          Regards,

          Akinbo

          Thanks for your comments Christophe. I am not aware that the log scale you mention has been created but I am aware that there are various reasons to believe that the gap between mathematics and physics will widen as we approach the Planck limit. You can check the review by Sabine Hossenfelder, http://www.livingreviews.org/lrr-2013-2 that I referenced in my essay to see the motivations in this regard.

          Cheers,

          Akinbo

          Thank you very much Miss Sujatha Jagannathan. I see you have an essay here. I will checK soon.

          Regards,

          Akinbo

          I liked the simplicity of the essay. I completely agree with your postulate to imagine points coming into and going out of existence exactly when needed. I call this the emergence of space from the actions of objects in time as opposed to the a priori existence of space as an infinity of points coming and going as a place for action and objects.

          You further argue that dividing an object with neural action does not involve energy, but obviously any thought of dividing does take energy; the energy needed to sustain that neural packet of a moment of thought. In fact, it would in principle take an infinite energy for the infinite thoughts of dividing infinitely...thank goodness most minds are not prone to this neurosis.

          There are two universes; math and physics, and math divides an object of our mind into an infinity of smaller objects with a neural action of our mind. Physics divides an object external to our mind into some physical limit of smaller objects with actions using other objects and of course using energy as well. Math represents objects as we imagine them to be and physics represents objects as they actually are outside of our mind. But our mind does use energy for all thought.

          The irony is that it is by the neural action of our mind that we imagine both the infinity of smaller objects in an imaginary reality as well as the finite atoms of real objects. In other words, math equally well describes both the infinite as well as the finite. In particular, can infinitesimal points exist in the lonely nothing of empty space? Or is it only objects, time, and action that exist? It is not only our science that makes an object out of empty space, something out of nothing, space seems to emerge from our neural reality as well.

          1.5, entertaining

          1.0, well written

          2.1, understandable

          2.0, relevance to theme

          6.6 total

            Hi Joe,

            I am of the view that the question, "Where did the universe come from?" is not stupid and is worth contemplating.

            By the way, the theory surrounding this predates Stephen Hawking. Among the earlier thinkers was the Belgian priest and mathematician Lemaitre and the Russian George Gamow. It was however Hubble's finding of the redshift-distance relation that let the horse out of the stable. Then, I think about 1973 or so, Edward Tryon introduced the possibility that rather than the universe having a beginning starting from a point of infinite density containing ALL the matter in the universe, it could have started from absolutely nothing. No matter-energy and no radius.

            I think there are a number of evidence that point in this direction, rather than the singularities of infinite density that Hawking and Penrose formulated. It is still work-in-progress and gaps to feel. Among the gaps in my opinion is the obsession to have ALL the mass in the universe to be present from the beginning. On the contrary, I have written elsewhere that it makes more sense that BOTH mass and radius have been increasing from zero in tandem. If positivity of energy is attributed to mass and negativity of energy is attributed to radius, then overall the Total energy sum from inception up till now remains ZERO, which is 'nothing'.

            But for unbelievers like you, you must find a better explanation for why the universe has not collapsed under the influence of the infinite number of masses acting over an infinite amount of time; Olber's paradox; the relative abundance of the elements, etc among the successes of the Big bang, as a work in progress.

            Coming nearer home, you must tell us who has been preventing the wedding between the Moon and the Earth, the Earth and the Sun despite the unrelenting strong love and attraction between them over billions of years. If you know who else could have been putting the marriage ceremony at bay other than Mr Expanding Space, please tell us.

            IMHO let's not use individual frailties that are not self-inflicted to muddle up our discussion. In Africa, there is a proverb that if you point a finger at people the remaining four are pointing at you.

            Regards,

            Akinbo

            Thank you Steve for your comments. I think you make some sense that mathematical division requires energy of some sort ("But our mind does use energy for all thought").

            On your statement, "I call this the emergence of space from the actions of objects in time as opposed to the a priori existence of space as an infinity of points coming and going as a place for action and objects", which partly supports my hypothesis, I cannot help wondering whether if in your theory, objects should stop acting for a moment, whether space would then disappear? I think not.

            We will continue our dialectic where we usually "meet" on this website.

            Thanks and best regards,

            Akinbo

            Some people did the exercice: www.scaleoftheuniverse.com/

            Based on today knowledge, the universe ranges from: 10^-35 to 10^27

            Quantum phenomena appear for quite large objects.

            http://www.cjoint.com/15fe/EBrsomy3XT2.htm

            If our mathematics applies to the large universe. Would it mean that the mathematics of very small objects applies in our scale?

            Exactly my opinion Christophe. Here is what Roger Penrose has to say 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.

            Hence, my asking assuming, without conceding that the system of real numbers applies to distance, how can a distance be divided if there is always a third element between two elements and going by geometrical considerations these elements are uncuttable into parts?

            Regards,

            Akinbo