Dear Branko,

Thanks for your comment. I don't think I agree that if divisibility is finite, the number of possible combinations can be infinite. With finite number of constituents and finite number of compartments, the number of combinations, even if astronomical, must be finite also. However, if the number of compartments and constituents is increasing, as would be the case for an expanding universe, the number of different possible arrangements in the system will also be increasing. This is illustrated by the second law of thermodynamics. Entropy of the universe is finite, but increasing with time.

Regards,

Akinbo

9 days later

Dear Akinfo,

You raised fundamental issues on point, space and time. I enjoyed reading your argument. You raised a solution, you wrote: I next propose a hypothesis of time as the separator of minimum lengths, enabling the physical manifestation of discreteness in otherwise 'syrupy' space." I would say if I may point it out that KQID states that space or extended line or matter is indeed 3D time, or time extension. That is why I made a slogan that space is the fetus of time and time is pregnant with space. Therefore, our Multiverse is the fetus of time and time is pregnant with our Multiverse. Crazy statement but logical? yes. Simple idea? Yes. Common sense and "of course" simple idea so obvious in Wheeler's sense? I would say, definitely yes.

You are the warrior of the truth, I comment you and keep on marching no matter what. I admire and share your spirit, I am with you marching no matter what they say and do,

Leo KoGuan

    Akinbo,

    Clever presentation. Does your last statement indicate your affirmation of Parmenides or of consciousness being the key to what is real? My "Connection: Mind, Math and Physics is comparatively mundane.

    Jim

      Thanks James for looking in. The essence of my essay is a refutation of Parmenides proposal that things do not change. I then try to illustrate what implication this has for physics. I will read and comment on your perspective this weekend.

      Akinbo

      Dear Akinbo,

      A. Given your interest in division, allow me to be divisive: Finding (as yet) no seconder, the motion lapses. Case closed.

      B. Given the above, your interest in DIALECTIC, and me now earnestly SEEKING an EXTENSION, I come as your old friend to close the case properly: I second the motion!

      I now CUT to the chase.

      1. As in good cooking: FIRST, catch your mathematical extension!

      2. You write: All mathematical extension that has magnitude can be mentally divided.

      3. You write: Therefore, no energy is required for division to be carried out.

      4. However, as every good physician knows: Mental activity requires energy.

      Conclusion: From such 3-step contradictions, all may be proven!

      With best regards, and loving your continuing enthusiasms;

      [link:fqxi.org/community/forum/topic/2491]Gordon Watson: Essay Forum[/link]. Essay Only.

      Dear Gordon,

      Thanks for your comments. Someone here also drew attention to the fact that mental division would require some energy to carry out. In a sense I agree.

      However, energy-wise physical division would be more expensive energy-wise as it would be a sum of the mental activity and the physical.

      There is the saying that "if wishes were horses beggars would ride". Therefore, mental division must come so much, more cheaper since it is a wish. Taking a fantasy trip to the Moon, would cost you much less calorie-wise than taking a stroll down the road.

      I will take a look at your essay now as I have some time on my hands at the moment.

      Best regards,

      Akinbo

      Dear Akinbo,

      1. Please accept my once-and-for-all apology for excess 'Aussie irony' in my response above (and, to be sure, hereafter). I blame over-stimulation from reading and re-reading your lovely words (and in anticipation). How about we share the indictment?

      2. Nevertheless: a contradiction is a contradiction (and not saved by (imho) unnecessary escapist fantasising). So may I suggest that you did oft misspeak -- and thus should fix -- each unnecessary (and distracting) reference to energy?

      3. Until that time, the contradiction remains.

      4. Yet, indeed, that FIX will not eliminate my FIRST emphasised point in my first above: Have you yet captured that mathematical extension? Or shall I find an engineer to help?

      PS: Thanks for the helpful comments on my essay. I'll reply soon; some thinking to do.

      Sincerely; Gordon Watson: Essay Forum. Essay Only.

      I really loved your well thought out essay. I was impressed by your quote "Ultimately, if extension cannot be its own separator into discreteness, the hypothesis proposed introduces 'time' as the separator of extension into discrete. By 'time', I mean duration of existence, i.e.extension can start to exist and cease to exist and as all minimum lengths do not have the same life span, the discrete nature of otherwise syrupy space becomes manifest. And the idea of perishing distance and how extension works when we walk about the room is intriguing. Well done it really makes me think.

      John C. Hodge mentioned in his post on my essay that your essay would be very interesting and he was correct! My essay is about Sorites Paradox; it explores discrete time units (where Plank's constant is made a cyclic-measuring-device or a Hamiltonian for duration)in contrast to your essay about discrete lengths (and Zeno's Paradox). I think there might be some overlap between our two points of view. I hope you get a chance to read my essay. I gave your essay a good mark. Yours Harri

        Thanks Harri for looking in. I also just read your essay. Yes, I think there is room to link our two essays, as you say 'discrete lengths' and 'discrete time units'. Note however that I suggest that what separates length or extension into discreteness is 'time'.

        I will rate your essay towards the end of competition to give it a lift when needed most.

        Regards,

        Akinbo

        Toward the OJO point:* studying the Akinbo point** until it perish.

        Dear Akinbo,

        1. FIRST, answering your title-question (Essay, p.1): No.

        2. SECOND, a request: Please define/explain in greater detail the Akinbo point** (this strange new point on p.5 of your essay), based on this preliminary attempt to clarify your text (p.5):

        "I [Akinbo Ojo] prefer to call that fundamental unit (which is extended, in contrast to the zero-dimensional point of some mathematicians), the [impure per Leibniz]*** "Akinbo point". The Akinbo point, my fundamental unit of length, is [somehow] featureless, save that it is a [somehow] extended thing." ???

        Please explain, for example: the connection between the original point and your identified extension. (PS: Was this extension discovered or created; by the gods; etc?) Perhaps compare this extension with extension by colour, or life-time, or its god(s); etc. And since it is NOT zero-dimensional: of what dimension is it?

        * reserving "the Ojo point" for a proposed gift to the mighty Ojo clan!

        ** here named; seeking to eliminate misunderstandings already wildly breeding.

        *** Though the immediate case I bring is against you (and not (YET) against the ancients or the gods), I and Leibniz (via his 1714b, para #2) seem to be as one on this one point of purity: A pure point, having no parts, cannot be extended, shaped or split:- yet (so goes my thesis) it may be forever named and claimed!*

        Regards; Gordon

          Dear Gordon,

          Thanks for the feedback and the opportunity to shed more light on possible grey areas on this topic.

          1. Good to see a No answer. So in your opinion what's the difference?

          2. FIRSTLY, there is no strangeness or originality in the extended point. As I discussed in my first essay, it dates back to the Pythagoreans and was a bone of contention between The Pythagoreans, Proclus, and partially Aristotle on the one hand holding the point to be the smallest possible finite limit to extension resulting from division, while Plato proposed that the point be of zero dimension. The inheritors of both schools of thought are for the former those holding a 'substantival' view of space, i.e. space exists independent of objects (Newton being a famous son of this family, and probably also Maxwell) and for the latter those of the view that space is a mere 'relational' concept that does not really exist (Leibniz, Mach and Einstein being famous sons of this school). Sometimes, there is an overlap and some straying. Witness for example that Einstein though of the latter school that says space is a fiction and a relational concept that does not exist comes round to propose that this unreal and non-existing thing when amalgamated with time becomes something real that exists, it can curve the path of moving bodies, and it can vibrate giving rise to gravitational waves which propagate at velocity, c.

          So from the foregoing going further down the scale, for a space that does not exist, its fundamental unit would be of zero dimension and does not exist. That makes sense. For a space that exists, following the idea dating back to Democritus that whatever exists must have some fundamental unit that also exists, since a multitude of what does not exist cannot make up what exists.

          SECONDLY, what does "having no parts" mean? This can have two meanings for a fundamental object. It could mean not existing, being of zero dimension and therefore not divisible and split into parts.

          OR it could mean existing, have a non-zero extension (since a multitude of zero existence and extension is zero existence and zero extension, while a multitude of non-zero extension is an even greater magnitude of extension), but not further divisible physically into smaller parts beyond some limit. Thus it CANNOT have parts. It cannot be split. A smaller part of it has no meaning and does not exist. It is suggested from empirical evidence that this limit to the divisibility of extension is ~ 10-35m (Planck length).

          So it really boils down to whether Space exists independent of objects OR Space does not exist but is merely a relational concept between objects, i.e. remove the objects in a location and nothing exists there anymore. As you can see it is an argument dating back centuries. There is an interesting entry in The Stanford Encyclopedia by Hugget, N. and Hoefer, C., Absolute and Relational Theories of Space and Motion.

          You seem to belong to the Relational school. Good for dialectic as I have someone whose position I can attack and who can attack mine as well.

          All the best,

          Akinbo

          *I think you may have misinterpreted Leibniz a bit given your point of view. Cant be extended can mean cannot be stretched. Only something that has parts can have a shape, i.e. central part and a border part or this side and the other side. An extended point has no sides, no central part and an outer part.

          If you read the first 7 paragraphs, which I consider sufficient, you will see that the pure point of Leibniz is a 'simple substance', the true atoms of Nature. Can this simple substance and true atom of Nature be of zero dimension?

          Dear Akinbo:

          To assist with my reply to your nice details above, could you help here please.

          1. Regarding those who take "the reals" to be continuous, how do they write/represent/denote the last real before 2 and the first real after it?

          2. Do you take "the reals" to be continuous?

          With best regards from this local realist; Gordon Watson: Essay Forum. Essay Only.

          Dear Gordon,

          As far as I know the answers I can give to your two questions are:

          1. There is no definite real before 2 nor any defined real after 2.

          2. I take 'the reals' to be continuous as do most, if not all mathematicians. I think the important question is how the real number line applies to physical reality. In this regard, I have a favourite quote from Roger Penrose's 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 could 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.... We should at least be a little suspicious that there might eventually be a difficulty of fundamental principle for distances on the tiniest scale. ...Why is there so much confidence (in the real number system) for the accurate description of physics, when our initial experience of the relevance of such numbers lies in a comparatively limited range? This confidence - perhaps misplaced- must rest on the logical elegance, consistency, and mathematical power of the real number system,..."

          My work seeks to demonstrate that this confidence is misplaced. That is also why although motion is well described using calculus, calculus itself makes use of the 'infinitesimal', dx a dubious quantity that simultaneously obeys both dx = 0 and dx тЙа 0. Mind you the term dubious is not mine. It is from an article in the Stanford Encyclopedia.

          Lastly, in contemplating how to fold a line constituted by an infinity of points, contemplate as well whether your type of 'point' can be folded or at what point does the folding take place.

          Thanks for the exchange.

          All the best,

          Akinbo

          Dear Akinbo,

          Overwhelmed by the stimulants on offer at your free self-serve open-access drug-store (especially your knowledge of the ancients), I'm now in rehab. And I am now required to pray "The Engineer's Prayer" should I find myself near your store again. So praying -- "I am a concrete engineer. I carefully distinguish between abstract and concrete objects. No abstract ocean floats a concrete boat. Amen" -- I throw this note to you:

          "I am a local realist* suspecting that you are similar. I seek to join you in working to reduce the ink and increase the truth in the world! Could this be true: We are two true local realists working to eliminate nonsense from BT, QM, SR, etc? And are we not yet sure where we differ? GW."

          The background to this note is this: You here express what I interpret to be a healthy open local realism. So, until my rehab is complete, I think it might be best for all if we concentrate on such "much more concrete" matters for awhile. (Perhaps leaving our creative jousting re "Euclid-v-Leibniz ++" until the off-season?)

          PS: Standing ready to reply to all your questions, it would be a big help if you'd NUMBER and repeat the questions in an Addendum; or edit the original via Q-numbers [eg, Q1. Q2. ++]. Thank you.

          * each term is defined in my essay.

          As always, with best regards; Gordon Watson: Essay Forum. Essay Only.

          I have considered your questions Akinbo, and copied the answers below...

          1st - the Mandelbrot's cusp at (.25,0i) is the minimum extent and highest energy represented in the Mandelbrot figure. But the theory would indicate that this translates into a minimum time step. However; for anything to persist longer than the Planck time, in this theory, it must have a non-zero size.

          2nd - particles act as probes of the properties of a given space, retaining and conveying information about separability and separation. I would say that once forms exist as self-contained independent units, which can move relative to each other, this defines or helps determine the dimensionality of space as well.

          3rd - I think part of the meaning of Math is that it preserves some features of natural law that are persistent, from cosmological era to era, from inception to its demise or the beginning of a new cycle, or from universe to universe in a multiverse scenario (more below).

          As for atoms of space, however; that concept speaks mainly to how the fabric of spacetime emerges, and one can't discern individual unit cells after that. If space and time are relativistically indistinguishable; then there is a lower limit of around 10^-13 cm - where particle separability is possible - in which Relativity is defined. And item 2 answers this.

          The Cosmology based on the Mandelbrot Set does not tell us whether a cold dark end is the universe's ultimate fate, or whether a new cycle would begin, as I can show you the graphical representation of both scenarios. Likewise; it supports the idea that the universe is singular and allows for the possibility of multiple universes. This suggests these possibilities coexist equivalently.

          All the Best,

          Jonathan

          Hi Akinbo,

          I liked your essay but I am still not fully convinced that a discrete physical model cannot be possible... although some of your ideas really made me think!

          I must admit, I was almost ready to give up trying to make sense of some of your points because I wasn't really following exactly what you were getting at. But then I think I got a better understanding... Please correct me if I'm wrong, but I believe your view is that in order for space/distance/point to exist in this universe, it must be constructed of something, or else it doesn't really exist in this universe. I think too many people will find it hard to abandon the notion of a background space that exists independent of matter, just like they might picture the big bang in their head as a point that explodes in a background space, rather than a point that expands and creates space itself. So from your perspective, to talk about a point between two objects in the physical world, that point must exist "on top of something", or else it really isn't a point in our universe. Maybe stated another way, you theory supposes that you can't have a true vacuum devoid of matter. I don't think you said some of this stuff, but I have a feeling like this is what you were getting at... but maybe I'm completely off.

          You said this with regard to dividing:

          "Physics does not fair better, even in the models where there is finite divisibility of length. In those models, there is a limit to the number of extended points or fundamental lengths, but there is also no distance between those points, since that distance will also consist of points. Further, one cannot resort to cutting at the boundary since as fundamental objects, both the boundary and its object are one and cannot be separate parts. So like, the case for math, where to cut is a problem."

          But what about a discrete physics model where there is a network of nodes, like what Stephen Wolfram postulates? I think in his model, 3-D space and matter is emergent, so that may be a loophole in your theory that allows for a discrete physical model. Maybe in this kind of network model, network connections(1) and non-connections(0) could combined to lead to emergent properties, which I think is similar to the idea you were describing in your theory when you tried to account for distinct properties in a physical continuum. In this type of network, I believe the lines/edges just help to define a "distance" in metric space between the nodes/verticies, and don't represent a 3-D distance at the most fundamental level... So maybe your ideas would gel with this type of network model since the lines in this model don't really contain any points.

          Maybe even imagining this kind of model pictorially is a little misleading. Maybe each node should be given a number and the structural relationship could be represented as sets of numbers, similar to how a graph is defined in graph theory. So rather than picturing a triangular network composed of three "points" and three "lines", you could consider the following isomorphic numerical representation:

          Vertex 1 connections: {2,3}

          Vertex 2 connections: {1,3}

          Vertex 3 connections: {1,2}

          I have more thoughts on this, but I don't want to get carried away and write more if I didn't get some of your ideas right in the first place.

          Please send a note to my essay forum when you respond so I get an email notification, and know when to check back on your page.

          Thanks,

          Jon

            Thanks Jon for finding time to read my essay.

            It may be that I have to improve and make clearer the points I was trying to put across. Especially as you ask, "I believe your view is that in order for space/distance/point to exist in this universe, it must be constructed of something", "too many people will find it hard to abandon the notion of a background space that exists independent of matter", "...a point that expands and creates space itself", "point must exist "on top of something", or else it really isn't a point in our universe"

            You are correct that the view is that whatever has the attribute of being extended must exist. Space/ distance/ point have extension and therefore must exist. Also all 'somethings' must exist. But given the economic and frugal ways of Nature, it is speculated that if it wants to create what exists, it would so to speak use one stone to kill two birds and intelligently make 'somethings' and 'space' of the same raw material. Hear this Newton from his paper [link:www.earlymoderntexts.com/pdfs/newton1666.pdf]De Gravitatione[/link]:

            "...it is clear that they (philosophers) would cheerfully allow extension (space) to be substance, just as body is, if only extension could move and act as body can" and

            "...space is capable of having some substantial reality. Indeed, if its parts could move..., and this mobility was an ingredient in the idea of vacuum, then there would be no question about it - parts of space would be corporeal substance" and

            "And my account throws a satisfactory light on the difference between body and extension (i.e. between a body and a region of space). The raw materials of each are the same in their properties and nature, and differ only in how God created them..." All from my 2013 essay.

            In essence, point is the fundamental unit of space, 'atom of space' if you prefer to call it so.

            As a result there cannot be point existing on top of something. Location is the substance, and substance is a location and the smallest unit of location/ substance is the non-zero dimensional 'point'. There cannot be more than one point at a point.

            Re: "But what about a discrete physics model where there is a network of nodes, like what Stephen Wolfram postulates?"

            The questions I would like to ask Stephen Wolfram if we met are: what is a node made of? Is it an extended thing or a zero dimensional object or a substance? What is a network connection? Is it a distance and therefore have the property of extension? If network is spatial, i.e. of space, is it infinitely divisible or is of finite divisibility? Is the network constituted of points?

            Knowing the frugal ways of Mother Nature, would it make nodes and networks of the same one substance behaving differently or two different types of substance.

            Finally, you seem to suggest that 'line' should be differentiated from 'distance', why?

            Many thanks for your time and looking forward to any further comments.

            Regards,

            Akinbo

            10 days later

            Dear Akinbo,

            It took me a while, but I'm finally getting back to you with my comments on your essay.

            Many authors in this contest have stated that mathematics is necessarily unchanging ("timeless"), and they conclude from this that the fundamental nature of the physical world cannot be mathematical. I think your point of view of "perishable" mathematics is very interesting, and I agree with you that it is possible to conceive of mathematical structures that can be "born" and "perish". As I said in my reply to your post on my forum, I think it is possible to define a mathematical structure that is related to another structure that acts as a time-counter, and relative to that time-counter, the first structure can evolve, even appear and disappear. That's why I have no problem in believing that a physical universe that is born, evolves and ultimately perish can be thought as nothing more than a mathematical structure.

            What you propose is original and ambitious, and as you say in your conclusion, it will be interesting to see if your hypothesis is falsifiable by real or thought experiments.

            Good luck in the contest and in your future research!

            Marc