Does division of extension mean the same in mathematics as it does in physics? by Akinbo Ojo

``Redefinition of things that are already defined is one way to resolve paradoxes and absurdities. But then such redefinitions must stand up to scrutiny and should be verifiable or falsified.''

That is they must be useful. Zeno and Penrose suggest a definition of division that is not useful in general.

``I like your definition of Multiplication and Division. It can resolve paradoxes of motion like Zeno's, if "Real numbers do not apply to distance" as you say.''

Division and therefore the real numbers such as 1/3, pi, etc. is a transformation that is not physical. Hence, my definition of the inverse of multiplication. There may be some argument about whether irrational, transcendental, etc. numbers are real because all distances along a line are either greater than or less than the irrational number. That is there is no distance along a line that equals the irrational number. This also suggests the problem with Penrose where again we have the ``divide'' definition issue. I suggest this as a way to avoid the things like Zeno's paradox, which are not consistent with observation (physical). After all we can go through a door.

My own contention is that the plenum is discrete and also continuous in some sense. Thus displaying a duality. Continuous because there is no distance between its lengths, but discrete because those lengths can perish or be created from Nothing. The fundamental unit of my plenum is the extended (not zero-dimensional) point.

Can this concept be reduced to a hypothesis and measurement? Mine, at least, has been applied to cosmology and the double-slit observations.

Dear Dr. Ojo! For a practising physician, syntropy is a very vital concept, because life is all 'we have'. In my opinion, Dr.Ulisse di Corpo very well speaks about: The Law of Syntropy' in his latestst e-book, based on Schrödinger, Szent-Györgyi and Fantappie. Retro-causality is a key concept of this medical approach which looks at conditioning and conditions. Best wishes and cordially: stephen (www.lifeenergyscience.it)

www.lifeenergyscience.it (typo/sorry).

Andrew,

Since I trust in the only compelling definitions of an ideal mathematical point as having no extension and of an ideal mathematical continuum as never losing its property to have three, two, or just one dimension/extension no matter how often it is cut into 3D, 2D, or 1D, respectively parts, I consider your "infinitesimal points" entertaining.

An infinitesimal length dx is still a length, an infinitesimal area dA is still two-dimensional, etc. Okinbo's splittable point was certainly not C. S. Peirce's best idea. I am claiming a better understanding in 2342.

Eckard Blumschein

Hi Akinbo,

Thank you for your comment on my blog.

I think I see where you are coming from with your essay and where you are trying to get to.

I have a clear idea about the subject.

I believe that the Universe is made of what I call Universal Bits (Existence/non-existence). They are the smallest of everything and cannot be subdivided. They are just bits of potential information, they are not material and they do not have a shape as such, but their apparent size, in any directions, is one Planck Length and they flick between existence and non-existence every Planck Time.

In order for a coherent world to develop, these Universal Bits must group into Coherent Basic Units (made of synchronised Universal Bits). Particles are simply a temporal pattern created by these Coherent Basic Units. But that's only my point of view ...

All in all, I thought that your essay was spot on track. I just rated it accordingly.

All the best,

Patrick

Dear Akinbo,

I am glad to be at contest again with you, as in 2013.

Simple but deep.'Yes' and 'No' in (v) is crucial for me.

More about: „How should we think of infinity?" You can see at RuÄ'er BoÅ¡ković [1, paragraph 391]. "Now, although I do not hold with infinite divisibility, yet I do admit infinite componibility". More you can see in paragraphs 391 to 396. Therefore I say: the mass, radius and any other fenomenon is finite but the number of their combination is infinite.

[1] Boscovich J. R.: (a) "Theoria philosophia naturalis redacta ad unicam legem virium in naturaexistentium", first (Wien, 1758) and second (Venetiis, 1763) edition in Latin language; (b) "A Theory of Natural Philosophy", in English, The M.I.T. Press, Massachusetts Institute of Technology, Cambridge, Massachusetts and London, England, first edition 1922, second edition 1966

Best Regards,

Branko Zivlak

Dear Akinbo,

I enjoyed your essay and I think it was nicely written. As far as extension in physics, things become a little more complicated if it involves also a temporal dimension, as in relativity theory. Zeno's paradoxes are resolved in special relativity because there is no motion in space but in spacetime. However, we all do not have to agree with the ramifications of this approach but it represents a solution.

Actually, Zeno's paradox of dichotomy is about motion being impossible. It cannot even commence since there will be always a point closer to the start than any other point ad infinitum. If we have to preserve the autonomy of this world, or to be more exact, its quasi-autonomy, then this paradox can be resolved only in the context of a tensless theory of time and existence. Another solution is the one given by Descartes that I also speak in my 2011 essay involving a continuous recreation of the world (at discrete time and space, i.e. a virtual reality). Obviously, the subject is more involved than that.

All the best.

Efthimios

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

Sorry, should be "Dear Akindo".

Again should be "Dear Akinbo"

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

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 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