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RECENT POSTS IN THIS TOPIC

Joe Fisher: on 4/2/15 at 14:37pm UTC, wrote Dear Dr. Prisinzano, I thought that your engrossing essay was...

Giovanni Prisinzano: on 3/24/15 at 21:16pm UTC, wrote Dear Akinbo, Mom has improved, but a full recover is difficult, because...

Akinbo Ojo: on 3/23/15 at 14:16pm UTC, wrote Dear Giovanni, I hope your old mum has fully recovered. In your response,...

Giovanni Prisinzano: on 2/28/15 at 16:33pm UTC, wrote Dear Akinbo, I thank you so much for your kind post and for your...

Giovanni Prisinzano: on 2/28/15 at 16:24pm UTC, wrote Dear Miss Sujatha, Actually I think that macro-world too can be numbered...

Giovanni Prisinzano: on 2/28/15 at 16:21pm UTC, wrote Dear Sir, thanks for your detailed post. It contains a lot of interisting...

Giovanni Prisinzano: on 2/26/15 at 15:24pm UTC, wrote Dear Tommaso, Thank you for your kind and thoughtful comment! It was a...

Giovanni Prisinzano: on 2/26/15 at 11:37am UTC, wrote Dear Koorosh, Thank you for your kind comment! Your statement that the...


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FQXi FORUM
October 14, 2019

CATEGORY: Trick or Truth Essay Contest (2015) [back]
TOPIC: If time is made of numbers by Giovanni Prisinzano [refresh]
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Author Giovanni Prisinzano wrote on Feb. 4, 2015 @ 21:46 GMT
Essay Abstract

The essay suggests a hypothesis about the nature of space and time. We assume that space is the set of all real numbers, while time is the set of positive real numbers “totally” (“linearly”) ordered in the increasing sense. We support these assumptions by considering some properties of continuous sets and by reinterpreting Dedekind’s axiom of continuity. We also suppose that under specific conditions, which can be found in systems travelling or operating at the speed of light, space and time lose continuity and become one and the same set, that of natural numbers. Lastly, we believe that our perspective may help to clarify some controversial problems of last century's physics, mainly concerning quantum theory.

Author Bio

Giovanni Prisinzano studied Philosophy at the University and at the Scuola Normale Superiore in Pisa, where he graduated in 1982 and finished his Ph.D. in 1986. He also worked at a post-graduate fellowships in Munich and Zurich Universities for two years. At present he is a Philosophy and History teacher in Italy's high schools.

Download Essay PDF File

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Lawrence B Crowell wrote on Feb. 5, 2015 @ 22:33 GMT
Giovanni,

Your essay was interesting, though there is something I have to take to task. I will also have to reread it to make a better assessment.

The problem I see with the idea that space involves positive and negative numbers and time only positive numbers is that this runs into some trouble with relativity. Time can be parametrized arbitrarily, and one can set zero at any point in spacetime.

Again I will have to reread your essay to make a firmer assessment of it. The discussion on the continuum was interesting.

Cheers LC

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Author Giovanni Prisinzano replied on Feb. 6, 2015 @ 16:04 GMT
Lawrence,

I thank you very much for your comment and for your interest.

I can't but agree with your remark that my idea of space as a set of positive and also negative real numbers is questionable. I'll have to think it over because, if it is incompatible with Relativity, as you say, I' ll consider the possibility to remove negative numbers from my view of space. After all a space made only of positive numbers is able to contain not only all existing events (which are at most a countable set) but also all the merely possible states of affair (which are, in my opinion, uncountably infinite). Maybe the inclusion of negative numbers in my explanation of space was due to the purpose to differentiate it as much as possible from time, which, unlike space, is progressive and irreversible. But it is possible that only positive numbers do exist outside our mind, and that space and time are made only of them.

Best regards,

Giovanni

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Lawrence B Crowell replied on Feb. 6, 2015 @ 23:12 GMT
I will try to reread your essay this weekend. My point about time and positive numbers is that one can set zero where you want. With calendars we have the Christian, Jewish and Islamic calendars that set their zero year at different points.

Cheers LC

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Eckard Blumschein replied on Feb. 18, 2015 @ 03:52 GMT
LC,

When Giovanni attributed the positive sign to time, I see this only reasonable on condition he referred to elapsed time, not to any event-related time scale, cf. Fig.1 in topic 1364.

You wrote: "one can set zero where you want". Yes, one is even forced to arbitrarily choose an event of reference if one ignores the alternative of referring to the only natural point zero (of elapsed time), the now.

Elapsed time exactly includes all past. Only elapsed time can be measured.

Eckard

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Eckard Blumschein wrote on Feb. 6, 2015 @ 04:09 GMT
Dear Giovanni,

Your essay is the first one I got aware of that provides a lot of rather uncommon thoughts which I tried to convey in my essays 369, 527, 833, 1364, 1793, and 2021.

I have to also appreciate your excellent style and a lot of valuable details.

Having read in particular Fraenkel (not Fränkel) 1923 with a bit more critical eyes, I arrived at less political correct conclusions. I agree: Dedekind's cut is not at all a cut.

I wonder if you will dare to answer LC's question as did I.

Best,

Eckard

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Author Giovanni Prisinzano replied on Feb. 6, 2015 @ 17:33 GMT
Dear Eckard,

thank you so much for your note and your appreciation of my essay! I'm new of Fqxi contests and a post like yours is a great pleasure for me.

I shall surely read all yours essays about the same, or a similar one, subject, but let me ask a naive question: How can I find any single essay by its number?

Unfortunately I have also to apologise in advance for my probable delay in answering to the next possible posts and in reading the new essays. I have to live suddenly from home, because my old mother, who lives alone and far away from me, has had a bad accident just yesterday and must undergo surgery in next days. Therefore I'm not sure if I'll be able to regularly follow the discussions of the forum. I'm very sorry for this!

Best Regards for you, Eckard!

Giovanni

P.S.: Obviously Dedekind cut is a cut only for sets of rational numbers, not of reals.

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Eckard Blumschein replied on Feb. 7, 2015 @ 11:12 GMT
Dear Giovanni,

Simply add the topic number to http://www.fqxi.org/community/forum/topic/ in order get the essay and the belonging discussion.

Dedekind's cut is considered as one way to create/define real numbers in contrast to rational ones. Other definitions include nesting intervals and equivalence classes. Please find Ebbinghaus quoted in 833. I agree with you on that a pebble-like number is a knife rather than a cut. That's why topology can so far not perform a symmetrical cut. I see you quite right with your criticism.

We all are not perfect. When you wrote "I have to live" you meant leave.

I will also be absent for some days for a surgery. Hopefully I will nonetheless

manage to submit a new essay "Physics Suffers from Unwarranted Interpretations".

I appreciate you writing Relativity and not relativity in your reply to LC on Feb. 6.

Best wishes for your mother too,

Eckard

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Author Giovanni Prisinzano replied on Feb. 16, 2015 @ 10:18 GMT
Dear Eckard,

obviously I meant “leave”, not “live”. The mistake was mainly due to my absent-mindedness in a difficult moment.

Much more serious is that I did not write “Fraenkel” correctly. My only “excuse” is that in a precedent book on similar arguments I wrote it corretly, but this can't clear my mistake.

My present condition is very complicated. Last week, in addiction to my mother's illness, I lost a person who was very dear to me, and I am very sorry to say that I cannot follow the forum by now.

Best regards for you!

Giovanni

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Amrit Srecko Sorli wrote on Feb. 6, 2015 @ 10:01 GMT
DEar Giovanni,

Yes, time has only a math existence.

see article

http://link.springer.com/search?query=sorli++amrit+

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Anonymous replied on Feb. 6, 2015 @ 18:00 GMT
Dear Amrit,

Yes, time has a math existence.

But, conversely, also math (or, at least, a part of it)has a physical and temporal existnce!

Thank a lot for yours reading suggestions!

Giovanni

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Amrit Srecko Sorli wrote on Feb. 6, 2015 @ 10:02 GMT
here is another paper

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John C Hodge wrote on Feb. 6, 2015 @ 20:52 GMT
Thanks for the thought provoking essay.

What you are showing is the (Greek) logic system is incompatible with the counting and geometry math of physics. (Or did I get it wrong?) Representing lines, surfaces, volumes, and duration as points produces paradoxes. Russell and Whitehead tried to unite logic and counting math - I think they assumed the relation but this is controversial.

When you use the terms ``space’’ and ``time’’, are you referring to the left side of the GR field equation or to the measurement of distance between objects and the measurement of duration between events? I think you don’t mean a void (Democritus) or a plenum (Aristotle).

The source of the paradoxes seems to be the logical problem of considering lines as many (unlimited number) points rather than as an extension. This distinction troubled the ancient Greeks. Democritus seems to have opted for the extension definition. (Yes, I know he discussed the idea of a volume of an object being composed of many thin slices. I take this to mean he conceived of calculus ``method of exhaustion’’ before Archimedes and Newton.)

I used 1/3 of a line in my paper to stay away from numbers such as $\pi$. Is there a point 1/3 along a line? Is 1/3 in the first or second class? Other points can be greater of less than 1/3. I conclude the correspondence of a real number with a point fails to be physical. That is a line is not composed of many points except as an abstraction.

I suggest your ``truth value’’ should include what is true for the model is true for object (measurement). For transformations to be useful, the inverse transformation must be unique and complete.

You may be interested in Photon diffraction and interference and 2015 contest paper for a different view of light.

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Author Giovanni Prisinzano replied on Feb. 25, 2015 @ 22:02 GMT
Dear John Hodge,

I thank you so much for your very interesting comments and apologize for the delay of my answer.

I don't know if greek Logic and Mathematics are incompatible with the modern science of nature, but they are probably incomplete because, for example, they did not afford the developement of the infinitesimal calculus (with the partial exeptions of Eudoxus and Archimedes)...

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Koorosh Shahdaei wrote on Feb. 7, 2015 @ 18:20 GMT
Dear Giovanni;

Thank you for your contribution. Although material i.e. particles are tangible, but space itself as a container is probably more difficult to describe, and time is the dynamics relating to material and space.

Having said that my view is that we are unable to get the whole picture, as both space and material have singularities and are discontinuous in my opinion and this is what I have also addresses in my article. Furthermore the physical objects have a quantity which bridges us to math, everything else without quantity is omitted by us.

Kind regards

Koorosh

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Author Giovanni Prisinzano replied on Feb. 26, 2015 @ 11:37 GMT
Dear Koorosh,

Thank you for your kind comment!

Your statement that the quantitative nature of physical objects is what permits a mathematical description of them is the winning idea of the science of nature. It goes back to Democritus (maybe also to Pythagoras), but has found its first effective achievement in Galilei's work.

I will read your essay as soon as possible.

My best regards,

Giovanni

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Member Tommaso Bolognesi wrote on Feb. 12, 2015 @ 10:24 GMT
Hi Giovanni,

you essay is certainly not running short of originality! I see you also have a book on these issues.

I find the idea of a continuous model of space and time (the reals) that becomes discrete when viewed by the eyes of a young Einstein riding the light beam very original and somewhat attractive, although I have problems in understanding whether the two pictures can fit into a unique, coherent vision of the physical universe.

(I have a tendency to believe that discreteness is all we need to explain the physical world, with continuity and infinity arising as limiting concepts - purely logical products of our ‘creative’ minds. That the human brain can be creative 'beyond naturalness' is confirmed, for example, by the construction of the Reals by Dedekind, and the implied mental procedures.)

You write:

From a logical point of view, a model maintains the “truth-values”, in the sense that all that is true of the object is also true of its model.

Shouldn’t it be the reverse, that is: all that is true of the model should be true of the object? What the models says about the object must be true, but the model is not required to tell all truths of the object (otherwise the two would coincide).

A final remark. It is a fact that the order of events in *subjective* time may be reversed when passing from an observer to another observer, but the Lorentz distance (spacetime distance) between two events is constant for all observers, i.e. invariant under the Lorentz transformation. The Lorentz distance and associated lightcone structure define the causality relation between events, which is fixed. Lorentz metric and causality are the objective aspects behind subjective time.

Then, what would be wrong in saying that space and time, taken separately, are purely subjective intuitions (following Kant) and that spacetime (Lorentz) distance is the objective physical quantity behind them?

Saluti da Pisa!

Tommaso

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Author Giovanni Prisinzano replied on Feb. 26, 2015 @ 15:24 GMT
Dear Tommaso,

Thank you for your kind and thoughtful comment! It was a pleasure for me to receive it and I regret not having been able to answer before.

I substantially agree with your remark that discreteness is what we need to describe the physical world (as evidenced by the power of fomalised languages and Turing machines), but I hold the opinion that space and time –...

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basudeba mishra wrote on Feb. 13, 2015 @ 16:55 GMT
Dear Sir,

Space, Time and coordinates arise from our concept of interval and sequence. When the interval is related to objects, we call it space. When the interval is related to events, we call it time. When we describe inter-relationship of objects or events, we describe the sequence by coordinates. Directions are arrangements of the sequences of intervals of objects in space. Dimension is...

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Author Giovanni Prisinzano replied on Feb. 28, 2015 @ 16:21 GMT
Dear Sir,

thanks for your detailed post.

It contains a lot of interisting suggestions, but I am not sure of having correctly grasped all its points. I shall endeavour to read your essay carefully.

Best regards,

Giovanni

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Sujatha Jagannathan wrote on Feb. 16, 2015 @ 06:44 GMT
Your thoughtful work assumes the assumptions of systematically numbered system of the Universe in mathematical sense but it puts forth more permissible subscripts and not the numbering of the macro-world!

Best Regards,

Miss. Sujatha Jagannathan

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Author Giovanni Prisinzano replied on Feb. 28, 2015 @ 16:24 GMT
Dear Miss Sujatha,

Actually I think that macro-world too can be numbered as well. Once we state that things (objects, or facts) are placed in a space-time made of numbers, it is possible tu put them in a one-to-one correspondence with numbers themselves. Moreover I think that the number of existing objects or facts amounts to a countably infinite set, while the set of state of affairs which are possible in a purely logical way in uncountably infinite.

I could not develop these points within a brief essay.

Kind regards

Giovanni

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Author Giovanni Prisinzano wrote on Feb. 18, 2015 @ 13:16 GMT
I want to thank very much all those who have read my essay and have posted the welcome and interesting remarks I see here.

Unfortunately I am not at home at present and I cannot answer the posts or follow the contest. My old mother, who lived alone, has had a serious accident for some days. Now she cannot move and I am engaged to help her constantly.

I promise to answer to everyone who has written or will perhaps write to me as soon as it will be possible.

I am very sorry for the delay and give you all my excuses!

Giovanni

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Akinbo Ojo wrote on Feb. 24, 2015 @ 19:31 GMT
Dear Giovanni,

Eckard Blumschein drew my attention to your essay and must I say I am glad I read it. In my opinion, it is one of the essays that must make the list of the Top 40 Finalists. The essay makes a good and sincere attempt to exorcise some outstanding fundamental devils in our physics and mathematics. Despite being such a good essay, I have some bones to pick and posers to raise,...

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Author Giovanni Prisinzano replied on Feb. 28, 2015 @ 16:33 GMT
Dear Akinbo,

I thank you so much for your kind post and for your appreciation of my essay! (AndI have to thank again Eckard for having been the first who resolutely has found it worth of attention.)

I cannot but subscribe you remark aboot Newton, who is absolutely a giant of thought, but I don't know if his views about space and time go deeper than those of all others I mention.

With regards to Dedekind's axiom of continuity, I specify that the dividing point is unique only in the sense that the line has to be divided in two part, if we want to view it as a geometrical representation of time. The left side of it represents the past, the right side the future, and the dividing or, better, uniting point, represents the present. This latter is unique for each reference-frame, because every reference-frame has its own present, but different observers, or reference-frames, can have a different present.

Finally I think that space, as well as the set of all real numbers, are not merely concepts, but are eternally existing entities, which cannot perish, as long as there is an Universe. Numbers (or space-time) are fundamental aspects of the Universe and are inseparable from it. I cannot say if it is possible for numbers to exist outside the Universe, because it is not possibile for me to conceive anything outside Universe.

All the best,

Giovanni

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Akinbo Ojo replied on Mar. 23, 2015 @ 14:16 GMT
Dear Giovanni,

I hope your old mum has fully recovered. In your response, "that space, as well as the set of all real numbers, are not merely concepts, but are eternally existing entities, which cannot perish, as long as there is an Universe.", I assume that this holds only if the Universe too is also eternally existing. Your statement suggests that if the Universe is perishable, then space is also perishable. I put this idea to good use in my essay.

Regards,

Akinbo

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Author Giovanni Prisinzano wrote on Mar. 24, 2015 @ 21:16 GMT
Dear Akinbo,

Mom has improved, but a full recover is difficult, because she is very old. Thanks a lot for your kind interest!

Your supposition is right: I cannot take for granted that space and time, as long as the Universe, are eternally existent beings.

I have already read your essay and I find your hypothesis that spatial distances can perish very original and interesting, as well as are unconventional and interesting your approach to the Parmenidean "spell" and your solution to Zeno'a paradoxes of motion. I find also several points of similarity between your perspective and mine, but I have to re-read carefully your essay, if I want to comment on it properly, as you deserve.

All my best regards,

Giovanni

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Joe Fisher wrote on Apr. 2, 2015 @ 14:37 GMT
Dear Dr. Prisinzano,

I thought that your engrossing essay was exceptionally well written and I do hope that it fares well in the competition.

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

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