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January 23, 2018

CATEGORY: Wandering Towards a Goal Essay Contest (2016-2017) [back]
TOPIC: Continuity, discreteness, and the limits of the mathematical representation of what happens by Giovanni Prisinzano [refresh]
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Author Giovanni Prisinzano wrote on Feb. 24, 2017 @ 21:45 GMT
Essay Abstract

The essay proposes an approach to the problem of divergence between the domain of the mathematical laws and that of aims and intentions based on the realtionship between reality and information. We show at first that a mathematical representation is possible only for those phenomena about which we have information. We shall then argue that, because of the discreteness of information, all mathematical model of reality must be discrete too. Since the latter includes phenomena such as subjective experiences, but also as motion and change, which we believe happen in a continuous dimension, we affirm that mathematical models cannot describe many of their aspects. Lastly, we suggest a hypothesis about why we have no information on intentionality and consciousness.

Author Bio

Giovanni Prisinzano studied Philosophy at the University and at the Scuola Normale Superiore in Pisa, where he graduated and obtained his Ph.D. He was also temporary research fellow at Munich and Zurich Universities. In recent years he worked on the philosophy of mathematics, and he published a book on this subject.

Download Essay PDF File

Satyavarapu Naga Parameswara Gupta wrote on Feb. 27, 2017 @ 08:11 GMT
Dear Prof Prisinzano,

Thank you for the nice essay on “Reality is discrete and Nice History of Philosophy starting from Pythagoras, Plato, Galileo, Archimedes etc… "

You are observations are excellent, for example…..

1. We shall then argue that, because of the discreteness of information, all mathematical model of reality must be discrete too. Since the latter...

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Satyavarapu Naga Parameswara Gupta replied on Mar. 3, 2017 @ 00:51 GMT
Thank you Giovanni Prisinzano,

Thank you for posting on my papers page,

Thank you for your kind words, I am waiting for your esteemed opinion on this Dynamic Universe model and for your future discussion...

Best Regards


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Alexander M. Ilyanok wrote on Feb. 27, 2017 @ 08:35 GMT
Dear Giovanni Prisinzano,

I read your essay today, and find that we are in even more agreement than usual. Your idea about “Consciousness is a function that represents itself, but is anincomputable function, in the sense that there is no information about it (information is computable), and we can never derive it from some algorithm” is very interesting.

I hold the view that...

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Author Giovanni Prisinzano replied on Feb. 28, 2017 @ 13:37 GMT
Dear Alexander Ilyanok,

I thank you very much for reading my essay and for your kind comments on it. I share your point of view on metaphysics and the obstacles it has often created for scientific research. I also agree on the fact that no physical theory (including those more established, such as Relativity and Quantum Mechanics) can be considered ultimate explanation of the world.

I will try to learn something about Femtotechnology and your deterministic approach to quantum mechanics, although my knowledge of physics is limited.

My best regards,


Lawrence B. Crowell wrote on Feb. 27, 2017 @ 16:15 GMT
Your paper is entertaining, and you are right in the sense that space and time are model systems. We can't isolate a quantum bit in a region smaller than a Planck length L_p = sqrt{Għ.c^3} or a Planck time T_p = L_p/c. This does not curiously mean that spacetime is gridded or chopped into blocks per se. The Fermi satellite result illustrates the lack of dispersion from burstars billions of light years away means space is continuous nearly 3 orders of magnitude smaller than the Planck length.

In some ways space and time or spacetime are something emergent from mental consciousness. It is an epiphenomenology built up from quantum entanglements, and how we interpret this according to continuous geometry is a matter of our mental model building. It is in some sense a matter of psychology.

Cheers LC

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Author Giovanni Prisinzano replied on Feb. 28, 2017 @ 13:46 GMT
Dear Lawrence,

Thank you very much for reading and appreciating my essay!

I was not aware of the results of the Fermi satellite and I'm happy to know that they can somehow support the point of view of the continuity of space-time.

On the other hand I do not think that space and time have a purely subjective nature. I think they have a physical reality (which I consider having a mathematically continuous dimension, except for special reference frames), but the limits of information and of our perceptual sphere do allow us to represent them only through discrete models.

Kind regards,


Joe Fisher replied on Feb. 28, 2017 @ 16:22 GMT
Dear Professor Prisinzano,

Please excuse me for I have no intention of disparaging in any way any part of your essay.

I merely wish to point out that “Everything should be made as simple as possible, but not simpler.” Albert Einstein (1879 - 1955) Physicist & Nobel Laureate.

Only nature could produce a reality so simple, a single cell amoeba could deal with it.

The real Universe must consist only of one unified visible infinite physical surface occurring in one infinite dimension, that am always illuminated by infinite non-surface light.

A more detailed explanation of natural reality can be found in my essay, SCORE ONE FOR SIMPLICITY. I do hope that you will read my essay and perhaps comment on its merit.

Joe Fisher, Realist

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Mark Pharoah wrote on Feb. 28, 2017 @ 22:40 GMT
You say,

"information and reality are inseparable. Not necessarily in the sense that they must co-exist, because information, being of mathematical nature, is eternal, or rather timeless, while reality changes, the things in the world are transitory; but in the sense that between information and reality there is a relationship similar to that between a system or a formal theory and its model. "

I have never read a convincing expository explanation of what information is. As I see it, the term functions as a conceptual tool which humans use to try to interpret the world, and that as such, does not actually exist 'out there' in the real world. Similarly, the concept of number only exists in the thinker because he accepts unquestioningly the premise that there are things with identity that match one another. From this premise he concludes 'there is more that one'... of this class of things, and therefore, that numbers are a sensible tool for modeling the world of identical things. However, if one denies this assumption, and instead entertains the premise that every instance is entirely unique, one denies the notion that mathematics exists also.

When it comes to consciousness and the application of maths, then, it is more that mathematics is a flawed tool for modelling objective reality itself (despite widespread faith in it as an accurate description of truths) than that it does not work well as a tool for understanding/describing/explaining consciousness.

I just thought I would throw that idea into the mix for you...

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Author Giovanni Prisinzano replied on Mar. 1, 2017 @ 15:22 GMT
Dear Mark,

I thank you very much for reading my essay, and for your interesting comment, which gives me the opportunity to clarify an aspect that perhaps in the text I have not explained very well.

You're absolutely right in saying that the term "information", which is used more and more often, is difficult to understand, not least because everyone tends to interpret it in the way...

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Lawrence B. Crowell wrote on Mar. 10, 2017 @ 18:55 GMT
I had forgotten that I had read your paper in the past. I reread it. I would agree largely that physical reality sits within the first order logic domain and that by the Löwenheim-Skolem theorem the cardinality of this set is countably infinite at most. This is largely because the fundamental unit of physical reality is quantum information, which consists of qubits as discrete elements. These do however have topological meaning, and just as homotopy depends upon diffeomorphisms on continuous manifolds so too physics requires this. The difference is that points and continuum sets that are transfinite in nature have no physical information content. We derive no information from them directly.

Cheers LC

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Author Giovanni Prisinzano replied on Mar. 12, 2017 @ 14:58 GMT
Dear Lawrence,

thank you very much for your further comments!

I totally agree that we cannot have direct information on transfinite sets. Information is discrete and computable, while infinite sets contain mostly uncomputable elements. But I'm not sure that some transfinite sets cannot have a physical meaning. Of them it is possible to have discrete models, as is done for example for real numbers. Moreover we don't know what space and time are made of. I know that the prevailing view nowdays is that they have a discrete and quantum structure. But it is not necessarily so. They may be continuous and composed of uncountable set of points (space) and instants (time). Important authors (as Russell and Grünbaum) have argued that only by admitting the continuum and the actual infinity we can solve Zeno's paradoxes.

Cheers, Giovanni

Vladimir Rogozhin wrote on Mar. 13, 2017 @ 18:41 GMT
Dear Giovanni,

I read with great interest your deep analytical essay with ideas and conclusions that will help us overcome the crisis of understanding in fundamental science through the creation of a new comprehensive picture of the world, uniform for physicists and lyrics filled with meanings of the "LifeWorld" (E.Husserl). My high score. I believe that the modern crisis of understanding in fundamental knowledge is the crisis of ontology. I invite you to read and evaluate my ideas.

Yours faithfully,


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Vladimir Rogozhin replied on Mar. 13, 2017 @ 20:28 GMT
My name is Vladimir Rogozhin

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Author Giovanni Prisinzano replied on Mar. 14, 2017 @ 10:21 GMT
Dear Vladimir,

I thank you so much for your kind interest in my essay and for the very high appreciation that you have given to it! I fully share your view that science and philosophy are inseparable (so was from the beginning until the Eighteenth century) and that their results may agree. But since I'm (at least partially) a Kantian, I have some doubts we will ever reach a final theory about the universe. I will read and comment with pleasure and as soon as possible your essay.

Yours sincerely,


Gavin William Rowland wrote on Mar. 16, 2017 @ 10:32 GMT
Dear Giovanni

I enjoyed reading your essay, and agree with your conclusions. Of course the whole question of mathematizable information rests on measurement, and if something is not directly measurable, as in consciousness, then there is no information upon which to formulate mathematical models.

You may find my essay "From nothingness to value ethics" of interest.

Best regards


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Author Giovanni Prisinzano wrote on Mar. 16, 2017 @ 16:04 GMT
Dear Gavin,

thank you so much for reading my essay, and for your kind comment, on which I agree. I posted my comment on your essay on your page.


George Kirakosyan wrote on Mar. 25, 2017 @ 07:41 GMT
Hi dear Giovanni,

I have read your amazing essay and just become a little bit shocked finding there a lot of my viewpoints, particularly, about on deeper interconnection of natural science and philosophy (or, with the art of logical thinking.) I am not philosopher but I seen this link is just inevitable to be get some serious shift in nowadays physics (as I see it are in the incredible crisis!)

You says for example "to see the invisible!" My dear, this just are a base point for my approach. You have talking on the significance of math that now become one of confusing aspects in present physics (meanwhile, in other areas nobody not see any complications on this matter!) So, I can say you much of compliments but let me read and to complete my evaluation of your work. Meantime I am very hopeful you can find time to look my work that I believe maybe interesting for you to read. Then we can summarize ours opinions! (I will grateful if you write some words in my page.)

In any case, I see mandatory my good support to you!

My best wishes.

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Author Giovanni Prisinzano replied on Mar. 28, 2017 @ 09:08 GMT
Dear George,

I thank you so much for your attention to my essay and the high appreciation that you gave to it! First of all, I am very pleased that you share the view of a deep connection between science and philosophy, which is at the basis of the history of thought, but has become increasingly difficult, for various reasons, in the last two centuries.

In recent days it was impossible for me to read your essay (or any other in the contest), but I will do it as soon as possible and I'll post a comment about it.

My best wishes for all,


George Kirakosyan replied on Mar. 28, 2017 @ 13:14 GMT
Dear Giovanni,

It is nice to see that you have come back in the "field of battle"! I wish you strong healthy (if you has been a little bit not well!)

And now I can say only that I was not at all mistaken in my hurried evaluation on your work, because I come fully convinced that you have well understanding where are the roots of a main problem, therefore your remarks will be very significantly to my.

So, Be well!

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George Kirakosyan wrote on Mar. 29, 2017 @ 04:34 GMT
Dear Giovanni

Thank you very much for your favorable words and valuable remarks. These are good support to me, a morally only, but it is also the support. I see mainly we are like-minded people, and let me just tell some small remarks only:

1. You says //the nature of fundamental particles (and QR) has not yet been clarified// - but you already know one crazy guy who says "I know this" and he points on the large works and on the concretely results (see Refs)

2. Then you says //I am not a mathematician and nor the physicist ...etc.//

My dear, the philosophy was a father of all sciences, then the philosophers must have more priority to instruct and evaluate of mathematicians and physicists (as their non-thankful sons!) than the opposite!

However, I think everything is in the usual rule of things!

Be well and many successes to you!

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George Kirakosyan replied on Mar. 29, 2017 @ 09:27 GMT
Thanks once more - for good lesson.I got it now!

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Author Giovanni Prisinzano replied on Mar. 29, 2017 @ 17:01 GMT
Be well and all the best to you too, dear George!

I'll look at your other papers.

(However: no “lesson” from me. That is not the way I do)

All my best whishes again,


Peter Jackson wrote on Apr. 5, 2017 @ 13:47 GMT

I found that a very accomplished essay with a well developed and argued thesis. I also largely agree, but a few questions below, and you avoid the problems of logic. I suspect you'd like the 'Law of the Reducing Middle' I proposed in an earlier essay to replace the problematic 'excluded' middle. The 'reducing middle' is a Bayesian, 'Bell' or quantum mechanical curve. It suggests NO two things in the universe are identical, so 1=1 is never quite true! I think that was 'It from Bit'; 'The Intelligent Bit' 2014, but I think you'd also like last years (scored top).

This year my essay shows how QM's orthogonal Cos2 curves CAN be produced by classical interactions! (Of course few scientist even dare look!). The model is simply founded on extension of Pythogorus theorem to 3D dynamics.

Do we not need a certain degree of discretion in continuity? i.e. must the rotation defining a spherical 'body' not be considered as discrete from any other bodies rotation?

Do you think that without such discrete 'motions' anything could 'exist' at all?

Fundamentally we argue the same of mathematics limitations, but you invoke a new, interesting and well justified rationale. All in all an exceptional essay worth an exceptional score, which I hope help gets you into the finalists. I do hope you get to read min before the deadline and comment. There are other slightly more philosophical elements.

Very best of luck in the contest.


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Author Giovanni Prisinzano replied on Apr. 6, 2017 @ 09:36 GMT
Dear Peter,

I was very pleased to receive your comments with beautiful words of praise about my essay! I also began to read yours, which seems dense, thoughtful and original (I also intend, as soon as possible, to read that of 2015, so high rated and commented), but I don't know if I'll be able to comment on it properly before the deadline, considering I lack an adequate background in Quantum physics and have little free time, by now. For this I apologize.

Thank you for your encouragement and good wishes, although I don't think I have real chances to get into the finalists rose. I am not a physicist and my rate in the contest is not high, despite your considerable contribution, for which I am very grateful to you.

All the best regards,


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