If time is made of numbers by Giovanni Prisinzano

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

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

DEar Giovanni,

Yes, time has only a math existence.

see article

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

here is another paper

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

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.

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

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

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

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

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 the perception of differentiation between the internal structural space and external relational space of objects. Since we perceive through electromagnetic interaction, where the electric and magnetic fields are perpendicular to each other and both move perpendicularly, we have three mutually perpendicular dimensions. These are invariant under mutual transformation (if we treat length as breadth or height, the object is not affected) and can be resolved into 10 different combinations. Past, Present and future are segments of the sequences of intervals of time that are strictly ordered - future always follows present; present always follows past. However, while future always follows present in an ordered sequence, any past event can be linked to the present bypassing the specific sequence. This proves unidirectional time. Since past and future are not invariant under mutual transformation, time is not a dimension. Since the intervals are infinite, space and time are an infinite continuum. We use segments of this analog reality by choosing a fairly repeatable and easily intelligible interval as the unit like taking out water from the river by a pot. This is the empirical definition of space and time.

Number is one of the properties of all substances by which we differentiate between similars. If there is nothing similar at here-now, the number associated with the object is one. If there are similars, the number is many. Our sense organs and measuring instruments are capable of measuring only one at a time. Thus, 'many' is a collection of successive one's. Based on the sequence of perception of such one's, many can be 2, 3, 4....n. In a fraction, the denominator represents the one's, out of which some (numerator) are taken. Zero is the absence of something at here-now that is known to exist elsewhere (otherwise we will not perceive its absence at all). Infinity is like one: without similars. But whereas the dimensions of one are fully perceptible, the dimensions of infinity are not perceptible. There cannot be negative infinity to positive infinity through zero, as it will show one beginning or end of infinity at the zero point, which is non-existent at here-now. No mathematics is possible with infinity, as all operations involving it will have undefined dimensions - thus indistinguishable from each other. Irrational numbers were used in India since antiquity based on the above principle.

The simplest answer to Zeno's paradox is that velocity is related to the mass of the body that is moving, the energy used (force applied) to move it and the total density of and the totality of the energy operating on the field. These are all mobile units against the back drop of the field that is static with reference to these. Middle of the distance is related to the frame of reference, which is static, while the other aspects are relatively mobile. Thus, it is like comparing position and momentum. They do not commute. Hence there is no paradox, which is borne out of experience. While the middle of the distance is gradually reduced, the velocity is not reduced by the same proportion. Hence the runner will reach the end point.

Long before Euclid, geometry (called 'khila panjara' meaning closed continuum) was used in India (seen in Shulva Sootras). Since numbers are discrete, we can use scalar numbers with suitable units in geometry, but the analog field cannot represent numbers. This has misled modern mathematics. Further details can be seen in our essay.

Regards,

basudeba

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

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

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, and I will do this by copying and pasting from your essay, then make my comment. Here goes...

"...many of the greatest thinkers in history, such as Pythagoras, Plato, Aristotle, Descartes, Spinoza, Kant and Einstein"

Isaac Newton's name is conspicuously missing. He has views that go deeper and are more reasonable in my opinion than the ones you name.

"What stays behind Zeno's paradoxes"

I agree with most of what you say here. I belong to the group that although mathematical tricks can resolve the paradox by seeming to make an infinite task completable in a finite time, most such methods still have the plague of having "seeming", "tending", "in the limit" dogging the claimed solutions.

You rephrase Dedekind's axiom of continuity in the following terms: "If all points of the straight line fall into two classes so that every point of the first class lies on the left of every point of the second class, then one and only one point exists, which is common to both classes, thus producing the union of them in a linear continuum."

Do you propose then that a line can only be divided at the 'unique' point and at no other place? The weakness of this Dedekind explanation is that it cannot explain the fact that a line can be divided in several places. I am therefore of the view that although interesting, Dedekind's proposal and its reformulation is inconsistent on the face of the fact that lines can be divided severally. Look at it this way, after dividing a line into two segments at your 'unique' point, are you now saying the segments become indivisible? Or is a line a living thing that can mutate and evolve another unique point after the first division? I propose my own hypothesis in my essay.

Finally, may I ask if your "space as the set of all real numbers" is an eternally existing entity or concept? If the Universe collapses at a Big Crunch will all those real numbers be still expressed somehow as a mathematical concept or in physical reality? Or do they perish? If they can perish at some future time, can some not be perishing today? Give this some thought.

I will not dwell much on the latter aspects of your well written essay mainly because I am of the opinion that the mathematical tricks therein have misled our physics in the last 100 years.

Best regards,

Akinbo