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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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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

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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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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

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