Mathematics and Reality

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  1. Per Wikipedia [see Primitive Notion], a point is defined as a primitive notion. A primitive notion is not absolute. It must be logically consistent within the broad context of knowledge.

  2. This means that “point” is a starting concept of Euclidean geometry; but it is not absolute within the wider context of knowledge.

  3. Per Wikipedia [see Point (geometry)], “points do not have any length, area, volume, or any other dimensional attribute. A common interpretation is that the concept of a point is meant to capture the notion of a unique location in Euclidean space.”

  4. A location in real space may be infinitesimal, but it is not dimensionless. It is also continuous with the surrounding space. This notion is similar to that of an irrational number on a number line.

  5. Therefore, a Euclidean point may act only as an idealization of a location in real space. It may be used only as an approximation of a real location.

  6. A real location cannot act as a primitive notion like a Euclidean point because it is not dimensionless. Therefore, in reality, the notion of location shall depend on the notion of a continuous space.

  7. Per Wikipedia [see Space (mathematics)] Euclidean space is defined as a set that includes points as elements. Thus unlike Euclidean space, the real space is closer to being a primitive notion.

  8. The concepts of space and point in Euclidean geometry are reversed compared to what they are in reality.

  9. This may have some fundamental implications on the way General Relativity and Quantum Mechanics are currently being interpreted in physics.

  10. The Euclidean space is rigid as it is based on the idea of rigid dimensions of matter. But this idea of rigid space may not necessarily apply to the more basic substance of electromagnetic field.

  11. The Disturbance theory looks at space as a continuous “electromagnetic field of zero frequency” similar to the unperturbed surface of a lake.

  12. As the unperturbed surface of a lake is disturbed, there come about discrete ripples. Similarly, as the continuous space is disturbed the idea of discrete frequency comes about.

  13. For the electromagnetic disturbance to propagate through it, the real space must be flexible. This flexibility of space seems to reduce as frequency increases.

  14. The real space seems to be rigid only at very high frequencies. This is similar to the case when an object moves at the speed of sound through air and the frequency ahead of it becomes extremely high. This makes the medium of air appear rigid to the fast moving object.

  15. Therefore, it is only when the frequency of electromagnetic disturbance is very high that space approximates the rigid space as postulated in Euclidean geometry.

  16. Thus, space, in reality, is continuous and it acquires a discrete point location only where matter is present.

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Comments

  • vinaire  On January 25, 2016 at 8:12 AM

    I am currently reading the book THE NATURE OF THE PHYSICAL WORLD by A.S. Eddington. This book was written in 1928 when the theory of relativity and the quantum theory were quite new. I shall highly recommend this book to others.

    You may find the original edition of this book at the following link.
    https://archive.org/stream/natureofphysical00eddi#page/n11/mode/2up

    This book is written by a very mature mind. Just read the INTRODUCTION to this book.

    .

  • vinaire  On January 25, 2016 at 10:08 AM

    Here is what I got out of the INTRODUCTION.

    This book goes into scientific philosophy. The “empty space” in an atom is actually full of “field”. It was thought of as “influence” but it may be looked upon as a more basic substance than matter. Still more basic substance is “concepts”; and underlying that is the substance of “consistency”.

    Our perception of the world is a broad overview compared to the scientific perception of the world that goes into the details of “fields”, “concepts” and “consistency”. The familiar world is subjective compared to the objective world of science.

    There are no familiar counterparts to scientific concepts like electron, quantum or potential. Science may explain them in more familiar terms only in future only when they are fully sorted out. For now these scientific concepts are abstractions. They are “part of the A B C of physics”.

    Eddington says, “The frank realization that physical science is concerned with a world of shadows is one of the most significant of recent advances… It is difficult to school ourselves to treat the physical world as purely symbolic.”

    We have to be prepared for the reality that Physics is aloof from familiar conceptions.

    .

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