Geometry of Reality


  • The Euclidean space is an idealization of dimensions of matter.
  • Space is not necessarily discrete like dimensions of matter.
  • Space is not necessarily rigid like dimensions of matter.
  • In reality, space is neither discrete nor rigid.

Here the word “discrete” is used in the sense opposite to “continuous” meaning “apart or detached from others; separate; distinct”. We can talk about dimensions in discrete terms, but we cannot do so with space. Space is a continuous whole.

Here the word “rigid” is used in the sense opposite to “flexible” meaning “firmly fixed or set”. We can talk about units for the dimensions of matter to be fixed, but not so for space.


  • A Euclidean point is an idealization of a location in space.
  • A location in space is not necessarily dimensionless.
  • A location is continuous with the space around it.
  • A location is approximated by a discrete point only when there is matter.

It is matter that fixes locations in space by virtue of being rigid. When there is no matter, we cannot fix or pinpoint locations in space.


  • Calculus approaches continuity from the direction of discreteness.
  • Calculus talks about gradually shrinking infinitesimals in that process.
  • We need mathematics that approaches discreteness from the direction of continuity.
  • Such mathematics will approach discreteness as frequency.

Calculus uses a matter-centric viewpoint that approximates continuity in terms of shrinking infinitesimals. When there is no matter as in the case of electromagnetic fields we cannot use rigid infinitesimals for reference. We may need to use lessening frequency to approach continuity. Here discreteness seems to be provided by frequency.


  • Mathematics considers a discrete point to be a primitive notion.
  • In reality, it is the continuous space, which is a primitive notion.
  • The rigidity of space is a function of disturbance in it.
  • Infinite frequency of disturbance generates total rigidity in space.

We cannot use dimensionless Euclidean point as primitive notion because it is not seen as expanding into a continuous space. But we can use continuous space as primitive notion because we can see it as shrinking to generate a dense point that approaches discreteness. It is this “density” that can be associated with rigidity.


  • Discreteness starts to form as space is disturbed.
  • This discreteness increases with frequency.
  • At a certain threshold  frequency, rotational fields start to form within the electromagnetic fields.
  • The first stable form of such rotational field is the electron.

It is postulated that electromagnetic field is the disturbed space. As this disturbance increases as frequency, pockets of rotational electronic fields appear in the wider electromagnetic field.


  • As these rotational fields grow the high frequencies at their center starts to collapse to form a hard nucleus.
  • The next stable form of this rotational field appears to be the hydrogen atom.
  • Mass is naturally created in the nucleus as the frequency of disturbance increases the most at the center.
  • The mysterious factor here is the role of “frequency”.

Mass is naturally created in the nucleus as the frequency of disturbance increases. The task now is to understand the nature of this disturbance.

The theory of special relativity talks about contraction of space and dilation of time at speeds approaching the speed of light. Such conclusions are subjective because the “observer” in that theory is limited in its observation by the speed of light.

Objectivity exists to the degree observer uses the whole universe as its reference. This means using all physical and mental senses. The moment one uses part of the universe as its reference one’s viewpoint descends into subjectivity. Thus mathematics employed by Einstein’s theory of Special Relativity is subjective.

Objectivity is the consistency among inputs from all physical and mental senses. To the degree this consistency is missing, observation is incomplete and subjective.



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