*Reference: Tertium Organum*

The following is a summary as well as a commentary on Chapter 5 of Tertium Organum by P D Ouspensky.

A 4D body is the tracing of the movement in space of a 3D body in the direction of Time. Higher dimensions seem to appear as different aspects of the same reality. For example, spirit, mind and body could simply be different dimensions of one and the same life.

Because of the dimension of time everything in the universe seems to be changing. Different things may be changing at different rates, but they all are changing. The totality of the universe, like the center of mass, may appear to be relatively unchanging.

**But there is nothing in this universe that appears to be absolutely constant.**

Abstractions, such as, the scientific principles, provide patterns underlying sets of concrete phenomena. Still deeper patterns underlie them. There can even be infinity of layers of patterns, each being a greater abstraction of the previous layer. If universe is a sphere whose surface represents concrete phenomena, then abstraction shall proceed in the radial direction toward the center.

**Thus, abstraction could be looked upon as the fifth dimension.**

Since abstraction is a pattern common to a number of changing phenomena, it would change at a lesser rate. The deeper is the abstraction the more constant it would appear. The deepest abstraction shall appear as the ultimate constant at the center of the spherical model above.

**This ultimate abstraction may very well serve as God.**

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A subject starts with some fundamental premise or premises. It then builds up a logic structure based on the relationships observed in the universe. When one talks about skipped gradient of understanding in a subject, one is talking about skipped understanding in the logic structure.

Mathematics started with counting. So the fundamental premise it adheres to is that of discreteness. The whole logic structure of mathemetics is built upon the idea of discreteness. All of arithmetic is built around the general idea of discreteness. Algebra simply plays on the logic structure of arithmetic.

It becomes interesting when one looks at space. Mathematics looks at space as made up of discrete elements called points. Foundations of mathematics shook when irratioanl numbers were discovered while calculating the hypotenuse of a right angle triangle. Ultimate disctreteness came under question.

So space seems to have a property of being continuous as opposed to being discrete. We carve discrete portions out of space in terms of objects. Points in space are suppositions. They can never be isolated. Only locations can be isolated in terms of objects.

Quantum mechanics is caught between the mathematical supposition of points and the actuality of locations as defined by objects.

Quantum Mechanics is a mess.

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The skipped gradient of Study Tech is simply a missing logic structure, where something is being taken for granted. Memorization of “mathematical facts” hides skipped gradient in a person’s understanding. All people who “hate math” are suffering from skipped gradient.

Quantum Mechanics is suffering from a SKIPPED GRADIENT, by taking for granted that the world is discrete (space is made up of points).

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Hi Vinaire – Health*

‘But there is nothing in this universe that appears to be absolutely constant.’ What about atoms in a crystal?

Anyway, I agree, Quantum Mechanics is a mess…consider this…when we approach near light speed, time slows. So if I jump on the space ship and leave Earth for a week at near light speed, I come back and it’s many years later on Earth. That is only one dimension of ‘leap’. From Earth to Sun…representing ‘near light’ speed. Is there a similar ‘leap’ from Solar to Galactic space/time? And is that the ‘near dark’ speed?

Until we understand dark matter/energy, quantum everything will be a mess.

Have a wonderful day!

Granny

You can have light speed only if you become light.

Anything that approaches light speed must turn into light.

Light and light speed go together.

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Wait…isn’t darkness the actual constant??

Light here refers to the electromagnetic waves. So there is invisible light, dark light… all kinds of lights.

There can be an eternal landscape, which can be divided into past, present and future based on the narrowness of the span of consciousness. If the span is considerable to encompass the whole landscape at once then we shall just have an eternal present.

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The most fundamental premise of mathematics is the discreteness of counting. This ultimately leads to the continuity displayed by the irrational numbers.

This gives us a scale. At one end of this scale is discreteness. At the other end of this scale is continuity. In between we have the singularity of the idea of existence, which then divides into the ideas of things, which then divide into catagories, sub-categories, sub-sub-categories ad infinitum to individual characteristics and further breakdowns of those characteristics, until we arrive at the idea of the ultimate common denominator. This ultimate common denominator has to be continuous as it underlies all things..

This is the scope of mathematics.