Tuesday, June 28, 2016

Dynamic Interacting Nature of Number

Before proceeding further, I will once again attempt to make clear the distinction that I make as between the two notions of number - in effect particle and wave aspects - that continually interact in experience as analytic to holistic (and holistic to analytic) respectively.

I define firstly the Type 1 aspect (where the number in question is referred to as the base).

So every base number here is defined with respect to a default dimensional number of 1.

Thus 2, for example in Type 1 terms is defined as 21.

I then define the Type 2 aspect (where the number in question is referred to as the dimensional number).

Every dimensional number here is now defined, in inverse fashion with respect to a default dimensional base of 1.

Thus 2 now in Type 2 terms is defined as 12.

Now it is vital to appreciate these two aspects of the number system operate in a dynamic relative fashion as complementary, where they keep switching (both in base and dimensional terms) as between analytic and holistic meanings respectively.

Thus when we start by defining the base in Type 1 terms as analytic, the corresponding dimensional number is then defined - in complementary Type 2 terms - as holistic.

However if we alternatively start by defining the base in Type 1 terms as holistic, the corresponding dimensional number is then defined - in complementary Type 2 terms - as analytic.

So with respect to our example of "2", it thereby keeps switching in experience as between both analytic (particle) and holistic (wave) aspects in both base and dimensional terms.

This then can be intimately linked to the psychological manner we experience numbers (and indeed  all phenomena).

The base number can be directly linked to the psychological perception of that number.
However the dimensional number is then linked - in complementary fashion - with the corresponding psychological concept of the number.

So in analytic terms, 2 as a base corresponds with the standard quantitative appreciation of the actual number (as comprising two independent units).

However in holistic terms, 2 as a dimension corresponds with the - largely unrecognised - qualitative appreciation of the number as potentially applying to all numbers (defined with respect to 2 as a dimension).  For example square or rectangular measurements with respect to a field would be 2-dimensional. However all measurements of such fields, which would be necessarily finite in nature would correspond with the quantitative analytic notion of 2 (as dimension). So the holistic notion is quite distinct in being understood as potentially applying to all such measurements (in infinite fashion).

So the key distinction as between analytic and holistic aspects respectively is that the former applies in a finite quantitative manner (in actual terms); the latter however applies in an infinite qualitative manner (in potential terms).

By far the greatest and most profound reductionism therefore in Mathematics is the way in which holistic (i.e. potentially infinite notions) are continually reduced in an actual finite manner.

Therefore though once again the holistic notion of number properly is qualitative in nature (applying in an infinite potential manner), it is effectively reduced from a conventional mathematical perspective in merely quantitative terms (as applying directly to actual finite data).

Whereas psychologically, the analytic interpretation of number is directly rational (in a linear manner), the corresponding holistic interpretation is directly intuitive in nature, which then indirectly can be expressed in a circular (paradoxical) rational fashion.

So in Conventional Mathematics, the constant reduction of holistic notions in analytic terms is directly associated with the corresponding reduction of intuitive appreciation is a merely rational manner!

Therefore, using 2 as an example, here is a brief outline of how one experiences the true dynamic interactive nature of number!

When the perception of "2" is formed in a rational analytic manner, this links up directly in complementary fashion with the corresponding concept of "2" (implicitly in intuitive holistic terms) as potentially applying to all instances of "2".

Then in reverse fashion, we also have in experience the perception of "2" implicitly in an intuitive holistic fashion that links up directly with the corresponding rational analytic interpretation of the concept of "2" (as applying in reduced fashion to all actual data).

Whereas the rational analytic interpretation of "2" as a perception corresponds with its impersonal quantitative nature, the intuitive appreciation of "2" by contrast corresponds with  unique qualitative identity. So when we are aware of  a particular example of "2" as a unique qualitative expression of the notion of "twoness" then we are appreciating the number in a holistic - rather than analytic - manner.

So expressed in an equivalent manner, when we experience the number "2" we keep switching in dynamic fashion as between the analytic notion of 2 and the holistic qualitative notion of "twoness" both with respect to perception (as base) and concept (as dimension).

Without the potential of "2" to exist in holistic terms (as infinite), we could not recognise any actual example of "2" in an analytic manner (as finite). likewise in reverse without actual examples of "2" in analytic terms, we could not move to form potential notions of "2" (as applying in all circumstances).

In fact the true dynamics are even subtler than represented here as a continual interaction likewise necessarily takes place as between the external notion of number (as object) and its internal counterpart (as mental interpretation)!

However the crucial point to appreciate is that the true notion of number is of a dynamic relative nature, entailing both quantitative (analytic) and qualitative (holistic) notions in complementary fashion.

And of course by extension, this applies to all mathematical and scientific notions.

However, we have attempted to convince ourselves - quite wrongly - that the nature of number is inherently static and absolute and can be successfully abstracted from the rest of experience.

When properly understood, this view is revealed as quite untenable. Worse still, its widespread acceptance has greatly distorted the very way we look at reality (in mathematical and scientific terms).

Though, in a general manner, I had held these notions for several decades it was only now (around 2005) that I began to see them in a novel fashion  that gradually began to reveal for me the true nature of the great unsolved mathematical problem i.e. the Riemann Hypothesis.

And this quest for radial mathematical understanding (where quantitative and qualitative aspects are equal interacting partners) then became inseparable from my on-going psychological quest for the experience of spiritual union.