Thursday, December 24, 2015

Wholes and Parts (9)

In the last two blog entries, we have seen how 1) the holistic interpretation of number is directly related to its ordinal nature and likewise 2) that such holistic interpretation is intimately connected with the true inherent dynamic interactive nature of space and time.

This therefore implies that the ordinal nature of nature is directly concerned with the manner in which number is given a unique location with respect to both space and time.

Now, to spell this out more fully, we must once again remember that in dynamic interactive terms, the analytic and holistic interpretations of number are necessarily complementary with each other.

Therefore, when in analytic terms, we interpret the cardinal natural numbers in a 1-dimensional manner i.e. as lying on the number line, the ordinal nature of these numbers is then properly interpreted directly through intuition, in a complementary holistic manner (where they have a location in complex space and time).

However, as always we can switch reference frames.

Therefore, in an alternative manner we directly intuit in holistic manner, the cardinal natural numbers, again in 1-dimensional manner as lying on the number line, the ordinal nature of these numbers is appropriately interpreted in a complementary analytic manner (again with a location in complex space and time).

What this means from a psychological perspective, is that we keep switching as between conscious and unconscious type interpretation with respect the the nature of the natural numbers in cardinal and ordinal terms.

Now, with conventional mathematical interpretation, these two-way dynamic interactions are reduced in a static analytic fashion.

So the holistic aspect is reduced to the analytic in a merely linear (1-dimensional) fashion. The ordinal aspect of number is thereby reduced in a cardinal fashion. Likewise, the time dimension of number is ignored with space treated in linear fashion.

Properly understood, the dynamic nature of number is bound by two aspects that lie at opposite extremes to each other.

Therefore from the analytic perspective, number approaches the totally rigid state of absolute form.

Again in formal explicit terms, Conventional Mathematics interprets the natural numbers in an absolute manner. However properly understood, their nature always is merely relative, whereby a rigid absolute type interpretation can indeed be ever more closely approached, without however fully attained.

However at the other extreme from this fixed analytic aspect, we have the pure holistic interpretation of number (where complementary poles of recognition simultaneously interact with each other in a directly intuitive manner). In fact here, number approaches a pure energy state (without form) in both a physical and psychological manner.
Again, this pure energy state of number which in the limit is ineffable, can be ever more closely approached without being fully attained.

However, as stated before we can switch reference frames so that the holistic aspect is directly intuited from the relatively  fixed forms of natural number and then the complementary aspect - though of a highly dynamic interactive nature - now analytically interpreted with respect to separate frames.

Successful understanding therefore in this regard needs to be extremely refined with respect to both rational and intuitive modes of understanding. So rational understanding is required to cover the entire spectrum from fully linear to fully circular modes.
Likewise intuition is required to cover the entire spectrum from fully immanent to fully transcendent modes.

Once again to finish this entry, with the dynamic interpretation of number, we move away from the conventional - and utterly misleading - notion of number as in some sense existing in abstraction from experience.

Rather number is now seen as the inherent encoded basis of all phenomena (in both physical and psychological terms). And in this understanding both its physical and psychological aspects are understood as fully complementary. And the quantitative and qualitative aspects of number are likewise understood as fully complementary.

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