Thursday, December 1, 2011

Cardinal and Ordinal Numbers (2)

As we have seen every number can be given both a cardinal and ordinal meaning which are quantitative and qualitative with respect to each other.
And where the ordinal number is the last in a group of numbers, the ordinal can be represented as the reciprocal of the cardinal.

So if we write 1^4 this can be given a quantitative meaning - where 4 is a cardinal number representing the dimension (or power) in question whereby 1^1^1^1 = 1 (in reduced quantitative terms).

However 4 equally here has an ordinal meaning as the 4th dimension (where 4 dimensions overall are considered). So here the 4th dimension represents 1/4 (of all four dimensions)
Thus to express 4 with respect to the ordinal number 4 (as the the 4th dimension) we obtain the value of 1^(1/4) = i.

So i here has a qualitative interpretation as imaginary i.e. the indirect expression of holistic unconscious meaning in conscious terms.

Of course 1/4 here can be given a quantitative meaning so that 1^(1/4) = i represents a number on the circle of unit radius.

Now interestingly if we now consider the 4th dimension as one of 5 dimensions it no longer can be represented by 1/4!

Whenever a number ≠ 1, a complementary relationship exists between the dimensional power and its reciprocal (that are quantitative and qualitative with respect to each other).

Once again in the default case = 1, both this dimensional number and its reciprocal are identical (in Type 1 terms) so that qualitative is reduced to quantitative meaning.