Monday, December 13, 2010

The Art of Perspective: DaVinci

All the problems of perspective are made clear by the five terms of mathematicians, which are:--the point, the line, the angle, the superficies and the solid. The point is unique of its kind. And the point has neither height, breadth, length, nor depth, whence it is to be regarded as indivisible and as having no dimensions in space. The line is of three kinds, straight, curved and sinuous and it has neither breadth, height, nor depth. Hence it is indivisible, excepting in its length, and its ends are two points. The angle is the junction of two lines in a point.

Every number, expressible and inexpressible sits upon a template for organizing the numberness of the number. We call this template a base. The base of a number is a power series which escalates to infinity in one dimension, (it's post decimal dimension), and toward zero in the other pre-decimal dimension.

Here we have a vector going in either direction, toward infinity, and toward zero. For instance, base 10 mathematics uses 10 as its base and thus everything is power of 10. Behold:

116,651 = 1*10^5 + 1*10^4 + 6*10^3 + 6*10^2 + 5*10^1 + 1*10^0

Now if we wanted to add .1234 to this number our power series would extend like so:

1*10^-1 + 2*10^-2 + 3*10^-3 + 4*10^-4.

Now, when we represent the number, we only consider the segment between the highest and the lowest place value, where 1^10^0 would always be considered the origin of both vectors. So, when you are seeing a number, you are always only seeing part of an infinite series which is lit up between extremes.


Now in Base-2, or Binary, the same rules hold true as in base 10, except that everything is a power of 2.

So instead of the chain extending like this:

1,10,100,1000,10000 ...

It extends like this:

1,2,4,8,16,32,64,128,256,512,1024,2048 ...


.5, .25, .125., .0625, ...


Our Base 10 system of representations is not without its paradoxes. Behold:

1/3 = .333333...
1/3 = .333333...
1/3 = .333333...
3/3 = .999999... = 1

In such an instance the bare bones of our structure to contain the Number is laid bare, extending infinitely toward 9*10^-INF which is also Zero. So, even with an eternity to work with, we can never finish the task of writing this number.


What is the Point?

Well, just that the number seems to be describing the relationship of one thing to another in a very specific sequence, where the sequence conveys a large part of what the representation refers to.

Suffice it to say, when we introduce the concept of number it's a how much/how many indication. Each number occupies one infinitessimal point on a line known as the "real number line". The end points (which do not fall on the line) are INFINITY and -INFINITY.

The number is a point. A geometric object which describes itself only in relation to other objects and as part of some system.

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