Number Beauty

0 (zero) is an enclosure of empty space. I'm talking about the glyph, the symbol, and not just the number (the un-number?)

If there is a proto-number, zero is about as close an any official number gets to it. We have here pure unification, and the presence of an absence.

Perhaps we should think of this glyph, this "0," not in terms of the encircling line, but only in terms of the space inside this encircling line. The line is just a way to point at the space. The emptiness is the thing, the (no-)thing.

The simple beauty of it, of man's favorite shapes. He rolls down the street all the time. He lives in terms of cycles. He symbolizes eternity with this circle. He races his fastest cars in circles. He lives on a globe.

The circle is also an opening, a feminine symbol. Whereas the 1 is obviously a male symbol, among many other things. Perhaps the 0 is a womb, the void from which all other numbers are born. For all numbers are unities. Only 0 is empty, neither negative nor positive. And 0 is the fulcrum of the number line, smack in the middle of positive and negative infinity. 0 can symbolize the proto-being from which all other abstract beings derive.

1 is the perfect primary being. 1 stands in the void heroic. A thin man. A phallus. A line. How little we notice it, but 0 gives us the curve and only the curve while 1 gives us the line. Perhaps 0 is ideally drawn as a perfect circle, and 1 as a line without serif. These are geometrical absolutes. The 0 is pure continuity. The 1 is digital. Although the straight line is spatial and not truly digital, still the straight line is as close as the spatial can get to the digital. I don't think we can count that paradoxical point-without-extension, no matter how fascinating this (non-)point is.

The glyphs for 1 and 0 are too perfect to be an utter accident. I think they caught on for a reason, even if this reason was subconscious. Those who have studied a little math know that only 2 digits are necessary. Of course it's arguable that only 1 is necessary, but this is utterly impractical. Because we need 2 and only 2 digits for positional notation, which is immensely superior to the unary system.

Binary or base-2 is beautiful like sculpture is beautiful. Symbolic Logic, that beloved pet of philosophers, is nothing but a breed of base-2 math. Well, that's one way to describe it. The bit is fundamental to human thought. And 2 or duality is part of this, and obviously fundamental to human thought.
Between 0, 1, and 2, we have the most important numbers to human beings. Binary uses only the 0 and 1, but implies the 2 by using 2 digits. The 2 is the hidden structure of these 0s and 1s.

Right/wrong. Self/world. Mind/matter. Self/other. Theism/Atheism. Up/Down. Left/Right. Male/Female. Good/Evil. Love/Hate. Negative/Positive. True/False.
Wisdom/Foolishness. Etc. Etc. Etc.

We think largely in binary. And I am anything but the first to notice or mention this.

2 is the possibility of movement, of time. Of course one doesn't need the digit 2, as positional notation in base-2 allows one to imply the 2. And every other number as well.

And the operators in Logic allows one to connect 2 or more bits into a composite bit.

Generally, I think the mind unifies. But most unities are acheived at the cost of negation. Good is a negation of Evil, and the reverse. Mind is a negation of Mind-independent, and so on.

Fortunately, at the greatest levels of abstraction, we can enjoy a sense of existence as something unified. We have the monism of Parmenides, Hegel, and many others. We have concepts like Being, the All, the One. All of this is beautiful. If we are 0's, we are in love with 1, or Unity.

I think the Christ myth involves unity. And I think other spiritual heroes symbolize unity. Jung talked of the Circle and Square of playing this role for the psyche.

Nicholas of Cusa used a proto-calculus to represent knowledge of God. Man is a polygon that increases its number of sides. But true knowledge of God is a polygon with an infinite number of sides, or a Circle.

That's the ticket right there --the Circle is the limit approached by a polygon with more and more sides. Add as many sides as you like. You won't have a circle exactly, but you are moving always (and forever) in that direction.

Why is the number e so beautiful? How sad it is that so few know of it! We all know pi. And pi is an eternal sort of number. We can see or almost see pi in any circle. One might argue that any circle outside the mind is an imperfect circle. But that aside, pi can exist all at once, spatially, implied by the form, real or imagined, of a circle.

e can do this do, yes, but e is more often associated with process, with change, with time. e is the constant associated w/ perfectly continuous self-proportionate growth, just as pi is the constant associated with the perfect curve, that maintains its constant curvature exactly.

Now e is used to generate the equiangular or logarithmic spiral. Strange enough, the circle is also an equiangular spiral, but with a zero growth rate.
So e and pi are strangely related in the curves that are generated from them. But this is not all.

e to the power of imaginary pi is or equals negative one. pi is imaginary because another strange number is involved. the number is i, or the imaginary unit. This unity is neither negative nor positive but lateral. It's between negative and positive, and yet a unity, a digital exact number, whereas pi and e and never fully revealed nor can be.

If you know a little math, this is shocking, for pi and e are transcendental numbers quite primary to mathematics.. If 0 and 1 are the most important "usual" numbers, then pi and e are the most important unusual numbers. Just as 0 and 1 have a poetic relationship, so do pi and e.

Pi is a good symbol for eternity. And e is a good symbol for time. Then we have i which is quite important in its own way. It's rational like 0 and 1, but unlike 0 and 1 which are real, i is imaginary. So we have 0 and 1 which are the most basic of basic numbers, and pi and e which are the most exciting perhaps of high-tech numbers, and then i which is really quite simple to use but different from the rest in that it is imaginary. i is the square root of negative one, which did not exist until someone created this strange beast the imaginary unit. It should be noted that there is -i as well as i. And the imaginary number line runs perpendicular to the usual number line. And this forms a cross. 0 is at the absolute center of this cross that stretches to infinity (and beyond) in 4 different directions. Must we deal with 4? Not really. We just have 2 to the power of 2 here. We have 2 number lines that meet at 0, each of which moves in a negative and positive direction away from 0. 0 is the origin.

Here's the finale. e ^(i*pi) + 1 = 0. These five crucial numbers fit together somehow into one beautiful identity. And this is an eternal relationship. e and pi are discovered not invented. 0 and 1 are the ultimate reduction possible of numbers in the traditional sense. i is invented. But once invented it was a key that unlocked the relationship between these other four, and itself of course. i, the imaginary number, was a tool that revealed a deep structure in our fundamental and most exciting numbers. This is a sculpture of perfect beauty, that no one can claim, that is easily carried around in one's head.