Bastard Reasoning

What can be nothing one moment and something the next, yet disappears in the presence of anything? –  Robert Kaplan, The Nothing That Is (59)

IMG_0042 The other day, my fourteen year old son pointed out that life and death are not antonyms, “You can’t have death without life, therefore the opposite of life is not death, it’s nothing.” Nothing, as in, an absence- not even an absence- a void without context- Well, what is that? my other sons and I wondered… I had cause to think on this thought further as I was coincidentally reading The Nothing That Is: A Natural History of Zero by Robert Kaplan.

Zero is neither negative or positive, but the narrowest of no-man’s land between those two kingdoms. (190)

Kaplan takes the reader through the transition of numbers from mere adjectives to nouns in their own right, and then he hits us with the mystery and enigma that is zero. Either Kaplan is an extremely clear and gifted writer or my math skills are far more impressive than I ever knew. Alright, settle down, Jessica, that’s a bit of an overstatement. Maybe. It may be a simple thing for most people to get their heads around why any number to the power of zero is one, but I got through college algebra getting the answers right without knowing what it really meant, but which now, thanks to Mr. Kaplan, I do. The next day, I tried to get my eighteen year old son to appreciate how exciting it was that I actually understand the concept, but he wasn’t up for my enthusiasm at 8 am, if ever.

But I digress-  before Kaplan even gets into what zero is (or isn’t), he gives an account of the possible ways by which it came to be understood at all.

If you favor the explanation that the ‘O’ was devised by the Greeks without reference to their alphabet, its arbitrariness is lessened by noticing how often nature supplies us with circular hollows: from an open mouth to the faintly outlined dark of the moon; from craters to wounds. ‘Skulls and seeds and all good things are round,’ wrote Nabokov. (18)

One of my favorite images from this natural history is the method for computations that the ancient Hindus used: a board covered in sand to mark the numbers, subtractions, and additions as they went along. Kaplan tells us their word for “higher computations” is dhuli-kharma, ‘sand-work.’ But what is most intriguing to me  is the more metaphysical idea that the way in which they expressed zero (mostly as a place-value marker- which was a huge development) was by a simple finger impression, a dent of nothing formed by something…there is something perfectly beautiful in that…

Once zero was an official thing then things got a little complicated. Zero takes us out of the realm of  nouns into travels as a verb and things get a lot freaky. A number to the power of zero is one, but what of zero to the power of zero? How can that equal one and also, zero? What about division? Division is the first clue, in fact, that we have problems comprehending the magnitude and minuscule nature of the slippery zero.

‘Allez en avant et la foi vous viendra,’ said French mathematician d’Alembert: ‘Just go ahead and faith will follow.’ (157)

That math so elegantly sums up all the mystery and power of our universe is something I find fascinating. I love books such as this that make some of that wonder accessible to my rather limited mind.

After all, maybe, like zero, we are all indivisible in our center. Knowing we’re nothing, but only in the context of our absolute something. I kind of love that idea- we are one with zero. Kaplan draws from a gallimaufry of disciplines in  a poetic, profound and valiant attempt to describe zero, that “pure holding apart,” concept to which zero lends and points itself. The poetic justice of taking our psychologically linear perspective and wrapping it around into the perfect symbol- 0, stretches all boundaries of philosophy and meaning: circumference – everywhere; center – nowhere* …by the end of the book I felt as though my skirt had been caught up in the door of a moving car driving around in circles and I was just holding on for my life. When it stopped,  all I could do was smooth the tangents from my shirt, straighten the x-axis of my skirt and say: Kids,  I got nothing, I have no answers.  But whew, that was fun!

Opposites are an illusion of language. Something and nothing, you know, are equally false substantives. (218)

*Sphaera cuius centrum ubique, circumferentia nullibi

**“…space, which is everlasting, providing a situation for all things that come into Being, but itself apprehended without the senses by a sort of bastard reasoning…” Plato’s Timaeus quoted (63)


11 responses to “Bastard Reasoning

  1. If you can think of it then in essence it exists. Zero offers a something, thus nothing has the potential of existence. What then is nothing, akin to the absence of something. Dark is the absence of light photons, but what remains may still be a something.

    Ancestors and philosophers talk about two worlds, they might describe with different words, but basically a material or spiritual world. It could be suggested that the eternal dark is the absence of motion of energy, a quality of a spirit world that is sleeping, dreaming rather than in motion. It could be suggested that what is manifested as appearance or activity is energy released from its sleep, our senses evolved to see motion rather than the invisible non-motion of energy.

    What is death, marked with the zero, is an absence of motion, energy falling away back into the ocean of dark dreaming sleep.

  2. I think it’s time your sons staged a non violent coup and started running the universe. We need such wisdom at the helm of every country.

  3. Fractal geometry and the insights of the science of Chaos are based on Complex Numbers. Unlike all other numbers, such as the natural numbers one through nine for instance, the Complex Numbers do not exist on a horizontal number line. They exist only on an x-y coordinate time plane where regular numbers on the horizontal grid combine with so called “Imaginary Numbers” on the vertical grid. Imaginary Numbers are simply numbers where a negative times a negative creates a negative, not a positive, like is the rule with all other numbers. In other words, with imaginary numbers -2 times -2 = -4, not +4. The Complex Numbers when iterated – subject to constant feedback – produce Fractal Scaling as is shown by the Mandelbrot set:

    z -> z^2 + c

    where c = any complex number.

    • There once was a red headed bunny
      when laid eyes on Fibonacci said-
      “I’ll be your honey!”
      What started with two
      very soon grew
      to numbers so large it’s quite funny.

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