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Even or Odd . . . or, What?

Not long ago, I read a book about math (The Joy of x, by Steven Strogatz) that mentioned the oddity (if you'll forgive the pun in advance) of the number two being the only even prime number. The thought that came to my mind (not for the first time) was how arbitrary the concept of “odd and even” really is.

Think of it. Is there anything inherently different about numbers that are even, contrasted with those that are odd? Well, yes . . . even numbers can be divided by two without leaving a remainder, while odd numbers always leave a remainder (and it's always 1). But that's really just the definition of an even number: a category that we, as counting humans, have created.

Before going any further with this notion of numbers, it's important to note that I'm only talking about those that mathematicians refer to as “natural” numbers (or sometimes as “counting” numbers). Fractions need not apply. Once we start letting fractions in the door, the whole notion of “odd” and “even” becomes, if not irrelevant, at least so abstruse that it's far beyond the scope of a brief essay. So: whole numbers.

And although the concept can be applied to negative numbers (and maybe even to zero, if you're liberal enough with your definition), there's no need to complicate the issue that way. What applies to the oddness and evenness of counting numbers applies equally to their pessimistic cousins, the negatives.

So: positive, whole numbers. One, two, three, four, etc., ad infinitum, some odd, some even.

But is there any intrinsic difference between odd numbers and even ones, separate and apart from the definition by which we humans have categorized them? Sure, the binary nature of odd and even seems to be a fundamental aspect of nature: night and day, black and white, north and south, east and west, left and right . . . wait!

Maybe “left and right” is a clue to why dualism, and thus the division of the numeric world into odd and even, seems so natural. We have (most of us) two arms with their attached hands, two legs with feet ditto, two eyes, two ears . . . okay, only one each of nose and mouth, but even there we have two nostrils and bilateral symmetry of teeth.

Perhaps if life on Earth had evolved in a triangular-prismatic form, we might not make so much of numbers divisible (or not) by two, but by three. If we got around on three legs and manipulated our world with three hands, might we be not only more stable and agile, but also more inclined to think of numbers as being, not odd or even, but “tercial,” “vacal,” and “surplal”? We may not have invented those words exactly, but surely the concepts of numbers evenly divisible by three, numbers vacant of a unit (i.e., one less than a multiple of three), and numbers surplus a unit (i.e., one more than a multiple of three) would have presented themselves quite naturally.

And perhaps we would have seen more threeness in the world around us. Night, twilight, and day, for example. Light, dim, and dark; open, closed, and leaky; short, tall, and middling; right, wrong, and ambiguous.

It's hard to imagine any sense of threeness relative to concepts such as north and south, up and down, or even east and west. But perhaps their immutable dichotomy might bestow on them some of the mystery and mythology that we, as binary creatures, now attribute to trinities. Living in a world of trilateral symmetry might mean a very fundamental difference in the way we would understand life, the Universe, and everything.

Trinary thought is more subtle and complex than binary. If a number can be, not only spot-on, but also just a little lean or just a bit fat, then other phenomena would inevitably be perceived as 'just so,' or 'a bit this way,' or 'a bit that way.' Analysis of one's immediate experience would be that much more complex. And with that extra bit of mental stimulus, would the human brain have evolved to be a bit faster and, dare we imagine, a bit more flexible and even tolerant? A bit less inclined to yea-or-nay judgment?

And if the world of tripedal humanity might be that different, try wrapping your mind around the universe of sentient, philosophical millipedes.