Monday, May 26, 2008

Something about Nothing

One of my favorite mathematical non-fiction books (yes, this is a genre) is Charles Seife's cogently written, entertaining book called "Zero: the biography of a dangerous idea." If reading 200+ pages of math history and equations, then may I tempt you with a cornucopia of zany appendices, such as "Create your own wormhole!" and "A proof that Winston Churchill is a Naval Orange." The wormhole I built based on his easy step-by-step directions has been great family entertainment, but let me forewarn you: your hat WILL blow off.

Anyway, an email yesterday from a fantastic former student (one who thinks about math on a 3 day holiday weekend) got me thinking about nothing again, and by nothing, I mean zero, the number, the concept, the beautifully symmetric symbol . . . Nirvana. While reading in her Mexican-American history book, she came across the following Mexican-American paragraph (printed her without permission):

"Considerable discussion has taken place about whether the Olmeca or the Maya
discovered the concept of the number zero circa 200 BC. (The Hindus discovered
the zero in the 5th century AD, and not until 1202 AD did Arab mathematicians
take the concept to Europe.) Notwithstanding, the fact is that before the time
of Christ, the Olmeca were using a more accurate calendar than that used in the
West today."
Now before you say "Olmeca? the tequila people?" Let me tell you about the Olmeca. They are considered to be the first significant civilization in Meso-American, and by "significant" I mean created beautiful pottery shards and embraced mathematics. Their culture is regarded as the mother of pre-Hispanic Mexico (notice when dealing with antiquity, "pre-" is a common modifier." The Olmeca are usually given credit for being the first Meso-Americans to comprehend the concept of zero (that means they thought about nothing quite literally.) Their calendar, hieroglyphic system of writing, and tequila recipe influenced the later cultures of the Mayan, Aztec, Mixtec, and Zapotec cultures.

But were the Olmecs (by which they are sometimes referred) actually the first to fathom zero, or people using and thinking about nothing outside of Meso-America, or was there a materialistic, jealous prehistoric cavemen who was envious of his caveman neighbor who had a "big, fancy rock," while he had "zero big, fancy rocks?" Before answering this question, it is important to distinguish among a ordinal number, a nominal number, a cardinal number, and a cardinal bird. The third is a medium-sized songbird belonging the genus-species Cardinalis-cardinalis, appropriately enough. But if you were to COUNT the number of cardinals you see on your fence chirping a barber-shop ditty, that number would be a "cardinal," or counting number.

The jealous caveman, when stating he has "Uggg-none", is using zero as a cardinal number. This is a pretty advanced usage of an idea, comparable to a student's realization of the link between practice and performance on a math test. An "ordinal" (not to be confused with the oriole bird) or ranking number refers to a relative position among other things, as in "the caveman with the most rocks wins FIRST place, the caveman with the next most rocks earns SECOND place, etc., right on down to the envious caveman with zero rocks in LAST place.

A "nominal" number is one that simply identifies something, such as a zip code, a player's jersey number, or our Social Security Number (mine is 314-15-9265, easy as pi to remember.) Zero can be used in any one of these three contexts, and its appearance throughout history has introduced it in each case at different times, the first of which was as a positional notation, i.e. as an ordinal number, or more appropriately, a symbol.

Dating back some 5000 years to ancient Mesopotamia, the Sumerian's cuneiform utilized a double-wedge to show an omission of a number. For example, when writing down a beautiful Babylonian babe's phone number of 104 (fewer digits required back then due to the unaffordability of phones), a young man would scribble down into his wet clay tablet the following:
The small, elevated double wedge essentially represents zero. The Mayans incorporated zero into their everyday counting, again as an ordinal, counting the days in their calender with "Day Zero. Their symbol for zero, although capable of warding off evil spirits, was not very efficient to write.
don't mess with the Mayan Zero

But the use of zero as a position holder versus the mathematical, cardinal zero are dramatically different. It wasn't until the Verdic mathematicians of India, did zero really turn into something that aided computation. They used a single dot to denote the number zero. The ancient Chinese came along and built upon the Hindu math, giving us our current symbol of the open dot, much quicker to "draw" than Mayan version.

Of course from there, the zero became commonplace, and even lead to the contemplation of infinity, yes infinity. The concept of nothingness and the concept of the infinite are really one in the same, as elucidated in this classic poem by Jonathan Swift:

So, naturalists observe, a flea
Hath smaller fleas that on him prey,
And these have smaller yet to bite 'em,
And so proceed ad infinitum . . .

And infinity gets us to quantum physics, the quest for Unification, the equation of the Universe, and ultimately, the meaning of life. Maybe the Mayan symbol is more appropriate after all.


Anonymous said...

My favorite number is 012 because it has a zero in it.

Anonymous said...

Celtic great Robert Parish went by the nominal usage "00." That's "double zero," not "oooooooh," although his play, along with DJ, Ainge, and Bird did warrant their fair share of superlatives and interjections.

Anyone who wasn't the Lakers won ZERO championships against them.

Brenda said...

I'm glad the email was put to good use!