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Inasmuch America has a large population of Latin Americans, it seems to me that people, or some people, might want to know about them, and what they are, and where they came from. Most Latinos of the south are either a mixture of Spanish and Indian, or sometimes pure Indian. We have some idea of the Spaniards. They were European. But what were the Indians? What is their contribution to the great numbers of–whether you like it or not–new Americans? In particular, what are their blood lines? Are they, as nativists insist, of very low IQ–83–and have they enstupidated the Spanish? Horrendously primitive?
Without thinking about it, I had the entrenched idea that they were just that. I wasn’t conscious that it was either an idea or entrenched–just a fact. It didn’t occur to me that I knew virtually nothing about these people, or that there was anything to know.
What pulled me up short was their architecture. Throughout a large region, sort of Yucatan through parts of Honduras, you find ruined cities of monumental architecture that would match most of what is found in the ancient Near East. A great deal of it is overgrown with jungle. To get to major sites like Palenque, you walk through dim trails with unexplored walls and passageways. But the existence of these ruins did not set well with the idea of primitive incapacity. The architecture was entirely Indian since they had no contact with Europe.
Aha! I thought with the brilliance of one who has been hit over the head by the obvious. Something screwy is going on here. How witless can you be and engineer these things? I started poking around. And found interesting stuff. For example:
The Maya invented a sophisticated base-20, positional-exponential number system, including zero. The invention of zero is regarded as major advance in mathematics, and occurred in India for sure and perhaps in other places, though never in Europe. Until Fibonacci brought zero back from the Hindu-Arab world, Europe used Roman numerals, a horrible system. I knew this, but had never thought about it. Well, it’s worth a little pondering.
In a positional number system, a number–7, say–has an absolute value–in this case unsurprisingly 7–as well as a different value depending on its position. For example, in the number 100,007, seven means, well, 7. In 100,070, its value is 70, and in 10,700, its value is 700.
“Exponential” means that each position in a number represents a different power of the base, in our case 10. Thus we have ten to the zero power equals one, to the first power, ten; squared, 100, cubed, 1000, and so on.
The Maya, using base twenty, had a similar progression, going 1, 20, 400, 8,000, 160,000 etc.. (Inevitably the choice of 20 as the base is attributed to our number of fingers and toes, though I have trouble imagining anyone actually counting on his toes.)
Neither of these ideas is obvious, or anywhere approaching obvious. Both eluded Archimedes, for example. They seem natural to us because were are steeped in them from the first grade and, since everyone has had high school algebra, exponents seem routine. Using a thing and inventing it are very different animals. Any bright freshman can sling definite integrals; it took a Newton to invent them.
Imagine that you are a Mesoamerican Indian somewhere in Central America trying to figure out how to deal with large numbers. The fact that you are interested in large numbers suggests that you are not stupid. You have never had high-school algebra or heard of exponentiation. I cannot imagine how you would get from here to “Eureka!” (though as a Maya you probably didn’t know Greek either).
The idea “Hey, what if I line up powers of 20, multiply them by sort of coefficients, and add them….?”–is a huge intellectual leap. So far as I can determine, it only happened twice. It never happened in Europe.
For the mathematically curious, the Maya system had a remarkable peculiarity. Number systems, or anyway all I have heard of, require a number of symbols equal to the base. For example, binary, base-2, has two symbols, 0 and 1; decimal, base-10, ten symbols 0-9; and hexadecimal, base sixteen, 0-F. So I thought, Oh help, I’m going to have to memorize twenty symbols of some weird sort. In fact, the Maya ran a base-20 system with only three symbols representing 0, 1, and 5. That is truly strange, but it works. If interested, the link above explains it nicely.
For the record, from The Story of Mathematics: “The importance of astronomy and calendar calculations in Mayan society required mathematics, and the Maya constructed quite early a very sophisticated number system, possibly more advanced than any other in the world at the time ….The pre-classic Maya and their neighbours had independently developed the concept of zero by at least as early as 36 BCE, and we have evidence of their working with sums up to the hundreds of millions, and with dates so large it took several lines just to represent them. ”
Curious from a Stone Age people, which they essentially were. I note that Europe did not invent zero.
It is often said that the Maya never invented the wheel. Actually they did. Hundreds of these wheeled pull-toys for children have been found. Several writers have commented that it is difficult to understand why the Maya were unable to make the mental leap to the idea of making full-sized carts. But of course they could. Thing is, there were no animals to pull them, such as horses or donkeys. Making a mental leap to horses does not get you a horse.
The Maya in the popular mind are thought to have been murdering, torturing savages given to human sacrifice. This is probably because they were in fact murdering, torturing savages given to human sacrifice. Why this is thought especially reprehensible is a mystery. The Romans sacrificed huge numbers in the arena so that the public could enjoy watching them die, crucified large numbers, and poured molten lead down the throats of criminals. In the European witch hunts, sort of 1450-1750, some 500,000 were killed depending on whose numbers you accept, mostly by burning alive. The Tudors hanged criminals, cut them down still alive, opened their abdomens and removed their bowels while still alive, and had four horses attached to their arms and-legs put them into pieces. And of course everybody and his dog put entire cities to the sword, from Joshua to Hiroshima. Despite their best efforts the Maya could not keep up with the moderns.
The invention of writing is among the major intellectual achievement of humanity and one that occurred at most three or four times on the planet, and perhaps fewer. Specialists argue, idiotically in my view, over whether Chinese was or was not influenced by earlier writing. Specialists have to do something with their time. What is not arguable:
Wikipedia: “It is generally agreed that true writing of language (not only numbers) was invented independently in at least two places: Mesopotamia (specifically, ancient Sumer) around 3200 BC and Mesoamerica around 600 BC. Several Mesoamerican scripts are known, the oldest being from the Olmec or Zapotec of Mexico.”
The Maya script is logosyllabic and said to be functionally similar to Japanese, to which it is utterly unrelated. It is not “proto-writing,” but actual real writing. This was not immediately known because the script had not been deciphered, but now about ninety percent can be read. This doesn’t help as much as might be expected since the Spanish Christians, as destructive as the Muslims of today, burned almost all Maya books–codices actually–and so everything we know comes from inscriptions carved on buildings. Imagine how we would look to Martians with the same problem. The book to read if interested is Breaking the Maya Code.
The aesthetic is a matter of taste but these to my eye appear artistically respectable. The Maya of today do nothing in math and technology, but retain a fine sense for design and the use of color.
Again from The Story of Mathematics: The Maya “were able to measure the length of the solar year to a far higher degree of accuracy than that used in Europe (their calculations produced 365.242 days, compared to the modern value of 365.242198), as well as the length of the lunar month (their estimate was 29.5308 days, compared to the modern value of 29.53059).” Try to imagine how they did it.
It is interesting that Europe invented neither writing, zero, nor its number system, but the Mesoamericans did all three. Perhaps the Indians were enstupidated by the admixture of Spanish blood. While this is all good fun, it again raises the question of how and why groups pass through periods of intellectual fertility and then stop, as the Maya certainly have. Always there is some pat genetic explanation that doesn’t make sense, can’t be established, or both. But the Indians did what they did. Interesting stuff, no?