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 insisted by web louts hostile to Mexicans, of very low IQ–83–and has their Asian blond enstupidated the Spanish? Were they 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.
Chiapas. Compares well with a lot of Roman monumental architecture. There are lots of these: Palenque, Tikal, Piedras Negras, Copán, Yaxchilan, Teotihuacan, Caracol, Uxmal, etc.
Chiapas. Time and the weather have not treated this building well, but it seems to me that these things must take considerable engineering talent. Phredfoto
Pyramid at Chichén Itsá. For scale, note people at lower left.
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. 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 neighbors 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. ”
Finally, they invented a base-twenty abacus that, since it uses only the numbers 1, 5, and 0, would be tricky to explain here. For those interested,
Curious from a Stone Age people, which they essentially were.
Various sources assert that the Maya could perhaps add and subtract (they certainly could) but could not multiply or divide. A problem with this theory is that only four Maya documents remain, the rest having been burned by the Spanish clergy, and societies do not carve grocery lists into monuments. However, a densely populated, complex urban people engaged in trade with other city-states and constructing elaborate buildings would almost have to be administratively numerate. A Maya civil engineer constructing a wall twenty feet by thirty would have little idea how many bricks he needed unless he could multiply the number in a horizontal row by the number of rows necessary to build his wall. Further, if he needed two thousand bricks and porters brought them ten at a load, he would have to divide two thousand by ten to order his material. Putting it simply, the said engineer (a) needed a functioning number system, (b) had on and so (c) probably used it.
He probably would have used the base-twnety abacus which the Maya also invented. While I have found it simple to use, explaining it here would take considerable spaqce. For those interested,
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 manage the mental leap to 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. Well, say some, why didn’t they make wheeled carts and push them?
Note that if men are used to pull a cart,they are pulling the weight of both the cart and the load. In the absence of steel, a cart sturdy enough to bear much weight would involve heavy wooden beams, heavy wooden axles, and heavy wooden wheels that, being rimmed with wood, would wear out with extreme rapidity. If the cart weighed five hundred pounds, and the cargo another five hundred, then the human pushañullers would have to translate a thousand pounds per mile to deliver five hundred. Dividing the load up and having the pushapullers carry the weight individually would require much less work, and no maintenance of wheels. Do you suppose they thought of this?
Many lightly read and growly web louts assert that the Maya were a Stone Age people. This lack of metals may explain why the Spanish so easily stole their gold and silver.
In fact metallurgy appeared in Latin America–which of course was not then Latin–quite early. Iron did not appear at all.
From Pre-Colombian Ecuador
Wikipedia: “South American metal working seems to have developed in the Andean region of modern Peru, Bolivia, Ecuador, Chile, and Argentina with gold and copper being hammered and shaped into intricate objects, particularly ornaments. Recent finds date the earliest gold work to 2155–1936 BCE. and the earliest copper work to 1432–1132 BCE. Ice core studies in Bolivia however suggest copper smelting may have begun as early as 2000 BCE.”
In South and Mesoamerica, Gold, silver and copper in pure form or alloys were made lost-wax casting into intricate objects. In lost-wax casting, you make a wax figure–a statue, bell, or ornament perhaps. You coat it with clay, leaving small holes at top and bottom. You then pour molten metal into the top hole. The wax melts and runs out the bottom hole, leaving the metal to harden in exactly the shape of the original artifact. It is not three-D printing, but neither is it primitive.
Maya Civilization Keeps Growing
The general public knows little of the Maya and, until recently, archaeologists were not much better. This is changing. For example, some 60,000 Mayan structures, previously unknown, were recently found in the Guatemalan rain forest. A few snippets and link:
BBC: “Results from the research using Lidar technology, which is short for “light detection and ranging,” suggest that Central America supported an advanced civilization more akin to sophisticated cultures like ancient Greece or China….The archaeologists were struck by the “incredible defensive features,”which included walls, fortresses and moats….
“With this new data it’s no longer unreasonable to think that there were 10 to 15 million people there,” said Mr Estrada-Belli,..Another discovery that surprised archaeologists was the complex network of causeways linking all the Maya cities in the area. The raised highways, allowing easy passage even during rainy seasons, were wide enough to suggest they were heavily trafficked and used for trade…..”
To call the Maya a Stone Age people is correct if you disregard gold and silver, and deeply satisfying to web louts of twilit understanding, but a tad deceptive to those who think. These were people who invented writing, hydraulic cement, paper (as much paper-like as papyrus anyway), the wheel, the planet’s best number system at the time, elaborate water-management systems, paved roads, schools, astonishingly accurate astronomical observations, and densely populated cities requiring the organized supply of food from outlying farms. This they did as a small, almost totally isolated people in a rain forest. The Roman Empire (for example) had the advantage of intellectual and cultural contact with many contemporary and older civilizations–Greece, Persia, Phoenicians, and the Hellenistic world among others, and yet did not invent a number system. In fact Europe in its entirety did not invent one, or the wheel, or writing.
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 m y 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 almost 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 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).”
It is well not to make more of a people than they were, but also not to make less. In their Classic Period (200-900 A.D.) the Maya were far ahead of the Nordic peoples of Europe, though they did not come close to the Greeks. (Who did?) In the book of civilization, they belong on the same page with Egypt.The Gauls, Huns, Hittites, and Europe outside of the Roman Empire would serve as footnotes. Papua-New Guineans they were not.