Why did the peoples of the New World fail to invent the wheel?
Answer this one. We're always fascinated by reports of ancient cultures like the Incas who performed great feats of civilization despite the fact the wheel was unknown to them. How could a halfway with-it civilization not invent the wheel? Rocks roll. Lightning knocks down trees and the trunks roll. Skulls roll. It must have been the axle, specifically, that they didn't invent, but it shouldn't take Isaac Newton to think of an axle. Was there some cultural commitment to dragging litters and hoisting loads on beasts of burden (and slaves) that inoculated these civilizations against the concept of wheels?
Yuhas and Brazle, huh? Boy, we don't get too many retired Cardinals pitchers writing in to the Straight Dope. Glad to see you guys are still keeping your minds occupied.
Now, then: let's not be too critical of the Incas. First of all, we note a peculiar pattern here. It wasn't just the Incas who failed to invent the wheel; every other civilization in the New World (with one exception, which we'll get to in a minute) managed to overlook it as well. For that matter, the ancient Americans also had to struggle along without the true arch, the cart, the plow, the potter's wheel, the bellows, glass, iron, and stringed instruments. But it's unfair to attribute this sorry technological record to either lack of IQ or (as far as the wheel was concerned) an infatuation with transport via brute strength. The fact is that most civilizations in the Old World didn't invent the wheel either--instead, they borrowed it from some other culture. The wheel appears to have been first used in Sumer in the Middle East around 3500 BC, whence it spread across Europe, Asia, and North Africa. It didn't arrive in Britain until 500 BC. This orderly diffusion pattern makes it conceivable that all the wheels in use today are directly descended from the invention of a single gifted individual--an individual, however, who was such a dope that he failed to sign his name on the patent application, thus assuring his (or her) eternal anonymity. We might therefore attribute Inca wheellessness to the absence of a pre-Columbian Thomas Edison.
But there are other factors involved. The principle of rotary motion, as you point out, is pretty obvious, and was well known throughout the New World as well as the Old. The Incas, for instance, are thought to have used wooden rollers to haul the giant stones they used to build their cities. Unfortunately, the New World suffered from a conspicuous scarcity of draft animals. The only beast of burden known in the Americas was the llama, a delicate critter restricted to certain parts of the Andes, which was used solely as a pack animal. Without draft animals you cannot do extensive hauling with sledges, and without sledges it will never occur to you that the wheel would be a handy thing to have. When the Incas had to transport heavy objects, they relied on manpower, often to the considerable sorrow of the men doing the powering (some 3,000 of 20,000 workers died dragging one particularly massive stone, according to chronicles). Consequently heavy hauling in the New World was restricted to the occasional special project. The Sumerians, on the other hand, had considerable experience with what we might call regularly scheduled sledge service, and even so it took them 2,000 years of fumbling before the idea of the wheel finally dawned. Not that it just popped out of the blue. The general sequence of friction-reducing inventions is thought to have been runners, rollers, rollers held in place by guides, rollers held in place by guides and thickened on the ends to make them roll straighter, the wheel and axle, and from there it's pretty much a straight shot to the Chevy Impala.
But you wanted to know about that exception I mentioned. The wheel evidently was familiar to the ancient Mexicans, the only known instance of its having been invented independently of the Sumerian version. Unfortunately, it apparently never occurred to anyone at the time that wheels had any practical application, and their use was confined to little clay gadgets that are thought to be either toys or cult objects. Another example of good technology gone to waste. Reminds me of Pac-Man.