Let me take this thread in entirely a different direction.
I read somewhere that the fact that there was no beast of burden (like the horse) available to Native Americans was a key factor in the scale of civilization in North America (remember, horses were introduced by Europeans). Another factor is the disease thing, which resulted from the Americas being physically isolated from the rest of the world. With the Chinese, there was cross-exposure to each other’s diseases over the years, and so when there was European incursions, disease was much less of a “force multiplier”.
Yes, I was told that in grade school, too. But is it that clear? Your own source, Doobieous, say this:
Perhaps some clarification is in order. I have no evidence concerning where the Arabs learned to manipulate numbers. What I am addressing is the source of the shape of their numerals. Your own source strongly intimates that they did NOT get those shapes from India. (I concur, based on the visual evidence given with your cite.) The authors of your source speculate that the numbers may have derived from the Arabic alphabet. Perhaps, but I’d like to see a comparison. Based purely on the samples of Arabic writing I have seen (i.e. on poor evidence at best) I would say that the China-to-Arabia transmission of numeral shapes IS the simplest explanation, of the three theses discussed in this thread. Again, almost the only thing needed to do to create most of the (European) Arabic numerals is to write the Chinese numerals but not lift the brush between strokes. (There ARE a couple of numeral-characters that need simplification, but the similarity is still obvious to the eye, and there ARE a couple of numerals that are not obviously related, unless one accepts the (in some cases great) similarity of the other numerals.)
Yes, it’s true, I am going largely off the surface observations, and the historical observation that transmission was possible, at that time in that place. I know of no scholarly research into this question but my ignorance is not proof the thesis is wrong. I will keep looking; in the meantime, the best remaining evidence is to make the experiment yourself. Get a brush pen, and write the Chinese characters in the proposed “Arabic style.” I only wish I could point you to a better source for the “real” written shape, rather than the “screen” shape.
Actually, an excellent point. But the main difference between my thesis and the “official” one is where the Arabs got the knowledge from; the common idea does not credit tha Arabs with creating their system, either.
As for giving the Chinese credit for “everything it seems,” I can only partly deflect the criticism by pointing out 1) that it is probably in part a reaction to my upbringing that gave ALL credit to the West for everything important and normal, 2) I don’t (really!), it just kind of came out that way in this thread, and 3) maybe I view my words differently when I write than you do when you read them. For example:
…seems so obviously true to me that I wonder what it is you (plural) think I’m saying. (I must really have come on too strong!)
On the other hand, while you may (or may not) be imputing more to my words than I am thinking, I am certainly not immune to error:
Okay. I DO fail to see how XCVII - or for that matter “twelve” or the English system of measurement - is obviously derived from or indicative of a base 10 system. (Yes, we do now use Base 10 encipherment in all dealings, but don’t those systems indicate that the people who created them were NOT thinking decimally?) If you wish to point out that base 10 is different from “decimal” I won’t argue, but I would like some real world examples. In the GQ thread How did ancient Greeks do mathematics? I read that the Greeks had this system:
BUT
Isn’t it possible to do arithmetic and even math without Base [anything]? Every number is just representative of an amount, in a naturalistic sense. That is, when you count fifteen oranges, you don’t think about it in “bases” (that’s one ten-orange plus five unit-oranges) you just have 15 of the things. Or, why couldn’t the Roman system be seen as, say, Base 1000 with a lot of simplification of the writing of the numbers? I really don’t see it as obvious that the Roman system derives from “base system” thinking. But maybe that’s just me.
Quote:“Isn’t it possible to do arithmetic and even math without Base [anything]? Every
number is just representative of an amount, in a naturalistic sense.”
Maybe something is messed up here but there are or were cultures that didn’t use bases - I can’t remember the name of one now.
But they counted one, two, three, many.
The natural way to represent an amount was equal to the number of fingers on a hand (base 5), on two hands (base 10), on two hands plus the hands themselves (base 12).
The French used a system of base 20, at least they did at some time because their numbers written longhand (like twentyeight) show it.
Unless you want to go one, two, three, many, you have to have some kind of system.
If on the other hand you wish to have every number be that number no more no less, then you have to have a new and original name for each and every number. This is why children working out mathematics by themselves can “invent” bases 4, 5, 6, 7, and so on but get stuck on base 11, 12 18, and so on, they usually don’t grasp that they need a new symbol for 11, 12, 18, etc…
If that doesn’t answer your question, please rephrase it.
Oh, I’m gonna keep using these #%@&* codes 'til I get 'em right.
I’m going to resurrect this thread solely for the purpose of responding to the erroneous assertion by {:-Df that a ‘base’ is somehow different from a method of representing numerals with words or symbols. I refer the reader to the last post of {:-Df above for the argument made.
When a culture adopts a positional system of numerical notation, such as we use, it is easy to understand the ‘base’ of the system; as noted at the site M-W Dictionary On Line, one definition of the word “base” is:
. But, mathematics doesn’t depend on notation for its concepts; understanding this is simple when one notes that cultures in the Middle East used varying methods of mathematical notation to conceive of and manipulate common mathematical principles. Thus, the concept of a “base” for ordering of numerals is not dependent on the written system but instead on the way the culture thought about numerals.
For example, the Romans used a system of numerical nomenclature that clearly was base-10 in concept. There are ten basic words for the numerals we demoninate one through ten; thereafter, with few exceptions, the numerals were denominated by combining a word representing a multiple of ten with a word for the added numerical value we would place in the units column. To say the number 44 was to say, in essence, “four tens and four”. Now, that is base-10 thinking, even if the written expression of that thinking lacked the sophistication later introduced to Europe through the Arab culture (which may have been derived from the Indian culture, but, until someone manages some scholarly examination of the subject and concludes otherwise, does not appear to have come from the Chinese culture). In order to clarify how something can be NOT base-10 in thinking, one only has to look at our words eleven and twelve, which to not derive from the concepts “ten and one” and “ten and two”.
Getting away from the numbers game, one of the reasons the Chinese wouldn’t have fared too well is basic cultural snobbery. The Chinese felt westerners were unclean and barbaric, and tended to believe that westerners weren’t quite the same kind of animal as the Chinese, biologically speaking. The Chinese carried this poor judgment so far as to declare that western bullets could not harm them. Boy, were they in for a surprise.
The Opium Wars probably provide the closest clue as to what would have happened. It’s true that the Chinese were a significantly society in many respects, but they just thought a little too much of themselves to keep it up.
I, for one, sure wish they had a better grasp of reality - I can trace part of my lineage back to the 12th century, and somewhere in there it shows I’m a direct descendant of some Chinese royalty, but all that went up in smoke over a century ago…
This topic is much discussed in the above mentioned book “guns germs and steel…”
There ware many conditions that allowed the eurpoeans to dominate the americas. The most important of them was by far disease. Also, but of lesser importance, steel, horses, communications (common use of writing), ships, etc…
A specific example mentioned in the book was the total domination of the Incas by a few spanish. A man on horseback, with stirrups, armor, and a sword could easily kill many inca warriors who were on foot.
I think a major point of difference between America and China was the numbers of population and the density of population. Compared to China, north America was pretty much empty. On top of that, Chinese society and culture were way more developed than native American cultures.
If China had been so sparsely populated as north America and the culture so primitive, maybe today there would be vast parts of China under a western system of government like is the case in Australia, Canada etc.
BTW, I once saw a very interesting work of fiction that told the story the other way around: The native Americans sail to southern Spain and establish a beachhead there which keeps expanding as they send more people and reinforcements. It is all done with historical acccuracy as far as geography, historical figures etc. It was kind of shocking in a way. It had maps of how the indian empire expanded in Spain with time etc.
The reason that the Spaniards could defeat many times their numbers of Incas were psychological and not just due to their superior capabilities of their weapons. The Incas had never seen a horse or a cannon. The shock of these magical items played a large part in the battle. The reference to think of here is War of the Worlds, which was written as a metaphor for European/American contact.
The example from Jared Diamond’s Guns, Germs, and Steel that labdude refers to is the battle of Cajamarka. At that “battle” around 80,000 Incas faced 168 Spaniards, 62 of whom were mounted. The Natives had come to talk, not to fight. The men around their king, Atahuallpa, were unarmed. The Europeans used their advantages wisely. They kept their armored troops hidden until at a signal they rushed out to attack. The cavalry had tied rattles on their horses to create more noise. The infantry fired cannon and blew trumpets ( also unheard of ) to panic the Natives. The Incas did indeed panic. In their terror, many were trampled and others were suffocated underneath their fellows. The Spaniards cut their way through the throng and captured Atahuallpa. During this whole time not a single Inca raised a weapon against a Spaniard. The Europeans responded by attacking the fleeing Incas, spearing the stragglers until after nightfall. Around 6 or 7 thousand Incas were killed. Due to the nature of the Incas divine monarchy, once the Inca king was in their power, the Spaniards had won.
A note about cavalry:
People tend to believe that the heavy cavalryman has the advantage over infantry. Assuming comparable equipment and training, this is not so. The man on foot does not have to worry about staying on his horse, so he can concentrate fully on staying alive. The advantage of cavalry is mobility. Also, horses have horsesense. Despite what you may have seen in Braveheart, horses are too smart to charge into a wall of spears.
The reasons for rise of the medieval knight were largely cultural. Since the western Europeans believed that this was the best way to fight, they neglected to develop infantry. When the flower of the French chivalry finally did meet up with well trained infantry ( the English archer and the Swiss pikeman ) the knights tended to get decimated.
A note about terminology:
Light and heavy do not refer to the amount of armor that a company is wearing. They refer to the type of weapon. Heavy troops ( cavalry and infantry ) carry hand to hand weapons; light troops carry missile weapons.