A while back I read an interesting article, I forget exactly where. There is a tribe in Africa that can only count to three (3). And not even that really, because their “3” is just translated as “many”. “One-Two-Many”. For some reason this strikes me as rather sad. But it did get me to thinking. What is the highest certain civilizations, esp. in the past, were able to count?
I know in ancient cultures that were reasonably advanced, “thousand” seems to be pretty universal. From the classic Latin “mille” to the Anglo-Saxon word for thousand. (I looked it up in my dictionary. Our word thousand is actually derived from an Indo-European word for “to increase, swell” and a Proto-Germanic word for “hundred”.)
But consider the word million. It is derived from the Latin root “thousand” and the quasi-Latin suffix “-ion”. That couldn’t be a (relatively) recent word, could it? And I don’t think there is a Classic [i.e., ancient] Latin word for million. Is there?
As to what cultures I am asking (what is the highest they could count?): I of course mean ancient Greece, ancient Rome, the Anglo-Saxons. Plus the Incas, the Mayas, the Aztecs. Any ancient society that was advanced enough to count high at all.
And even if you don’t have an exact answer to this question, tell whatever you know. I find this subject fascinating.
It’s claimed that Pirahã, a language of Brazil, has no numbers at all. It’s claimed that there are words meaning “small quantity” and “large quantity” but none that give an actual count of anything:
There were words for very large numbers in ancient India:
Not exactly related, but similar, there’s a general rule in computing that the only reasonable numbers are zero, one and infinity.
It’s been stated and restated many times in different ways by different speakers, but you generally need to cater for something to:
[ul]
[li]Never occur, ever[/li][li]Occur once and only once[/li][li]Occur an arbitrary/indefinite number of times[/li][/ul]
There is some argument as to whether it really should be 0, 1, 2 and infinity, as the concept of a paired set is sometimes useful, but in very broad terms, the reasoning behind this rule is that:
You can use a simple conditional test to trap things that should never occur
You can use a variable to store a single value
For anything bigger, you need an array, a table, etc - and these are generally of arbitrary size.
George Gamow tells a version of this story in the opening pages of One, Two, Three . . . Infinity (originally pub. 1947, but revised one (or more?) time(s), and perhaps still in print?)
He states this was the case for certain tribes of Hottentots, who allegedly could count up to (and including) 3, then “many” after that.
Actually, he starts by telling the story of two Hungarian aristocrats who couldn’t count beyond 3, along with another jokey story about the alleged famous stupidity of Hungarian aristocrats. (Apparently the butts of “dumb blonde” or “Pollack” or “Italian” style jokes of the time.) Then he notes that it was actually true of various Hottentot tribes.
It’s thought, at least by some, that the proto-Indo-European word for “seven” was borrowed from proto-Semitic; perhaps “six” was similarly borrowed, though not “eight”, “nine.”
Could it be that the proto-IE people could count only to five (or six) when they first contacted speakers of pre-Semitic? AFAICT the question is too speculative to even be controversial. The proto-Semites’ “seven” might have had some special religious significance to them, leading to its propagation.
I remember Terry Pratchett’s Discworld trolls count as follows:
One, two, three, many.
Many-one, many-two, many-three, many many.
Many many-one, many many-two, many many-three, many many many.
Many many many-one, many many many-two, many many many-three, LOTS.
Of course, Pirahã is an extreme outlier in terms of its simplicity and crudeness. Last I heard, the general consensus was that some relatively recent (i.e., no more than two or three generations ago) calamity had wiped out all of the tribe’s elders, or perhaps even all of the adults, taking most of their culture with them.
And not entirely seriously, but Richard Adams has his rabbits in Watership Down able to count to four, and then just “many” (“hrair”), which depending on context can be roughly translated to “five”, or “thousands”, or “uncountable”. He was probably influenced by accounts of the similarly-limited human tribes.
I read somewhere (sorry no cite) that “none”, “one”, “two”, (maybe “three”, not sure), “a few”, and “many” are pretty much hard wired into our brain. Everything else with respect to numbers and counting has to be learned. I suppose if you don’t have any sort of complex trade or bartering you don’t need any more than that.
I don’t know how scientifically proven this is but it does explain the above mentioned tribe’s lack of numbers above 3 and the similar tribes described in Senegoid’s post.
In terms of high counting, Archimedes’ Sand Reckoner was his attempt to find out how many grains of sand could fit into the universe.
That required a means of writing down large - very large - numbers. (Space is big. I mean, really big.) The Greeks didn’t have such a system, so he invented one. He started off with the concept of a myriad myriad (i.e. 10,000^2) and took it from there.
Back to the OP. You’re thinking about the question wrong. What’s the largest number we can count to today? There are names for particular large numbers, like a googolplex, but that doesn’t mean we are limited to any particular size for our numbers. We have procedures that can write out any number of any size. The basic procedure is to use scientific notation, as in 10[sup]100[/sup] for a googol and 10[sup]10[sup]100[/sup][/sup] for a googolplex. This quickly gets unwieldly for super-duper large numbers so many other schemes have been devised, all of them with this sort of recursion procedure.
Recursion goes way back. The Greeks had it. Their largest standard numeral was a myriad or 10,000. If they needed multiples of a myriad they wrote that number on top of it. The Romans did a variation of this, in which they used a bar meaning multiply by 1000, so that M with a bar over it was equal to a million.
For super-duper large numbers the Greeks created them through multiple recursion exactly as we do. Aristotle devised this system in order to estimate the number of grains of sand in the universe.
Most civilizations that had any sort of advanced math would have figured this out and devised their own system. They may, like us, have had names for particular large number that were of interest to them but they had ways for reaching any number they needed to use that were exactly parallel to ours.
There doesn’t seem to be a practical limit in English. We use -illion as a suffix for each cluster of three orders of magnitude, using Latin as a root for those prefixes. Thus “vigintillion” for a number consisting of 20 sets of three zeroes, or 10^60. The practical upper limit would be where we run out of Latin names for numbers, and we can arbitrarily back-form new Latin numbers using ISV. Googol would be, in that notation, -illion preceded by Latin 33, preceded by Ten. Maybe “ten tre-trigintillion” or something, my memory fails me. Actually, since trillion has four sets of 3-zeroes, it would really only be “ten duo-trigintillion”
Vedic Indians (by at least the early first millennium BCE) had invented names for successive powers of ten than went up to what we call a trillion, which is probably the record for actual named number words in an ancient civilization. As Exapno notes, however, any culture could count to whatever number they needed to by devising some kind of linguistic workaround.
Of course I heard the “one, two, more than two, more than two…” as related to Amazon tribes.
I suspect like the “fifty words for snow” (not true) it’s a cultural fabrication to make a point. Anyone should you would think be able to count to ten with both hands, and twenty if not wearing shoes. (and then for men, 21). It should not be that hard to go from there to naming each quantity in any culture. Almost every culture is going to habitually encounter situations of greater than 2, even if it’s “how many guys in this hunting party?” or “how many kids do you have?”
Daniel Everett’s claim is that the Pirahã can get along just fine without numbers except for one meaning “small quantity” and another meaning “large quantity.” So, md2000, it’s not true that every culture is going to have situations where they have to count. Even if it’s true, as Chronos says (and this isn’t universally accepted), that this situation arose because at some point in the past all the adults in the culture were wiped out, the fact is that this was certainly at least three generations ago. Today, their culture (with the usual amount of adults) gets along fine without counting. (At least, unless we assume that Everett is simply lying about everything, and most of his claims have been checked out by other people.)
I understand that not every culture came up with finger counting as we know it. Some never thought of it at all, others came up with variations like including the knuckles; IIRC, there was one that counted with the space between fingers, which gets you 8 not 10 for both hands. Interesting to think how we could have ended up with a base 8 number system, and no doubt thinking that was the base most natural to humans the way I see the same said about base 10.
I don’t understand this, and it seems a bit of an over-generous comment wrt a culture on the lamer side of the mathematical concepts continuum.
“Cultures” that haven’t figured out how to count do not have a practical way of saying, “This tree usually produces 547 fruits, but this year produced 796.” And the notion of representing higher numbers can’t be solved with ‘some kind of linguistic workaround,’ because the next guy over won’t have any idea what you are saying when you tell him “The wildebeest migration count is down by a couple hundred thousand this year.”
