Posted on 01/14/2008 11:42:57 PM PST by forkinsocket
You may not realize it, but when you tell the grocer you'd like a half-dozen eggs for your family of six, you're using a primitive numbering system. Anthropologists believe that such object-specific counting, in which words like "half-dozen" and "six" denote the same quantity but refer to different objects, preceded abstract counting systems, in which any number can describe any object. Now, a study of Pacific Island languages suggests that counting systems can also evolve in reverse, becoming more object-specific. People on the Polynesian island of Mangareva take object-specific counting to the extreme. They tally some things, such as unripe breadfruit, using one type of number sequence, whereas they count ripe breadfruit and octopus using another. At the same time, the islanders add up various other objects using an abstract counting system similar to the one English speakers use.
There is ample evidence that object-specific counting systems do precede abstract systems in cultural evolution. So the coexistence of supposedly primitive and advanced counting systems in the same culture piqued the interest of psychologist Sieghard Beller and anthropologist Andrea Bender of the University of Freiburg in Germany. They took a fresh look at counting systems that had been previously recorded in the Pacific islands, and, in the 11 January issue of Science, they argue that what appears primitive may not be.
The researchers compared Mangarevan and three Melanesian languages to Proto-Oceanic, the extinct tongue from which all four evolved. Most scholars believe that Proto-Oceanic employed an abstract counting system. But Mangarevan and another of the daughter languages use object-specific counting systems--making them less abstract than the ancestral language. The authors attribute this unexpected reversal to cultural necessity. The two languages lack written notation, and their object-specific sequences--which count certain items in units of two, four, or eight--would simplify mental arithmetic. (It's easier to subtract two dozen from six dozen than 24 from 72.) Such arithmetic would have been essential as the islands became important trade centers.
The work "draws attention to the point that numbers are tools," says Heike Wiese, a linguist at the University of Potsdam in Germany. "A number system may be simple not because a culture can't make it any better, but because it is most efficient." Peter Gordon, a psychologist at Columbia University, cautions that the conclusions depend upon reconstruction of Proto-Oceanic. That the extinct language really used an extensive abstract system is "not entirely uncontroversial," he notes.
Yeah, the usual six inches would be overlooked.
That's why 007 advertised his "length of experience." Left nothing to doubt.
Huh?
Half-dozen can be used for more objects than just eggs. A half-dozen ice cubes, a half-dozen stars, a half-dozen pigs, a half-dozen movies. There, just used half-dozen for other objects.
In American English you’ve got the passel, the gob and the shitload.
I think they mean, in the example, “half-dozen” is only for eggs..
Then, abstracted, any quantity of six.
First a number designation was object specific, then abstracted to the same quantity of any object. The number became abstracted from its specific context.
I think.
bump
Lol!
What if they are counting the number of eggheads writing stupid articles like this one?
A better example might be Japanese where the words are modified for counting different things like people, time, the floors in a building, etc. English does this as well, but not nearly to the same extreme level of Japanese. For example, we use ‘primary’ and ‘first’ differently (where ‘primary’ is the first in a group or series while ‘first’ is a more general term).
So first primary is less specific than primary primary. A dozen dozens are a gross, but why is a dozen 12? Why not ten?
The ancients developed a digital numbers system long before computers. Theirs is based on 10. The computer is based on 2. Which is the more advanced?
Old joke: Why aren’t there more women in science, engineering and math?
Because they’ve been told since adolescence that this [-——————] is eight inches.
(If told in person that would have been fingers spread not very far apart)
A dozen is a handy number. It's easily divisible by two, three or four. If two three or four guys split the cost of a dozen doughnuts, it's easy to figure out how many doughnuts each guy gets.
There are a lot of hypotheses about the origins of the dozen. E.g., we have a jury of twelve because there were twelve apostles. But 13 is unlucky because there were 13 in attendance at the Last Supper -- 12 apostles plus Jesus. The thirteenth was Judas Iscariot, who had already turned traitor.
I’m still waiting for a scientific study that explains why liberals are incapable of understanding economics. Now that would be worthwhile.
Neither. They both represent a number but are not the number itself. Base-2 is certainly an advance over unary, but after this point all that really matters is how you want to store your data. Base-2 can be sort of bulky but hexadecimal makes base-2 operations fairly easy. Base-10 is obviously the most common system and most people have memorized basic arithmetic in it. I would recommend learning numerals in a way that you can solve problems in any base and not try to find the 'best' base (which many would argue exists but isn't useful for arithmetic--e).
Or maybe a “half dozen” is just a representative of the equivalence class which is “six”. Sounds simpler.
Or is it the other way ‘round?
Three Chem E's share a dorm room. One day a ChemE comes back with a brand new bike.
"Wow! Where'd you get that?" asks a roommate.
He replies, "Darnest thing. I was walking along the Engineering quad when this beautiful blonde came by riding a bike. She jumped off the bike, tore off her clothes and said "Take anything you want."
"Ooooh, good choice," said the roommate, "those clothes would have never fit."
But obviously not so different that you can use one to describe the other in your explanation....
I would recommend learning numerals in a way that you can solve problems in any base and not try to find the ‘best’ base (which many would argue exists but isn’t useful for arithmetic—e).
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Thank you for the clarification and the erudicity.
How does one learn numerals in a way that will apply to any base? Aren’t all numerals representative of a specific base? Isn’t the best base a function of its application?
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