Polynesians May Have Invented Binary Math(news.sciencemag.org)
news.sciencemag.org
Polynesians May Have Invented Binary Math
http://news.sciencemag.org/archaeology/2013/12/polynesians-may-have-invented-binary-math
4 comments
one, two, three, four, five, six, seven, eight, nine, ten
finger overflow!
(ten plus) one, (ten plus) two, ...
For base ten, you can just put a pebble down for each overflow, and the fingers will always count the units. If you were using base eleven, you would count [1,2,3,4,5,6,7,8,9,A],[10,11,12,13,14,15,16,17,18,19],[1A,20...], so a given finger wouldn't always correspond to the same digit.
finger overflow!
(ten plus) one, (ten plus) two, ...
For base ten, you can just put a pebble down for each overflow, and the fingers will always count the units. If you were using base eleven, you would count [1,2,3,4,5,6,7,8,9,A],[10,11,12,13,14,15,16,17,18,19],[1A,20...], so a given finger wouldn't always correspond to the same digit.
But your writing system overflowed before your finger overflow. That's not very intuitive. Each finger represents a unique glyph until suddenly on the last finger it takes two glyphs to represent it.
If you were using base eleven you'd put your pebble down when you hit dec(11) aka base11(10). That pebble represents dec(11). Then first finger would be dec(12) aka base11(11) and once again your first finger represents 1.
So in base11 [1,2,3,4,5,6,7,8,9,A] - pebble - [11,12,13,14,15,16,17,18,19,1A]
A pebble and five fingers would be dec(16) instead of dec(15) but your five fingers still represent 5. The pebble represents 11 instead of 10.
But really, once you're into double digits you normally wouldn't be counting on your fingers anymore. You write 10.
If you were using base eleven you'd put your pebble down when you hit dec(11) aka base11(10). That pebble represents dec(11). Then first finger would be dec(12) aka base11(11) and once again your first finger represents 1.
So in base11 [1,2,3,4,5,6,7,8,9,A] - pebble - [11,12,13,14,15,16,17,18,19,1A]
A pebble and five fingers would be dec(16) instead of dec(15) but your five fingers still represent 5. The pebble represents 11 instead of 10.
But really, once you're into double digits you normally wouldn't be counting on your fingers anymore. You write 10.
This is exactly the system that Robert Forslund advocates as an explanation of certain ancient numbering systems in "A Logical Alternative to the Existing Positional Numbering System" (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.44....).
Oh, base 10 leads to redundancy when finger counting. Because all ten fingers is the same as 0 fingers plus token. Base 11 wouldn't have that problem.
I don't understand "[..] so a given finger wouldn't always correspond to the same digit."
I don't understand "[..] so a given finger wouldn't always correspond to the same digit."
Show me "4*5" in base-(9+1) hands. Now try it in base-(9+2)
show ten fingers, close both fists, show ten fingers.
(ten plus ten)
show ten fingers, close both fists, show nine fingers. (eleven plus nine)
Anyway...there are other alternatives if you're going to attribute the origin of our numeric system to the number of fingers we have. A base 6 system would be really likely as well. One hand could represent the most significant digit, and the other could represent the least significant digit. Then you could easily count to 35 with your fingers before you finger overflow.
Or you could do a binary finger count where every finger represents a different significant digit. Then you're at 1023 before you finger overflow. This is more unlikely given the large number and the unintuitive idea that each finger represents exponentially more value than the previous one. Plus you end up with some really awkward finger positions to represent certain numbers.
But I'm just not buying the idea that base ten is most likely because we have ten fingers. I'd say the base 6 system is best for our fingers. Overflow in one hand just naturally increments the finger count in the other hand. And as with the base eleven or two systems, each finger always represents the same written glyph.
show ten fingers, close both fists, show nine fingers. (eleven plus nine)
Anyway...there are other alternatives if you're going to attribute the origin of our numeric system to the number of fingers we have. A base 6 system would be really likely as well. One hand could represent the most significant digit, and the other could represent the least significant digit. Then you could easily count to 35 with your fingers before you finger overflow.
Or you could do a binary finger count where every finger represents a different significant digit. Then you're at 1023 before you finger overflow. This is more unlikely given the large number and the unintuitive idea that each finger represents exponentially more value than the previous one. Plus you end up with some really awkward finger positions to represent certain numbers.
But I'm just not buying the idea that base ten is most likely because we have ten fingers. I'd say the base 6 system is best for our fingers. Overflow in one hand just naturally increments the finger count in the other hand. And as with the base eleven or two systems, each finger always represents the same written glyph.
A finger is a natural 1, and 45 is 2deci, thus your hands make a natural decimal-base.
Note that when you tried to show base-(9+2), you made a mistake in counting. It looks like you treated "all fingers" as 9+2, and "all but one fingers" as 9. That's inconsistent. Unless you have 6 fingers on one hand?
Note that when you tried to show base-(9+2), you made a mistake in counting. It looks like you treated "all fingers" as 9+2, and "all but one fingers" as 9. That's inconsistent. Unless you have 6 fingers on one hand?
> show ten fingers, close both fists, show nine fingers. (eleven plus nine)
But now the number of fingers you held up doesn't equal the number of items you were counting.
Also, that's not base 11 any more than me holding up 4 fingers 5 times would be base 4.
But now the number of fingers you held up doesn't equal the number of items you were counting.
Also, that's not base 11 any more than me holding up 4 fingers 5 times would be base 4.
"But now the number of fingers you held up doesn't equal the number of items you were counting."
That's true in either case though. Once you finger overflow the real representation is up to interpretation of what came before and what the known base is. That's why (as stated in a previous response) I think base 6 is most appropriate for our hands. You can accurately and naturally represent numbers 0 to 35 with no weird shenannigans.
That's true in either case though. Once you finger overflow the real representation is up to interpretation of what came before and what the known base is. That's why (as stated in a previous response) I think base 6 is most appropriate for our hands. You can accurately and naturally represent numbers 0 to 35 with no weird shenannigans.
I do think it's interesting how so many cultures who were (allegedly) once on the forefront of science and technology have "fallen behind the curve." And no doubt history will continue to repeat itself.
How is calculating in binary easier? I think it's easier to do relatively complex calculations in base10/12 in our head than to write an immense amount of numbers down then trying to work with them further. Wouldn't one page of calculations turn into ten? Or maybe I'm too tired to think straight...
You only have to remember 3 facts for addition: 0+0 = 0, 1+0 = 1 and 1+1 = 10. The last is the only carry situation, further simplifying memorization. THe same thing holds for subtraction, multiplication and division, very few facts to memorize.
I'm guessing that Polynesian civilizations didn't deal with millions and millions of any particular item, so that they rarely did a one page calculation. Indeed, the article claims that "80" is a large number for the ancient Mangarevans.
But this article totally misses out on the real issue - who owns the Intellectual Property of Binary Math? Previously, we thought it was Leibniz, and clearly, we've been paying his heirs for the use of their Intellectual Property, but now we have to trace down the descendants of these fantasically Inventive Mangarevans, and give them the Lion's Share of the money previously given to the (now know to be false) owners of Binary Math Intellectual Property.
I'm guessing that Polynesian civilizations didn't deal with millions and millions of any particular item, so that they rarely did a one page calculation. Indeed, the article claims that "80" is a large number for the ancient Mangarevans.
But this article totally misses out on the real issue - who owns the Intellectual Property of Binary Math? Previously, we thought it was Leibniz, and clearly, we've been paying his heirs for the use of their Intellectual Property, but now we have to trace down the descendants of these fantasically Inventive Mangarevans, and give them the Lion's Share of the money previously given to the (now know to be false) owners of Binary Math Intellectual Property.
It wasn't pure binary. It was a decimal system with three large binary steps superimposed.
I bet they invented polymath.
How does having 10 fingers matter in a base ten system? If we're going by finger count a base11 system seems more appropriate - we'd have a unique symbol for each finger. And that way you can count all the values of the first position with your fingers and you only move to double digit numbers when you run out of fingers.
Anyway, as alluded to in the article, we should be using a base12 system: http://io9.com/5977095/why-we-should-switch-to-a-base+12-cou...