While not intended to be used mathematically, the I Ching hexagrams developed around 1000AD represented the binary numbers from 0-63 (2^6), as discovered by Leibniz who was quite fond of binary himself.
Polynesian people used a kind of binary number system 600 years ago (2013)
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Re: Polynesian people used a kind of binary number system 600 years ago (2013)
#12Computers use base two because their most natural unit can occupy one of a couple states: 0 or 1. One, two, base two. Human hands, on the other foot, have ten fingers. Since our favorite mapping between things and integers is finger counting, we naturally end up with more than two states. Zero, one, two, three, four, five, six, seven, eight, nine, and the fully-extended state, ten. That's eleven states, which is why…
Zero was introduced well after base ten was in use.
Re: Polynesian people used a kind of binary number system 600 years ago (2013)
#13Of course, we all know what they would have used if they were real pros:
Re: Polynesian people used a kind of binary number system 600 years ago (2013)
#14Earlier quoted context omitted.
Imagine you had two fingers and not ten. Try counting in binary. That should clear up the anomaly.
You can count from zero to two on two fingers, so two-fingered aliens may invent numerals for zero, one and two. If they develop that into a place value system, it will be (fingers+1)-ary, or in their case trinary.
you can count from zero to three :)
Re: Polynesian people used a kind of binary number system 600 years ago (2013)
#15The ability of the Polynesians to settle huge stretches of the Pacific might be one of the most impressive human achievements ever. Odds are they reached South America even if we never find direct evidence (there is some).
There's a study that found Polynesian DNA markers in indigenous Brazilian remains. It's probably what you are referring to by the some evidence. https://www.nature.com/news/dna-study-links-indigenous-brazi...
I've visited Mangareva. It's a lovely island and a step in the journey to get to Pitcairn Island.
Re: Polynesian people used a kind of binary number system 600 years ago (2013)
#16The ability of the Polynesians to settle huge stretches of the Pacific might be one of the most impressive human achievements ever. Odds are they reached South America even if we never find direct evidence (there is some).
> Odds are they reached South America even if we never find direct evidence (there is some).
Isn't sweet potatoes in Polynesia (which originated from South America) pretty much a proof?
Re: Polynesian people used a kind of binary number system 600 years ago (2013)
#17They find that the former Mangarevans combined base-10 representation with a binary system. They had number words for 1 to 10, and then for 10 multiplied by several powers of 2.
Interesting. Perhaps this is the very first use of binary-coded-decimal?
Re: Polynesian people used a kind of binary number system 600 years ago (2013)
#18Of course, we all know what they would have used if they were real pros: https://en.wikipedia.org/wiki/Factorial_number_system
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Re: Polynesian people used a kind of binary number system 600 years ago (2013)
#19Computers use base two because their most natural unit can occupy one of a couple states: 0 or 1. One, two, base two. Human hands, on the other foot, have ten fingers. Since our favorite mapping between things and integers is finger counting, we naturally end up with more than two states. Zero, one, two, three, four, five, six, seven, eight, nine, and the fully-extended state, ten. That's eleven states, which is why…
Fully extended is one set over none extended: base ten.
It makes sense if you think of all of them extended as a set, rather than one less than a set. And so by the time positional notation came around, it was cemented that all of them extended was a set. (It took us a while to get 0 and positional notation.)
Just look at Roman numerals:
A finger. A hand. Both hands. A hand representing both hands. Both hands representing both hands. Etc.
Re: Polynesian people used a kind of binary number system 600 years ago (2013)
#20Computers use base two because their most natural unit can occupy one of a couple states: 0 or 1. One, two, base two. Human hands, on the other foot, have ten fingers. Since our favorite mapping between things and integers is finger counting, we naturally end up with more than two states. Zero, one, two, three, four, five, six, seven, eight, nine, and the fully-extended state, ten. That's eleven states, which is why…
It's been speculated that prior to base ten (or maybe alongside it) people used base twelve (using knuckles) hence anachronisms like dozens (inches, hours), 60 (minutes) and 360 (degrees), etc.