Originally posted by wolfgang59Oops, my mistake. Two hands. 12x2 + 2x2.
3x4 on EACH hand using fingers,
use one hand for units
use other hand for '12's
that gives a possible 12x12 = 144.
I guess 156 includes using the thumb on the '12's hand??
But if you're going to use one hand for units, then isn't it 14x14? And just using fingers it's 5x5.
Originally posted by AThousandYoung12 is a much friendlier base than 14. I was only GUESSING how the original poster got 156. the natural answer is 144 of course but then you would be left twiddling your thumbs ....
Oops, my mistake. Two hands. 12x2 + 2x2.
But if you're going to use one hand for units, then isn't it 14x14? And just using fingers it's 5x5.
😀
Originally posted by wolfgang59Maybe a previously unknown mutation had occured in ancient Babalonia that left everyone with 6 fingers on each hand instead of 5.
12 is a much friendlier base than 14. I was only GUESSING how the original poster got 156. the natural answer is 144 of course but then you would be left twiddling your thumbs ....
😀
BTW, in India, the time count for music there uses the knuckles of the hand to count up to 16 with emphasis on certain beats. Sounds like the same kind of thing the ancients used for counting stuff not time.
Originally posted by nihilismorYou're both wrong. Apparently they used base 60,
This is coincides with what I've turned up. However, I have read that they worked with a base 30 system (not 12) which contradicts the website cited earlier in this thread.
http://www-history.mcs.st-andrews.ac.uk/HistTopics/Babylonian_mathematics.html
Sorry, out for a while.
Clarifying: You use the thumb as a pointer to 'count'. So its still counting pyhsically using your hand. So you notch your thumb to your knuckles and that will indicate what number you are in your singles digits.
The 156 comes from combining the 2nd digit hand and 1st digit hand. 12x12 on the 2nd digit hand=144. Then you can count to 12 on your single digit hand. 144+12=156.
I had some reasonable answer to explain base 60 following this counting scale, but I don't remember it. Meh. thinking outside of base 10 hurts me anyways.
Originally posted by tamuziThe Babylonian's used base 60.
Isn't 360 an adoption from the babylonian Base-12 system. Not to mention that so many numbers go into 360.
The history on the babylonian base-12 is related to counting with the segments on each finger (4*3) So you could count to 156 on your two hands instead of our minuscule 10.
I find wikipedia good for mathematics but for history of maths there is a better site.
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_numerals.html
As noone knows why base 60 was used I prefer the explanation that they went for 360 days in the year and partied hard for the missing days. I don't believe it but a good story can be more fun than the reality.
Originally posted by deriver69...I quoted it first!...
I find wikipedia good for mathematics but for history of maths there is a better site.
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_numerals.html
As noone knows why base 60 was used I prefer the explanation that they went for 360 days in the year and partied hard for the missing days. I don't believe it but a good story can be more fun than the reality.
Originally posted by deriver69One possible reason for using base 60 is that it makes it easier to mentally calculate a wider range of divisions than base 10.
I find wikipedia good for mathematics but for history of maths there is a better site.
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_numerals.html
As noone knows why base 60 was used I prefer the explanation that they went for 360 days in the year and partied hard for the missing days. I don't believe it but a good story can be more fun than the reality.
The ease of calculating divisions is related to the number of prime factors of the base. 10 has two prime factors (2,5), 60 has 3 (2,3,5).
The same reasoning might explain why 360 was chosen for the number of degrees in a circle. If we wish to split a circle in thirds, for example, we can simply place 120 degrees in each third. If the circle had, for example, 100 degrees in it then we could not split it into three equal portions using a whole number of degress.
Originally posted by deriver69It is indeed. I'm actually at St Andrews doing maths at the moment, and I sat through a lecture course last year which was basically based on this site (lectured by those who wrote it). It was really interesting, and for some reason I've subsequently spend quite a lot of time browsing this site. Curiously, I found a few papers to read this way that are helping me with my dissertation...
So you did, it is an excellent site isnt it
It may well be that several of the reasons for using 360 were considered whenever they decided upon 360 degrees for a circle.
I like the year calendar one best however, as the divisibility argument could be used for picking 60 or 120 degrees whereas a year in days suggests 360 specifically.
(I don't doubt in the slightest, though, that divisibility played an important role, however)