# Base 10 math

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#### bdewoody

##### Guest
I wonder if the only reason we generally use base 10 math is because we have 10 fingers. So if we had evolved with eight digits would we be using base 8 or does base 10 have some deeper significance in mathematics.

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#### Mee_n_Mac

##### Guest
bdewoody":kui9x39u said:
I wonder if the only reason we generally use base 10 math is because we have 10 fingers. So if we had evolved with eight digits would we be using base 8 or does base 10 have some deeper significance in mathematics.

My guess is your guess is as good as any. That is we use base 10 because we have 10 fingers. But others used other systems, the Mayans used base 20 (fingers and toes ?) and I think the Babylonians used something else again. The Greeks used 1- 9 but then had 10, 20, etc. What's that make their system ?

Had we evolved to have 8 fingers we'd be using octal ... or hex perhaps.

A

##### Guest
I wouldn't know - I think in Base 16.

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#### a_lost_packet_

##### Guest
bdewoody":xca5g8tp said:
I wonder if the only reason we generally use base 10 math is because we have 10 fingers. So if we had evolved with eight digits would we be using base 8 or does base 10 have some deeper significance in mathematics.

Well, thank the Romans.

If someone else with a different base system had conquered the known world, we'd likely be using theirs.

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#### bdewoody

##### Guest
a_lost_packet_":1w1vya9x said:
bdewoody":1w1vya9x said:
I wonder if the only reason we generally use base 10 math is because we have 10 fingers. So if we had evolved with eight digits would we be using base 8 or does base 10 have some deeper significance in mathematics.

Well, thank the Romans.

If someone else with a different base system had conquered the known world, we'd likely be using theirs.
Actually I think in this case we have the Arabs to thank. Roman math had no zero. That concept was introduced by arab mathematicians, also negative numbers.

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#### SJQ

##### Guest
Apparently, the Babylonians (it might have been another group in that area/around that time) used base 12, derived from the number of knuckle bones of the four fingers on one hand. The thinking is that it was easier for the sheep-herders to count their flock - more counts per hand.

Base 60 was also used, but it is an extension of base 12. 60 has a lot of integer divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30), which was useful in a pre-floating-point world. Another extension, to 360, made dividing circles easier for survey and astronomy purposes. We still use remnants of these systems: 60 seconds = 1 minute; 60 minutes = 1 hour; 360 degrees equals one full turn, demonstating the utility of the bases.

During the initial development of the metric system, the French tried to rationalize the circle, by dividing a right angle into 100 "grads" (360° = 400 grads) instead of 90°, but aside from a few specialized fields (surveyors, I think, may use the grad, but I don't know of anyone else), grads didn't catch on.

I think the resistance to grads was largely because of the British Admiralty's development of circumnavigation techniques. The earth turns 360° in 24 hours, thus an hour is 15 degrees (360/24). When you are determining longitude by comparing local noon (measured with a sextant) against an accurate clock (chronometer) set to Greenwich Mean Time (GMT), the arithmetic was simpler with degrees than grads. Remember, we are talking of a period from the early 1700's to the mid 1900's - there were no calculators, and definitely no GPS. Navies and air forces still teach navigation by these techniques - it is "Plan B" for when the "electrickery" goes south on you.

SJQ

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