Decimal/Talk

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Decimal is the number system humans use because of the fact that we have ten fingers.

I heard that some cultures prefered to use the hexadecimal system because they didn't count their fingers on their hands. But instead, they counted with one hand using one thumb to touch on the finger tips and the bends at their finger joints. (There are 16 points on each human hand, hence a hexidecimal system.) However, the decimal system became so wide spread internationally that it dominates now.

I heard about this over twenty years ago from my high school teacher. I don't know his source of this information. I am wondering if any wikipedians out there can confirm this.


If the counting finger-joints technique were more prevailing than counting fingers, human society could have adopted the hexadecimal system which is much better compatible with binary computers nowadays.


The ancient Mayan civilization used base 20 in their numbering system. Their numeric symbols denote values from 0 to 19. (source: http://www.eecis.udel.edu/~mills/maya.htm)


Avoid fallacies in arguments. Just because the people that use decimal do so because they have 10 fingers doesn't mean that all humans use decimal. Nor does it invalidate any of these base 16 or base 20 systems. The article should point out that not all people use decimal (and I will edit it). --drj


I don't think there are any societies that used base 16 though. The highschool teachers story seems suspect. Base 20 is of course fingers and toes. But where does base 12 come from? --AxelBoldt


12 presumably comes from months of the year. Many calendars have 12 months in a year (not just because it is nearly the number of lunar months in a year). Imagine you are an early geek into factors and astronomy. Observe: 360 days in a year, aha! that factorises easily with nice factors like 12, 60, 24, etc. The base 16 claim seems very dubious to me. Fingers and toes didn't occur to me though it is plausible. --drj.


I think the 12, 24, 60 business came from the Babylonians/Persians? Somewhere that direction and long before Greece. --rmhermen I said "geek" not "greek"! Bablylonians/Mesopotamia is the generally agreed source I believe. --drj


Are roman numerals a number system? What is the base?

It's a number system, but not a positional one, so it doesn't have a base. --AxelBoldt

So perhaps the article on number systems should mention it?

Yes it should. --AxelBoldt

In the US weighing system, one pound = 16 ounces. In Chinese weighing system, one catty = 16 taels. Though they are not number systems, but at least it give some hints why the number 16 is involved in measurements universally. In any systems that use division, any power of 2 is a good candidate for convenience sake. For example, a gallon = 4 quarts = 8 pints = 128 fluid ounces = 1024 fluid drams etc.

Looks like human are attracted to the power of 2 and astronmonical periods and our fingers and toes.

A old British pound = 20 shillings one old shilling = 12 pences

20 and 12 can still be explained, but 1 mile = 1760 yards??? how did they come up with that number?

Have you heard the story about how the butt size of the Roman horses decided the rail guage in the current US railroad system?


In decimal counting, the Fibonacci numbers repeat the sequence of the last digit over a period of 60. Every other number system with base less than 14, repeats in less than half of this (often 24).

Base   Period of last digit of Fibonnacci Numbers
  2      3
  3      8
  4      6
  5     20
  6     24  (last two digits too)
  7     16
  8     12
  9     24
 10     60  (unusually big)
 11     10
 12     24  (last two digits too)
 13     28
 14     48

Karl Palmen