Why have we chosen our number system to be decimal (base 10)?

Expanding on the comment by J.M., let me quote from the (highly recommended) book by Georges Ifrah The Universal History of Numbers (Wiley, 2000, pp. 21-22):

Traces of the anthropomorphic origin of counting systems can be found in many languages. In the Ali language (Central Africa), for example, "five" and "ten" are respectively moro and mbouna: moro is actually the word for "hand" and mbouna is a contraction of moro ("five") and bouna, meaning "two" (thus "ten"="two hands").

It is therefore very probable that the Indo-European, Semitic and Mongolian words for the first ten numbers derive from expressions related to finger-counting. But this is an unverifiable hypothesis, since the original meanings of the names of the numbers have been lost.

Ifrah then goes on to explain that

...the hand makes the two complementary aspects of integers entirely intuitive. It serves as an instrument permitting natural movement between cardinal and ordinal numbering. If you need to show that a set contains three, four, seven or ten elements, you raise or bend simultaneously three, four, seven or ten fingers, using your hand as cardinal mapping. If you want to count out the same things, then you bend or raise three, four, seven or ten fingers in succession, using the hand as an ordinal counting tool.


I think the answer here might be, that the guys who thought base 10 was a good idea had the largest sticks.

If one trusts the wikipedia, the Babylonians had a base 60 system, which can still be felt today with this "60 minutes in an hour" nonesense, and a (related) base 12 system was widely in use too. There are still unique words for "eleven" and "twelve", as well as expressions as "a dozen". After all, you can count to twelve using a single hand.

Then, there was the base 1 latin system, and (wikipedia again) a base 20 system for the mayan.

Something as easy as "base 10 is natural for humans" does not explain it all. =)


Because it makes the metric system so much simpler :).

Tags:

Number Systems

Related

Eleven unit squares inside a larger square Algorithms to find simple closed curves on a surface Finite rings of prime order must have a multiplicative identity Number of common divisors between two given numbers How do you go about doing mathematics on a day to day basis? Proving: $\cos A \cdot \cos 2A \cdot \cos 2^{2}A \cdot \cos 2^{3}A ... \cos 2^{n-1}A = \frac { \sin 2^n A}{ 2^n \sin A } $ Prove that $\prod_{k=1}^{n-1}\sin\frac{k \pi}{n} = \frac{n}{2^{n-1}}$ $|G|>2$ implies $G$ has non trivial automorphism If $a > b$, is $a^2 > b^2$? Similar matrices have the same eigenvalues with the same geometric multiplicity Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem) Discriminant of a monic irreducible integer polynomial vs. discriminant of its splitting field

Recent Posts