Base 10 Number System Explained

[mtanti]

I read that we use a base 10 number system because we have 10 fingers. What does that have to do? If that was the case then we would use the 10 symbol digits (0-9) when counting on our fingers and not start form 1 and end at 10.

 

[CRGreathouse]

The most common base systems used in the world's languages are (in order): base 10, corresponding to the number of fingers; base 20, corresponding to the number of fingers and toes; and base 5, corresponding to the number of fingers on a hand. This alone makes a case for the digit-base connection. (Heck, the "digit" of a number and a "digit" of a person are even the same word in English.)

The idea that 0 is a number is a revolutionary idea and is newer than the development of language.

 

[mtanti]

Yes but you are not using your fingers as the set of numbers unless one of them is zero. It's like a base 9 system, starting from 1 till 9 and then introducing a new magic number to continue counting... I don't think this extra digit, zero, comes from the fact that we have 10 fingers.

 

[arildno]

The number "10", in ANY base system, is its own BASE REPRESENTATION of the base number itself. What's your problem here?

 

[CRGreathouse]

I don't think this extra digit, zero, comes from the fact that we have 10 fingers.

The concept of "ten" is much older than the concept of "zero", which is itself older than the concept of positional notation.

 

[mtanti]

So how did the concept of base ten notation take off from the fact that we have 10 fingers?

 

[CRGreathouse]

So how did the concept of base ten notation take off from the fact that we have 10 fingers?

Breaking numbers up into powers of ten seems to have been recursively putting objects in bijection with the number of fingers: ten objects <--> ten fingers, ten groups of ten fingers <--> ten tens <--> one hundred, one hundred groups of ten fingers <--> ten hundreds <--> one thousand. Th Greek 'coded' number system shows rather direct influences of this concept (e.g. "nine hundred" was represented with a single symbol).

The base-10 positional system was based on the fact that 10 was already the basis for the spoken language.

Here's a link (found on the Phrontistery) about the origins of numeration:
http://www.scit.wlv.ac.uk/scit/modules/mm2217/intro.htm

 

[mtanti]

So base 10 originated after each finger was given a numbered name and then it developed? Why wasn't 10 expressed as 1 digit then?

Could it be that the first time a list of numbers was written it was like this:

1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
etc

and the modern way to list numbers is like this:

00 01 02 03 04 05 06 07 08 09
10 11 12 13 14 15 16 17 18 19
etc

which means that at the introduction of zero, the list was shifted forward?

 

[CRGreathouse]

So base 10 originated after each finger was given a numbered name and then it developed? Why wasn't 10 expressed as 1 digit then?

1. Speech originated long before writing. Fingers weren't always given numbered names, although by my understanding this was common in South America, but the collection of fingers typically corresponded to a short name.*
2. In many systems 10 is expressed as a single digit. It was a coil in ancient Egyptian (medju), $\iota$ (iota) in ancient Greek and X (ex) in classical Latin. In fact, reprsenting 10 as more than one symbol was pretty rare until fairly recently. In Europe it didn't really happen until Leonardo Fibonacci introduced Hindu-Arabic numerals.

* I've already mentioned base-5 and base-20 systems. In fairness, I have heard of a duodecimal (base-12) system, as well as a system that is essentially base-100, but I've only heard of one of each of these as numeration systems. There is some evidence that Proto-Indo-European was base-12, which would explain words like "dozen" in Germanic, Italic, Celtic, and Cyrillic languages.

 

[CRGreathouse]

Could it be that the first time a list of numbers was written it was like this:

1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
etc

and the modern way to list numbers is like this:

00 01 02 03 04 05 06 07 08 09
10 11 12 13 14 15 16 17 18 19
etc

which means that at the introduction of zero, the list was shifted forward?

No, not really. The development of zero as a number and of positional number systems happened in historic times, so we know almost precisely how it happened. (This is in contrast to the development of most languages, which must be reconstructed since they are older than writing.)

The first form of number writing would probably have been chits or tallies. Knots, as used by the Inca, may also have been used early on. Carvings in wood and stone were early records of numbers (only the latter generally surviving, of course); clay tablets were also used in Mesopotamia. Certainly none of these used digits as we know them.