So I'm a humanities/arts kind of guy, on the opposite side of the spectrum from math, so forgive me if this is a bit simplistic.

Anyway, I've been working with post-tonal music lately, where notes are based on a 12-tone chromatic system, rather than the scale centered 7-tone system. Everything is dealt with in integers between zero and e (11).

Basically, it got me thinking about why we base our number system around 5. We have 0-9, and then start the cycle over again with 10, a two digit number. When you have nine apples and add a tenth, nothing special happens. I'm not questioning the laws of math, because when you have two whole things and add two more whole things, you always have four whole things. I'm just curious as to why the rollover starts with ten.

Is it because of our hands? We have five fingers on each hand obviously. Or is there another reason why we have a number system based on 10?

The laws of math don't change when you label things differently. Say we have 0 1 2 3 4 5 6 7 8 9 $ 10. The "$" represents what we know as ten, so 5+5=$ and we start the cycle over again after that. The laws of math would still function properly, we're just notating how we perceive numbers differently, no?

I always assumed it was based on like, hands. I don't know enough offhand to really confirm or deny that changing to base-12 math or whatever would change anything, though I assume Bolt does

Umm...we use a base 10 system...

It's probably due to our fingers, yes, though perhaps the real reason someone thought of it (as opposed to it just happening in a more primitive fashion) is lost to us.

But yes, all numbers we use are just symbols. And besides a possible spatial or psychological advantage in using base 10, there's nothing really special about it.

And people involved in computers, especially very low level programming and hardware, need to get used to base 2 and base 16 (and I hear 8, but I rarely see that). You can have any base you really want, you just need to think up a unique symbol for each digit you want.

Yeah, I feel like base 8 would be much more elegant. It would still provide a reasonable size for numbers we deal with, and 10, 100, etc would all be divisible by 2 and 4 and 8 and, as you go up, more powers of two.

I think the 10 based system was developed before people even thought about multiples.

Hex is not too bad.

The reason for bases 8 and 16 is that it is incredibly easy to convert to binary. 16 is still better than 8 due to the arbitrary byte size convention, where 2 hex digits happens to be a byte on all modern machines.

I'm not even speaking in terms of computers, I just think the base being more factorable is ideal.

I just had a lecture about this in math. We could calculate in any base, but the hindu-arabic system was the best against its rival, the roman numeral. There was also the mayan system used in America, which was base 20 that had place values of 1, 20, 360, and 7,200.

Since we naturally count on our fingers as children, however, base 10 makes the most sense.