[benjer3]

This has been on my mind for a while, and I would like to see what others think.

What would be the best numeral system for everyday use? Of course, some systems are better in certain situtaions, as in binary for computer logic, but isn't the only reason we use a decimal system that that's how it has (virtually) always been done? Did it only arise because we have ten fingers and ten toes?

I personally believe that the qualifiers of a good system would be that there aren't too many or too few digits and that "ten" is easily divisible by common numbers. Specifically, I like the thought of using an eight- or twelve-based system. I believe that a thirty-based system would work very well because it can be divided by the three lowest prime numbers, but it would have far too many digits.

[Quag]

perhaps non base 10 would be workable. but when learning mathematics base 10 is by far the easiest for a child. My daughter is in grade 2 and still uses her fingers for math and is one of the strongest in her class. I can't imagine trying to teach non based 10 to my son. The concept of adding and subtracting is hard enough to learn. Perhaps base 5 would work as it would be 1 hand but base 10 seems far supoerior to base 5 to me.

[unreality]

What about octal? It's more that much more divisible than base 10 (10 divides 1,2,5,10 ... 8 divides 1,2,4,8) but as a power of 2 it has certain advantages to use as a base system.

The reason I say that instead of a more factorable system like duodecimal (12 divides 1,2,3,4,6,12) or sexagesimal like the Babylonians used (60 divides 1,2,3,4,5,6,10,12,15,20,30,60) is because the octal system would be easy to learn for kids. If you just stick your hands out in front of you and tuck your thumbs under your palms, there ya go, you have digits 0-7.

But it's not that worth it since octal doesn't really provide that many more advantages over decimal (it's actually less efficient in terms of how many digits, requiring something like log(10)/log(8) times as many digits), other than breeding a future generation of good programmers because of how easy it'd be to convert to binary or hexadecimal

I'm a fan of going back to sexagesimal if everyone can remember a bunch of symbols. I think binary is the most 'pure' but sexagesimal is on the opposite end of the spectrum. Think about doing fractions in sexagesimal, it'd be very easy, much easier than base 10.

"one third" in decimal = 0.3333333333333333333333333333333...etc

"one third" in sexagesimal = 0.[20] where [20] is a single digit representing our decimal "20"

lots of other fractions could be expressed conveniently without so many repeating digits:

fraction :: sexagesimal version

1/2 :: 0.[30]

1/3 :: 0.[20]

1/4 :: 0.[15]

1/5 :: 0.[12]

1/6 :: 0.[10]

1/7 :: 0.[8][34][17]...(repeats those 3 digits forever) ... this one is gonna be messy no matter what base system is used pretty much

1/8 :: 0.[7][30] (think [7.5] being half of [15] which is 1/4)

1/9 :: 0.[6][40] (think [6 + 2/3] being a third of [20] which is 1/3)

1/10 :: 0.[6]

etc. I'd rather teach a kid sexagesimal fractions than decimal versions. Then again the major drawback is having so many symbols. So I'm gonna have to go with binary... its purity is appealing, despite being the most inefficient (digits per number) of the systems

[benjer3]

I'm a fan of going back to sexagesimal if everyone can remember a bunch of symbols. I think binary is the most 'pure' but sexagesimal is on the opposite end of the spectrum. Think about doing fractions in sexagesimal, it'd be very easy, much easier than base 10.

Yeah, that's the main reason I've thought of base 12 and base 30. 2, 3, and 4 are very common numbers, so duodecimal or even sexagesimal would work well with that. I think the main reason 5 is so common is the decimal system and our fingers. With that and number of characters, I like duodecimal the best.

Not that I'm saying that we should change. I like decimal , too. It would be virtually impossible, anyway. Quag is right about teaching it, though I've read that ancient Egyptians counted in base 12 by counting the finger knuckles with the thumb.

[Guest]

i've always been a fan of the balanced ternary system.

it's simple, and very easy to work in (admittedly, division can be a bit tricky).

mathematically it's the most effiecent number system, short only of base e.

basically i imagine a dollar that increased by powers of 3, and by allowing trade, you essentially have balanced ternary.