There is the argument that mathematics would be further along had mankind adopted the base 12 or base 60 number system.

]]>2. It's arbitrary from the point of view of numbers. Aliens with 6 fingers quite probably will have a base-6 number system. But the math remain the same.

3. Just the semantics will change not the actual math, but even then they will look prettier. Of course the drawback is you have to revert all past papers written in the decimal system.

4. Compact length. Numbers in the binary are lengthy while for larger bases you progressively gain more compact displays. This argument is thus in favor of the duodecimal compared to decimal.

You have a point in 1. and 3. but they are historical reasons and not mathematical. It's like the transition (but not as important) to having zero, if people weren't willing to change math would suffer.

True reasons about the drawbacks of the duodecimal system are that it doesn't divide perfectly 5, though dividing 3 is a greater advantage, and you have to memorize more multiplications. However, the paper I cited describes why in the end it is better that the decimal. It is not by chance that Leibniz and Pascal supported it.

]]>well it's very nice that you are for the duodecimal system,but there are four problems that come out if we look at it:

1.People are used to counting and doing math in the decimal system and we would have to wait the next generation to apply that number system.

2.People based the decimal system as you might know on the number of fingers on both hands together.it's more intuitive to start doing math in the decimal system.It's not arbitrary!

3.We would have to redo math! Most of today's math especially the fields which use numbers in any way would have to change their theorems and everything.

4.you said yourself that the binary system may be a little better than the decimal in some way.so then why is it not better than the duodecimal?

So you see you're not totally wrong but you're not totally right either.it's like the argument between which is better e or pi.there's just no way to tell the winner but since they became competition at the same time the race between them will be a tight one,but the decimal system has already beaten many other,like the base 60 number system and the hexadecimal system.Still i agree that the binary system is better in simple math than both because it has less symbols and it might be better in the elementary math like addition and subtraction and such stuff,but it might not be as simple in calculating the integral of x^1101 as x goes from 1010010 to 1011011.

]]>you're welcome.i find those interesting,and wonder why mathematicians don't care about them at all.

Apart from topology (why?), maybe it's that these numbers are dependent on the decimal base system which is arbitrary.

Maybe only the binary system might offer some insight whenever the number base is directly involved due to it being the minimal base available.

I'm an advocate of the duodecimal (12) system. We lose perfect division with 5 but gain that with 3, 4 and 6. Especially 3, it is a more important prime factor than 5 since it comes earlier. Google The Case Against Decimalisation pdf.

]]>i will always remember them...

also...prime numbers don't seem interesting at first glance,but now they have infected the number theory world...:)

]]>Thanks for the link!

]]>