Base-12 Math

[uppi]

Maybe instead of trying to use one base representation XOR the other, we could instead employ each representation based on the convenience it lends to the subject at hand?

So that every subfield invents its own base representation to go along with its own unit system?

I cannot think of any advantages that would outweigh the confusion that different base representations would create.

 

[Rashiminos]

So that every subfield invents its own base representation to go along with its own unit system?

I cannot think of any advantages that would outweigh the confusion that different base representations would create.

We should eliminate base-2 entirely. Trinumeracists unite!

 

[warpus]

Base-1 all the way. We have unlimited storage these days anyway. I mean, not really, but what the hell.

 

[Hygro]

144 is a very natural 100 to me. divisible by a lot of nice numbers

 

[Timsup2nothin]

144 is a very natural 100 to me. divisible by a lot of nice numbers

This would be why dozen and gross got their own special names, which are normally reserved for powers of ten. They are too convenient to ignore. Does make one wish we had an extra finger on each hand. Base twelve would have been the norm all along and we could skip this whole base ten system as the comparatively off kilter mess that it actually is.

 

[Kyriakos]

Hm... What relative values do the two unique symbols there have next to the 10 known ones (and their replacement after '5') from decimal?

Furthermore, if we were to benefit from altering numeric systems, wouldn't it be a more potentially helpful idea to replace one with a clear center (5 in decimal, 6 in this one) with one without a clear (integer) center? (eg -including zero- 9 numbers, or seven, evelen etc). Cause juxtaposing similar things usually reveals less info that doing that with non-similar ones.

 

[Borachio]

Base-1 all the way. We have unlimited storage these days anyway. I mean, not really, but what the hell.

Er. Base-1 is what, Mr Soup?

Everything is ONE, I presume. So when you count something the answer is ONE, no matter whether there are 0, 1, 2,... inf. number of instances of it?

I like it. And the operations of addition, subtraction, multiplication and division are very much simpler too. Since the answer will always be ONE.

Spoiler :

1+1=1;
1-1=1;
1*1=1;
1/1=1.

I think, maybe, purists would use 0 instead of 1. I don't know though. I've not encountered Base-1 before.

0+0=0;
0-0=0;
0*0=0;
0/0 =0.

Yeah, that makes a bit more sense.

But I can't help thinking it's not very useful.

Spoiler :

Now, I bet you mean Base-2.

 

[Kozmos]

Why not go for Base 69 or Blase 420

 

[Kyriakos]

Blase

 

[warpus]

Er. Base-1 is what, Mr Soup?

In base 1 you can only use 1 symbol:

1 = 1
2 = 11
3 = 111
4 = 1111
5 = 11111

and so on.

Contrast this with base 2 - you can now use 2 symbols:

1 = 1
2 = 10
3 = 11
4 = 100
5 = 101

etc.

 

[CKS]

I don't see anything in the charts that makes base 12 easier or better (the only thing that looks easier is angles for fractions of a circle, and that has also redefined the size of the degree, so it doesn't count).

Now, base 8 has advantages for fractions&decimals, as 1/2, 1/4, and 1/8 now have only a single decimal place. Think how much better it would be if we hadn't used our thumbs for counting.

 

[Perfection]

The real benefit of base 12 is that division by 3 or a power of 3 never results in continued fractions.

Octal is far inferior to hexadecimal because 8=2^3 whereas 16=2^2^2, that property makes it far more useful for binary based computers.

 

[Borachio]

In base 1 you can only use 1 symbol:

1 = 1
2 = 11
3 = 111
4 = 1111
5 = 11111

and so on.

Contrast this with base 2 - you can now use 2 symbols:

1 = 1
2 = 10
3 = 11
4 = 100
5 = 101

etc.

OK. Then that's just like Roman Numerals without the refinements of V and X etc. But where's the identity element in base-1?

 

[Gori the Grey]

How does one turn a speaker up to eleven in a base-12 system?

 

[Borachio]

Well. At the risk of stating the obvious, 13?

 

[Gori the Grey]

Is that even louder than 11 on a base-10 speaker?

'Cause then I'm all for it.

Or is 12 to 13 a slightly smaller increase than 10 to 11?

'Cause then I'm against it.

 

[Borachio]

I think it has to be slightly quieter in proportion. But clearer louder as an absolute.

I mean. 13 is just plain bigger than 11, isn't it?

Well, it always used to be. Plus you get to annoy the heck out of the tridecaphobics. That's got to be bonus, imo.

 

[Gori the Grey]

Then I don't know how to feel. Because you want your (base-10) 11 for those times when you want to kick it up, so I want my kick to be as substantial as possible.

But what I'm trying to kick it up in is volume. So I want my volume to be as loud as possible.

Quite a quandry.

The bit about tridecaphobes might help resolve the quandry. Particularly if 13 is Satanic. But do base-12 tridecaphobes fear 13? Or 15? Or some other number?

 

[Perfection]

Of positive integer bases binary of course would provide the biggest bump from 10 to 11 a full 50% boost.

However I would consider ternary as well because you still get a substantial 33% boost and 11 is 4 which is death. And what's more black than turning your amps up to death? None more black!

 

[Borachio]

But do base-12 tridecaphobes fear 13? Or 15? Or some other number?

Frankly I don't know.

But I don't see why not. It doesn't matter what the base is. 13 is still 13.

Er. If you see what I mean. Hang on. I've got to work this out.

Spoiler :

0,1,2,3,4,5,6,7,8,9,A,B.

13 in base 12 is 11! (Now, why did I need to work that out? It should have been obvious to me.)

But it's still 13 really. We just call it 11. (Or 1 mod 12. Or something.)

But there's your 11. Again!