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/sci/ - Science & Math

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6520749 No.6520749 [Reply] [Original]

What does /sci/ think about the dozenal system (base 12)?

>> No.6520753

How am I supposed to count with my fingers then?

>> No.6520776
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6520776

>>6520753
>How am I supposed to count with my fingers then?

Use the creases on your fingers where they bend. Some cultures actually do these rather than counting the fingers.

>> No.6520780

base 11 is superior

>> No.6520783

>>6520776
*this

>> No.6520787

>>6520749
I don't know why you think base 12 is good. What would we call this system?

0, 1 -> 10, 11, 12 -> 100, 101, 102, 103, 110, 111, 112, 113, 120, 121, 122, 123, 130, 131, 132, 133, 200, 201, 202, 203, 210, 211, 212, 213, 220, 221, 222, 223, 230, 231, 232, 233, 300,301,302,303,310,311,312,313,320,321,322,323,330,331,332,333->1000,1001,1002,1003,1004...

>> No.6520815
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6520815

based Footfall aliens had base-12 mathematics

>> No.6520820

>>6520749
No better, and in fact objectively worse, than base 6.

Best base in terms of compactness of representation: e. Obviously irrational bases are impractical. So therefore the best base in terms of how efficient the representation is, is 3, followed by 2.

At the point we have two primes, so we can start considering choosing a base that is closest to 3 but that yields a finite expansion of more rational numbers than any previous base. This would give us the next good base as the primorials; 6, then 30, then 210.

12 is nowhere on this list for all the right reasons. 12 is a shit-tier base, no better than 6, probably even worse than 10.

In summary:
3>2>6>30>210
no others need apply

>> No.6520829

>>6520787
digitary base
Why the fuck wou;d you ever do this except for writing a message in code

>> No.6520896

>>6520820
>Trinary
Interesting, what's your logic behind this one?

>> No.6520920

>>6520896
It has to do with the calculation that you use to prove that exp(1) is the "best" base. Under those criteria, 3 is "better" than 2, because it is closer to exp(1) in a specific way.

But there's no need for me to explain it in detail: the blog is dead but archive.org has a copy
http://web.archive.org/web/20131015070453/http://www.burtonmackenzie.com/2007/12/whats-most-optimal-numeric-base.html

>> No.6520927
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6520927

>>6520920
>All the opinions I recall reading on this, though, have suggested that we're currently too deeply ingrained in binary physical implementations such that switching would probably be a bit of a setback given our 50ish years of optimizing for binary implementations. I suspect that if a ternary implementation really is better, it will only get explored if we hit a wall with Moore's Law for our current setup.

Very intredasting. Thanks for that m8.

>> No.6520937
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6520937

>>6520927
It's kind of cool to think about. There were some experiments with base-3 computers in the past:

http://en.wikipedia.org/wiki/Setun

>> No.6520950

>>6520749
>No 1/5

Fuck off. Also <span class="math"> [/spoiler]>Having multiple factors of 2
Fucking retarded. Base 30 or 210 are the only logical choices.