9 ms·

I would prefer base-12; it has a lot of benefits. See http://en.wikipedia.org/wiki/Duodecimal http://en.wikipedia.org/wiki/Duodecimal, especially http://en.wiki

I would prefer base-12; it has a lot of benefits. See http://en.wikipedia.org/wiki/Duodecimal http://en.wikipedia.org/wiki/Duodecimal, especially http://en.wikipedia.org/wiki/Duodecimal#Comparison_to_other_numeral_systems http://en.wikipedia.org/wiki/Duodecimal#Comparison_to_other_... Instead of changing our clocks, we could just change our numbering system. Having 50 (that's 5 x 12) seconds per minute, 50 minutes per hour, and 20 hours per day seems perfectly reasonable.

baddox 16y ago
Choosing a radix is a balance between the number of prime factors (and brevity) and the number of symbols to keep track of. I think twelve strikes a good balance as well.
- zeteo 16y ago
  But 12 only gains you one more factor that's not a power of 2, and is 30 times more difficult to implement (operation tables have 144 cells for base 12, compared to 4 cells for base 2).
  - eru 16y ago
    That's why you should use the digits -n/2 to +n/2 for base n. That shrinks the tables by a factor of four.
    - zeteo 16y ago
      Oh no, I just knew someone would come and argue for balanced n-ary on this thread :)
- ars 16y ago
  In that case 3 is your number. (Because it's the closest number to e, 2.71) There is a currency based on it (with the provably least number of coins necessary to make any kind of change), ternary logic, balanced ternary is especially cool, etc.
  - pavel_lishin 16y ago
    Why is being close to e a good thing?
    - eru 16y ago
      Actually, the best number depends. Basically, you want to have as few operations as possible, but you also want them easy. Having base b for number n, you need log_b n digits where each digit is an element of (0..b-1). So working on those representations takes something like f(log_b n, b) operations. Where the function f depends on the operation you are looking at. A good base should keep f small in relation to all n. One very natural choice for f, I can't remember which at the moment, leads to e being the best base in theory---so 3 being good in practice. If you are working with something like trees on disk (yes, data structures are very intimately related to numbering systems---read Okasaki's Purely Functional Data Structures for more information) a very big b, i.e. branching factor in this case, like 1024 is useful: Loading a new digit/node from disk into memory takes a long time, but once it's in memory, your operations will be fast.
eru 16y ago
I'd like to use base-11. Prime numbered bases eliminate lots of special cases.

baddox 16y ago

Choosing a radix is a balance between the number of prime factors (and brevity) and the number of symbols to keep track of. I think twelve strikes a good balance as well.

zeteo 16y ago
But 12 only gains you one more factor that's not a power of 2, and is 30 times more difficult to implement (operation tables have 144 cells for base 12, compared to 4 cells for base 2).
- eru 16y ago
  That's why you should use the digits -n/2 to +n/2 for base n. That shrinks the tables by a factor of four.
  - zeteo 16y ago
    Oh no, I just knew someone would come and argue for balanced n-ary on this thread :)
ars 16y ago
In that case 3 is your number. (Because it's the closest number to e, 2.71) There is a currency based on it (with the provably least number of coins necessary to make any kind of change), ternary logic, balanced ternary is especially cool, etc.
- pavel_lishin 16y ago
  Why is being close to e a good thing?
  - eru 16y ago
    Actually, the best number depends. Basically, you want to have as few operations as possible, but you also want them easy. Having base b for number n, you need log_b n digits where each digit is an element of (0..b-1). So working on those representations takes something like f(log_b n, b) operations. Where the function f depends on the operation you are looking at. A good base should keep f small in relation to all n. One very natural choice for f, I can't remember which at the moment, leads to e being the best base in theory---so 3 being good in practice. If you are working with something like trees on disk (yes, data structures are very intimately related to numbering systems---read Okasaki's Purely Functional Data Structures for more information) a very big b, i.e. branching factor in this case, like 1024 is useful: Loading a new digit/node from disk into memory takes a long time, but once it's in memory, your operations will be fast.

eru 16y ago

I'd like to use base-11. Prime numbered bases eliminate lots of special cases.