Alberto Monteiro wrote: > > David Hobby wrote: > > > >>> However, a base 12 counting system would have been much better; > >> > >> No, it wouldn't > > > > Well, a little better. > > > A little worse. > > > Depending how you count, you can > > argue that 12 "has more factors" than 10. This must be worth > > something, since I don't hear anyone pushing for prime bases such > > as 11. Agreed, it's not a big deal. It might be more to make a > > number base feel "comfortable" than a great aid in calculations. > > > The problem with base 12 is that it has _2_ twice and _3_ once > when you factor it, so that the "practical man" rules to check > if a number is divisible by another would get a higher degree > of confusion. Base 6 would be a much better choice than base 12.
I'm not sure what you mean. I don't find the divisibility tests confusing. Some are simpler than others, yes. And we may well disagree on how to compare degrees of simplicity. > I don't see many advantages in base 6 over base 10: > the only one that comes to my mind is that base 10 has simple > rules to check if a number is divisible by 2, 5, 3, 9 and 11; I think the rules for 4,6 and 8 are also simple. (Again, here's a link for background: http://www.jimloy.com/number/divis.htm ) > with > base 6, there would be simple rules for 2, 3, 5 and 7; maybe > losing 11 and gaining 7 could count as a minor improvement. I would say that there are also simple rules for 4, 8, 9 and 10 when working base 6. (This is making base 6 look good. But there should be a way to lift divisibility rules from base 6 to base 12 (=2*6), at the price of adding some complexity.) > OTOH, base 12 would have simple rules for 2, 3, 4, 6, 11 and 13, > and since the base-10 rules for 4 and 6 are one bit less simple > than the rules for 4 and 6 in base-12, we would _lose_ the > rules for 5 and gain the rules for 13 - which is a bad trade. Again, I would count more rules as "simple". I see that you are counting the base 10 rule for 4 as "one bit less simple" than the base 10 rule for 2. Would the base 10 rule for divisibility by 8 be "two bits less simple"? This is fuzzy, as I said. I would count the base 10 rule for 3 as much less simple than the base 10 rule for 8, even. I guess it depends on what size numbers one is expecting to use the divisibility tests on-- I'm imagining large numbers as input. ---David The divisibility by 3 test runs in linear time, Maru. _______________________________________________ http://www.mccmedia.com/mailman/listinfo/brin-l
