What's a good numerical base?

[KrazyHorse]

Originally posted by Thue
Just for the record, I just proved that no non-integer base can represent all numbers on the continuous number line.

This is not true. Any rational can do it, and many algebraic non-rationals can do it too.

[KrazyHorse]

For example:

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

[Thue]

So where was the error in my "proof"... *looks*

Bugger, I failed to take into account that 11 could be bigger than or equal to 100 .

[Lord Avalon]

Originally posted by Boris Godunov
I'm going to go with Tom Lehrer on this one, and suggest Base 8.

Tom Lehrer

However, base 8 has been done. See Larry Niven's Kzinti, or nonhumans in Wendy & Richard Pini's ElfQuest.

[RGBVideo]

Originally posted by Thue


Good luck memorizing the multiplication tables in that system for calculating without an electronic calculator. Quick, what is 43*57?

Also, good luck memorizing the 50 additional number symbols you will need.

the question was about an alien civilization with presumably higher avg intelligence than humans

also, the latter is actually pretty easy to do

[KrazyHorse]

43*57 is easy because it's a difference of easy squares 2500-49=2451