" I've read that innovation company 3M have a similar policy to encourage the exceptional stuff that turns up from time to time with the crazy stuff "

Sure, but they also have a distillation process. That was my point.

" I like the 0.1 as one third (you wrote one tenth but surely it is one third) in base three "

You are confusing things. 0.1 *means* one third in base three, just as 10 means three. "One tenth" in base three is an irrational number just like one third in decimal. There's a lesson to be learned here: we should be careful not to make too much of paradoxes, more often than not they betray the fact that we are approaching the problem from the wrong angle.

One day I'd like to discuss an invention of mine, the exponential number system. It consists of treating all numbers as logarithms, which transforms all multiplications into sums and gets rid of infinities once and for all. As a bonus, it gets rid of the fact that there are more 1s than 9s in the world (there's a name for that, I forgot what it is) It's pretty cool, maybe some day I'll bring it up.

Have fun,

Aurino