That this is possible at all is counter-intuitive to me, and hence fascinating. Even more fascinating is that he does not have a solution for 10958 in the ascending case.
There's not a lot interesting about "facts about numbers" when you place such a low upper bound on your achievements. If he'd only done this up to 100, he'd never have had trouble finding a solution for 10958. But why 11111? Why not 111111111111?
To me this is just as interesting as any other arbitrary list of permutations of symbols.
Intuitively, this problem seems isomorphic to the famous NP-complete problem, 3SAT[1]. Instead of picking binary states, you have to pick symbols to insert, and where, that yield the desired outcome. If this intuition is true, then if you can write a program to generate these expressions (in polynomial time) then you'd have also proven P=NP. You could probably brute force it though as the difficulty scales with the length of your target number.
I didn't read the article... but why 1 to 9? Is it because we have 10 fingers and 10 symbols that represent numbers? We're this numbers chosen for another reason?
Is that actually why base 10 became the norm? I've never really learned why exactly decimal was chosen, and I'd be interested in learning about what historical evidence there is for its origin.
It's often claimed, but I'm not aware of any strong evidence for it.
In particular, since our hands can show "10" the natural base this would imply is base _11_ and not 10.
Another argument I've heard presented is that since 10 is divisible by 2 and 5 this simplifies many common calculations. There were groups in the past advocating use of other bases (in particular 12 but also 16).
The mayan's number system is base 20 (though the digits are are drawn out of sub digits in base-5).
> Another argument I've heard presented is that since 10 is divisible by 2 and 5 this simplifies many common calculations.
To me, it always seemed like 5 was only a common number because of its place in base 10, not the other way around. There doesn't seem to be any reason that 2 and 5 would have been chosen as more significant than 2 and 3 or 2 and 7.
> The mayan's number system is base 20 (though the digits are are drawn out of sub digits in base-5).
I think I remember learning in school that one of the ancient Mesopotamian civilizations (Sumerian, I think, but I could be wrong) used 60 as the basis for their system because it was divisible by 1, 2, 3, 4, 5, and 6.
11? How so? If I have 10 fingers I can count from 1 to 10. When I start again I count from 11 to 20. Again from 21 to 30. In base 11 it would go 1 to A, 10 to 19, 1A to 28, etc. It doesn't make sense.
Right, but that doesn't really say anything about causation; there is definitely a linguistic link between the body parts and numerical digits in this word, but that could have easily developed after base ten became common for other reasons.
