amused
gwengothelf is evidently bored at work today - and I'll let her explain what she has been thinking about:[QWP, Friends-Locked post]
"At work today, the idea came up of counting to large numbers on your fingers, the arbitarily chosen number being 1,000,000.
So, I worked out that if you assume all 10 fingers have 3 possible states (straight, bent, down) then you can represent 3^10 (59049) discrete numbers on your fingers. This assumes 8 fully motile fingers and 2 thumbs. People who don;t have high digital dexterity might have problems with this, but playing piano or guitar will hell with the ring finger independence. I thought about doing something with different bending angles or bends at different joints, but my fingers just don;t work like that!
So, I could count to 59,049 on my fingers. That's pretty cool, but not 1 million, so I had to expand that. On to toes.
Toes present a bit of problem, nowhere near as independently motile as fingers, I eventually settled into dividing each foot into 2 - big toe and rest of toes, each having 2 states (curled and uncurled) giving an extra 2^4 (16) states on top of the fingers. This now gives us a method of representing (2^4)*(3^10) discrete values.
Wow! That's 944,784 different values - that's a big number using only my digits and no external mechanisims.
Still, it's not 1,000,000 though... so I had to find more ways of representing numbers. I dismissed head position as you would need to watch your digits, so added eyebrows.
Although I have 2 independently motile eyebrows, only one more 2 state representation is needed, so I went for eyebrows raised and eyebrows lowered giving (2^4)*(3^10)*(2^1) discrete values.
So, that is 1,889,568 discretre values - meaning I could count from 0 to 1,889,567 using 10 fingers, 4 toes and a eyebrow and represent each number on the way.
Obvioiusly, I could eradicate the eyebrows if I had more motility in my toes, or could get 1 toe to do 3, rather than 2 states.
Due to it's mixed base nature, this would only really be of any use for counting as working out the representation for an arbitrary number would be tricky at best :)
So, if you're ever really bored... you know what you can do. I suggest limbering up your fingers first! :D"
