Like maybe when you add 7 and 6, let's say, one algorithm is to say "I'll see how much it takes to get to 10" -- it takes 3, and now I've got 4 left, so I gotta go from 10 and add 4, I get 14. That's an algorithm for adding -- it's actually one I was taught in kindergarten.
But there are other ways to add -- there's no kind of right algorithm. These are algorithms for carrying out the process the cognitive system that's in your head.
The way they did it was -- of course, nobody knew anything about photosynthesis -- so what you do is you take a pile of earth, you heat it so all the water escapes. You weigh it, and put it in a branch of a willow tree, and pour water on it, and measure you the amount of water you put in. When you're done, you the willow tree is grown, you again take the earth and heat it so all the water is gone -- same as before.
There has to be a reason you can say "how many cars did they wonder if the mechanics fixed?" but not "how many mechanics did they wonder if fixed the cars?" And the reason can't just be "because that's what a child is more likely to hear" because then you have the problem of infinite regress
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