In article <mailman.7792.1393994283.18130.python-l...@python.org>, Ben Finney <ben+pyt...@benfinney.id.au> wrote:
> Roy Smith <r...@panix.com> writes: > > > I stopped paying attention to mathematicians when they tried to convince > > me that the sum of all natural numbers is -1/12. > > I stopped paying attention to a particular person when they said âI > stopped paying attention to an entire field of study because one > position expressed by some practicioners was disagreeable to meâ. > > Would you think âI stopped listening to logicians when some of them > expressed Zeno's paradox of the impossibility of motionâ to be a good > justification for ignoring the entire field of logic? > > Rather, a more honest response is to say why that position is incorrect, > and not dismiss the entire field of study merely for a disagreement with > that position. I *was* partly joking (but only partly). Still, there's lots of stuff mathematicians do which I don't understand. I cannot understand, for example, Andrew's Wiles's proof of Fermat's Last Theorm. I can't even get past the first few paragraphs of the Wikipedia article. But, that doesn't sour me on the proof. I can accept that there are things I don't understand. I don't know how to speak Chinese. I don't know how to paint a flower. I don't know how to run a mile in 4 minutes. But I accept that there are people who do know how to do those things. I can watch a friend pick up a piece of paper, a brush, and some watercolors and 5 minutes later, she's got a painting of a flower. I watched her hands hold the brush and move it over the paper. There's nothing mystical about what she did. Her hands made no motions which are fundamentally impossible for my hands to make, yet I know that my attempt at reproducing her work would not result in a painting of a flower. But, as I watch the -1/12 proof unfold, I don't get the same feeling. I understand every step. I wouldn't have thought to manipulate the symbols that way, but once I've seen it done, I can reproduce the steps myself. It's all completely understandable. The only problem is, it results in a conclusion which makes no sense. I can *prove* that it makes no sense, by manipulating the symbols in different ways. The sum of any two positive numbers must be positive. I can group them and add them up any way I want and that's still true. But, here I've got some guy telling me it's not true. If you just slide this over that way, and add these parts up this way, it's -1/12. That does not compute. But it doesn't not compute in the sense of, "that's so complicated, I have no idea what you did", but in the sense of "thats so simple, I know exactly what you did, and it's bullshit" :-)
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