Working with the set of real numbers
Roy Smith
roy at panix.com
Wed Mar 5 06:29:43 CET 2014
In article <mailman.7792.1393994283.18130.python-list at python.org>,
Ben Finney <ben+python at benfinney.id.au> wrote:
> Roy Smith <roy at 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 â€œI
> stopped paying attention to an entire field of study because one
> position expressed by some practicioners was disagreeable to meâ€.
>
> Would you think â€œI 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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