Re: The Warm Equations

Ted Nolan <tednolan> <ted@loft.tnolan.com> wrote:

Interesting to note the way margins of a real-life space venture are run:
>
Two astronauts have been stuck at the ISS for an extra two weeks,
so far, because their ride has flat tires, and it's not a crisis,
and nobody has had to volunteer to step out the airlock.

This passage from "The Purloined Letter" (Poe) leads me to believe
Sherlock Holmes' predecessor, C. Auguste Dupin, prefers warm equations:

    As poet and mathematician, he would reason well; as mere
    mathematician, he could not have reasoned at all ...

    I dispute the availability, and thus the value, of that reason which
    is cultivated in any especial form other than the abstractly
    logical. I dispute, in particular, the reason educed by mathematical
    study. The mathematics are the science of form and quantity;
    mathematical reasoning is merely logic applied to observation upon
    form and quantity. The great error lies in supposing that even the
    truths of what is called pure algebra, are abstract or general
    truths. And this error is so egregious that I am confounded at the
    universality with which it has been received. Mathematical axioms
    are not axioms of general truth. What is true of relation-of form
    and quantity-is often grossly false in regard to morals, for
    example. In this latter science it is very usually untrue that the
    aggregated parts are equal to the whole. In chemistry also the axiom
    fails. In the consideration of motive it fails; for two motives,
    each of a given value, have not, necessarily, a value when united,
    equal to the sum of their values apart. There are numerous other
    mathematical truths which are only truths within the limits of
    relation. But the mathematician argues, from his finite truths,
    through habit, as if they were of an absolutely general
    applicability-as the world indeed imagines them to be. Bryant, in
    his very learned 'Mythology,' mentions an analogous source of error,
    when he says that 'although the Pagan fables are not believed, yet
    we forget ourselves continually, and make inferences from them as
    existing realities.' With the algebraists, however, who are Pagans
    themselves, the 'Pagan fables' are believed, and the inferences are
    made, not so much through lapse of memory, as through an
    unaccountable addling of the brains. In short, I never yet
    encountered the mere mathematician who could be trusted out of equal
    roots, or one who did not clandestinely hold it as a point of his
    faith that x2+px was absolutely and uq. Say to one of these
    gentlemen, by way of experiment, if you please, that you believe
    occasions may occur where x2+px is not altogether equal to q, and,
    having made him understand what you mean, get out of his reach as
    speedily as convenient, for, beyond doubt, he will endeavor to
    knock you down.

Danke,

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