Quotation for the week: Davis and Hersh

Philip J. Davis and Reuben Hersh’s book The Mathematical Experience was an early attempt to open the philosophy and culture of mathematics to a general audience. The authors don’t spare themselves or their colleagues from a little gentle ridicule in places, as in their portrait of the “ideal” (i.e. archetypal) mathematician:

The mathematician regards his work as part of the very structure of the world, containing truths which are valid forever, from the beginning of time…

The objects which our mathematician studies were unknown before the twentieth century; most likely, they were unknown even thirty years ago. Today they are the chief interest in life for a few dozen (at most, a few hundred) of his comrades. He and his comrades do not doubt, however, that non-Riemannian hypersquares have a real existence as definite and objective as that of the Rock of Gibraltar or Halley’s comet. In fact, the proof of the existence of non-Riemannian hypersquares is one of their main achievements, whereas the existence of the Rock of Gibraltar is very probable, but not rigorously proved…

He finds it difficult to establish meaningful conversation with that large portion of humanity that has never heard of a non-Riemannian hypersquare. This creates grave difficulties for him; there are two colleagues in his department who know something about non-Riemannian hypersquares, but one of them is on sabbatical, and the other is much more interested in non-Eulerian semirings…

The ideal mathematician feels prepared, if the occasion should arise, to meet an extraterrestrial intelligence. His first effort to communicate would be to write down (or otherwise transmit) the first few hundred digits in the binary expansion of pi.

If you can provide really satisfactory reasons why that last suggestion should or shouldn’t work, you might be on your first steps toward becoming a philosopher of mathematics…


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2 Responses to Quotation for the week: Davis and Hersh

  1. Vincent says:

    I should believe that if a meeting would occur that the extraterrestrial must have encountered pi due to it’s natrual occurence in almost all mathematics. The use of binary should be fairly simple to deduce its meaning as base 2 greatly simplifies the translation of other base systems like decimal or hexadecimal. Or if you like, a quote from the film Mean Girls will suffice:
    When asked why Lydsay Lohan likes math; “Because it’s the same in every language.”

  2. strathmaths says:

    The question this leaves open is, I guess, whether maths is really “natural” or whether it’s just something that seems natural to human beings. Would we expect maths to be more universal than, as Davis and Hersh put it, “life and death, love and hate, joy and despair”? And even if it is universal, (why) would we expect an alien intelligence to be interested in it?

    (Each of the Voyager space probes carries a disc — the so-called Voyager Golden Record — which is intended to give a sample of Earth culture to any extraterrestrial that comes across it. The contents of the disc make interesting reading as an attempt to grapple with the problem of what ETs might actually be able to make sense of…)

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