Sunday, January 23, 2011

The Urysohn Metrization Theorem: an alternate account

[from: The Journal of Proctoscopic Philosophy, (to appear)]

            We have seen that belief in the intellectual curiosity known as the “Urysohn Metrization Theorem”, oddly widespread, can be adequately accounted for in adaptationist terms.  However, an even simpler explanation lies ready to hand.

            The underlying puzzle is known in cosmology as the Horizon Problem.  To wit:  How can far-flung regions of the universe, well outside one another’s event horizons, share certain arbitrary and contingent values of various parameters -- for instance, the uniform temperature of the Cosmic Microwave Background Radiation?    In mathematics, the problem is the same:   How can some random fragment of patriarchal European ideology -- in this case, the U.M.T. -- be held to so tenaciously by scholars who have never met one another?
            The solution to both problems is the same:  Cosmic Inflation.  You see, many billions of years ago, all the world’s mathematicians were packed together tightly into a tee-ny, ti-ny region of space, no bigger than a thimble.  One of them (possibly Urysohn) somehow took it into his head that, if a space is regular and second-countable, it must be metrizable (whatever that is supposed to mean).  All the other compactified mathematicians nodded their little heads vigorously and followed like sheep.   Then the cosmos went -- VROOM ! -- and that’s where we are today.
           Simple, really.

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