[SPORK, FUNNY] Donald Rumsfeld... the poet?
deafbox at hotmail.com
Sun Apr 13 19:28:22 PDT 2003
>As we know,
>There are known knowns.
>There are things we know we know.
>We also know
>There are known unknowns.
>That is to say
>We know there are some things
>We do not know.
>But there are also unknown unknowns,
>The ones we don't know
>We don't know.
>-Feb. 12, 2002, Department of Defense news briefing
This reminds me of the shy reals. We all know
Cantor's diagonalization argument that the
cardinality of the reals is qualitatively
greater than the cardinality of integers. So
we say the integers are countable, while the
reals are not. The rationals are also countable.
As are the algebraic numbers, which include
many (though only a countable number) if
irrationals, such as sqrt(5) and cuberoot(3).
Of course, there are plenty of real numbers that
aren't algebraic that we can describe by other
methods, such as pi, and e.
But here's the interesting thing: all the
finitely describable numbers are themselves
countable. The remaining reals, the "shy"
ones, are the uncountable bulk of reals, even
though I cannot name one of them.
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