In the early 1920's, two guys named Banach and Tarski were exploring a
rather obscure branch of mathematics, later called by physicists and
mathematicians, "a
somewhat surreal corner of set theory". They came up with some theorems known
as the
Banach-Tarski theorems (BTT). Now remember, these were not speculations but
theorems which they could prove. Here is just one example of what comes out
of BTT:
start with a solid sphere, like a bowling ball with no finger holes. This one
sphere can be
cut into five pieces so that two of them can be reassembled into another solid
sphere
identical to the original; the remaining three pieces (guess what's coming)
can also be
reassembled into another solid sphere identical to the original. And so on.
Surreal indeed!
But people just viewed it as an oddity with no application to the real world
until...
After QCD was thoroughly tested and accepted by most physicists, a fellow
named
Augenstein, who knew about BTT and QCD, looked at the math involved in both
and
showed that the rules governing sets and subsets in BTT were formally exactly
the same
as the rules that described the behaviour of quarks and other entities in QCD.
One
example of something that happens in the real world of physics is this: when a
single
proton is accelerated and smashed into a metal target, it can produce many new
copies of
itself. This is exactly like the proliferation of bowling balls described by
BTT! Thus again
pure math became applied math decades later.
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