Invisible wrote:
> [Strictly, a *universal* Turing machine is a simplified programmable 
> computer, if you want to nitpick.]

More completely, a Turing machine is a (very simple) machine with the 
program in ROM. A universal Turing machine is a Turing machine whose 
program (in ROM) is an interpreter for a program stored in the RAM. 
That's the sense in which it's "programmable".

The benefit is that if you can prove something is true of the universal 
turing machine, you can prove it's true of all turing machines, because 
the universal turing machine can be programmed to be like any other 
turing machine.

Mike Raiford wrote:
 > Why would someone want to do this? (other than the obvious self-abuse?)

Because it's math. If you can prove that X, with enough work, is 
equivalent to any Y, and then you prove some property of X holds, then 
you can prove that property holds for every Y.

If you can prove that (for example) you can't solve a problem with Iota 
calculus, and you can prove that Iota calculus can solve any problem a 
normal desktop computer can solve, then you can prove your desktop 
computer can't solve it.

By being very very simple, you make it easy to prove things about it 
that you'd never really want to *do* in actual real life.

-- 
Darren New / San Diego, CA, USA (PST)
  Ever notice how people in a zombie movie never already know how to
  kill zombies? Ask 100 random people in America how to kill someone
  who has reanimated from the dead in a secret viral weapons lab,
  and how many do you think already know you need a head-shot?

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