On 4/8/2012 11:50, Warp wrote:
> Darren New<dne### [at] sanrrcom>  wrote:
>> A TM can calculate an answer *isomorphic* to the answer of an arbitrary
>> problem, but it can't solve the actual problem as stated.
>
>    I don't really understand what the difference is.
>
>    The only isomorphism I'm familiar with is graph isomorphism,

"isomorphic" means there's a one-to-one mapping from one thing to another 
thing. But that doesn't make them the same. It just means there's a mapping.

So a WAV file might be isomorphic to the position of the speaker at each 
given sample, but that doesn't mean a WAV file is an actual sound. It can be 
mapped to an actual sound.

A Turing machine can decompress a representation of an MP3 file into a 
representation of where the speaker would be at each given moment, but it 
can't actually play the music.

-- 
Darren New, San Diego CA, USA (PST)
   "Oh no! We're out of code juice!"
   "Don't panic. There's beans and filters
    in the cabinet."

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