On 4/8/2012 19:15, Kevin Wampler wrote:
> I think perhaps this is the crux of the difference in out viewpoints. I
> don't consider a "normal" computer as any more capable of programming a UTM
> in the sense you seem to mean it than a normal TM is.

A TM can't encode any sort of tape for any other TM.

> Both have to operate
> on some encoding of the TM that the initial program is for, and I don't see
> why binary digits represented by electrical means are any less of an
> encoding than abstract symbols on a tape.

We're confusing two things here. One is that real computers can perform 
computations that TMs can't, because TM's don't have cameras, microphones, 
etc. One TM can't program another TM at all, because a TM can only write to 
its own tape.

The other point is that humans can do things computers can't because we're 
capable of encoding things directly from reality with our inputs. (E.g., we 
can look at a hand-written representation of a turing machine program and 
mentally turn it into an actual turing machine program without outside 
assistance.)

I just found it amusing that programming a Universal Turing Machine is one 
thing a Universal Turing Machine can't do without assistance.

-- 
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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