>> I implicitly assumed that any machine that can't process it's own 
>> program isn't worthy of the title "computer", that's all. ;-) But yes, 
>> I see what you're saying.
> 
> So, your brain is weaker than a Turing machine? Cool.

This is not exactly news. A Turing machine has unbounded memory, 
remember? ;-)

> It's the simplicity of the machines that make them amenable to 
> universality, not the complexity. Remember that the Von Neumann 
> architecture was a breakthrough.

Uh... wuh?

>> As for being able to perform infinite instructions in finite time... 
>> surely that just makes it even *harder* to predict what the machine 
>> will od, no?
> 
> Not if it can process its own input. Think about how the halting problem 
> works, and why... If the machine has unbounded state, it might run 
> forever without ever getting into the same state twice. But if you can 
> run the computer forever without it actually taking forever, then you 
> can say definitively "no, that machine never stops."
> 
> And a machine that can run an infinite number of instructions in finite 
> time *always* stops. ;-)

Really? And by "infinite" do you mean Aleph0, Aleph1, or some larger 
cardinallity? ;-)

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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