Chris

On Sat, Jan 23, 2010 at 1:35 PM, Christopher Menzel <cmenzel@xxxxxxxx> wrote:
>
> So it appears that the content of your claim that "there are many computational
> processes which cannot be completely summarized" is nothing more than the
> fact that there are undecidable computational problems.  What I don't understand
> is why you are using your own idiosyncratic terminology for expressing this
> exceedingly well known and rather elementary fact about the limits of
> computation.  Surely the only effect of doing so is to obfuscate what
> is otherwise entirely clear.

It makes you think about it, yes. It is entirely normal that those who
are most familiar with this old result will have the most difficulty
seeing it in a new light.

>> Or you could look at Stephen Wolfram's idea of "computational irreducibility". It
>> appears to me to be saying the same thing:
>

> Yes, although he appears to be citing undecidability to illustrate a more general
> claim about the predictive limitations of theories.

I'm glad you are able to see this.

So what is important is this idea that there are "predictive
limitations of theories."

My comment to Ali was that the "predictive limitations of theories"
might explain why our "theories" of language (grammars) have failed to
usefully disambiguate natural language, and that we might be able to
do better by treating syntactic predictions purely as a process,
distinct from theories about that process.

-Rob

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