dkomo  wrote or quoted:
> Perplexed in Peoria wrote:

[...]

> > I think that Dawkins is talking about Kolmogorov complexity here.  To
> > my mind, the key point about Kolmogorov complexity is that it insists
> > that the language used to describe the object must be rich enough to
> > say things like "repeat N times" and more complicated
variations of that
> > phrase.  It doesn't limit us to a fixed set of phrases.  (But, in thus
> > unleashing descriptive power, it makes itself somewhat ambiguous and
> > very non-operational as a metric.)
> 
> I just had a series of exchanges with John Wilkins about this very same 
> thing on talk.origins. 
> I claim that Dawkins is using the term  "description" in a different 
> way than it is used in Algorithmic  Information Theory.  Dawkins 
> intends his written descriptions to be *meaningful* and easily 
> understood.  No such restriction is put on descriptions in AIT. [...]
> And Dawkins doesn't care if his descriptions are 
> of minimal length or optimal in some other sense.  He just wants to use 
> a consistent set of descriptions of different organisms to gauge the 
> relative complexities of those organisms.
> 
> Frankly, I wish people would stop even mentioning Kolmogorov complexity 
> as some kind of a metric to consider.  Whatever utility this idea has 
> for AIT, the sad fact is that there is no known method for even 
> computing the length of the minimal program that will output a given 
> string, nor to tell if a particular such program is of minimal length. 
> As a general metric for complexity, Kolmogorov complexity is useless.

"Length of shortest description" in some language is a fine metric -
*until* you allow partial recursive functions into the mix.

As soon as the descriptive language becomes universal, it becomes
exceedingly difficult to prove that a description is really the
shortest one in the general case - and all you can typically do
is place some distant upper and lower bounds on the value.

It's a good argument for sticking to standard, recognised 
non-Turing-complete compression functions as the specified
descriptive language in such metrics.  At least with these
you can prove that the description you have is the shortest
in a reasonable quantity of time.

Choose a "bijective" compressor and the proof is simple, each
pattern has precisely one program that generates it - so it
*must* be the shortest one possible.
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