Re: question on algorithmic complexity

Brian D. Harper (bharper@magnus.acs.ohio-state.edu)
Fri, 19 Jan 1996 15:57:49 -0500

Bill Hamilton wrote:

>Eddie Olmstead writes
>
>>I agree with Bill that randomness alone is not a measure of complexity.
>
>Hmm, I would say that randomness alone is not a measure of meaningful content.

agreed. There is no objective measure of "meaningful content" IMHO

>
>>However, I think I know where Brian is going. A simple sequence of
>>"HTHTHTH..." is not complex because you could write one simple algorithm to
>>generate it. The order is very simple--like a NaCl crystal with an endless
>>repeation of a simple pattern. There is order, but very little information.
>
>Agreed.
>
>>However, to generate the sentence "DNA is a complex molecule", it takes a
>>much larger (but still finite) set of algorithms--rules of spelling,
>>grammer, etc. of the English language. The order is much more complex, but
>>it contains information precisely because isn't simple repition--like a DNA
>>strand. A totally random sequence doesn't obey any rules. Thus, it is
>>complex and disordered. Thus, we are looking for "ordered complexity" if
>>you will.
>
>I think Brian would say "organized complexity".

agreed. "ordered complexity" is an oxymoron, sorry eddie ;-).

[...]

>But I'm looking forward to this discussion. C'mon
>Brian :-).
>

I hope to finish up this weekend. With all this buildup I hope
people aren't too disappointed with the final product :-).
Actually, I have an ulterior motive in this. I'm writing an
article on this (maybe two) and what I'll post will be one
section of the article. Since my hope was to get constructive
feedback, I don't mind these little interludes. If there is
enough interest I could go on and post other sections as I
write them.

Now, one more quick point. I think both Bill and Eddie
misunderstood what I wrote, which means that I must have
mis-spoke somehow. I think AC is a very good definition
of complexity but not a good definition of organization
(as it stands). Organized thingies are complex but not
all complex thingies are organized. For example, a
monkey typing randomly at a keyboard will produce a
document more complex than a Shakespeare play :-). This is
the reason for the term organized complexity. Shakespeare's
play is both organized and complex. The monkey's masterpiece
is only complex. So, AC is a very good (IMHO) definition of
complexity. Complexity plays an important role in organization,
but there's more to organization than complexity.

Now organization ----> design is another matter entirely :-).
This has to be considered very speculative. Now if we
take design in the van Tillian sense (and I generally do)
then AC cannot say anything about design. AC cannot measure
purpose, meaning, mindfull intent or any of these things.
The best one can say is that these are metaphysical conclusions
that are perfectly reasonable in light of the evidence.

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Brian Harper |
Associate Professor | "It is not certain that all is uncertain,
Applied Mechanics | to the glory of skepticism" -- Pascal
Ohio State University |
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