pitfalls of complexity

[Mike_Cahill at sil.org]

Dear Rob,

I mostly just listen to people on this list, but can't resist a comment on
your concluding paragraphs:

      "Another nice thing about randomness as an explanation for homonymy,
      idiosyncrasy, and most other problems which vex us in language, is
      that it short circuits the debate on complexity. The idea is that if
      a
      system exhibits random patterns it is already maximally complex.
      Stephen Wolfram calls this "computational irreducibility." He has
      gone
      into it quite extensively. Though not for language. His shock claim
      is
      that the vast majority of systems are already maximally, and thus
      equally, complex (in the sense of being universal computers.)

      If that is true and systems exhibiting random patterns, in particular
      language, are computationally irreducible, then it may not be a
      question of comparing the complexity of languages and deciding if
      they
      become more or less complex over time. The important question may be
      do they exhibit random patterns. Because if they do they may already
      be maximally complex."

This connects randomness, computational irreducibility, and complexity.
Randomness = maximally complex. This of courses hinges on what you mean by
complex, and there can be at least two ways of looking at that. If an
entity is nonuniform with multitudes of parts, then it appears complex. But
that apparent complexity could be the result of randomness (think of sand
dunes shaped by wind) or it could be what you might call "specified
complexity," with a code and system behind it (think letters written on a
beach). The DNA of any organism is quite complex, but is far from random.
If you randomized the peptide chains that compose it, that molecule might
still have the appearance of complexity, but scrambled (random!) DNA is
unsystematic and useless.

A specified complexity would be amenable to analysis and computational
treatment, while random complexity would not. So I'd agree with the
statement that "systems exhibiting random patterns ... are computationally
irreducible". But the part I left out, in the ellipsis ("in particular
language") is what the point is. I'm not so sure that randomness short
circuits the debate on complexity as much as avoids it.

Finally, when you state that
      And why is randomness so important? Because paradoxically it allows
      us
      to find more patterns (if patterns are regular then rules limit how
      many we can find.)

I'm wondering what you mean by randomness. Randomness by definition is the
lack of pattern.

A nice exercise to start the morning with.

Mike Cahill