complexity and heat, an analogy in the history of science

Eric Watt Forste (arkuat@pobox.com)
Wed, 13 Aug 1997 17:50:13 -0700

One of the interesting things about the history of thermodynamics
is the way the English word "heat" was revealed to be devoid of
meaning. "Heat" turns out to map loosely to temperature, to
conductive energy flow, and to stored thermal energy. The traditional
English word does not map precisely to any of these things. In
modern scientific usage, "heat" serves as a taxonomic word, referring
to phenomena of interest to thermodynamicists without referring to
any particular one thing. (In non-scientific usage, it continues
more or less to refer to the fictitious caloric, just as some --
not all -- modern non-scientific astronomical talk makes use of
the Ptolemaic model.)

I suspect that a similar disintegration is happening to the word
"complexity". Although it is now clear to us that "heat" has no
referent, and that the real measurable thermodynamic quantities
are several different things, each of which has its own technical
name, things were not so clear in the nineteenth century when
the hard work was being done in laying the foundations of
thermodynamics.

All the really good discussions of "complexity" I've seen on this
list seem to point toward a developing taxonomy of different types
of complexity. There are several different competing definitions,
and like the three definitions of "heat" they may all be right.
That means each one of them will need a name of its own, so we can
stop inadvertently confusing them, and if we can't agree which one
is the "real" complexity, it may very well turn out that complexity
is as chimerical as caloric, a half-baked idea that has played its
role in the history of science to date, but, turning out to have
no referent, must now be discarded.

I'm presenting this discussion from the perspective of some readings
in analytical philosophy, as applied to the history of science,
and I'd be delighted to have my perspective broadened by a
mathematician specializing in the study of complexity. Or by
anyone else, for that matter.

The only definition of complexity I can bring to mind at the
moment is the one that I think is used in algorithmic
information theory, which is the length (in bits) of the code
needed to produce the full string. This definition allows all
sorts of lossless compression to be applied to a given
bit-string to squeeze out redundancies that, properly speaking,
shouldn't count toward complexity. I can think of worse
definitions, but this AIT definition has mismatches with
"ordinary usage" of the word "complexity" as well. Before
delving into these, I'd like to see what alternative
definitions people have to suggest. I know John K Clark
recently put forth several alternative definitions, with
criticisms, and it was his post that triggered the thoughts
that led up to my writing this.

--
Eric Watt Forste ++ arkuat@pobox.com ++ expectation foils perception -pcd