Reliable Computing 4: 105–107, 1998.
1998 Kluwer Academic Publishers. Printed in the Netherlands.
A Brief Description of Gell-Mann’s Lecture and
How Intervals May Help to Describe Complexity
in the Real World
1003 Robinson, El Paso, TX 79902, USA, e-mail: firstname.lastname@example.org
Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA,
On March 10, 1997, Murray Gell-Mann, the 1969 Nobel-prize winning physicist,
presented the 1997 Fessinger-Springer Memorial Lecture on The Quark and the
Jaguar: From Simplicity to Complexity. Dr. Gell-Mann won the Nobel prize for
being one of the authors of the famous quark theory. He is currently a professor and
the Co-Chairman of the Science Board of the Santa Fe Institute, the world-renowned
institution devoted to the study of complexity.
What is complexity: a problem. Gell-Mann started his El Paso talk with the
fundamental question: “What is complexity?” As an example of increasing com-
plexities, he showed three neckties: a tie with a simple repeating geometric pattern
(simple stripes), a tie with a more complicated repeating pattern, and a tie with a
non-repeating, complex picture. How can we formalize this difference in complex-
A formalization: Kolmogorov complexity. The striped tie is simple because we
can characterize its pattern with a very short description. A more complicated tie
requires a longer description, while a description of the third (“artistic”) tie prob-
ably requires an elaborate description. It is natural to formalize this difference in
the following way: By the complexity of a pattern p (word, binary sequence, etc.)
we mean the length of the shortest program (in some ﬁxed programming language)
that can generate p. This length is called algorithmic information complexity or
Kolmogorov complexity, and denoted by K(p). It was introduced in the 60’s, inde-
pendently, by three researchers: A. Kolmogorov, R. Solomonoff, and G. Chaitin
(for a modern survey, see, e.g., ).
Problems with Kolmogorov complexity. Kolmogorov complexity seems like the
perfect answer to the fundamental question, since the more complex the pattern, the