Best of All Worlds
Frederick
In best of all worlds, Leibniz surpasses Newton
SCIENCE
>http://www.dallasnews.com/health/columnists/tsiegfried/stories/072103dnlivtomcol.618db.html
07/21/2003
By TOM SIEGFRIED / The Dallas Morning News
When Gottfried Wilhelm von Leibniz declared that humans inhabit the best of all possible worlds, he
really meant that the universe is a cool place because it permits the pursuit of science.
In modern translation, says mathematician Gregory Chaitin, Leibniz meant that God is a computer
programmer.
Whether you take "God" in a devout religious sense (as Leibniz did), or as metaphorical shorthand
for the ultimate nature of the universe, is beside the point. Dr. Chaitin's message is that the
practice of science today reflects a new "digital philosophy" that was articulated by Leibniz more
than three centuries ago.
A mathematician, philosopher, physicist and lawyer, Leibniz devised calculus independently of Isaac
Newton, invented a primitive calculating device, and rediscovered the binary number system
(previously used by musicians in India more than a millennium earlier). Expressing information
using the binary digits 0 and 1 (as modern computers do) stemmed from Leibniz's desire to apply
logic to the cosmos.
It was through logical analysis that Leibniz concluded that the world God created was the most
nearly perfect possible. After all, Leibniz reasoned, God could have made a universe in any of many
possible ways – some complicated, some simple.
Suppose, for instance, that God made the world the way a child might make abstract art – splashing
dots of color on a sheet of paper with a crayon. Even for an apparently random pattern of dots,
Leibniz showed that it would be possible to devise a mathematical formula describing their
positions. In other words, you could use the formula to plot a curving line that would pass through
all the dots – in the order they were made.
For most patterns of dots, though, the formula would be extremely complicated. A "better" world
might be built by arbitrarily changing certain aspects of nature. But events in such a world,
though obeying some complicated formula, would appear to be utterly chaotic, beyond the power of
human scientists to comprehend.
"When a rule is extremely complex, that which conforms to it passes for random," Leibniz observed.
To say that the world is ruled by "laws of nature," then, is not very meaningful unless the laws
are relatively simple. You could in principle find a rule to describe the world no matter how
random it looks. But unless the rule is short and sweet, you have not discovered a very useful law.
Fortunately, the world that humans actually inhabit succumbs to rather simple formulas; scientists
can describe all sorts of processes with only a few fundamental equations.
"God has chosen the most perfect world," Leibniz wrote in his Discourse on Metaphysics, "the one
which is at the same time the simplest in hypothesis and the richest in phenomena."
In Leibniz's writings, Dr. Chaitin sees the precursor of his own seminal work in describing nature
in terms of information. He was a pioneer in the development of algorithmic information theory, a
method for gauging the complexity of a scientific theory.
A good theory, Dr. Chaitin explains, compresses lots of observations about nature into a concise
mathematical statement – best expressed as an algorithm, or computer program. The algorithmic
information content of a theory is the length of the shortest program that can reproduce all the
observations.
"The smaller the program is, the better the theory," Dr. Chaitin writes in a recent paper (online
at arXiv.org/math.HO/0306303). That is, a good theory, or law of nature, reduces complex data to a
short (or simple) formula.
Leibniz's anticipation of this concept, plus his invention of binary digits, planted a 17th-century
seed that is only now flowering in many scientific pursuits based on information processing. Dr.
Chaitin cites recent advances in quantum information theory and quantum computing, the use of
holographic information descriptions of black holes, and models of computation studied by Edward
Fredkin (originator of the "digital philosophy" terminology).
"The digital philosophy paradigm is a direct intellectual descendant of Leibniz," writes Dr.
Chaitin, of IBM's research laboratory in Yorktown Heights, N.Y. "The human race has finally caught
up with this part of Leibniz's thinking."
The digital view of nature also represents a subtle revision of a more ancient philosophy –
practiced by the followers of Pythagoras – often summarized by the statement that "Everything is
number; God is a mathematician." Today, says Dr. Chaitin, the proper credo should be "Everything is
software; God is a computer programmer."
This "digital" philosophy has become a new paradigm for science, and it's just what science needs
to cope with the complexity that eludes description with traditional Newtonian physics, based on
analysis of mass and motion, or matter and energy.
"In our new interest in complex systems, the concepts of energy and matter take second place to the
concepts of information and computation," Dr. Chaitin asserts. The godlike authority of Newton and
his materialist philosophy must yield to the new digital philosophy in order for science to extend
the human ability to comprehend creation.
Newton's vision is the history of science; Leibniz's is the future.
"Newtonian physics," Dr. Chaitin avers, "is now receding into the dark, distant intellectual past."
E-mail tsieg...@dallasnews.com
--
Best,
Frederick Martin McNeill
Poway, California, United States of America
mmcn...@fuzzysys.com
http://www.fuzzysys.com
http://members.cox.net/fmmcneill/
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Phrase of the week :
"It has yet to be proven that intelligence has any survival value."
Arthur C. Clarke
Mark Twain said : " When we remember we are all mad ,
the mysteries disappear and life stands explained . "
:-))))Snort!)
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