Chaitin, creativity, biology and mathematics

I was looking today, once again, at Gregory Chaitin’s most recent work which is described in his book Proving Darwin.  I realized that much of what has been written about this work (even what I have written) doesn’t give adequate attention to the crucial shifts in perspective that metabiology proposes. Chaitin says concisely:

According to metabiology the purpose of life is creativity.  It is not preserving one’s genes.  Nothing survives, everything is in flux, ta panta rhei, everything flows, all is change as in Heraclitus. (emphasis my own)

Metabiology explores randomly evolving artificial software (computer programs) in the hope that it will reflect randomly evolving natural software (DNA).  Chaitin’s work is built on many ideas, in mathematics and in biology.  One of the most significant of these is the observation of the infinite complexity of mathematics and its ‘incompleteness’ which allows the equivalence to be drawn between math creativity and biological creativity.  But Chaitin also subscribes to the view that the world is built out of mathematics,

that the ultimate ontological basis of the universe is mathematical, which is the hardest, sharpest, most definite substance there is, static, eternal, perfect.

And he goes on to say that:

…our physical world is but an infinitesimal portion of the world of mathematical ideas, which includes all possible physical universes, and which is all that exists, all that really is…But, following Godel, our knowledge of that perfect world is always incomplete, always partial, and constantly changing.

Chapter Eight is given the title What Can Mathematics Ultimately Accomplish?  And here Chaitin characterizes the living mathematics he has observed:

Math evolves, math is completely organic.  I am not talking about what Newtonian math might ultimately be able to achieve, nor what modern Hilbertian formal axiomatics might ultimately be able to achieve (see Jeremy Gray, Plato’s Ghost: The Modernist Transformation of Mathematics, Princeton University Press, 2008), http://press.princeton.edu/chapters/i8833.pdf and not even what our current postmodern math might ultimately be able to achieve.  Each time it faces a significant new challenge, mathematics transforms itself. (emphasis my own)

The idea that life itself is creativity, and that our knowledge of it is always incomplete, is a view of things that I believe mathematics easily inspires.  My own experience with mathematics has always led me in this direction, both within the confines of my very personal experience as well as when I explore ideas in science, philosophy and art.  It’s a provocative and optimistic view.  Mathematics seems to be coming from us, yet it keeps giving us images of the larger thing of which we are a part, to the point of showing us that we can never fully know that larger thing.  We are seeing something about us and the world.

Chaitin considers the political and theological implications of these ideas as well, which he addresses in chapters 6 and 7.  All of the ideas on which Chaitin’s work is based are big ideas, and there are many references in the text to related thoughts.  And it does seem to be the big ideas to which Chaitin is devoted when he concludes:

Even if almost everything in this book is wrong, I still hope that Proving Darwin will stimulate work on mathematical theories of evolution and biological creativity.  The time is ripe for creating such a theory.