A Dialogue between Gregory Chaitin and Israel Rosenfield

The structure of DNA that has been revealed by the recent decipherment of the human genome bears a striking similarity to the structure of mathematics that is suggested by Gregory Chaitin’s work. Just as most of the genome is "junk", i.e. probably more or less random sequences without any clear function, so too, Chaitin's work shows that there are very few numbers that are not random. In a more general sense we could say that the axioms of mathematics are like the "genes" of the human genome. There are not enough of them to generate all of mathematics anymore than there are enough genes to generate a complete individual. And just as what are for the moment unknown (and perhaps unknowable) mechanisms that are responsible for the construction of the full individual, so too, there is much that is unknown ? and perhaps unknowable ? about the construction of mathematical theorems that are not derived from the known axioms. So in Chaitin’s world of mathematics there are, on the one hand, non-random numbers that can be produced from algorithms (genes) that are "shorter" than the numbers themselves ? as there are "genes" in the genome that produce proteins of much greater complexity than the genes themselves; yet, on the other hand, there are the vast majority of numbers that are random ? without any order (they can only be described by numbers as long as themselves), just as most of the DNA in the genome also appears to be random. We do not have any broad understanding of the relationship between the junk DNA (which is not necessarily always junk) and the genes that make up the same molecules of DNA; nor do we know how the various bits and pieces of mathematics might fit into a larger whole. There is then, an "incompleteness" inherent in the structure of mathematics; by analogy we might say, DNA, too, is "incomplete" because its structure alone does not contain all the genes necessary for the "construction" of a human being. And DNA fails to give us all the clues ? indeed, the most important ones - about how and why complex forms of life ever emerged on the earth since bacteria and other single cell organisms are so successful, so adaptive, that there seems little reason for life to have ever evolved into multicellular organisms, let alone fish, mammals and ultimately human beings. And we will be asking as well if these approaches to complexity in mathematics and the emergence of advanced forms of life sheds any light on human psychology. For it is generally assumed in the neurosciences that the brain is a rule obeying organisms, that it has innate (genetically determined) structures that in some sense represent "universal grammars" of, for example, vision, thought and language that can account for our visual and linguistic abilities. This is a view that seems at odds with Chaitin’s vision of mathematics, as it does with the present realization that DNA does not appear to contain enough information to fully account for the complexity of living organisms. And yet another, considerably more complex view of DNA, the brain and human psychology is beginning to emerge. The decipherment of DNA by the organism is not passive, but the consequence of numerous mechanisms (mostly unknown for the moment) that involve signaling from one cell to another, splicing of the DNA and so on; and the brain is not a passive organ, interpreting environmental stimuli according to predetermined programs. The brain too is "splicing" ? i.e., creating the phenomena we are aware of - our feelings, memories, thoughts and actions. For the brain is an organ that is actively reacting to stimuli. Mind is the consequence of the dynamic interactions of the brain, the body and the environment. And all of these activities are part of a larger whole that includes consciousness, whose complexity may be beyond our ability to ever understand. Complexity, then, from numbers to the structure of mathematics, and from primitive reproducing organisms to conscious human beings will be the subject of our dialogue




Israel Rosenfield is professor of history at the City University of New York. He received his M.D. from the New York University School of Medicine and his Ph.D. from Princeton University. He is the author of several non-fiction titles and writes frequently for the New York Review of Books. He has recently published his first work of fiction entitled Freud's Megolomania, Norton,(New York), 2000 which depicts the discovery of Freud's last manuscript, Megolomania. Rosenfield's scholarly work in the areas of the history of science and the philosophy of mind are placed within the stucture of a novel revealing a final reconsideration of key elements within Freud's foremost theory of psychoanalysis.