The historian and writer George Dyson starts off by documenting Turing and von Neumann's basic achievements. Dyson has a book out next week on this very topic, and given his past writings on technology and computing I am looking forward to it. As Dyson tells us, the basic groundbreaking idea of Turing and von Neumann was not just a machine which performs calculations at superhuman speed. It was the concept of a shared program and the then startling idea that you could code

*both*the data and the instructions for it in the same language (binary) in the same machine. This idea really is one of those "big ideas", simple to state but absolutely revolutionary in its impact. Turing and von Neumann's greatness thus lies not in conceiving the physical manifestation (or 'instantiation' as programmers would say) of a computing recipe but in their abstract generalization of the very idea of a programmed computer.What is not always recognized is that Von Neumann went a step ahead and floated an even more remarkable notion, that of a machine which contains instructions for assembling copies of itself. Von Neumann immediately tied this to biology; but this was a few years before Watson and Crick discovered the specific mechanism in the form of DNA base pairing. Unlike the "dynamic duo", nobody remembers von Neumann as making a signal conceptual contribution to biology. I remember the writer John Casti lamenting the general public's lack of recognition of von Neumann as the man who first really thought of the mechanism of heredity on the general basis that mathematicians are used to. As Casti pithily put it in his wonderful book 'Paradigms Lost': "Such are the fruits of the theoretician, especially one who solves 'only' the general case". To be fair, biology is an experimental science and no amount of theorizing can nail an experimental fact, but I suspect mathematicians would widely commiserate with Casti's lament.

The biologist Sydney Brenner then follows up by recognizing Turing's contributions to biology. In 1952 he wrote what is considered the first paper on nonlinear dynamics in which he described pattern formation in chemical reactions and possibly in developmental biology. We are still trying to understand the implications of that discovery even as nonlinear dynamics itself has become an enormously fruitful field with deep applications in modeling almost any complex natural phenomenon.

Finally, mathematician Barry Cooper from the University of Leeds points out a tantalizing question stemming from Turing's work; are complex, emergent phenomena strictly computable? This is partly a question about the limits of 'strong' reductionism and one that I have explored on this blog often. We don't yet know the answer to this question, to whether we can compute higher-order phenomena starting from a few simple particles and fields bequeathed to us by the particle physicists. As we tackle problems as complex as the future of the cosmos and the source of consciousness in the twenty-first century, this question will continue to hound scientists and philosophers. It waits for an answer as profound as Turing's answer to Hilbert's famous Entscheidungsproblem.

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