Answering Descartes: Beyond Turing.

The first half of the 20th Century was filled with a stunning group of scientists, Einstein, Bohr, von Neumann and others. Alan Turing ranks near the top of this group. I am honored to write in this Centennial Volume commemorating his work. How much do we owe one mind? His was a pivotal role in cracking the Nazi war code that profoundly aided the defeat of Nazism. His invention of the Turing machine has revolutionized modern society, from universal Turing machines to all digital computers and the IT revolution. His model of morphogenesis, the first example of a “dissipative structure”, to use Prigogine’s phrase for it, is one I have myself used as a developmental biologist. I rightly praise Turing, but seek in this chapter to go beyond him. The core issue is the human mind. Two lines of thought, one stemming from Turing himself, the other from none other than Bertrand Russell, have led to the dominant view that the human mind arises as some kind of vast network of logic gates, or classical physics “consciousness neurons”, to use F. Crick’s phrase in The Astonishing Hypothesis (1), connected in the 10 to the 11th neurons of the human brain. I think this view could be right, but is more likely to be wrong. My aim in this chapter is to sketch the lines of thought that lead to the standard view in computer science and much of neurobiology, note some of the philosophic claims for and doubts about the claim, but most importantly I wish to explore the emerging behavior of open quantum systems, their new physics, and, centrally, our capacity to construct what I will call non-algorithmic , non-determinate yet non-random TransTuring Systems. As we shall see, Trans-Turing systems are not determinate, for they inherit the indeterminism of their open quantum system aspects, yet non-random due to their classical aspects. They are new to us, and may move us decisively beyond the beauty but limitations of Turing’s justly famous, but purely classical physics, machine. Beyond the above, I shall make one truly radical proposal that I believe grows out of Richard Feynman’s famous “sum over all possible histories” formulation of quantum mechanics,(2). This formulation is fully accepted as an equivalent formulation of quantum mechanics. I will show that Feynman’s formulation evades Aristotle’s Law of the Excluded Middle, while classical physics and, a fortiori, algorithmic discrete state, time, classical physics, Turing machines, obey the Law of the Excluded Middle. Following philosopher C.S. Pierce, who pointed out that “Possibles” evade the Law of the Excluded Middle, while Actuals and Probable obey that Law,(3), and Alfred North Whitehead,(4), I shall propose for our consideration a new dualism, Res potentia and Res extensa, the realms of the ontologically real Possible and ontologically real Actual, linked, hence truly united, by quantum measurement. In contrast, the dualism of Descartes, Res cogitans, thinking stuff, and Res extensa, his mechanistic world philosophy, have never been united. I believe Res potentia may be a consistent and new interpretation of “closed” quantum systems prior to measurement. These ideas and other much less radical ones resting on open quantum systems lead to new and testable hypotheses in molecular, cellular, and neurobiology, and, hopefully, a new line of ideas in the philosophy of mind including proposals about: how mind acts acausally on brain, an ontologically responsible free will, what consciousness IS, the experimentally testable loci of qualia as associated with quantum measurement itself, the irreducibility of both qualia and quantum measurement, the unity of consciousness, i.e. the “qualia binding problem” and its cognate “frame problem” in computer science. From these, technological advances in numbers of directions may flow.