Stuart Kauffman (Vermont/Santa Fe)
The Turing Machine has transformed modern society. Yet is is a subset
of classical physics, a discrete state discrete time, and absolutely
definite Cartesian machine. Parallel tracks, starting with Bertrand
Russell's "sense data statement", and the McCulloch Pitts "Logical
Calculus of Ideas Immanent in the Mind" led, with the Turing Machine
to Strong Artificial Intelligence, the view that mind must be a
complex Turing machine, or network of formal logical gates. The
Turing Machine defines "algorithmic".
Hidden in the above framework of ideas are two concepts: 1) knowledge is propositional and representational, as by bits in a Turing Machine or McCulloch Pitts network. 2) All knowledge is so representable. However, the famous FRAME problem, based on these assumptions, has plagued computer science since Turing, never solved.
Critically, humans and dogs solve the frame problem, often easily. Dogs presumably do so without propositional knowledge. These facts suggest that the entire framework above is wonderful, but very limited despite its evident power.
I will discuss an entirely new framework. Closed quantum systems, prior to measurement, propagate the Schrodinger equation unitarily. These are the basis of quantum computers, no more powerful, but faster than classical physics computers due to parallel search. In sharp contract, Open Quantum Systems in an Environment, are able to lose phase information into the enviornment, a process called "decoherence" hence do NOT propagate the Schrodinger wave equation unitarily since phase information is lost. Decoherence allows an open quantum system to "decohere to classicality" - at least for all practical purposes, FAPP. It is debated whether decoherence is or is not the same as quantum measurement. The latter is governed by the Born rule where the square of an amplitude is its probability of being measured. It is not clear that the Born rule applies to decoherence.
New physics arises during decoherence, including the Quantum Anti Zeno effect where decay between states is not an exponential half life, and decoherence can affect chemical reactions.
Radically, it now appears that RE-coherence from classical (at least FAPP) to partially or fully quantum coherence. This is supported by the Shor Quantum error correction theorem and other theory.
The above suggests that open quantum systems may be able to HOVER indefinitely between quantum coherent and classical FAPP behaviors. This is entirely new physics, but seems correct.
The Poised Realm
My colleagues, quantum physicist, Gabor Vattay of Eotvos University, Budapest, and Samuli Niiranen and I have defined a Poised Relam for open quantum systems. The X Y plane has on its Y axis, quantum coherent at the origin, and classical FAPP up the Y axis by decoherence and back to quantum by recoherence down the Y axis. The X axis is Order, Criticality, and Chaos, as tuned by tuning Hamiltonians.
We believe the Poised Realm is a new feature of reality. Vattay has shown that the rate of decoherence varies across the X axis, and that the energy level distribtution varies in a characteristic way from the ordered half plane, to criticality, to the chaotic half plane.
Different molecules may be located at different X axis positions, more or less able to hover between quantum and classical.
Trans Turing Systems
The above authors have defined a non-algorithmic Trans-Turing system comprised of quantum superposition states, pure states, and classical degrees of freedom in the Poised Realm. This system is neither deterministic due to quantum superpostion states and quantum measurements in the Trans-Turing system, nor is it random, due to the classical degrees of freedom. Thus it is an entirely new, non-algorithmic class of "information processing systems", where we will need to redefine "information" for the Poised Realm.
I believe Trans-Turing Systems are constructable, go beyond Turing, and may have powerful implications for the Mind-Brain system. Decoherence allows "mind" to act ACAUSALLY on brain, answering Descartes' problematic dualism of Res Cogitans and Res Extensa, itself bound by classical physics and the causal closure of classical physics. It is possible, and testable by diverse approaches, that Trans-Turing systems are located in synapses and post synaptic neurotransmitter receptors, and that quantum entanglement plays a role in the Binding problem of neuroscience. Just conceivably, conscious experience is associated with quantum measurement, again a testable hypothesis.