The Non-Algorithmic Trans-Turing System

In my past blog I described the Poised Realm for open quantum systems in an X Y coordinate system of Order Criticality and Chaos out the X axis and decoherence up the Y axis from quantum to classical behavior and recoherence down the Y axis.  I gave grounds to think the Poised Realm is real and is either a, or “the” pathway from the quantum to the classical world.

Next, recall that Turing machines are absolutely definite. In Turing machines, there are no weird “the cat is simultaneously both dead and alive” states as in the Poised Realm before superpositions decohere. Most cognitive and computer scientists are persuaded that the mind must be algorithmic, like a computer.  This view dominates neuroscience, computer science, artificial intelligence, and the philosophy of mind. On this view, we are machines.

My purpose in the present blog is to try to persuade you that we can have information processing systems, “Beyond Turing,” that are not at all algorithmic. We can have information processing systems that partake of the weird “simultaneously both dead and alive” superposition states before they slowly decohere, hence Trans-Turing Systems are not definite.

More I think our mind-brain systems may be such systems.  If so, much science needs to be done to understand and test these early hypotheses.  I will discuss this hope in later blogs.

I now describe the non-algorithmic Trans-Turing System. It will contain embodied information and operate in the quantum, Poised Realm and classical worlds with processing of embodied information and actions at the quantum, poised realm and classical levels.

A liposome is created by placing amphipathic molecules, such as cholesterol, in water. These form bilipid layers that in turn form hollow vesicles containing water inside.  Such bilipid layers are very similar to cell membranes.  Consider anchoring a number of chromophores by trans-membrane proteins to the insides and outsides of such liposomes.

Such liposomes are open quantum systems, subject to decohrence and recoherence, perhaps as chlorophyll may be made more recoherent by absorbing light from chromophores in the antenna protein in the center of its absorption bands.  Again this is testable, for example, by observing a narrowing of absorption bands upon such light stimulation.

Vattay has found in his simulations that higher amplitude modes are more likely to decohere. This is reminiscent of Fermi’s Golden Rule which states that quantum systems are more likely to drop from a high energy state to the lowest energy state rather than to intermediate energy states.

When a quantum amplitude decoheres to classicity FAPP, at some degree of decohrence it IS part of the classical world FAPP.  But the Hamiltonian of the classical system must be comprised by such classical degrees of freedom that are “sufficiently classical “FAPP degrees of freedom. If decoherence is the only pathway to the classical world, there are no “just classical” degrees of freedom.  Therefore, at some point, the now classical FAPP degree of freedom must modify the Hamiltonian of the rest of the classical system.

Alternatively, motion out the X axis may give a sudden, all or none, transition to classicity, as in our hopes above to recapitulate the von Neumann R process in the Poised Realm. Again,the now classical degree of freedom alters the classical Hamiltonian of the total system.

But then the classical dynamical behavior of the classical aspects of the liposome systems changes.

Now consider an electron in the physicist’s “classical box” with infinite potential barriers. The physicist calculates the behavior of the electron in the box using the Schrodinger equation and the box as THE BOUNDARY CONDITIONS. But if the shape of the box is changed, so too are the boundary conditions and the behavior of the electron will change.

This implies that when the quantum amplitude falls to classicity FAPP or traverses the X axis towards chaos, and changes the classical Hamiltonian of the liposome system, the BEHAVIOR OF THE REMAINING QUANTUM DEGREES OF FREEDOM CHANGE, perhaps light electrons which remain Poised Realm mixed or pure states.

Consequently some different amplitude in the poised realm peaks to high amplitude values and tends preferentially to decohere to classicity FAPP, or classicity out the X axis, again altering both the classical Hamiltonian and thereby again altering the boundary conditions of the still remaining quantum degrees of freedom.

It is clear that this behavior is new.  It is not closed system quantum behavior describable by the Schrodinger equation. It is partially behavior in the Poised Realm with both weird superposition states and pure states, and partially classical FAPP or X axis classical behavior, and the system is also receiving driving quantum and classical inputs as a liposome with light of different wavelengths impinging upon its chromphores.  But its behavior is not merely classical.  And the behavior in the poised realm is not describable by the Schrodinger equation since decoherence is dissipative. Nor is it “quantum random” which will bear on a responsible free will later.

Given Shor’s theorem, recoherence of partially decohrent degrees of freedom, or fully classical FAPP, as chlorophyll and its antenna protein suggest, should be possible.  Recoherence classical FAPP degrees of freedom will again alter the Hamiltonian of the classical system and the resulting quantum behaviors of the total system. Thus this liposome system, open quantum and classical system has deeply novel behaviors, passing from quantum through the Poised Realm to classical FAPP or classical X axis behaviors and back to more or fully quantum behaviors.

It is obvious that this liposome system is NOT ALGORITHMIC, for its behavior is clearly NOT DEFINITE.  Superpositions of mixed states persist for a short time allowing constructive and destructive interference, and the Born rule may apply to which amplitude becomes classical passing out the X axis. Indeed, this system IS NOT A CARTESIAN MACHINE, nor is it a closed quantum system that we are familiar with. Yet this system clearly is both EMBODIED and receives quantum and classical and poised realm inputs, and emits quantum, classical and poised realm behaviors. Thus its quantum, poised realm, and classical behavior enabled by the constraints in the system, have embodied information and therefore a semantics.  It is the start of a Trans-Turing System.

Now generalize to a collection of such liposomes interacting with one another and their world via emitted and absorbed photons and other quantum degrees of freedom, and classical behaviors and poised realm behaviors.

In later blogs I will identify the collection of interacting liposomes with quantum entangled neruotransmitter receptors in the synapses in your brain. From this I hope to get to conscousness, qualia, and the Unity of Consciusness.  We have been disenchanted machines since Newton. I hope to show that we can become re-enchanted in our full humanity.

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