Roger Penrose: The Singular Mind

• Roger then looked to quantum mechanics for possible answers to account for consciousness.
• Quantum mechanics contains non-computable elements, most notably, the underlying cause of a wave function collapse.
• Operating from the position that human consciousness is a non-computable factor, Penrose formulated Orchestrated objective reduction (Orch OR).
• Orch OR is a theory that attempts to explain how quantum mechanical processes in the brain result in consciousness.
• A central idea in quantum mechanics is that any particle can exist in multiple states simultaneously.
• This is known as quantum superposition.
• When a measurement is taken, the wave function "collapses" to one and only one state.
• Once it's collapsed, it then becomes a matter of classical mechanics.
• Objective-collapse theory is the idea that there exists an objective threshold of some physical quantity and that exceeding this threshold causes the wave function to collapse.
• Researchers still haven’t been able to determine what this threshold might be.

• Microtubules consist of tubulin proteins which contain a dipole that gives them ferroelectric properties.
• Ferroelectricity is a property observed in certain materials characterized by the presence of a spontaneous electric polarization without the presence of an electric field.
• Electric polarization refers to the separation of the center of positive charge and the center of negative charge in a material, much like the north and south poles of the globe are separated by a distance.
• These tubulin proteins can exist in many states – or as Roger and Stuart Hameroff propose, a superposition of states.
• Microtubule structures are highly influential in the brain.
• Along with actin and other cytoskeletal structures, microtubules self-assemble to establish cell shape, direct growth, and organize functions including those of brain neurons.
• Roger contends that consciousness depends on biologically ‘orchestrated’ coherent quantum processes in collections of microtubules within brain neurons.

• What would such a theory look like?
• Roger focuses on a small part of consciousness: understanding.
• There are theorems of logic, most particularly Gödel's theorem and Turing's analysis of computation, that lead Roger to believe that human understanding is not a computation.
• Computers run on algorithms.
• What we do when we understand a mathematical proof does not involve following an algorithm:
• "A proof is an algorithm using certain kinds of rules and you have to use them correctly. For it to be a proof, you must believe that those rules only give you true statements.”
• “It's that belief, that it only gives you true statements, which enables you to demonstrate the truth of a proposition, which you can see must be true.”
• “Nevertheless, it cannot be derived by means of whatever rules you start with. As long as you believe those rules only give you truths, then you must believe this Gödel statement is also true and not derivable by means of those rules." - Roger Penrose

• "If you're a mathematician, you very strongly get the feeling that it's a bit like geology or archeology or something. You're exploring a world and discovering things which are out there. You don't invent the theorems, you discover truths, which are in some sense out there in a world, but they're not the world." - Roger Penrose
• Only a small part of the mathematical world encompasses the whole of the physical world.
• A beautiful theorem of pure mathematical work occasionally finds a real-world application sometime after its discovery.
• But the more we discover in physics, which is governed by equations and geometrical ideas, the more we reduce them to mathematics.
• And in that mathematics, we gain enormous precision in how we describe and understand the way the physical world operates.
• "You have to resort to mathematics when you try to probe reality at its deepest levels." - Roger Penrose
• Both the world of mathematics and physics relate to the world of conscious experience.
• Roger thinks it is a hopeless task to build everything from this world, or empirically, because sensory experiences are difficult to describe in a precise way.

• Roger speaks briefly on the history of geometry in mathematics, beginning with Euclid's parallel postulate.
• The parallel postulate states that if given any straight line and a point not on it, there "exists one and only one straight line which passes" through that point and never intersects the first line, no matter how far they are extended.
• Any geometry where the parallel postulate does not hold is a non-Euclidean geometry.
• Non-Euclidean geometry includes hyperbolic, spherical, and elliptic geometries, plus many more branches.
• Conformal geometries are sets of transformations that preserve angles.
• These are, at their fundamental levels, physical laws that describe the physical world in different and increasingly refined ways.

• Quantum computers are special in the sense that they (for now) can only solve very specific problems.
• "Ordinary" computers are designed to solve almost any algorithm that you can impose upon them.
• But as computer chips become increasingly smaller, they will be eventually restrained by quantum mechanics.

• Conformal Cyclic Cosmology
• One idea Roger is currently most interested in is conformal cyclic cosmology.
• According to this hypothesis, the universe undergoes repeated cycles of expansion, referred to as eons, each starting from its own Big Bang and finally coming to a stage of accelerated expansion which continues indefinitely.
• It was Einstein's positive value cosmological constant that inspired this hypothesis.
• Because this constant is accelerating the universe's expansion, it means that, from the conformal point of view where angles are preserved, the universe will be spacelike at its end.
• Since the Big Bang singularity is also spacelike, it might be possible to match conformally the end of our universe to its beginning.
• State Reduction Experiments
• State reduction experiments look to the state change of the measured system caused by a measurement conditional upon the outcome of the measurement.
• These experiments are some time away, but Roger is excited by their prospects.
• Consciousness

"Not biological experiments, but just physics experiments that are being done there. Whether you will see the quantum effects in microtubules is quite possible...but to see any direct evidence of connections with consciousness, I think it's a long way off because that's really such a slippery subject." - Roger Penros