Quantum Physics versus the Singularity

Ever since famous mathematician/physicist Sir Roger Penrose (born 8/8/1931; see picture below) published his best-selling book "The Emperor's New Mind" in 1989 and its sequel "Shadows of the Mind" in 1994, there is an intense discussion going on within philosophical circles and especially the Artificial Intelligence (AI) community about the role and effect quantum physics, quantum biology and quantum theory in general could have for AI and whether quantum theory can possibly improve the understanding of the workings of our brains.

Penrose's position is bold and he essentially believes that current day computers and hence AI can never reach the highest levels of human intelligence because human understanding (as demonstrated by our ability to understand complex mathematics for example) is non computational and hence exceeds the capabilities of machines. He also argues that human consciousness can only be explained when taking quantum effects in our brains into account.

Penrose versus the Singularity

Penrose's theory delivers some of the most profound and strongest arguments against the currently so popular school of the technological "Singularity" in AI. The concept of a technological singularity has been introduced by science fiction author Vernor Vinge in 1993 and entered mainstream popular science with Ray Kurzweil's book "The Singularity is near" in 2005.

According to Kurzweil and his follower singularitans the ever accelerating pace of performance and power of computers will at a certain point in the not so distant future (according to Kurzweil around the year 2045, see chart below) lead to machines with AI that will be smarter than humans in every respect by then.

Once that singularity point is reached, machines will have the abilities to and will start to improve themselves in exponential steps and reach superhuman intelligence levels that are unimaginable to us (with IQ scores of say 10,000 or even higher).

There will then be a "run-away" effect of computer intelligence and we humans will be dominated by such super intelligent machines. This theory is supported by some prominent figures like Bill Gates, Elon Musk, the philosopher Nick Bostrom and even by the famous physicist Stephen Hawking.

Kurzweil's own stance towards these predicted developments is more optimistic. He has even launched a Singularity "University" to spread his views (and make some money with his own predictions). He sees only positive aspects of such a super intelligence for mankind. He thinks, that along the way of developing super intelligent machines we will solve many big problems for mankind like longevity and environmental problems.

He also expects that humans and machines will simply merge over time. According to Kurzweil, humans will soon have all sorts of nano machines inside their bodies and brains and our brains will be directly connected to the Internet and the IoT, the Internet of Things (an idea picked up by Elon Musk lately with his neural lace project). On the other side, machines will become more human like in their behaviour and their appearance. After all, the border line between humans and machines will become fuzzy and fade out, Kurzweil believes.

Some of the singularitans take a much more negative stance than Kurzweil, however. They expect that there will be a major threat that these super intelligent machines will get out of control and might eventually even eradicate the human race. Especially Musk, Bostrom and Hawking have issued warnings along this line of arguments (and Musk uses it to justify his neural lace and OpenAI projects to produce "good and friendly" AI - an absurd and nonsensical idea in my eyes).

It is interesting to notice, that none of the popular proponents of the singularity theory is a specialist in AI. Only Kurzweil (see picture on left) used to work in AI some decades ago when he worked on optical character recognition and natural language processing using neural nets and hidden Markov models. Just recently however, Kurzweil became an employee of Google and gives a lot of public speeches about the advances of AI and his own predicted singularity. He promotes Google services and products along the way and working on his self-fulfilling prophecy. He must have received quite a convincing financial package from Google to give up his intellectual independence to act as a Google promoter and evangelist at this late stage of his life and career at 68 years of age.

Now, Penrose and especially Hawking are also no real AI experts (even though Penrose has published several popular science books over the last 3 decades in which he discusses AI and related computability topics at length and depth). However, they are both accomplished and highly respected scientists, mathematicians and physicists and very smart people and therefore deserve to be taken much more seriously than your typical singularitans like Bill Gates, Elon Musk or Nick Bostrom and the likes. Penrose and Hawking have at least a scientific reputation to lose.

It is quite surprising to see Penrose and Hawking to arrive at the opposite sides of the spectrum of opinions about the singularity and the question where AI will eventually end up. Decades ago, Penrose and Hawking have been close friends and collaborators working together very successfully on the theory of black holes. Now, however Hawking thinks, the Singularity will happen soon and may even be the doomsday of humanity.

Penrose believes the opposite, namely that AI will never reach the human level of intelligence and will never really outsmart humans. Machines may beat us at certain skills like playing CHESS or GO and may drive autonomous cars and do all sorts of seemingly intelligent activities, but they will not arrive at anything that requires consciousness or real understanding or an insight into what they do. Or, as the philosopher Dan Dennett would put it: they may become competent without having any comprehension.

The singularity and AI proponents have all the money and PR behind them. Lots of publications and media are supporting and covering their views pretty much every day right now. Especially the big AI firms with their vested interests all try to sell us how good the world will become with super intelligent AI and machines - without ever proving that this is even possible.

Since I am usually in favour of non mainstream thinkers, I will focus here on the much less discussed views of Roger Penrose and his few collaborators (who have no big corp backing either) and try to explain and evaluate their scientific arguments against the impossibility of computer based higher levels super intelligence and consciousness.

Please be aware, that the topics discussed in the following chapters cover highly complex mathematical and physical theories and are difficult to understand in detail (in stark contrast to the singularity stance which is more a set of believes in the future of computing and an AI "religion" rather than a scientific theory. Their only argument is the ever increasing power of computers out of which intelligence and consciousness is expected by them to somehow suddenly emerge. None of the singularitans has ever given any serious indication how this will happen).

Due to the inherent difficulties of the topics discussed, I can only cover these topics here in a very superficial manner (I need to condense some 1000+ pages of some difficult books of Penrose's down to some 30+ pages). I therefore advice readers that want more substantive and detailed information to do their own further research. My suggestion is to read some of the popular science books of Roger Penrose or - if you want a lighter meal - at least watch some of his speeches and interviews on Youtube.

My goal here is to give an easy to understand overview of the interesting discussion how AI might relate to quantum theory, quantum physics and quantum biology and to show that there are serious theories predicting that the singularity will not happen (at least not any time soon) and that AI may face substantial, unsurmountable theoretical and practical limits.

Penrose's two key Arguments

Penrose's arguments against the possibility of super intelligent machines are based on and motivated by reflections about and conclusions taken from Goedel's Incompleteness Theorem and the limits of algorithms and computability on one hand, and considerations about quantum mechanics and quantum theory on the other hand.

He believes that our intellectual understanding and our consciousness are caused by and are based on quantum level effects in our brains (that only happen in living organisms and don't exist in machines). In his eyes, "understanding" is a fundamental aspect of intelligence and requires consciousness. For Penrose understanding is a non computational ability of our brains and makes us and keeps us superior to any current or future AI system or anything we would consider an "intelligent" machine.

These are very strong and bold statements that challenge the singularity camp and even the whole AI community and their ongoing massive efforts to develop just that: intelligent and conscious machines.

Goedel's Incompleteness Theorem

The first main argument of Penrose outlined in his Emperor's new Mind book is based on Goedel's Incompleteness theorem and its proof. (Since I have just recently covered this subject at length in another post - see: "Goedel's Incompleteness Theorem and the Emergence of AI" - I will not explain or discuss the Incompleteness theorem here again and refer the interested reader to my prior post instead (also see the chart summary below).

Penrose argues that Goedel (and Turing) proved that machines cannot solve certain (mathematical) problems like proving the consistency of certain axiomatic systems or solving Hilbert's Entscheidungs Problem (and many more problems of theoretical computer science and mathematics known today).

However, he argues further, we humans can intellectually "step outside" these underlying theories and go beyond them and prove exactly the limitations of axiomatic systems and even universal turing machines. Hence, we can prove what machines cannot do - as Goedel (and Turing and others) showed. Machines are limited to what algorithms can do, no more, no less, and no matter how "smart" such algorithms might be or become (by self-enhancement in AI for example).

Humans are not limited to algorithmic thinking. Certainly, we can think in algorithmic ways and often do so as for example when we do simple arithmetics and divide two large numbers or do certain other sequential quasi mechanical calculations. But we are not limited by these (simple) algorithmic procedures. We often solve problems with intuition and immediate insights instead that skip and go far beyond algorithmic procedures as the complex proof of Goedel's Incompleteness theorem shows. This is also exemplified and especially true for our theories of the infinite as introduced by Cantor. In principle, argues Penrose, machines cannot "construct" and "understand" completed infinite entities and even uncountable infinities and prove theorems about them as we can !

According to Penrose, we humans have the ability to "step outside" of the algorithmic boundaries and procedures when we do mathematics (and other conscious thinking). We then often have sudden "insights" and just "see" possible solutions instantaneously in our minds without the need of any step by step algorithmic calculations. These sudden insights constitute a critical part of what we call "understanding", a feature of consciousness that machines never have. When machines beat us in Chess or GO they don't even "understand" that they have done just that ! As a matter of fact, they don't even know what Chess and GO are, they just shuffle bits around without any conscious knowledge of what they are doing or achieving with it.

Penrose's analysis what Goedel's theorem says and the consequences it has for AI and our understanding of mathematics has been criticised and discussed from many angles. With his opinion he continues and extends arguments along the historic line of well known AI critics like Weizenbaum, Dreyfus, Searle and others, but on a deeper, much more scientific level.

I will not discuss this issue here further as I have discussed most of them already in my post about Goedel in some detail. In general, I think that Penrose's arguments related to the scientific and philosophical consequences of Goedel's theorem are valid and substantial in their core and that Goedel's theorem poses a major threat to the goals of AI and the claims of the singularity camp.

However, even if Penrose is right about Goedel and the consequences of his proof as we will assume from here on, he still must explain how our brains can actually "step outside the box" and do "non algorithmic thinking", how exactly do we do this, what are the underlying mechanisms and how can they be explained ? The answers to these questions are to be found in quantum physics and quantum effects in our brains according to Penrose.

Quantum Theory and the Quantum Mind

To solve these problems, Penrose reverts to quantum mechanics, quantum theory in general and quantum gravity and quantum biology specifically (the biology part is mostly covered by his colleague and collaborator Stuart Hameroff). His main idea and argument is that our understanding of complex (mathematical) issues is caused by certain quantum processes in our brains. These quantum processes are not computational or algorithmic and hence cannot be executed or resolved by today's computing machines.

Several critics of Penrose argued that quantum theory has nothing to do at all with AI and how our brains work and shall therefore be kept out of AI theories and be constrained to physics where it belongs. One key argument of his critics is that such core AI phenomena like intelligence and consciousness are currently still so ill defined and little understood that it makes things only worse when bringing quantum theory into the mix.

Quantum theory is itself barely understood in many areas yet and is still considered counter intuitive by physicists and non physicists alike despite its undeniable practical success and extreme precision when tested experimentally.

Key concepts of quantum theory like: Heisenberg's uncertainty principle, particle entanglement, superposition of particles and their states (i.e. particles can be at two places at once), quantum tunnelling, the wave/particle duality and the quantum state wave function and its collapse as a result of measurements/observations and all their consequences are still hard to grasp for any non physicist. There are several incompatible interpretations of these effects vigorously disputed still even among physicists today - some 100 years after quantum mechanics was established.

Even though these arguments have a point, I think that this line of criticism is unfair to Penrose. He is undisputedly one of the leading theoretical physicists in the world and should be allowed to use his highly specialised knowledge and insights to try to solve thousand years old problems as difficult as it may be to follow his thinking sometimes.

Despite all the fundamental conceptual problems that might still exist with quantum theory, it is probably the most successful and most precise physical theory mankind has ever created. It would not be justified in any way to exclude quantum theory derived arguments from discussions about consciousness. If there is a serious line of scientific arguments explaining the emergence of consciousness that pulls us into the nanoscale regions of our universe and brains then so be it. Penrose at least - as the only established scientist known so far - puts forward a clear and testable theory of how our consciousness might be explained to emerge from minute quantum effects in our brains.

After all, difficult problems like what are intelligence and consciousness might require just such difficult and complex scientific answers. Otherwise, if the answers were easier to obtain, the problems should have been resolved already ages ago! Penrose puts forward a real testable theory about our brains and minds - in stark contrasts to the singularity camp that only believes in the emergence of strong AI at some point in the future without giving any solid scientific reason or justification why this shall actually ever happen other than the exponentially increasing power of computers.

Platonism and Quantum Reality

Besides being a leading physicist, Penrose is also a philosopher and platonist. He admits this with no hesitation. He thinks - like Plato did and many other famous mathematicians after him like Cantor and Goedel - that mathematical objects do exist independent of humans and that true mathematical statements say something about a kind of reality that exists independent of us. As a matter of fact, platonists believe that abstract objects and forms like numbers, circles, triangles etc are the "real reality" and that our physical world is just an imperfect approximation and implementation of these abstract forms and objects.

When applied to our brains and minds, platonism leads to the so called dualism which has been made popular by Descartes. Descartes argued that our mind and our thinking happen and exist in a different realms than physical matter like every day objects or our bodies and brains. Mind is different from matter. Matter constitutes the physical world we live in but our mind constitutes our mental reality of thoughts, ideas and consciousness.

For modern science, dualism is not acceptable as it postulates a reality above and independent of matter that cannot be tackled by scientific methods. Our mind and consciousness would not be part of our material world and the physical and other scientific laws of this world would not be applicable or in any sense verifiable in the sphere of mind.

Penrose is a scientist and platonist. So he tries to get rid of and solve the duality problem created by Descartes between mind and matter with his new approach. He tries to explain consciousness and at the same time how consciousness and matter can be reconciled in the same world. He hence tries to kill two birds with one stone. He tries to resolve the problem of a separate mind from matter by bringing consciousness back into our physical reality and the material world. To bridge the gap between consciousness and the physical world he brings quantum theory into the game.

His main idea is simple. He argues that we have a Quantum Mind ! That is to say, according to Penrose, our mind is influenced by and based not only on standard physical and chemical processes like the firing of our neurons in our brains but also on frequent and essential quantum effects. Whenever these quantum effects happen we have moments of conscious experiences ("now" moments) and awareness in our minds. And whenever these conscious moments happen, our minds and the physical quantum world overlap and coexist at the same time in the same reality ! That is Penrose's proposed solution to the centuries old problem of dualism.

His approach also justifies Penrose's platonism and his view that mathematical objects are real in a sense and that mathematicians study abstract objects that exist independent of us and discover truths rather than invent them. In the short and sudden conscious quantum moments we have direct - non computational - access to and experience of the realm of abstract objects buried in the quantum world. In these short moments, our minds and the quantum reality are one and the same thing. That is why we can often just "see" mathematical truths in an "aha" or "now" moment without any need or use of algorithmic calculation.

But how exactly do these "aha" or "now" quantum moments of consciousness come about and how can they be explained ?

The Copenhagen Interpretation of Quantum Mechanics

Penrose did not only try to justify his platonistic view of mathematics and resolve the dualism issue, he also tried to establish the objectivity of consciousness by brining quantum theory to the table. He actually even went an additional step further along the way and argued against the classical observer based and probability interpretation of quantum mechanics (the so called Copenhagen interpretation, see below) of the famous 1922 Nobel Prize in Physics winner Niels Bohr.

Bohr was one of the founding fathers of quantum physics. He developed the "Bohr model" of atoms. He postulated that electrons must revolve around the nucleus of an atom in stable orbits with discrete energy levels. Electrons can jump from one energy level (or orbit) to another by assuming or omitting quantised energy packages (in form of electromagnetic waves; see chart below). Even though this simple model has since been augmented and improved, its core principles are still considered valid in today's physics and chemistry.

Bohr was also an amateur philosopher like Penrose and believed in the principle of complementarity by which he meant that objects and physical entities could be described and independently be analysed with seemingly contradictory terms or properties like in the famous quantum wave and particle duality. Hence, Bohr was convinced that for example light can behave both like particles and waves at the same time depending only on the experimental settings and observations chosen. He felt confirmed in his views by de Broglie's theory that even electrons and matter can be described as waves (which was experimentally confirmed in 1927).

Bohr's view of the ontological status and consequences of certain quantum effects like Heisenberg's Uncertainty Principle led to the Copenhagen Interpretation of quantum physics (which in several enhanced versions is still the most commonly taught interpretation of quantum mechanics today) caused many discussions among the leading physicists of his time.

Especially Albert Einstein, who had revolutionised physics himself in many respects and who himself had contributed to the emergence of quantum mechanics (for example by explaining the photo-electrical effect), had a more classical, deterministic and causalistic understanding of quantum physics.

He tried to argue on several levels against Bohr's more indeterministic interpretation of quantum physics. This led to the famous communication between Einstein and Bohr in which Einstein said, that he is convinced that God does not throw dice when making decisions. Einstein was trying to make fun of Bohr's non deterministic views of quantum events. Bohr responded humorously: " Einstein, don't tell God what to do!".

Bohr's Copenhagen interpretation claims that quantum scale physical systems cannot be understood as having definite physical properties prior to or unless being observed. Between observations no definite statements can be made about quantum objects, only probabilistic statements about their expected states. According to this interpretation and understanding of the quantum world, quantum theory can only predict the probabilities of the results of future observations. This makes the quantum theory more a theory of what we can know about the physical world, rather than a theory about the physical world itself.

Bohr therefore also had no problem with the so called superposition of particles that often plays a decisive role in quantum mechanics. According to the superposition effect, a quantum particle can be at two different places or states at the same time. However, when a particle is observed, this superposition "collapses" and the particle is only found in one concrete state or place after the observation. This effect is called the collapse of the wave function (see chart below).

The underlying wave function -used everywhere in quantum mechanics - was derived by Erwin Schroedinger (picture on left) in 1926 who won the Nobel Prize in Physics for his work in 1933. Schroedinger's famous mathematical partial differential equation describes the changes over time of quantum particle movements.

According to the Copenhagen interpretation of quantum mechanics, Schroedinger's wave function equation (see below) is the best and most precise way to describe the state change and movement of quantum particles. The equation is used in all major areas of quantum theory, quantum mechanics, quantum field theory, quantum gravitation and string theory even though there are also other equivalent formulations of the underlying mathematical principles describing the movement of quantum particles like Heisenberg's matrix operations.

Due to the minute scale of the measured subatomic particles the observation process itself will have substantial effects on the measured system and the outcome of the observation. The act of the observation influences the possible states and locations subatomic particles can be in and the collapse of the wave function reduces the number of states and locations the particles can assume after measurement to only one of all the possible states. Heisenberg has also derived a theoretical and practical limit for any quantum measurements with his famous Heisenberg Uncertainty Principle.

Since Bohr's time a variety of several alternative interpretations of quantum mechanics and quantum effects and especially the collapse of the wave function have been put forward such as the many-worlds interpretation, the de Broglie-Bohm interpretation and the objective quantum decoherence interpretation or objective reduction (OR) which is what Penrose supports.

Objective Reduction

As a platonist Penrose could not agree with the observer base, non objective Copenhagen interpretation of quantum mechanics. Bohr believed that the wave function collapses when an observation is made by some conscious being. This is unacceptable to Penrose. He would not accept that it requires a conscious observer to determine the outcome of a quantum measurements and he does not believe that quantum objects or events would not have a clearly defined ontological status of existence when not observed between measurements.

Even Schroedinger himself was puzzled by the Copenhagen interpretation of his own formula. He did not agree with the consequences of the observation dependent interpretation of quantum mechanics and constructed his famous "Schroedingers Cat" Gedankenexperiment to show how ridiculous and counterintuitive such an interpretation actually is (see cartoon).

To counter this interpretation, Penrose postulates a so called objective reduction to explain the collapse of the wave function. For this view he assumed that the collapse of the wave function is a "real" physical process in which observers play no special role.

He argues that the stability of the wave function depends only on the energy difference between the superpositional states of particles (assuming no outside disturbance). The wave function will collapse into a single state when this energy difference of the states exceeds a certain threshold. The resulting single state is defined by a probability function of the amplitude of the original wave function.

To arrive at this objective reduction, Penrose made a bold step by combining Einstein's general relativity theory with quantum theory into Quantum Gravity. According to Einstein's general relativity theory, every mass causes a certain curvature or warp depending on its size in the structure of the space-time in its surrounding. This bending and deforming of space-time causes the physical effect that we call "gravity". Usually such gravitational effects are only noticed in relation to large and massive objects like our earth, the moon, our sun and black holes for example. But they have effect on much smaller scale as well as Newton's famous apple that hit his head demonstrates.

Penrose argues that gravity also plays a role in the quantum world of the tiniest atoms or sub atomic particles. The mass of these tiny particles also produces minute space-time warps around themselves and cause a disturbance of the spacetime when and wherever they move. These disturbances are obviously very, very small. He suggested that at the Planck scale (at 10^ -35 meters) in which these quantum particles operate the curved spacetime is no longer continuous, but discrete. So every such particle generates its own "blister" in spacetime on which gravity at a "one graviton" level exerts a destabilising force.

If a particle is in superposition with itself and in two different places at the same time, it therefore creates, according to Penrose, two distinct tiny disturbances simultaneously in their surrounding space-time geometry causing two superposed gravitational fields (see chart below). But, again according to Penrose, it takes energy to maintain the superposition of these two fields. If no energy is added to the combined system, then over time they will vanish and collapse into one single location with just one associated gravitational field. This is Penrose's argument in a nutshell for the possibility of the objective reduction explaining the collapse of the wave function with no need of any (subjective) observer !

This objective reduction also explains, according to Penrose, why we do not ever experience any macro objects of larger size like cars, humans or stars in superposition and in two locations at once. The energy required to experience such superposition of macro scale objects for a measurable timespan to be maintained would be immensely high. However, electrons and any subatomic particles can be in several places at once until the space-time warp separation reaches the objective reduction threshold and causes the collapse of the wave function - which could be already after some fractions of nano seconds - or in certain circumstance thousands or millions of years later.

The greater the mass of an object, the faster its potential superposition will undergo an objective reduction. At the quantum level superpositions may take millions of years to reach the threshold level for objective reduction and hence the particles may sustain superposition for ages ! However, if we consider an isolated object with a macro scale mass of say 1 kilogram, then the objective reduction threshold would already be reached after only 10^ -37 seconds !

This objective reduction time window and its effect brings up more interesting questions. For example: at what specific amount of mass can an object no longer appear in superposed states and no longer be seen in several locations at once ? Penrose estimates that the macroscopic effect kicks in at the scale and size of usual dusk particles. He has proposed concrete experiments to test this hypotheses.

?Stuart Hameroff - or an Anesthesiologist's View of Consciousness

With his objective reduction, Penrose had solved a major problem in quantum mechanics of how to avoid the dependance of the quantum world on subjective observation. He also had explained in the Emperor's new Mind book that our brains are not limited by Goedel's theorem like classical computers are. His thought was, that the "extra power" that our brains have over computers come from quantum processes that happen in our brains and are not computable.

In his book however, he had not been able to propose where exactly in our brains such quantum processes occur and what role they play in explaining our higher intelligence, understanding and finally our consciousness. He only indicated that our retinas interact with photons and that this interaction requires quantum level interactions. Penrose left the question open where substantial quantum processes occur in the brain that can explain and cause our consciousness.

Stuart Hameroff (see above), an emeritus professor for psychology and anesthesiology and current director of the Center for Consciousness Studies at the University of Arizona proposed to Penrose where the required quantum effects may take place in the brain.

He is working since the early 1990s closely with Penrose on his quantum consciousness theory and brings in the molecular, chemical and biological knowledge needed to defend Penrose's theory. As a practising anesthesiologist at the time he was also an expert on human consciousness as he took patients in and out of consciousness every day during his professional work.

Hameroff suggested to Penrose that the place of the quantum processes might actually be found and maintained in the so called Microtubules !

Hameroff was convinced that consciousness - contrary to the popular opinion of the singularitans - does not emerge from the signalling between the neurons and synaptic plasticity in our brains, but that consciousness emerges from a deeper level layer inside the neuron cells. Consciousness emerges according to Hameroff on the level of the microtubules that are an essential structural and functional part of all brain cells (including glial cells) and occur in massive amounts inside neurons.

In his first book called Ultimate Computing published in 1987 (before he met Penrose) Hameroff already discussed the computational abilities of microtubules. In this book Hameroff argued that the microtubules could be the key information processing units in the brain rather than the neurons with their electrical potential signalling. When he then later read Penrose's Emperor's new Mind, he saw a possible combination of his approach with Penrose's quantum approach. This collaboration between Penrose and Hameroff led Penrose to publish his book: Shadow of the Mind in 1994. They have cooperated and refined their combined theory ever since until today.

Some prominent physicists like Max Tegmark have argued in recent years against Penrose and Hameroff that such quantum phenomena in microtubules cannot have any significant influence upon how our brain creates consciousness or intelligence. Even if these quantum effects would happen in our brain, argues Tegmark, they would be too short lived (he calculated a time of only 10^ -15 seconds) and hence wouldn't persist long enough in such a "warm, wet and noisy" environment of our brains to have any measurable effects. However, Penrose and Hameroff and colleagues have shown in several replies to Tegmark lately, that Tegmark made mistakes in his assumptions and calculations and that microtubules can indeed execute quantum effects in the brain at the temperature of the brain and in time frames necessary to execute substantial influence on our consciousness and thinking processes as Penrose and Hamerhoff had proposed.

What exactly are Microtubules ?

Microtubules (short "MT") are part of all eukaryotic (human) cells. They have a variety of functions and make up an essential part of the cytoskeleton of the cells. They can be found pretty much anywhere in the cytoplasm of our cells and neurons. They are nano sized hollow cylinder shaped molecular structures (see scheme below)

MTs are important within the cells for several different and important processes and functions. As mentioned, they are foremost a major structural component of cells and form part of the cytoskeleton (with microfilaments). They are also making up the structural components of the cilia and flagella that are needed by cells to move around autonomously and provide mobility for the cells when needed. The MTs achieve this by fast repeated cycles of growth and contraction.

Microtubules self assemble within the cells from two tubulin molecules (alpha and beta tubulin - shown as yellow and white balls in chart above). They attach to each other in alternating sequences and form linear, planar and cylindric 3-D shapes. The cylindric forms can change their length from a few nanometers to 50 micrometers in very short timeframes allowing cells a stable but flexible structure and to contract and expand to allow the cells to be mobile. MTs are also essential for the cell division process and pull the chromosomes inside the cell nucleus apart so cells can divide (during mitosis and meiosis).

Each neuron in our brain contains approximately 10^9 microtubules (see picture left)! In the dendrites and the cell body they are organised as a fractured network connected by microtubule associated proteins (MAPs).

In the axons of the neurons they are usually long continuous, non fractured tubules.

They function in the axons as a kind of conveyor belts for motor proteins and allow the transport of molecules and especially secretory vesicles from dendrites through the cell body and the axon to the synapse membranes and hence are an important part of the inter neuronal signalling processes and needed for synaptic learning and plasticity.

According to Penrose and Hameroff, the role of MTs for our consciousness comes from the fact that many proteins used in drugs bind to the tubulin proteins that make up the MTs. The drugs binding to the tubulin interfere with the MT dynamics (see picture above showing the build up and deconstruction processes of the MTs) and hence can strongly effect the cell functions and growth and even lead to apoptosis (the genetically programmed cell death). Several drugs can stabilise and de-stabilise the MT dynamics and can be used also for cancer treatments. MT polymers are very sensitive to extra cellular environmental effects. MTs can also influence and control gene expressions within the cells.

There are further strong medical indications that MTs play an important role in the generation and maintenance of our consciousness. Their dynamics and structure has been linked for example to the Alzheimer's disease which is a neuronal disease that leads to the stepwise loss of cognitive skills and consciousness.

Microtubules as Cellular and Quantum Computing Devices

Hameroff has suggested that the MTs can also be seen as powerful 3-D nano scale computing devices ! He showed how MTs can be used to model all basic classical computational operations (logical gates) with tubulin molecules as the cells of a cellular automata model. Such a cellular automata ("microtubule automata") would act upon their direct tubulin neighbours within the MTs cylindric 3-D structure by simple rules based on dipole coupling strengths (see also my post : "From the Game of Life to Consciousness").

Hameroff has then extended this idea to see the MTs as quantum processors acting as "quantum computers" with superposition of the tubulin protein molecule particles. He revised this model later and argued that the the MTs qbits (the quantum version of "bits") are based on oscillating dipoles forming superposed resonance rings in helical pathways on lattice like substructures of the MTs (see A below). This means that the superposed states are not tubulin molecules or parts thereof but rather the potential pathways that make up the computation processes of the MTs.

Sherrington had first proposed in 1951 to see the cytoskeleton of our cells as a kind of cellular level "nervous system". MTs can therefore be seen as molecular nano computers and have accordingly been nick-named "nano brains".

The latest improved and revised approach by Hameroff and Penrose has been confirmed in 2013 by experiments of Bandyopadhyay et al in Japan.

Orchestrated Objective Reduction (Orch OR) and Microtubules

With trillions of microtubules in our brains doing all their individual computations according to Penrose and Hameroff, it is hard to see how all these potential quantum processes going on in the microtubules can cause a stable and unified consciousness and experiences (a similar problem arises on the neural network level). Somehow the activities of the quantum processes in the microtubules have to be synchronised and "orchestrated".

Hameroff and Penrose have argued that this synchronisation or orchestration of the quantum activities of the microtubules is caused by the microtubule associated protein (MAP) attachments sites on the microtubules. They "tune" the quantum oscillations in lattice like substructures of the microtubules and thereby regulate the objective reduction or self collapse of the wave function in certain co-ordinated frequencies that can be measured.

Each time such a collapse occurs, a very short "conscious now" event happens. Sequences of such individual events create an experienced "stream of consciousness". Our actual experience of a continuous stream of consciousness is an illusion caused by an effect similar to when we watch a movie. A movie is not a continuous stream but a fast display of a sequence of framed still images just displayed at rapid speed of 25 frames per second. The same happens with our "conscious movie" that we experience. The many conscious "now moments" just happen so often that our brains experience them as a continuous flow without noticing the non conscious moments in between.

The scheme below shows the increasing resonating oscillations of these processes on the microtubules (1, 2, 3) and the emergence of the conscious effect (between the states 3 and 4 of the microtubule) caused by the microtubule quantum oscillations reaching the threshold for the objective reduction causing the conscious "now" moment and the associated collapse of the wave function, after which new oscillations emerge and the process repeats.

Predictions and consequences of the Orch-OR model

The Orch-OR theory allowed Penrose and Hameroff to derive several very interesting consequences and predictions. Hameroff proposed that quantum particles can "tunnel" between neurons and other brain cells like astrocytes using so called gap junctions (direct connections of cells with no myelin barriers between - see chart below).

In this way a complex and powerful communication network between all brain cells can be established that does not even need or require the firing of neurons and their communication via synapses - a kind of base level high bandwidth wireless communication between our brain cells ! This consequence of their theory was confirmed experimentally in 1999.

Hameroff and Penrose further suggested that EEG signals and waves are caused by the underlying synchronisation of the quantum vibrations of the microtubules in certain neurons which project their axons to the top of our brains right under our scull where they can be easily measured as EEG waves.

Hameroff further theorised that conscious activities underlying the EEG signals can be derived from their model. According to their model, microtubules are using cross gap junctions entanglements to form dynamically larger groups of synchronised oscillating microtubules.

Hameroff suggested, that their model explains how consciousness is forming and acting in the brain. Consciousness in the brain can be seen as moving association patterns of quantum entangled zones of microtubules. These zones "move around" in the brain in the form of dynamic fields of synchronised microtubule networks combining the activities of neurons and glial cells !

Non synchronised zones of the brain would "only" execute unconscious brain activities. This aspect of the Penrose-Hameroff theory is confirmed by the recently discovered so called Posner clusters that can form and interact even via longer distances in the brain (see details in chart below).

Penrose and Hameroff also claim that their model can explain the formation of long term memories better than currently known models. Current neural models assume that learning and memory formation is essentially build by modifying synapses of neurons (synaptic plasticity). However, according to Hameroff these synapses are membrane structures that cannot sustain and represent long lasting memories. Such long term potentiation needs the underlying microtubules to sustain.

Their theory also predicts that neurons themselves can learn as individual cells ! An individual neuron can use its microtubules to learn to recognise and process patterns - without other neurons and synaptic plasticity.

Since the microtubules can do their own computations and learning in any cell they occur in, this also explains why even already very simple organisms and microbial cells that do not have any neurons or brains can still be intelligent to a certain degree (pls see also my recent post: "Intelligence without Brains") !

Finally, one more very interesting consequence of their theory is that it also gives a framework how the famous "binding problem" in AI can be resolved ! How do the neurons know which other neurons are engaged in one and the same single task across the brain ? The dynamic zones of entangled synchronised microtubules and Posner clusters described above might provide a solution for the binding problem.

Quantum Biology

Since Penrose published his "Shadows of the Mind" in 1994 explaining the Penrose- Hameroff model of quantum computing microtubules in the brain, a whole new science of Quantum Biology has emerged with many more concrete and confirmed examples of quantum processing in living, biological organisms.

Quantum processes have been studied since and found in our eyes (already postulated by Penrose 1989), in the magnetic field based orientation in bird brains and in photosynthesis processes in all plants and various cells. Quantum processes, especially quantum tunnelling are now also considered as essential factors in several genetic processes such as DNA mutations.

Conclusion

According to Hameroff: "Orch OR is the most rigorous, comprehensive and successfully-tested theory of consciousness ever put forth."

As a matter of fact, Penrose and Hameroff have proposed 20 concrete scientifically testable consequences of their theory (some mentioned above). So far, 6 of them have already been confirmed while none of them has been refuted.

However, the Penrose-Hameroff approach to explain the emergence of higher intelligence and consciousness is also without a doubt the most complex theory for these topics ever proposed. The theory combines and links together such diverse areas of science as: philosophy (platonism), computability theory (universal Turing machines), mathematical logic (Incompleteness theorem), quantum mechanics, general relativity theory, quantum gravitation, quantum biology, cellular automata (microtubule automata), cognitive neuro science, anesthesiology and cellular micro biology all into one complex theoretical framework !

It is obvious that such a wide approach must attract criticism and fire from all sides. Surprisingly though, even after some 30 years the theory stands strong and is un-refuted so far and scientific evidence is increasingly supporting more facets of this framework.

With his young age of 86 years now, Sir Roger Penrose is still intellectually sharp like a razor and very creative and active. He is still publishing new books and presenting his work and theories around the world. With Hameroff he continues to refine his consciousness theory whenever new criticisms come up.

When compared to the singularity approach, Penrose and Hameroff win hands down. The singularity proponents have no scientific base to defend their claims that once computers get more and more powerful super intelligence and consciousness will somehow suddenly pop up and emerge. Their prediction is that this will happen around the year 2045 or no much later.

However, as Hameroff and Penrose have shown with their analysis of the computational power of the microtubules that exist in all our brain cells (and even communicate with glial cells), the assumptions and forecasts of Kurzweil and the singularitans when the singularity will actually occur are doomed.

Their calculations and estimates so far take only the classical brain models as a basis in which the neurons are the main drivers for intelligence and consciousness. Hence only the estimated numbers of neurons and their connections in our brains, not including the microtubules or glial cells, are taken into account so far.

So, even if the Penrose/Hameroff theory turns out to not be correct at the end of the day, they have certainly shown already that microtubules play a key role in our brains and that our brains are much more computational sophisticated and powerful than the singularity camp wants to admit.

Kurzweil has predicted that by 2023 single computers will reach the processing power of a single brain with around 10^18 calculations per second and by 2045 will achieve around 10^28 computations per second to beat all human brains taken together (around 10 billion people). This would then somehow cause the singularity.

However, these calculations are way off according to Penrose and Hameroff. There are around 100 times more cells in the brain than just neurons and they all play a part in the emergence of consciousness and higher intelligence. Each of these brain cells contains an estimated average of 10^9 microtubules and each of the microtubules can execute millions of quantum computations within a second.

This gives around 10^13 brain cells times 10^9 microtubules times 10^6 calculations per second on average which gives an overall estimate of 10^28 calculations per second for just a single (!) brain and hence 10^38 for all humans taken together (by around 2045). So, the singularity estimate is false and off by a factor of about 10^10 ! It seems like the doomsday scenarios of the singularity camp and followers must be postponed.

And these estimates do not even take into account that the cells in the brain would be quantum entangled and hence would compute and communicate instantaneously with now noticeable time delays and therefore would actually be much faster (!) than any current computers, not slower than computers by a factor of 10^6 as Kurzweil assumes in his own estimations.

Anyway, no matter how this all ends up and turns out to be, the Penrose-Hameroff model is a fascinating theory to study with many new and unique ideas about how our brain works and how higher level of intelligence and consciousness might emerge out of the basic quantum space-time structure of our universe.

It also provides a humbling perspective for all AI enthusiasts who still believe that AI can solve all the world's problems in the next few years. There may well be substantial theoretical and practical limitations for what we possibly can do with our current type of computer technology that we better take into account more seriously.

E.Schoneburg

Hong Kong, June 6, 2017