Gaps in Penrose’s Toiling
Rick Grush & Patricia Churchland
Philosophy of Dept., University of California, San Diego
Journal of Consciousness, 2, No. 1, 1995, pp. 10-29
Keywords: mathematical truth, unknowable algorithm, quasi-crystals
The core part of this article is the Grush and Churchland’s discussion of the soundness of the processes by which mathematical truth is ascertained. The authors say that for convenience they will grant Penrose’s claims that human mathematicians are not using a knowable sound algorithm in exercising mathematical understanding, and thus arriving at ascertainible or unassailable mathematical truths. They also go along with his claim that there is no sound but unknowable algorithm. Instead they concentrate their discussion on the soundness of the brain procedures involved. They basically argue against the soundness of such procedures. They point out, and Penrose agrees with them in saying, that mathematicians sometimes make errors. The authors admit that anyone can make an error while applying a fundamentally sound procedure but they argue that the complexities of mathematics make it hard to distinguish an error of application from an unsound procedure. Therefore they claim that Penrose can only substantiate his claim by specifying procedures that are short enough for it to be easily checked that the application of procedures has been correct.
The authors point to the case of the famous 19th century mathematician, Cauchy, who denied the possibility of the existence of infinite sets. The existence of such sets is now a basic part of mathematics as taught to students. The authors argue from this that there are no sound procedures, but only procedures that are usually reliable, or which are useful on a trial and error basis.
Penrose replied to Grush and Churchland in the next volume of the Journal of Consciousness Studies. In his reply, he decides to concentrate the argument on the question of Pi 1 sentences, which assert that particular computations, such as Goldbach’s conjecture and the Lagrange theorem do not halt. He considers that these sentences are in principle accessible by human reasoning and insight. In contrast to Grush/Churchlands contention that mathematicians use trial and error and general reliability, Penrose claims that mathematical understanding is more precise than anything in science or philosophy. Penrose accepts that individual mathematicians make errors, but says the point is that there is an argument to be found which gives access to the mathematical truth.
The rest of the Grush/Churchland article is a disappointment relative to the reasonably coherent discussion of mathematical truth. As philosophers, they are more plausible in terms of arguments relative to logic and maths than in physics or neuroscience, where Penrose and Hameroff are better placed in terms of scientific knowledge. They appear to waste a lot of time on the proposition attributed to Penrose that quasicrystals are evidence of non-algorithmic physical processes. In fact, Penrose suggested that their relationship might be non-local, rather than non-algorithmic. More to the point, even if there was nothing unusual about the quasi crystals it is not apparent why this would by itself falsify the OR form of quantum wave reduction proposed by Penrose.
The attack on Hameroff’s proposals for microtubules as the basis of quantum activity in the brain contains factual errors. Grush/Garland claim physiological evidence that consciousness can occur without microtubules. This turns out to be based on two claims relating to the drug colchicine used in the treatment of gout. Colchicine depolymerises microtubules without patients losing consciousness.
However, Penrose/Hameroff point out that the blood/brain barrier prevents most of the drug from reaching the brain. It was further claimed that when colchicine was delivered direct to the brains of animals they also did not lose consciousness. The Penrose/Hameroff reply is that brain microtubules are more stable than microtubules in the rest of the body, not having polymerisation cycles, nor the exposed beta plus ends found in body microtubules.
Grush/Garland also come up with the rather strange objection that the microtubules do not extend the full length of the axons to the actual synapse. The answer is that the connection is made by other elements of the cytoskeleton without which the microtubules could not even perform their known function of transporting neurotransmitter and other molecules to the synapses. This answer also applies to their connection with the cell membrane and the dendritic spines.
There was a further argument about anaesthetics. G&C claiming ion channels are the main target for anaesthetic gases. P&H do not deny the importance of these, but argue that the same changes that happen in hydrophobic pockets in membrane proteins also happen in microtubules, with the action on the latter ablating consciousness.
G&C reasonably ask how quantum activity in microtubules in individual neurons could be extended across the wider brain. In this article, Hameroff has suggested communication via gap junctions. While this is also very controversial it does provide a structure to fill the apparent gap pointed out by G&C.
The Grush & Garland article, published in 1995, have begun to look a bit dated. There are references to ‘promising research programmes’ presumably in the area of mainstream ideas about consciousness, whereas there is sadly little sign now that we are any closer to a a mainstream theory of consciousness, and this nowadays beginning to be openly acknowledged by mainstream science. Instead, recent papers suggest a much greater caution as to the timescale needed to establish nature of consciousness on the part of both neuroscientists and some AI experts. In contrast, Hameroff can at least point to the correlation of cytoskeletal activity and synaptic function, which G&C claimed to be unconnected plus some evidence for the existence of quantum coherence in the brain.
In particular, G&C also give a large amount of space in their article to neural net computers. These were very much in vogue in the 1990’s because they used or at least simulated the parallel processing of data seen to be used by the brain. There seem to have been hopes that neural nets would break the log jam in AI and robotics. As late as the turn of the century, Max Tegmark suggested that the promise of neural net computers leading to an understanding of consciousness, suggested that there was little need to look to the quantum level for an explanation. Little now seems to be heard about neural nets, suggesting that this route to imitating the brain has not proved very fruitful. P&H merely point out that whatever the merits of neural nets, they are certainly based on a sequence of algorithms and have no bearing on mathematical understanding relative to Gödel. P Despite the many shortcoming of the Grush and Garland article it is often referred to a definitive refutation of the whole of the Penrose/Hameroff model, without even a reference to the existence of a reply by Penrose and Hameroff.
Reply to Grush & Churchland
Roger Penrose & Stuart Hameroff
Journal of Consciousness, 2, (2), pp. 99-112
One interesting thing about this reply is that exists at all. Commentators on quantum consciousness are apt to quote The Grush & Churchland article as a comprehensive dismissal of the Penrose/Hameroff model, without even mentioning that there was a reply, let alone bothering to discuss any of the points raised.
Penrose and Hammeroff claim that Grush & Churchland’s (G&C) arguments are misleading and that with respect to the physiological evidence of the brain they are factually incorrect. With respect to Penrose and non-computability, their main argument is said to hinge on the statement that mathematical thinking can contain errors. Penrose says that he does not deny this, but does not see it as invalidating the Gödel argument. Penrose also say that G&C claim that he said that in some and perhaps in all instances human thought was sound but non-algorithmic. He states that this is incorrect, and that he never denied that human thought and even rigorous mathematical thinking could be in error.
Penrose says that he wishes to restrict the argument to Pi 1 sentences, which are sentences that assert that a particular computation does not halt. An example of a Pi 1 sentence is the Goldbach conjecture, which states that ‘every even number greater than 2 is the sum of two prime numbers. It is an assertion that the computation does not halt in the sense that it says that a programme looking for an even number that was not the sum of two primes would never find it and would therefore never come to a halt. Penrose says the issue is as to how accessible to human reason Pi 1 sentences are. P G&C also claimed that there was no evidence that non-computability was involved in quantum gravity. Penrose replied that there was some evidence. This relates to the work of Geroch and Hartle, which showed that there was no algorithm for certain problems related to the superposition of four dimensional space-time, which is in turn closely related to Penrose’s version of quantum gravity.
The latter part of the reply is devoted to G&C’s criticisms relative to the physiology of the brain. They claimed that a drug called colchicine, which is used for the treatment of gout, acts by depolymerising microtubules, but does not result in the loss of consciousness. In reply, Hameroff says that this argument fails to take account of differences between microtubules in the body and microtubules in the brain. The brain microtubules are much more stable. In its medical use colchicine does not penetrate to the brain, being excluded by the blood-brain barrier, but in animal experiments, where it has been administered to the brain, it is shown that brain microtubules do not depolymerise. P Grush & Churchland argue that if microtubules were responsible for consciousness, consciousness would be distributed through out the body, because there are microtubules in all cells. Against this, Hameroff stresses the substantial differences between body cell microtubules and neuron microtubules, the latter being in much denser networks, particularly in the dendrites.
G&C also queried how microtubules communicated with the cell membrane and in particular with the synapses, since axons stop some way short of the synapses. Hameroff answers that the connections are made by smaller cytoskeletal proteins and some incoming communication is via second messengers. P They also question how microtubules encode information. Hameroff points the suitability of the cyclical lattice for information, although more complex arguments for amino acid structures and quantum tunnelling appear in later papers. He also quotes Vassilev (1985) for evidence of signal transmission. Here again, there seems to have been some more recent data for signalling since the Penrose/Hameroff reply was published.
Brainshy: Non-Neural Theories of Conscious Experience
Patricia Smith Churchland
In: Towards a Science of Consciousness II: The 1996 Tucson Discussions and Debates: Eds Stuart Hameroff, Alfred Kaszniak, Alwyn Scott MIT Press 1998
In this paper Churchland seeks to refute the consciousness approaches of Chalmers and Penrose.
With reference to Chalmers, who famously characterised consciousness as the ‘hard problem’, Churchland wishes to show that consciousness is no harder than many other outstanding problems in neuroscience, such as motor control, learning or memory. Churchland seems to mock the idea that consciousness may be a different type of problem from these other neuroscience problems.
However, with these other problems there is general agreement that however hard these problems may be, they could in principle be solved by a system of algorithms for manipulating energy, protein and other brain materials. What would emerge is a dynamic not in principle different from other aspects of organisms or even inanimate matter. It is less easy to do with consciousness, because what we know about electricity, about protein and about other brain molecules does not allow for them producing a new property not seen elsewhere in the universe.
Churchland further attacks the zombie notion, which is essentially the argument that the brain functions of receiving, processing and responding to data could be achieved without the help of consciousness, and without giving rise to consciousness. Consciousness is indeed absent from the standard neuroscience description of the brain, which is causally closed.
Churchland tries to evade this by saying that because we can conceive of such a brain does not necessarily mean that it could exist, and therefore we shouldn’t base anything on this argument. It is certainly true that we don’t know enough about consciousness, to say whether or not humans could have evolved without it. But that does not get us away from the fact that brain processes, as described by current neuroscience, do not have a requirement for consciousness, and do not produce it. Subsequent discoveries may show that the brain processes do require consciousness, but that is not the current state of neuroscience. It is somewhat ironic that the mainstream, which does everything it can to belittle consciousness and still more freewill, rushes to its defence when it is suggested that a sophisticated brain might operate without consciousness.
Like other mainstream writers, Churchland seeks to fudge the question of qualia. She admits briefly that there are ‘prototypical’ qualia such as pain or blueness, as in the blueness of the sky, but then dives off into discussing grey areas such as thought or experience of limb positions. She asks whether these qualify as qualia. This proves to be rather a sleight of hand, because she now doubles back on the ‘prototypical’ qualia, and claims that they are only a starting point for investigation and not a full characterisation of their class. In this way, she manages to chip away at the qualia problem by introducing categories that might not be qualia, and thus might lead themselves to easier explanation. Even if this approach was successful in the grey areas, it would still leave the ‘prototypical’ qualia of pain and the blueness of blue unexplained, so really Churchland hasn’t progressed at all, although her readers may be left with the impression that she has.
Churchland goes on to give us a bit of a lecture on philosophy, and in particular the fallacy of argument from ignorance. Basically she is saying that ignorance about something does not allow one to draw any conclusions about it. One can only draw a conclusion about oneself, to the effect that one is ignorant about the property under discussion. In particular, it is wrong to draw the conclusion that (1) we can never explain the property, (2) that science can never deepen our knowledge of the property, or (3) that the property can never be explained.
Only a few modern thinkers such as Colin McGinn support something like the (1) and (2) positions, so the question is really as to whether the third position stands up. In justifying her stance, Churchland targets some straw men, for instance that because we don’t know the cause of a noise in the night, we are not justified in supposing a supernatural or alien origin, rather than gettinging to grips with the possibility of explaining consciousness from existing science.
The difference between Churchland’s noise in the night and theories of consciousness is that we are not as ignorant about biology and physics as we are in the case of the noise in the night. We know enough about these to determine the type of things that are possible with them. A system of algorithms instantiated in neurons could in principle drive other neurons to perform brain processes, such as motor control, learning and memory, the precise mechanism of which is as yet unknown, but we know enough about the components of the brain, to know that they do not produce a property not detected in the rest of the universe, and consciousness falls into this category.
The last part of Churchland’s paper deals with the Penrose/Hameroff model. Churchland remarks with truth that the details of the Penrose/Hameroff theory are highly technical. This seems too much for her, and she decides to skate round the main issues, but still attempts to refute the theory.
Penrose did invoke the Platonic idea of mathematical truth, but in terms of the theory as a whole, this concept could be seen as only an image for what Penrose is proposing. Churchland, however, makes it look like the centrepiece.
Her approach to the core of Penrose’s argument about consciousness, that it requires something that is not based on algorithms that can only be found at the quantum level, is garbled. She states that Penrose requires operations at the quantum level, but does not state why. This has the effect of making the whole thing sound improbable, without her having to engage with Penrose’s arguments. Penrose developed a detailed argument for how quantum gravity might be involved, but instead of trying to refute this, Churchland treats us to throw away lines such as ‘quantum gravity were it to exist’ and ‘no adequate theory of quantum gravity exists.’ Of course, scientific knowledge could never progress at all if every hypothesis was treated like this. Meanwhile Churchland offers no reasoned or detailed refutation of Penrose. We are also told that ‘mathematical logicians generally disagree with Penrose’, but their arguments are not presented, so we have no chance to judge.
Churchland attempts to disparage the microtubule part of the Penrose/Hameroff theory. She points out correctly that anaesthetic molecules bind to protein receptors in the cell membrane. However, the evidence appears to suggest that these molecules permeate down to other cell proteins including microtubules, so she has hardly made the case against microtubular consciousness on this basis.
Strangely she misses the strongest argument against the theory which is the tendency to rapid quantum decoherence in the conditions of the brain. She make think she is referring to this when she mentions the possibility of coherence being swamped by ‘millivolt signalling’. However, the problem is not signalling as such, but the overall activity of the environment. In fact, since this paper was written, microtubules have been shown to be involved in signalling.
Subsequent to this the tone of the article sinks to a rather unprofessional level. Any proposal made by Hameroff is ridiculed for being only a ‘might’, a possibility, but how can science develop without ‘might’ proposals. Churchland also seems to think that the microtubule proposal did not explain how it linked to consciousness. This is factually incorrect, with regard to the detailed work of Penrose and Hameroff.
More neural than thou
(Reply to Patricia Churchland’s ‘Brainshy’)
Both in 1996 Tucson discussion and debates
In her ‘Brainshy’ paper in 1996, the philosopher, Patricia Churchland, attacked the Penrose/Hameroff model as well as the view points of Chalmers and Searle.
Hameroff’s reply in this paper criticises Churchland for ignoring a number of brain features thought relevant to consciousness, including the probabilistic element in the firing of synapses, the role of gap junctions and dendrite-to-dendrite exchanges in brain processing, glial cells and the role of the cytoskeleton. He particularly criticises the lack of mention of the role of the cytoskeleton in regulating the neuron and its synapses.
The latter parts of the paper seem to concentrate on redescribing parts of the Penrose/Hameroff model rather than specifically criticising Churchland. This discussion begins with the comment that Churchland is contemptous of Penrose’s Platonism. Hameroff counters by asking, ‘what is fundamental reality’. He remarks that as far back as 1971 Penrose tried to provide a description of the quantum mechanical geometry of space at the Planck scale by proposing quantum spin networks, which are suggested to encode the volumes and areas of physical space, but may also encode non-computational understanding and possibly the qualia.
Hameroff also covers the question of anesthetics and consciousness in this article, pointing to evidence that anesthetics act in hydrophobic pockets in protein, which are also seen as a possible site for quantum coherent activity.