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Penrose & Hameroff 3Articles relevant to the Penrose/Hameroff model of quantum consciousness, by Hameroff, Tuszynski, Chaitin and others, plus Grush & Garland criticism of Penrose and reply to Grush & Garland. 1.) Conduction pathways in microtubules, biological quantum computation and consciousness - Stuart Hameroff et al 2.) Search for quantum & classical modes of information processing in microtubules - Stuart Hameroff & Jack Tuszynski 3.) Gaps in Penrose's Toilings - Grush & Garland - Philosophical criticism of Penrose's consciousness ideas 4.) Reply to Grush & Garland - Penrose & Hameroff 5.) Cytoskeletal involvement in neuronal learning - Dayhoff & Hameroff 6.) Mathematical Intelligence - Giuseppe Longo 7.) Neural mechanism that randomises behaviour - R.H.S. Carpenter - Vision research suggestive of quantum processing in the brain. 8.) Godel & Turing - Chaitin - Sees the reasons for Godel's incompleteness theorem as linked to the nature of physics. 1.) Conduction pathways in microtubules, biological quantum computation and consciousness Stuart Hameroff, Alex Nip, Mitchell Porter & Jack Tuszynski Biosystems, 64, 2002, pp.149-168 The article examines the plausibility of quantum computing in the brain. In respect of this, Hameroff views proteins as information processing or computing systems. In a quantum computer, superpositions of particles would be in two or more states or locations simultaneously. Classic computers utilise binary bits of 1 or 0. Quantum computers have superpositions of 1 and 0 at the same time. These superposed particles are called qbits. The qbits are entangled with one another. When the wave function collapses, the resulting classical data is the output for the computer. Quantum computers are expected to be particularly effective as search engines. This advantage may be particularly relevant for perception and hence survival in living organisms. Quantum computation has become more feasible since proposals for quantum error correction. This would involve an algorithm running on a computer that detects and corrects any localised decoherence that might otherwise lead to the collapse of the whole system. It has been suggested that microtubules could support an algorithm for quantum error connection. Hameroff suggests that the folding of protein could be based on a quantum computation. He also suggests that the structure of microtubules could be favourable to quantum error correction, and some amino acid groupings such as tryptophan and histidine may be involved in this. Fröhlich originally proposed (1968) that there could be quantum dipole oscillation in hydrophobic pockets in order to regulate protein conformation. Roitberg et al (1995) demonstrated functional protein vibrations that depend on quantum effects centred in two hydrophobic areas. Matsumo (2001) claimed to observe quantum coherence in actin. Actin is related to cytoskeletal contraction. Meyers and Overton showed a correlation between anaesthetic potency and solubility in lipids. At the time, it was assumed that this meant the lipids in cell membranes, but Wulf and Featherstone (1957), Frank and Lieb (1982-94), Halsey (1989) and others suggest they act in hydrophobic pockets in target proteins. The solubility is indicated to be an effect of van der Waals forces. The anaesthetics act on neurotransmitter receptors, such the GABA and serotonin receptors, second messenger proteins, enzymes and tubulins. A molecule just entering a hydrophobic pocket may not be enough, it must be the right type of molecule. Hallucinogen are seen to bind at serotonin receptors. This paper examines amino acid pathways in microtubules such as those for tryptophan and histidine and their possible involvement in electron mobility and quantum tunneling. Hameroff suggests that the conditions in microtubules could allow tunnelling over 3nm rather than the more normal one nanometer. Conformational states of tubulin are also suggested to be determined by London forces within the tubulin interiors. Electron conduction between tryptophan and histidine amino acids may be important in this respect. Beck F, Eccles J.C. (1982), Quantum aspects of brain activity and the role of consciousness: Proceeding of the National Academy of Science: USA 89 (23) 11357-11361 Franks N.P. and Lieb W.R. (1984), Do general anaesthetics act by competitive binding to specific receptors: Nature 310, 599-601 Fröhlich H, (1968) Long range coherence and energy storage in biological systems: Int J. Quant Chem 2 6419 Fröhlich H, (1970) Long range coherence and the action of enzymes: Nature 728 1993 Fröhlich H, (1975) The extra dielectric properties of biological materials and the action of enzymes: Proceedings of the National academy of Science 72 4215 Halsey M.J. (1989) Molecular mechanism of anaesthetics: General Anaesthesia – Fifth Edition Wulf R.J, Featherstone R.M. (1957), A correlation of van der Waals constants with anaesthetic potency 2.) Quantum & classical modes of information processing in microtubules Stuart Hameroff & Jack Tuszzynski Biochemical energy is provided to microtubules in several ways, including from tubulin bound GTP which is hydrolysed to GDP. Van der Waals forces operate between the amino-acid side groups . Hameroff suggests that the tubulins could be the computing bits of a calculating system. Hameroff and Tuszynski say that by using the Protein Data Bank and the Tinker molecular dynamic package, they have demonstrated quite a high negative charge on tubulin at normal pH, with 40% of this concentrated in the tail-like ‘C’ terminal of the monomer. It is also indicated that mapping of electrostatic charges in the tubulin shows two wells of positive charge near the junction between the alpha and the beta monomers, which mapping work suggests would result in quantum tunnelling. W. Bras (1) has demonstrated microtubules align parallel to magnetic fields, and this is also considered as likely to allow electron tunnelling. Work by Binhi et al (2) indicates the existence of unpaired electron spins for networks in protein interiors, which are shielded from the environment and lead to functional quantum interaction at physiological temperatures. The conclusion of the article is that work on microtubules and the component tubulins suggests several mechanisms for quantum information processing. (1) W. Bras, Magnetically aligned microtubules: PHD thesis, John Moore University (2) V.N. Binhi & A. V. Savin, Molecular gyroscopes and biological effects of weak extremely low frequency magnetic fields: Physical Review E 65: 051912 1&8211: 0519 R.R. Rizi et al, Intermolecular zero quantum coherence in the human brain: Magnetic resonance medecine: 43 627-32 (2000) W. Richter et al: Functional magnetic resonance imaging with intermolecular multiple quantum coherence: Magnetic resonance imaging 8, 489-494 (2000) 3.) Gap’s in Penrose’s Toilings Rick Grush and Patricia Churchland Philosophy Dept., University of California San Diego Journal of Consciousness Studies, 2, No. 1, 1995, pp. 10-29 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. 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. 4.) Reply to Grush & Garland Roger Penrose & Stuart Hameroff Journal of Consciousness, 1995, 2 (2) pp. 99-112 and: www.quantumconsciousness.org 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. 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. 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. 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. (1) Vassilev P. et al, (1985) Intermembrane linkage mediated by tubulin: Biochem. Biophys Res Comm. 126 pp 559-65 Jibu M, Hagan S, Hameroff S, Pribram K.H., Yasue K, (1994) Quantum optical coherence in cytoskeletal microtubules: Biosystems 32 pp 105-209 Jibu M, Yasue K, Hagan S, (1995) Water laser as cellular vision Oedaira H. and Osaka A.C. (1989) Water in biological systems: Kodansha Scientific 5.) Cytoskeletal involvement in neuronal learning Judith Dayhoff, Stuart Hameroff et al European Biophysics Journal, 1994, 23:79, 93 Experimental evidence suggests that the cytoskeleton may be involved in information processing, cognition and learning. Mileusne et al (1980) (1) correlated tubulin production with peaks in learning. Cronly-Dillon (1994) (2) also correlated increase and reduction of tubulin production in the visual cortex to learning. Conventionally learning is associated with synaptic plasticity. Both Lynch & Baudry (1987) (3) and Friedrich (1990) (4) suggest that LTP depends on the rearrangement of the synaptic cytoskeleton. Matsumoto and Saka (1977) (5)and Hirokawa (6) (1991) suggested links to excitability of membrane receptors and ion channels and to synaptic transmission. Desmond and Levy (1998) (7) found changes in dendritic spines mediated by cytoskeletal actin during learning. Kwak and Matus (1988) (8) and Aoki and Siekevit (1985) (9) suggested that microtubules depolymerised in the event of lack of input. The last quoted found that signalling in and regulation of dendritic spines depended on phosphorylation of microtubule associated proteins (MAPs). (1) Mileusne et al (1980) (2) Cronly-Dillon (1974) Possible involvement of microtubules in memory fixation: J. Exp. Biol 61 443-454 (3) Lynch & Baudry (1987) (4) Friedrich (1990) Protein structure, the primary substrata for memory: Neuroscience 35 (5) Matsumat & Saka (1977) (6) Hirokawa (1991) (7) Desmond & Levy (1998) (8) Kwak & Matus (1981) (9) Aoki C. & Siekevit P. (1985) Journal of Neuroscience 5 2465 2483 6.) Giuseppo Longo Journal of Consciousness Studies, vol. 6, 1999, Nov/Dec. The article attempts to refute Penrose’s argument that the Gödel theorem indicates that there is some form of non-computable processing in the human brain. The reasoning is difficult for the non-specialist to follow. However, the gist appears to be an argument that proofs that go beyond formal systems can be derived from numerous mental and historical experiences, some of them from outside mathematics. The problem that does not appear to be dealt with is whether or not these may not themselves involve non-computable processes. 7.) A Neural Mechanism that Randomnises Behaviour R.H.S. Carpenter Physiology Laboratory, University of Cambridge Journal of Consciousness Studies, vol. 6, No. 1, 1999, pp. 13-22 The abstract starts by pointing out that the time taken to react voluntarily to stimulus is far longer than can be accounted for by known nervous system processing. The strength of response is shown to rise in proportion to the incoming sensory data, until a critical level at which action is taken is reached. However, the rate of rise fluctuates randomly from trial to trial. This claim is based on studies of neurons in the frontal eye field and the time taken between presenting a visual stimulus and making a saccade (an eye movement). The saccade itself is very quick, lasting only 20-30ms, but the system is not designed for speed in other respects. The average gap between presentation of the stimulus and the saccade is 200ms. Normal processing in the nervous system is claimed to account for at most one third of this time. The shortest route from the retinal receptors to the eye muscles passes through the superior colliculus and should take only 60ms. However, the colliculus receives input that comes ultimately from the parietal cortex and the frontal eye fields. The control is inhibitory, otherwise the eyes would be constantly darting towards each and every stimulus. The blanket inhibition has to be lifted for a saccade to be made. The colliculus lacks the information to make useful decisions, because it registers only where things are in space, but not what they are. The biggest problem is seen to be in a series of trials the response time varies over a surprisingly large range. While the average saccadic latency is 200ms, on some 5% of trials the latency is either less than 150ms or more than 300ms. In the first stage of the latency period neurons distinguish between a target stimulus and distractors. This takes about the same period of time, about 70ms, whether the eventual latency period is short or long, so the whole of the variability is concentrated in the latter part of the latency period. The article suggests that this means that the variability is not due to noise in the sensory pathways, but to something introduced by the brain. The randomness of the reaction times is seen as a function of deliberate randomisation by neural processes in the brain. Carpenter says that the underlying process is obscure, although he points out that its is consistent with the Penrose/Hameroff model, and that the delay periods involved are similar to those seen in Libet’s experiments. Carpenter goes on to speculate as to what evolutionary advantage would favour randomisation. He argues that there would be an adaptive advantage in the resulting unpredictability, as opposed to deterministic responses that would be easier for a predator or prey to predict. Carpenter, R.H.S. Oculomotor procrastination in Eye Movements Cognition and Visual Perception (1981) Carpenter, R.H.S. Movement of the Eyes (1988) Carpenter, R.H.S. Human saccadic latency to targets of differing contrast and probability: Evidence for neural randomisation Carpenter, R.H.S. and Williams M.L.L. Neural computation of log likelihood in the control of saccadic eye movements Nature 377 pp59-62 Godel & Turing Chaitin Godel showed that the connection between proof and truth was shaky. In mathematics and in other formal systems statements can be true but unprovable. Some mathematical propositions might be undecidable, and this demolishes the idea of a closed consistent body of rules, and replaces it with incompleteness. Chaitin discusses randomness. Something is random if there is no pattern or abbrevaited description. Then there is no algorithm shorter than the thing itself. On this basis, mathematics can be shown to be shot through with randomness. This has implications beyond mathematics because the laws of physics are mathematical. The laws of physics are seen as algorithms that map input data or initial conditions onto output data or the final state. The possibility of the universe as a computer is examined. Quantum mechanics imposes a lower limit on the time taken for each step in processing, and the universe has a finite age, so only a finite amount of information can have been processed in the life of the universe. This is suggested to mean that there is a cosmological bound on the fidelity of mathematical laws. Random or patternless sequences of a given length require the longest programmes. A random sequence of length k requires a programme of length k. These random or patternless sequences comprise the majority of sequences. Such programmes, where the number of bits equals the number of observations are random and useless. The minority of non-random sequences require a programme that is shorter than k. The shorter the programme, the less random the sequence, and the greater the pattern present in the sequence. This links to information theory. Messages are coded or compressed to eliminate redundant information. Any information source that is not random can be compressed. The definition of randomness is the reverse of information theory. Chaitin also relates this to the Occam's razor concept in which the simplest theory, or in other words the shortest sequence, is seen as the best theory. Simplicity here meansd not ease of calculation, but the number of arbitrary assumptions that have to be made. A scientific theory is valuable, if it allows one to compress many observations into a few hypotheses. The minimum quantity of information needed to define a string is equated to the complexity of the string. Most strings of length n have complexity n, and these are random. Only the non-random minority have less complexity. Where a string is random, the programme describing it has has to expand in direct relation to the length of the string. Although randomness can be measured and defined, a given numprograber cannot be proved to be random. This is seen as being related to Godel's incompleteness theorem. The fundamental unit of information is the 'bit', and this is defined, and this is defined as the smallest item of indication a choice between two things. In binary notation, one bit is represented by either a '0' or a '1'. In the 1960's, the Russian mathematician, Solomonoff, represented a scientist's theory as an algorithm predicting future observations, and in the case of competing theories about observations, the model will select the algorithm comprising the fewest bits. This is the same idea as Occam's razor. Any specified series of digits, such as 123, can be generated by an infinite number of algorithms. However, the bast programme is the smallest one. The smallest programmes are called minimal programmes, and there may be one or many minimal programmes for a given series of digits. The concept of the minimal programme is closely related to the concept of complexity. The complexity of a series of digits is the number of bits required to get the series of digits as output. There the complexity equals the minimal programme for the series. It is emphasised that non-random distributions are exceptional. It is easy to show that a series of digits is non-random by finding a programme that is shorter than the series, but will generate the series. To demonstrate that a particular digit is random, it is necessary to demonstrate that there is no small programme for generating it. Chaitin's version of Godel predicts that such proof of randomness cannot be found. Given that quantum mechanics depends on random outcomes this indicates a limitation to axiomatic systems. Godel had shown that it was not possible in mathematics to have a mechanical system of proofs without the need for human judgement or insight. Before Godel, Hilbert had wanted a formal system with a finite list of axioms or initial assumptions and rules of inference. This is the definition of a formal system. A formal system has an algorithm for testing proofs that will check one-by-one all the theorems of a particular system. The randomness of numbers that are larger than the formal system cannot be proved. This is taken as being related to Godel's incompleteness theorem. Godel's theorem was based on the Cretan liar paradox, referring to the Cretan who says that 'all Cretans are liars', or alternatively, 'this statement is false, although Godel preferered 'this statement is unprovable'. If the unprovable statement was true, it meant that the formalisation of number theory was incomplete. At the same time, if the statement was provable, it would also be false, and number theory would be inconsistent. Much of Chaitin's discussion focuses on the concept of algorithmic information theory. He asks how many bits of information of information the smallest programme takes to calculate an individual object. Between two objects there may be mutual information that measures the commonality of the objects. This is regarded as a fundamental concept. Knowing the amount of commonality reduces the amount of information needed to describe the objects. Randomness in a particular object implies the lack of common features with another object. Chaitin seems to criticise mainstream mathematics for shrugging off the implication of Godel's theorem and the slightly more accessible work of Turing on the halting problem, which essentially dealt with those things that a computer could not do. The view has tended to be that the problem did not apply to normal mathematics, but Chaitin thinks they may be wrong in this respect. His view of algorithmic information theory suggests that randomness and incompleteness may be more pervasive than generally thought. Chaitin considers that there may be a deeper reason for incompleteness that is linked to physics. Physics contains the notion of entropy or the amount of disorder in a system, which also relates to the arrow of time. The size of a computer programme is a similar concept to the amount of entropy in a system. The idea or programme size relates to the Occam's razor concept of preferring the simplest system. The problem with the concept of the smallest or simplest programme is that one cannot be sure that one has the smallest programme. Such mathematical truth would require an infinite amount of information, while any system of axioms contains only a finite amount of information. |
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