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Penrose & Hameroff 8


Summaries and reviews of further papers and books relevant to the Penrose/Hameroff Orch OR theory plus Fefermann on Godelian argument, alternative approaches by Georgiev and Brian J. Ford on single-cell organisms.


1.) Godel's first incompleteness theorem  -  summarised from various sources

2.) Penrose's Godelian argument  -  Solomon Fefermann  -  Dept. of Mathematics, Stanford

3.) Falsification of Penrose-Hameroff model of consciousness & novel avenues for development of quantum mind theory  -  Danko Georgiev  -  Laboratory of Molecular Pharmacology, University of Kanazawa

4.) Analysis of quantum decoherence in the brain
& Solitonic effect of the local electromagnetic field on neuronal microtubules  -  Danko Georgiev  -  Disagrees with Hameroff on structure of macroscopic quantum coherence in the brain.

5.) Electric and magnetic fields inside neurons and their impact upon the cytoskeletal microtubules  -  Danko Georgiev  -  Further work on possible structure of quantum activity in microtubules.

6.) The Essential role of mathematical cognition  -  Robert Hadley  -  Tries to reach Penrose's conclusion re: computers and brains without using Godel.

7.)  Sensitive Souls  -  Brian J. Ford  -  discusses sophisticated abilities of single-cell organisms

8.)  Roger Penrose  -  In:- Conversations in Consciousness - Susan Blackmore

9.)  Hameroff replies to criticisms




1.)

Godel's first incompleteness theorem

Summarised from various sources

Godel's first incompleteness theorem is the starting point for Penrose's approach to an explanation of the nature of mathematical understanding. In the later development of Penrose's ideas by Stuart Hameroff mathematical understanding has been enlarged to mean consciousness, presumably on the argument that we need to consciously feel or appreciate the truth of a mathematical statement that is not provable by the immediately available axioms.

The theorem states that a theory capable of expressing arithmetic cannot be both consistent and complete. For any consistent formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable by means of the axioms of the theory.

For the purposes of discussing Penrose's proposals relative to undertanding or consciousness the important phrase here is 'true but not provable'.

This true but not provable statement is called the Godel sentence G. Of course this is not just one sentence; in fact there are an infinite number of Godel sentences. Each set of axioms containing the minimum required piece of number theory has a corresponding Godel sentence G saying that G cannot be proved to be true by the axioms of the theory. If G could be proved within one of these theorems, say theorem T, then it would mean that T had a theorem G, which would contradict itself, because G says that T does not have such a theorem. If G did exist in such a form it would make T inconsistent.

That's not particularly easy, but it's about as simple as it can be made.

It may sometimes have been suggested that there is a way round by making G and additional axiom of T as an enlarged theorem to be called T'. However, this enlarged set of axioms will have a new Godel sentence and so on and so. This appears to be an infinite regress.

The truth and provability of the Godel sentence is taken as a formalised version of the 'Liar Paradox'. This last says: 'This sentence is false'. The sentence is not true, because if it was true it would be false, just as if the Godel sentence could be proved by the axioms, it would show that they were not consistent. However it is also apparent that the sentence cannot be false, because it would then be true. A similar and more concrete example is the 'Cretan Liar Paradox' where a Cretan says that all Cretans are liars. Since the statement relies on a Cretan it contains the same nemesis of itself.

The Godel incompleteness theorem relates to an undecidable problem such as the 'Halting Problem' which asked if the processing of some problem would ever halt. An example might be Goldbach's Conjecture, which says that every even number 4 or greater can be written as the sum of two prime numbers as in:-  2+2=4, 3+3=6 and 3+5=8. As here, it's easy to test this for a small run of even numbers and for quite a long run on a super computer, but the search for an even number that is not the sum of two primes could go on indefinitely. When Godel's incompleteness theorems were first produced, it was still hoped that a general algorithm might allow such undecidable problems to be tackled. However, Alan Turing, co-founder of the concept of computing by machines and breaker of the Nazi wartime codes, showed in 1936 that there was no programme that could solve the halting problem.  

For Penrose's approach to mathematical understanding and ultimately consciousness, the true but unprovable segment of the incompleteness theorem was taken to mean that the human mind could go beyond axioms that could be expressed as algorithms and run on a classical computer.

Reference:-
Godel's Proof  -  Ernest Nagel & James Newman  -  Routledge
 



2.)
 
Penrose's Godelian argument

Solomon Feferman, Dept. of Mathematics, Stanford

INTRODUCTION:  Feferman has a common cause with Penrose in opposing the dominant computational model of the mind, and considering that human thought, and in particular mathematical thought, is not achieved by the mechanical application of algorithms, but rather by trial-and-error, insight and inspiration, in a process that machines will never share with humans. His criticism of Penrose applies mainly to him extending his argument too far in areas such as mathematical soundness and consistency, and thus providing ammunition for the computational-mind camp.


This paper suggests that while Feferman makes some criticisms of Penrose, his position is nevertheless, much closer to Penrose than the view points found in mainstream consciousness studies. Feferman says, on only the second page of this paper, that he is convinced 'of the extreme implausibility of a computational model of the mind.' In a single sentence, he totally excludes himself from the Dennett/Churchland/Blackmore/Wegner etc. orthodoxy that dominates scientifically and philosophically respectable thinking about consciousness.

Feferman's criticism of Penrose is that the latter's argument relative to Godel's theorem does not strengthen the argument against the computational model, but may actually give it support by it being possible to dismiss Penrose's arguments at one point or another. There is  a detailed and highly technical analysis of Penrose's arguments, as presented in both the 'Emperor's New Mind' and 'Shadows of the Mind', that extends from page three to page ten of this paper. Feferman criticises Penrose's version of mathematical soundness as ambiguous, and there are also considered to be problems with Penrose's notion of consistency. Feferman says that even the tour-de-force of mathematical reasoning on pp. 3-10 of his paper does not cover all the technical errors made by Penrose. Feferman criticises Penrose for what he describes as 'slapdash scholarship' on the subject of the Godel theorem, which should have required particular care, given that it is central to his argument on consciousness. Having argued all this in pages of technical detail, Feferman then informs his exhausted reader that Penrose's case would not be altered by putting right the logical flaws that Feferman has spent all this time discovering.

Feferman emphasises that Penrose's argument relative to mathematical understanding rests primarily on the first part of Godel's first incompleteness theorem, to the effect that in a formal system of axioms, a sentence G(F) is not provable within the system of axioms (F). Penrose is indicated to have pointed out in his books that a formal system of axioms can be reformulated as a Turing machine (a computer). Feferman stresses that 'every theorem-generating machine can be recast as a formal system and vice versa', meaning that a computer can be reformulated as a system of axioms.

Feferman's own position is that the computational-mind argument is misleading in terms of the weight that it places on the equivalence between Turing machines and formal systems. The model of mathematical thought in terms of formal systems is considered to be closer to the nature of human thought, and particularly mathematical thought, than to the functioning of Turing machines. The Turing machine model would assume that given a problem, human reason would plug away, applying the same algorithm indefinitely, in the hope of finding an answer. Feferman says that it is ridiculous to think that mathematics is performed in this way. Trial-and-error reasoning, insight and inspiration, based on prior experience, but not on general rules, are seen as the basis of mathematical success. A more mechanical approach is only appropriate, after an initial proof has been arrived at. Then this approach can be used for mechanical checking of something initially arrived at by trial-and-error and insight.

Feferman views mathematical thought as being non-mechanical. He says that he agrees with Penrose that understanding is essential to mathematical thought, and that 'it is just this area of mathematical thought that machines cannot share with us. 'However, Feferman criticises Penrose for over stating his argument, and thus exposing it to criticism from the computational-mind majority. Much of this criticism relates to Penrose's arguments about mathematical soundness. He also rejects Penrose's platonism.

 


3.)

Falsification of Penrose-Hameroff model of consciousness & novel avenues for development of quantum mind theory

Danko Georgiev, Laboratory of Molecular Pharmacology, University of Kanazawa (2006)

INTRODUCTION: Georgiev thinks that consciousness could be related to Penrose's objective reduction (OR), but is critical of the Hameroff model for how Orch OR could occur in the brain. Instead, he proposes that the cytosol could support Bose-Einstein condensates on a timescale of 10-15 picoseconds, which he regards as sufficient for neural processing.


Danko Georgiev is unusual among critics of the Penrose-Hameroff theory in attacking Hameroff on his own ground, in terms of the detailed functioning of neurons. One of Georgiev's main targets is Hameroff's proposals for quantum tunnelling via gap junctions between neurons. Hameroff has suggested this, as a means by which quantum coherence could extend from one neuron to many, and thus lie behind the gamma synchrony that can extend over large segments of the brain, and is recognised in conventional theories as a correlate of consciousness.

Georgiev faults the Hameroff model on gap junctions, because it relies on structures called dendritic lamellar bodies (DLBs), to communicate between the microtubules and the gap junctions. Georgiev points to a paper by De Zeeuw et al (1995), in which it was shown that the DLBs are not present in dendritic spines, and do not come closer than some tens of micrometres to gap junctions. However, DLBs are thought to be involved in gap junction synthesis. In his paper, De Zeeuw says that DLBs contain neither microtubules nor neurofilaments, but beyond this neither Georgiev nor De Zeeuw offer a description of what lies between the DLBs and the gap junctions. This seems to leave the question of what processes this area could support rather open.

Georgiev is not trying to refute the idea of quantum coherence extending between neurons, but instead advances the view that there is quantum coherence between neurons via actin filaments and other cytoskeletal proteins at the dendritic spines. Georgiev also cites a paper by Hatori et al (2001) suggesting that actin uses quantum coherence in the movement of muscles.

Georgiev dislikes Hameroff's emphasis on conscious processing as being concentrated in the dendrites. He claims that Hameroff's does not allow any consciousness in axons, and this creates a problem in explaining the problematic firing of synapses; only 15-30% of axon spikes result in a synapse firing, and it is not clear what determines whether or not a synapse fires. It is certainly true that Hameroff emphasises the dendrites, particularly as they are important for linking to the gamma synchrony, but I have not found anything in Orch OR that specifically denies the possibility of conscious activity in the axons.

Georgiev places considerable emphasis on the fact that it is experimentally shown that the insertion of electrodes into the brain can stimulate both conscious experience and motor action. He criticises the existing Hameroff theory for failing to integrate this form of electric current, although Georgiev does not feel that it invalidates the theory as such. Georgiev says that microtubules are likley to be, and need to be, sensitive to the external electric field, if something like the Orch OR theory is to be sustained.

Georgiev criticises Hameroff's requirement for microtubules to be quantum coherent for 25 ms. This has been generally regarded as an ambitious timescale for quantum coherence, and Georgiev objects on the grounds that enzymatric functions in proteins take place on a very much quicker 10-15 picosecond timescale He suggests that vital processes might be interrupted by Hameroff's lengthy coherence period.

Georgiev wants to base his version of OR consciousness on a 10-15 picosecond timescale. He claims that modelling of the cytosol suggests that Bose-Einstein condensates could be sustained for 10-15 picoseconds, which he considers long enough for them for them to be significant in neural processing. Such a rapid form of objective reduction would also remove the necessity for the gel-sol cycle to screen microtubules from decoherence, as it does in the Hameroff version of objective reduction.

Georgiev is also critical of the standard reutation of quantum mind theories, which involves coupling a quantum state to a thermal equilibrium bath in which it will decohere. Georgiev points out that living systems are far from thermal equilibrium, and this fact invalidates this traditional critique. Georgiev suggests that consciousness is a GHz phenomenon. This, once again, has the advantage of by-passing Tegmark's time to decoherence objection by using a timescale faster than his collapse time.




4.)

Analysis of quantum decoherence in the brain
 & Solotonic effect of the local electromagnetic field on neuronal microtubules

Danko Georgiev et al

Medical University of Varna/Kanazawa University

Published in Neuroquantology

INTRODUCTION: Georgiev is one of the few researchers actively investigating consciousness on the basis of quantum activity in neurons. He disagrees with Hameroff's model in a number of respects, including the function of gap junctions relative to the binding of consciousness, and instead proposes a mechanism based on quantum brain dynamics ideas, as developed by Jibu and Yasue and also Vitiello. However, despite rejecting Hameroff's mechanism, he still appears to rely on Penrose's idea of objective reduction of macroscopic quantum coherence giving access to consciousness at the fundamental spacetime level. His approach has the advantage of not requiring quantum coherence to be sustained for longer than Tegmark's calculated 10^-13 period for the collapse of quantum coherence within the brain, but having rejected Hameroff's scheme, he does not provide an alternative means of binding together the action of billions of neurons into the unified experience of consciousness.


The development of molecular biology during the latter part of the 20th century made it clear that neurons were highly complex, and from this it became apparent that features such as memory and some diseases such as dementias might be better understood in terms of molecular changes within the neurons. In these cases, it has been shown that not only are there changes in neuronal  firing, but also in cytoskeletal organisation, the cytoskeleton being composed of biomolecules that are the basis of life. The DNA of the cell nucleus contains essential information, but is viewed here as being driven by the transfer of information from the cytoskeleton.

In looking at the synapses between neurons, the author draws particular attention to the metabotropic links, as distinct from the ionotropic links that take the form of electrical signals via membrane ion channels. With the metabotropic links, neurotransmitters bind to G-protein coupled receptors (GPCR). These activate second messengers, which in turn act on protein kinases and phosphatises that modulate the cytoskeleton. The cytoskeleton in its turn signals protein production requirements to the nucleus of the cell. The fast electrical activity of the ion channels is contrasted with the slower biochemical processes within the neuron. Georgiev says that the Hameroff model only takes account of the biochemical and not the electrical activity. He disagrees with this exclusion of electrical activity, pointing out that Penfield's ground breaking research in the mid 20th century showed that conscious memories could be evoked by inserting electrodes into parts of the cortex.

Georgiev argues that in neurons, the electric field is not confined to the ion channels in the membrane, which is the conventional view, but that it can also act directly on the microtubules. This concept is in line with ideas put forward by Jibu and Yasue and also by Vitiello. The approach bof these researchers involves a quantum field theory of the electric dipoles of water molecules in the brain, and here, particularly within the neurons. The dipole rotational symmetry of the water molecules is proposed to break into the quanta of dipole vibrational waves or dipole wave quanta (dwq), which manifest as long-range correlations in water. As such, they transmit information in water.

These correlations are suggested by Georgiev to influence the conformation of the microtubule tubulin 'tails' that protrude from microtubules. The coherent behaviour of the tubulin tails can be modelled as solitary waves (solitons) propagating along the outer surface of the microtubules, and acting as a dissipationless mechanism for the transmission of information along the microtubule. Collisions of the waves formed by the tubulin tails are suggested to act as a computational gate for the control of cytoskeletal processes. It is already experimentally verified that tubulin activity controls the sites where microtubule associated proteins (MAPs) attach to microtubules, and also controls the transport of vesicles of neurotransmitters towards synapses. The output of the computation performed by the tubulin tails is here suggested to come via the MAP attachments and also the kinesin motor transport along the microtubules.

The author goes on to discuss the probabilistic nature of neurotransmitter release at the synapses, and the possible connection this has with quantum activity in the brain. The probability of the synapse firing in response to an electrical signal is estimated at only around 25%. Georgiev points out that an axon forms synapses with hundreds of other neurons, and that if the firing of all these synapses was random, the operation of the brain could prove chaotic. He suggests instead the choice of which synapses will fire is connected to consciousness, and that consciousness acts within neurons. Each synapse has about 40 vesicles holding neurotransmitters, but only one vesicle fires at any one time. Again the choice of vesicle seems to require some form of ordering. The structure of the grid in which the vesicles are held is claimed to be suitable to support vibrationally assisted quantum tunnelling. Georgiev also thinks that B-neurexin and neuroligin-1 proteins that form a bridge between the axonal and dendritic cytoskeletons are relevant to consciousness. Georgiev discusses Max Tegmark's paper, which conventional consciousness study thinking views as having completely dismissed the possibility of consciousness based on quantum coherence in the brain. In respect of this debate, Georgiev points out that the real question is whether the time to decoherence is greater or lesser than the timescale of dynamical changes in the brain. He agrees that if the decoherence time is shorter than the dynamical time, it is not feasible for quantum coherence to be involved in brain activity. In his 2000 paper, Tegmark has a decoherence time of 10^-13 seconds. It is suggested that neuronal activity is orchestrated via the conformational activity of tubulin subunits, and that this activity has a dynamical timescale that could fall within the Tegmark timescale. The conformational transition times within the tubular proteins of the microtubules coincides with transition times for the microtubules as a whole. Georgiev's answer to Tegmark is also an answer to the main thrust of the Koch and Hepp (2006) paper also purporting to dismiss quantum mind theories.

Georgiev's work represents something of a hybrid theory mixing the quantum brain dynamics model promoted in recent years by Jibu and Yasue ans also Vitiello with the quantum consciousness theory of Penrose and Hameroff. Georgiev thinks that the Hameroff scheme for instantiating quantum consciousness in the brain is flawed in a number of respects, and proposes a neuronal mechanism that is closer to quantum brain dynamics. Georgiev also rejects Hameroff's idea of quantum tunnelling at gap junctions between dendrites, citing a lack of suitable structures for coherence in the dendritic spines, where the junctions are located. Unfortunately, he does not propose an alternative method, by which the conscious activity in billions of individual neurons is bound together into the experience of unified consciousness, either by some connection to the gamma synchrony or by any other means.

However, he still appears to support the Penrose concept of objective reduction of the wave function as a result of macroscopic quantum coherence giving access to consciousness at the fundamental spacetime level. This implies that he thinks that at some stage, the solitons propagating along the microtubule undergo objective reduction and that this is the basis of consciousness.




5.)

Electric and magnetic fields inside neurons and their impact upon the cytoskeleton microtubules

Danko Georgiev, Medical University of Varna

http://cogprints.org/3190/

In this paper, Georgiev argues that any link between signals in the cortex and the microtubules has to be understood in terms of the local electromagnetic field. He dismisses a number of theories as to how the microtubules might support information processing and/or consciousness. For instance, the magnetic fields inside neurons are stated to be too weak relative to the background noise of the Earth's magnetic field to support information processing. Instead, he argues that attention needs to be focused on the electrical field, which is responsible for the signals passing along neuronal membranes via ion channels to synapses, and is seen as a necessary source of input into microtubules, if these are in fact involved in information processing or consciousness.

Evidence is claimed for the idea of a model based on structured water and positively charged ions. Magnetic resonance studies indicate that water in neurons is more structured than normal liquid water. A substantial part of the water in neurons is bound to various biomolecules. Much of the rest of the water is structured with high viscosity and dynamic correlations between individual molecules. Most of this structured water is around the cytoskeleton, and studies of this water have tended to indicate the presence of long-range dipolar ordering leading to internal electric fields or oscillations of electric fields.

It has been further suggested that structured water close to microtubules could generate solitons, a form of quanta propagating as solitary waves. The author suggests that this involves the C-termini tubulin 'tails' that project from the microtubules and are capable of multiple conformations. The properties of the tubulin tails are a function of the acidic aminoacid residues, which allows them to be highly flexible. Studies show that these tubulin tails interact with microtubule associated proteins. The carboxyl termini of the tubulin tails have been shown to undergo modifications when interacting with MAPs. The C-termini have also been shown to contain molecules (called chaperone molecules) that assist in the folding of protein, and in particular in ensuring that protein folds in the correct way rather than in a large number of other possible ways. A cycle of removal and restoration of a tyrosine residue from C-termini is a characteristic of stable axonal microtubules. Changes to protein side chains located near the C-termini appear to regulate the interaction between microtubules and MAPs. MAP proteins such as tau and kinesin bind most effectively with particular side chains. Differences in the binding of MAPs are suggested to modulate the function of microtubules.

Georgiev suggests that molecular studies allow the construction of models, by which microtubules can process electrical information. The C-termini are electrically charged and physically flexible and can undergo conformational changes, in response to changes in the vector of the electrical field. Solitons can transfer energy between the tubulin tails without dissipation. These solitons are suggested to be capable of directly effecting the scaffold of presynaptic proteins and the release of neurotransmitters from synapses.




6.)

The Essential role of consciousness in mathematical cognition

Robert Hadley, Simon Fraser University

Journal of Consciousness Studies, 17, No. 1-2, 2010, pp. 27-46

Hadley puts forward alternative possibilities to Penrose's argument from the Godel theorem, in order to reach a Penrose-type conclusion about brains and computers. He argues that a system that lacked consciousness would be incapable of certain concepts and certain proofs. Hadley refers to Kant's argument that the perception of an object requires the unity of consciousness. In modern terms, the difficulty of seeing how the unity of consciousness is achieved by the brain is referred to as the binding problem, and is not the same as, but is closely intertwined with the question of consciousness. The concept of objects is claimed to require certain assumptions about space and time, and also the categorisation of the objects themselves. Conscious experience may also be needed to understand the relationship of one object to another. In terms of mathematics, the natural numbers are an even set, which is conceived of as existing simultaneously. It is possible for human students of mathematics to think of an unbounded set of objects existing simultaneously, but this concept produces a circularity for computers.

There is also the question of understanding geometrically-based proofs, where to understand the proof, it is necessary to conceive a geometric design, as a whole or unit. This involves an argument concerning the situation where human perception is able to immediately see that an arrangement of dots comprises a hexagon, which is seen as a unit, whole or gestalt, although all that exists is a few printed dots, and there is no continuous hexagon printed on the paper. A computer analysis of the dots could generate the angles of relationship between them, but not by itself generate the idea of a geometrical objects such as a hexagon as a single cohesive whole. There needs to be a realisation that the dots at the corners of the hexagon (the only thing actually printed on the paper) belong together, and although something might be programmed in for particular dots, there is no way to generate this for arrangements of dots in general, from present forms of computation. It requires human conceptions about the parts of cohesive wholes belonging together to achieve this. Complex diagrams need to be perceived as integrated gestalt patterns.  Therefore the author argues that it is not necessary to accept Penrose's argument from the Godel theorem, in order to agree with his main conclusion that brains and existing forms of computer are different, and consciousness not possessed by computers is required for some human brain activities.

 

 

7.)

Sensitive Souls

Brian J. Ford

INTRODUCTION:  In the penultimate chapter of this book, the author describes the sophisticated behaviour of many single-cell organisms. This includes identification and location of prey, taking advantage of reproductive opportunities and complex navigation and awareness of position.  All of this is achieved without the support of the nervous systems and brains found in multi-cellular organisms. This has led some to suggest the use of quantum computing to support the marvelously complex behaviour of such cells, a form of computing that could subsequently have been passed down to the evolutionarily later multi-cellular organisms.


This review concentrates on the penultimate chapter of Ford's book, which deals with single-cell organisms. Organic cells are divided into two categories, prokaryocytes and eukaryocytes. Prokaryocytes seem to have constituted the earliest forms of life. Eukaryocytes are more sophisticated with nuclei, mitochondria and other organelles. More sophisticated organisms are comprised of eukaryocytes.

Ford discusses the various categories of microbe, starting with bacteria, which are prokaryocytes, and have the most primitive type of cell organisation. However, despite their single-cell organisation, bacteria have many senses, and can adapt their behaviour in response to what they sense in their surroundings. Some bacteria form patterns as they grow, suggesting a sense of position or orientation, while others move together to form communities of bacteria, with some resemblances to single organisms. In varying chemical environments, bacteria form varying patterns. There is also signaling between different genders of bacteria (traditionally known as plus and minus rather than male and female). The two genders can swim together and fuse. Bacteria can also direct chemical compounds at other organisms in order to destroy them. These lethal compounds are used to establish a territory. Communities of organisms destroy outsiders in this way. Ford suggests that microbes possess some form of communication. Some compounds are used to send signals to neighbours, either for the forming of communities or the finding of food. Some bacteria can sense desirable locations and avoid adverse locations.

Protozoa, such as the single-celled amoeba, have many senses including some vision, can inspect food before ingesting it, or congregate in numbers to identify, ingest or destroy bacteria, can construct shells out of sand grains, find mates and avoid adverse environments. All of this requires considerable sensory and motor coordination, and does not depend on any form of external control. Amoeba can adjust their rate of reproduction to the food supply, and also do not consume more food than they require. Single-celled eukaryocytes are also responsive to light. Many of the free-swimming protozoa have what are effectively eye spots, allowing them to rotate towards light sources. For instance, a species called Euglena has a flexible body that can change shape as it moves or swim fast, propelled by a whip-like thread at the front of the organism. The mechanism by which this structure can allow the organism to change direction involves the level of concentration of calcium ions within the organism, and implies some form of memory and data processing to achieve the form of navigation that are detected.

It has also been shown that amoeba detect their food rather than encountering it by chance, and that their feeding response is not automatic, but tailored to the amount of food that has already been consumed. The amoeba appears to have a switch to detect that it has consumed too little or too much food. In some cases amoeba appear to have an olfactory response to food stuffs. The amoeba is able to sense and trap prey, even when the prey species appears more agile than the amoeba.

In the case of free-swimming types of algae living in colonies, each cell sends out fibrils to connect to its neighbours. The cells transmit signals to one another, in order to coordinate the movement of the colony, without the need for any central control. The algae, spirogyra, can communicate in a rather similar manner for sexual reproduction. Somehow, these organisms have to identify mates, locate them and grow towards them. Again this seems to require sophisticated communication between single-cell organisms.

Protozoa have fine threads of actin and myosin proteins inside their cells, and these contractual proteins drive the cilia and flagella that allow the cell to move. The actin/myosin complex works by splitting ATP, and thus releasing metabolic energy. This energy allows the process of contraction. Although this explains the actual movement of the organism, it does not explain the cells complex response to its environment. Cells have refined senses to allow them to recognise one another, and even to cooperate with one another, based on appropriate senses and data processing. Small organisms also posses hard to explain proprioceptor organs that allow them to determine their position relative to external reference points, and to from that place themselves in adaptive locations. Ford argues that the remarkable thing is that amoeba can do most of the things that humans and other mammals can do, despite being only single-cell organisms.
 

 

8.)

Roger Penrose

In:- Conversations in Consciousness

Susan Blackmore

Oxford University Press (2005)

In this conversation there is an early disagreement between Blackmore and Penrose over the meaning of 'understanding'. Blackmore will not have it there is a distinction between an automatic response such as catching a ball, which at the moment of doing it, requires no conscious thought about the balls dynamics and dealing with a problem that requires conscious thought. Blackmore gives the impression of seeing herself make an important point. Maybe she wants to distance herself from Penrose position, because otherwise I find it hard to make sense of her argument.

The main substance of this conversation is a discussion of the Godel theorem, which forms the basis of Penrose's take on consciousness and understanding. He says that with simple mathematical statements, there is no argument as to which are true or false. These statements appear as objective facts. The question is how do we come to the realisation of the truth of these statements. Initially, we have axiomatic rules, which is applied give trustworthy conclusions. Godel shows that given that the rules give truths, it is possible to transcend the rules. If the rules only give truths, they must be consistent, but the statement which asserts the consistency of the rules lies outside the rules. The question is how do you ascertain the truth of the consistency statement or any other statement that transcends the rules. This according to Penrose, comes from understanding, and further to that it is claimed that the rule system is itself only an imitation of what understanding does.




9.)
 
HAMEROFF REPLIES TO CRITICISMS
In a recent talk Stuart Hameroff defends the Penrose/Hameroff quantum consciousness proposals against various criticisms. He discusses papers by McKemish and by Reimers. One paper claimed that useful coherence could not arise in hydrophobic pockets. Hameroff countered by asserting that the authors had only discussed the situation with respect to a single hydrophobic pocket. He says that it is accepted that a single pocket would not be useful. However, he says that his model is in terms of multiple hydrophobic pockets, where there could be different electron clouds capable of forming a dipole. He emphasises that many benzene and indole rings present in tubulin (the protein of which microtubules are made) are very close together. Electron dipole states switching at 8MHz is now considered a sufficient base for processing in microtubules.

Further to this, Reimers et al produced a paper showing that Frohlich type condensation was in three types weak, strong and coherent and claimed that microtubules could only support weak condensation at 8MHz, whereas Orch OR required strong or coherent. However, Hameroff says that in the context of electron dipoles forming in the dendritic microtubules 8MHz is sufficient. Hameroff indicates that he has moved away from the idea of Bose Einstein condensates, involving countless quanta locked in phase, as the basis of processing in microtubules. The single state of such a condensate is seen as less useful than a system involving many states. All that is required in his present model is synchrony and entanglement.

Hameroff goes on to discuss another important criticism of his model. This is the controversial area of the hydrolysis of GTP to GDP. Hydrolysis of GTP to GDP equates to conformal change through the release of a phosphate bond. This process is irreversible, leads to depolymerisation and treadmilling in microtubules with bits falling off one end, and being put on the other. This is suggested to make Hameroff's model impossible. However, he suggests this does not happen in the dendrites where microtubules are capped to prevent GTP hydrolysis. Thus the dendrites do not have polymerisation cycles. Therefore they are good for storing information and could be involved in learning. Here there is dipole switching between multiple hydrophobic pockets, and electron dipole states switching is sufficient.

Hameroff goes on to discuss suggested information processing within microtubules. Here the microtubule lattice is viewed in terms of topological qbits. The qbits are suggested not to be the individual tubulins but instead pathways along the microtubules. There is a choice of a number of such pathways. These pathways also allow for quantum error correction. If one tubulin gets out of alignment, it is pulled back by its neighbours, something that would not be possible with superpositions of individual tubulins. This is referred to as quantum error correction. Hameroff also criticises Reimer for attempting a refutal of his model on the basis of a 2D linear path, rather than the 3D paths around microtubules favoured by Hameroff and colleagues.










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