There is no real agreement within the cognitive sciences (and I include philosophers like Dennett and Searle as contributing to these) on how consciousness should be defined or approached, let alone what it may be, while the closest almost all cognitive scientists might get to QM is NMR technology used in structural and functional imaging. Meanwhile, in practice QM is a statistical mechanics. Some argue that it IS a statistical mechanics in an irreducible sense, but interpretations of the relationship between the formalism describing quantum systems and any "real" physical system remains open (and answers range from multiverse interpretations as one of a class of relative state interpretations to the truly esoteric). The last few hundred years within the sciences (including back when science was natural philosophy) have been dedicated in no small part to developing mathematical/formal languages which are as devoid of semantic content as possible, thereby allowing unambiguous statements to be made. Consciousness, whatever else it might entail, requires an explanation of understanding and meaning (i.e., we cannot explain consciousness without explaining what it is to understand one's conception of self as a unified agent distinct from even one's own body as well as one's environment the conceptual framework used to structure this self-aware perspective of the world around that self). However, formal languages are by DESIGN incapable of this. Meanwhile, the statistical structure of QM relates to physical systems in some unknown way. Combining the two, therefore, requires taking a mathematical language that is used to describe the dynamics of systems in ways we can't interpret or define in any one-to-one way and using this apparatus to model the quintessential exemplar of the very things it and all other formal languages were developed to avoid- subjectivity itself (and what it means).

I would suggest, before reading Penrose's books or Stapp's (3rd?) edition, that one acquires The Emerging Physics of Consciousness, published by Springer and in the same series (Frontiers) that Stapp's book is. Penrose's fellow developer of their Orch-Or quantum consciousness model, Stuart Hameroff, describes their model, but also included are other opinions from researchers in various fields (including a hero of mind, Alwyn Scott).

I think quantum mechanics fits to explain every occurrence :)

and Your another question is still missing its answer...

Http://www.sciencedaily.com/releases/2014/01/140116085105.htm

You can find the background to Pietro's link extensively discussed in two books by Roger Penrose: "The Emperors New Mind" and "Shadows of the Mind", which are both very interesting to read, whether you believe in the microtubule connection or not.

Thank You Piu...

Does Microtubules produces patterns of vibrations or they vibrate randomly.

There are several excellent books on the Physics of Consciousness, including Evan Harris Walker (very accessible and excellent), also Lockwood, Hodgson, Stapp, Penrose, et al.

This being said, i'm not sure I understand the alternatives you cite here: " is consciousness quantum mechanics, or is it a biological phenomenon ". Biology is, at bottom, quantum mechanics - there is no reality to any matter other than embodied in its wave functions.

There is no real agreement within the cognitive sciences (and I include philosophers like Dennett and Searle as contributing to these) on how consciousness should be defined or approached, let alone what it may be, while the closest almost all cognitive scientists might get to QM is NMR technology used in structural and functional imaging. Meanwhile, in practice QM is a statistical mechanics. Some argue that it IS a statistical mechanics in an irreducible sense, but interpretations of the relationship between the formalism describing quantum systems and any "real" physical system remains open (and answers range from multiverse interpretations as one of a class of relative state interpretations to the truly esoteric). The last few hundred years within the sciences (including back when science was natural philosophy) have been dedicated in no small part to developing mathematical/formal languages which are as devoid of semantic content as possible, thereby allowing unambiguous statements to be made. Consciousness, whatever else it might entail, requires an explanation of understanding and meaning (i.e., we cannot explain consciousness without explaining what it is to understand one's conception of self as a unified agent distinct from even one's own body as well as one's environment the conceptual framework used to structure this self-aware perspective of the world around that self). However, formal languages are by DESIGN incapable of this. Meanwhile, the statistical structure of QM relates to physical systems in some unknown way. Combining the two, therefore, requires taking a mathematical language that is used to describe the dynamics of systems in ways we can't interpret or define in any one-to-one way and using this apparatus to model the quintessential exemplar of the very things it and all other formal languages were developed to avoid- subjectivity itself (and what it means).

I would suggest, before reading Penrose's books or Stapp's (3rd?) edition, that one acquires The Emerging Physics of Consciousness, published by Springer and in the same series (Frontiers) that Stapp's book is. Penrose's fellow developer of their Orch-Or quantum consciousness model, Stuart Hameroff, describes their model, but also included are other opinions from researchers in various fields (including a hero of mind, Alwyn Scott).

"hero of mind", nice!

To be fair to him, as much as I personally have used his work to understand the mind beyond e.g., his contributions to neuroscience, consciousness, and related topics (in e.g., his The Nonlinear Universe, chap. 7), he's more of a hero IN mind (at least the mind that's mine),

Thanks for the reference, I only know his chapter in the Tuszynski book but "The Nonlinear Universe" indeed looks very interesting as well.

Interesting material Andrew!

Some more "material" can be found here:

# Eccles, J.C., Do mental events cause neural events analogously to the probability fields of quantum mechanics? Proc R Soc Lond B Biol Sci, 1986. 227(1249): p. 411-28.

# Koch, C. and K. Hepp, Quantum mechanics in the brain. Nature, 2006. 440(7084): p. 611.

It occurred to me that some 2-3 years of research might be redeemed somewhat from utter failure by providing sources for those interested in the literature on quantum theories of consciousness (and similar issues, such as the relevancy of QM to living systems in general or quantum-like theories of consciousness).

All but the final categories are books/volumes, though they range (and for the most part are arranged) in order from borderline-pseudoscientific sensationalist accounts to technical monographs. The final category consists of journal articles (as well as a journal largely devoted to this question). Apart from the main categories there is very little ordering, as I made the list by copying my sources (which, apart from the journal articles, are all hard-copies) and if I took the time to arrange it better I'd end up spending hours deciding what to include rather than first-found/first-chosen.

1) Sensationalist books:

Brown, J. (2000). Minds, Machines and the Multiverse: The Quest for the quantum computer. Simon and Schuster.

Wolinsky, S. (1993). Quantum Consciousness: The Guide to Experiencing Quantum Psychology. Bramble books.

2) Non-technical books

Stapp, H. P. (2009). Mind, Matter and Quantum Mechanics (3rd Ed.). Springer.

Stapp, H. P. (2011). Mindful Universe: Quantum Mechanics and the Participating Observer (2nd Ed.). Springer

Nadeau, R. (1999). The Non-Local Universe: The New Physics and Matters of the Mind. Oxford University Press.

Suarez, A., & Adams, P. (Eds.). (2012). Is Science Compatible with Free Will?: Exploring Free Will and Consciousness in the Light of Quantum Physics and Neuroscience. Springer.

Abbott, D., Davies, P. C., & Pati, A. K. (Eds.). (2008). Quantum aspects of life. World Scientific.

Pylkkänen, P. T. (2006). Mind, matter and the implicate order. Springer.

3) Volumes from Advances in Consciousness Research

Van Loocke, P. (Ed.). (2001). The physical nature of consciousness (Vol. 29). John Benjamins Publishing.

Gordon G. Globus. (2003). Quantum closures and disclosures: Thinking-together postphenomenology and quantum brain dynamics (Vol. 50). John Benjamins.

Gordon G. Globus. (2009). The transparent becoming of world: a crossing between process philosophy and quantum neurophilosophy (Vol. 77). John Benjamins.

3) Emergence: What it lacks in a physics even physicists can't call physical it makes up for as a buzzword:

Macdonald, G., & Macdonald, C. (Eds.). (2010). Emergence in Mind (Mind Association Occasional Series). Oxford University Press.

Seager, W. (2012). Natural Fabrications: Science, Emergence and Consciousness. Springer.

Murphy, N., Ellis, G. F., & O'Connor, T. (Eds.). (2009). Downward Causation and the Neurobiology of Free Will. Springer.

Clayton, P. (2004). Mind and emergence: From quantum to consciousness. Oxford.

Koons, R. C., & Bealer, G. (Eds.). (2010). The waning of materialism. Oxford University Press.

Horst, S. W. (2007). Beyond reduction: philosophy of mind and post-reductionist philosophy of science. Oxford: Oxford University Press.

4) From pretty basic to more technical:

Tuszynski, J. A. (2006). The Emerging Physics of Consciousness. Springer.

Torey, Z. (2009). The crucible of consciousness: An integrated theory of mind and brain. MIT press.

Barrett, J. A. (1999). The quantum mechanics of minds and worlds. Oxford University Press.

Green, H. S. (2000). Information theory and quantum physics: physical foundations for understanding the conscious process. Springer.

Ivancevic, V. G., & Ivancevic, T. T. (2008). Quantum leap: from Dirac and Feynman, across the Universe, to human body and mind. World Scientific.

Ivancevic, V. G., & Ivancevic, T. T. (2010). Quantum neural computation (Vol. 40). Springer.

Matta, C. F. (Ed.). Quantum Biochemistry: Electronic Structure and Biological Activity. Wiley

5) Some books on the interpretation(s) of QM, theoretical physics, and cosmology

Schlosshauer, M. A. (2007). Decoherence: and the quantum-to-classical transition. Springer.

Jaeger, G. (2009). Entanglement, information, and the interpretation of quantum mechanics. Springer.

MacKinnon, E. M. (2011). Interpreting physics: Language and the classical/quantum divide (Vol. 289). Springer.

Maudlin, T. (2011). Quantum non-locality and relativity: Metaphysical intimations of modern physics (3rd Ed.). Wiley.

Saunders, S., Barrett, J., Kent, A., & Wallace, D. (Eds.). (2010). Many Worlds?: Everett, Quantum Theory, & Reality. Oxford University Press.

Hemmick, D. L., & Shakur, A. M. (2011). Bell's Theorem and Quantum Realism: Reassessment in Light of the Schrödinger Paradox. Springer.

And finally, actual research (mostly)- journal articles

First, there's an entire journal almost wholly devoted to this issue and those like it: NeuroQuantology (www.neuroquantology.com). I'm sure some of the papers are excellent, but in my humble opinion, those who would think twice about any journals on parapsychology and/or alternative medicines which defy known physics may find this journal analogous.

Moving on-

Segalowitz, S. J. (2009). A quantum physics account of consciousness: Much less than meets the eye. Brain and cognition, 71(2), 53.

Asano, M., Ohya, M., Tanaka, Y., Basieva, I., & Khrennikov, A. (2011). Quantum-like model of brain's functioning: Decision making from decoherence. Journal of theoretical biology, 281(1), 56-64.

Khrennikov, A. (2011). Quantum-like model of processing of information in the brain based on classical electromagnetic field. Biosystems, 105(3), 250-262.

Acacio de Barros, J., & Suppes, P. (2009). Quantum mechanics, interference, and the brain. Journal of Mathematical Psychology, 53(5), 306-313.

Persinger, M. A., & Koren, S. A. (2007). A theory of neurophysics and quantum neuroscience: implications for brain function and the limits of consciousness. International Journal of Neuroscience, 117(2), 157-175.

Baars, B. J., & Edelman, D. B. (2012). Consciousness, biology and quantum hypotheses. Physics of life reviews, 9(3), 285-294.

Kurita, Y. (2005). Indispensable role of quantum theory in the brain dynamics. BioSystems, 80(3), 263-272.

Tegmark, M. (2000). Importance of quantum decoherence in brain processes. Physical Review E, 61(4), 4194.

Rosa, L. P., & Faber, J. (2004). Quantum models of the mind: Are they compatible with environment decoherence?. Physical Review E, 70(3)

Mavromatos, N. E. (2011, July). Quantum mechanical aspects of cell microtubules: science fiction or realistic possibility?. In Journal of Physics: Conference Series (Vol. 306, No. 1)

Hu, Huping, and Maoxin Wu. "Current Landscape and Future Direction of Theoretical & Experimental Quantum Brain/Mind/Consciousness Research." Journal of Consciousness Exploration & Research 1.8 (2010).

Louie, A. H. (2005). Any material realization of the (M, R)-systems must have noncomputable models. Journal of integrative neuroscience, 4(04), 423-436.

Longo, G. (2012). Incomputability in Physics and Biology†. Mathematical Structures in Computer Science, 22(5), 880-900.

Luz Cárdenas, M., Letelier, J. C., Gutierrez, C., Cornish-Bowden, A., & Soto-Andrade, J. (2010). Closure to efficient causation, computability and artificial life. Journal of theoretical biology, 263(1), 79-92.

Thaheld, F. (2003). Biological nonlocality and the mind–brain interaction problem: comments on a new empirical approach. BioSystems, 70(1), 35-41.

John, E. R. (2002). The neurophysics of consciousness. Brain Research Reviews, 39(1), 1-28.

Louie, A. H. (2007). A living system must have noncomputable models. Artificial life, 13(3), 293-297.

Smith, C. U. (2009). The ‘hard problem’and the quantum physicists. Part 2: Modern times. Brain and cognition, 71(2), 54-63.

Persinger, M. A., & Koren, S. A. (2007). A theory of neurophysics and quantum neuroscience: implications for brain function and the limits of consciousness. International Journal of Neuroscience, 117(2), 157-175.

And that's all the typing I can manage in one night. It's not exactly exhaustive, but then this isn't exactly a forum for exhaustive reviews. A final note:

For those with a fair amount of familiarity with mathematics (in particular, abstract algebras & measure theory or similar topics), I recommend Hall's Quantum Theory for Mathematicians (Graduate Texts in Mathematics). Despite the fact that we find "observables" in quantum mechanics to correspond not to what is observed but to a mathematical function, physicists like Dirac still managed to render alien the mathematical structure of QM: "Mathematicians tend to despise Dirac notation, because it can prevent them from making important distinctions, but physicists love it, because they are always forgetting that such distinctions exist and the notation liberates them from having to remember" (http://people.cs.clemson.edu/~steve/CW/395/CS483-part1.pdf)

Thank you Andrew .....

I enjoyed this paper by Capolupo and colleagues, which has also been commented and re-commented a lot:

http://www.ncbi.nlm.nih.gov/pubmed/23333569

As basically everyone else seems to be saying, there is no real agreement about concepts such as mind and consciousness among congnitive scientists, let alone, I would add, taking the adventurous path of quantum theories, about which, again, not all scientists agree, and apply them to consciousness and mind. There is a good number of philosophical speculation about mind: it is not suprising that those who attempted this combination, or at least some, took the path of neurophylosophy. I am not sure I can't be at least a little skeptical about this approach. A lot of data seems to have been gauged about the brain, and the relationship betweetn neural networks and neural activities, and consciousness. Some neuroscientists seem to maintain the idea that cosciousness equals to a mind-wandering state - thus identifying brain areas that are related to it, so the answer to your second question would be, according to some, the result of brain acitvity. It is interesting to note, though, that you're making some sort of false distinction between something that is in the brain and something that is the result of brain activity: what's the difference? Brain actiivty is in the brain anyhow. I wouldn't have any doubt in calling it a biological phenomenon in any case.

To complicate things furhter, a recent publication unveiled what we already knew and stated it clearly: data from fMRI investigation, which is what we base our speculations and theories on, have so many possible interpretations that it shouldn't be possible anymore, with a bit of common sense, to claim that something happens somewhere in the brain because fMRI data show such areas active under certain circumstances. If you find this interesting I can retrieve citation for you. I hope this helps.

Dear Manish, You have asked a long standing and important question for which there are protagonists (like Sir Roger Penrose with the Orchestrated objective reduction (Orch-OR) model; Christof Koch and Klaus Hepp) and antagonists. In addition to the literature quoted above, I would recommend you review the work of the late Gerd Sommerhoff who collaborated with Sir Peter Medawar and worked at University College London and Trinity College Cambridge (although he has become infamous for other reasons more recently). Subrata Ghosh, Satyajit Sahu, Anirban Bandyopadhyaya have also re-examined this question recently (see below). My own view is that we badly need a leap in theoretical understanding AND experimental results. Hope this helps.

References to the debate are below:

1. LaForte, Geoffrey, Patrick J. Hayes, and Kenneth M. Ford 1998.Why Gödel's Theorem Cannot Refute Computationalism. Artificial Intelligence, 104:265-286.

2. Feferman, Solomon (1996). "Penrose's Gödelian argument". PSYCHE 2: 21–32. CiteSeerX: 10.1.1.130.7027.

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4.http://consc.net/mindpapers/6.1b

5.http://users.ox.ac.uk/~jrlucas/Godel/referenc.html

6.Boolos, George, et al. 1990. An Open Peer Commentary on The Emperor's New Mind. Behavioral and Brain Sciences 13 (4) 655.

7.Davis, Martin 1993. How subtle is Gödel's theorem? More on Roger Penrose. Behavioral and Brain Sciences, 16, 611-612. Online version at Davis' faculty page at http://cs.nyu.edu/cs/faculty/davism/

8.Lewis, David K. 1969.Lucas against mechanism. Philosophy 44 231-233.

9.Putnam, Hilary 1995. Review of Shadows of the Mind. In Bulletin of the American Mathematical Society 32, 370-373 (also see Putnam's less technical criticisms in his New York Times review)

10.Tegmark, Max (April 2000). "Importance of quantum decoherence in brain processes". Phys. Rev. E 61 (4): 4194. doi:10.1103/PhysRevE.61.4194.

11.McKemmish, L.K., Reimers, J.R., McKenzie, R.H., Mark, A.E., and Hush, N.S. (2009). "Penrose-Hameroff orchestrated objective-reduction proposal for human consciousness is not biologically feasible". Physical Review E 80 (2): 021912–021916. Bibcode:2009PhRvE..80b1912M. doi:10.1103/PhysRevE.80.021912.

12.Georgiev, D.D. (2007). "Falsifications of Hameroff-Penrose Orch OR model of consciousness and novel avenues for development of quantum mind theory". NeuroQuantology 5 (1): 145–174.

13. Koch, Christof; Hepp, Klaus (30 March 2006). "Quantum mechanics in the brain". Nature 440 (7084): 611. doi:10.1038/440611a.

14.Hepp, K. (27 September 2012). "Coherence and decoherence in the brain". J. Math. Phys. 53 (9): 095222. doi:10.1063/1.4752474. Retrieved 8 August 2013.

15. Penrose, Roger (1989). The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics. Oxford University Press. p. 480. ISBN 0-19-851973-7.

16. Hofstadter 1979, pp. 476–477, Russell & Norvig 2003, p. 950, Turing 1950 under “The Argument from Mathematics” where he writes “although it is established that there are limitations to the powers of any particular machine, it has only been stated, without sort of proof, that no such limitations apply to the human intellect.”

17. Roger Penrose. Mathematical intelligence. In Jean Khalfa, editor, What is Intelligence?, chapter 5, pages 107-136. Cambridge University Press, Cambridge, United Kingdom, 1994.

18. Bringsford, S. and Xiao, H. 2000. A Refutation of Penrose's Gödelian Case Against Artificial Intelligence. Journal of Experimental and Theoretical Artificial Intelligence 12: 307-329. The authors write that it is "generally agreed" that Penrose "failed to destroy the computational conception of mind."

19. In an article at http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html L.J. Landau at the Mathematics Department of King's College London writes that "Penrose's argument, its basis and implications, is rejected by experts in the fields which it touches."

20. Princeton Philosophy professor John Burgess writes in On the Outside Looking In: A Caution about Conservativeness (published in Kurt Gödel: Essays for his Centennial, with the following comments found on pp. 131-132) that "the consensus view of logicians today seems to be that the Lucas-Penrose argument is fallacious, though as I have said elsewhere, there is at least this much to be said for Lucas and Penrose, that logicians are not unanimously agreed as to where precisely the fallacy in their argument lies. There are at least three points at which the argument may be attacked."

21. Dershowitz, Nachum 2005. The Four Sons of Penrose, in Proceedings of the Eleventh Conference on Logic Programming for Artificial Intelligence and Reasoning (LPAR; Jamaica), G. Sutcliffe and A. Voronkov, eds., Lecture Notes in Computer Science, vol. 3835, Springer-Verlag, Berlin, pp. 125-138.

22. Marvin Minsky. "Conscious Machines." Machinery of Consciousness, Proceedings, National Research Council of Canada, 75th Anniversary Symposium on Science in Society, June 1991.

23. Feferman, S. (1996). "Penrose's Gödelian argument". Psyche 2: 21–32.

24. Searle, John R. The Mystery of Consciousness. 1997. ISBN 0-940322-06-4. pp 85–86.

25. Penrose, Roger (1989). Shadows of the Mind: A Search for the Missing Science of Consciousness. Oxford University Press. p. 457. ISBN 0-19-853978-9.

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28. Stuart Hameroff, Roger Penrose. "Consciousness in the universe: A review of the ‘Orch OR’ theory". Physics of Life Reviews. http://www.sciencedirect.com/science/article/pii/S1571064513001188

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32. Hameroff, Stuart (2008). "That's life! The geometry of π electron resonance clouds". In Abbott, D; Davies, P; Pati, A. Quantum aspects of life. World Scientific. pp. 403–434. Retrieved Jan 21, 2010.

33. Roger Penrose & Stuart Hameroff (2011). "Consciousness in the Universe: Neuroscience, Quantum Space-Time Geometry and Orch OR Theory". Journal of Cosmology 14.

34. Reimers, Jeffrey R.; McKemmish, Laura K.; McKenzie, Ross H.; Mark, Alan E.; Hush, Noel S. (17 March 2009). "Weak, strong, and coherent regimes of Fröhlich condensation and their applications to terahertz medicine and quantum consciousness". PNAS 106 (11): 4219–4224. Bibcode:2009PNAS..106.4219R. doi:10.1073/pnas.0806273106. PMC 2657444. PMID 19251667. Retrieved 10 June 2013. Cite uses deprecated parameters (help)

35. Hameroff, S.R. (2006). "The entwined mysteries of anesthesia and consciousness". Anesthesiology 105 (2): 400–412. doi:10.1097/00000542-200608000-00024. PMID 16871075.

36. Hameroff, S. (2009). "The "conscious pilot"—dendritic synchrony moves through the brain to mediate consciousness". Journal of Biological Physics 36 (1): 71–93. doi:10.1007/s10867-009-9148-x. PMC 2791805. PMID 19669425.

37. Buhl, D.L., Harris, K.D., Hormuzdi, S.G., Monyer, H., and Buzsaki, G. (2003). "Selective Impairment of Hippocampal Gamma Oscillations in Connexin-36 Knock-Out Mouse In Vivo". Journal of Neuroscience 23 (3): 1013–1018. PMID 12574431.

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Hormuzdi, S.G., Filippov, M.A., Mitropoulou, G., Monyer, H., and Bruzzone, R. (2004). "Electrical synapses: a dynamic signaling system that shapes the activity of neuronal networks". Biochimica et Biophysica Acta 1662 (1–2): 113–137. doi:10.1016/j.bbamem.2003.10.023. PMID 15033583.

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49. Georgiev, D.D. (2009). "Remarks on the number of tubulin dimers per neuron and implications for Hameroff-Penrose Orch". NeuroQuantology 7 (4): 677–679. doi:10.1038/npre.2009.3860.1.

50. De Zeeuw, C.I., Hertzberg, E.L., Mugnaini, E. (1995). "The dendritic lamellar body: A new neuronal organelle putatively associated with dendrodentritic gap junctions". Journal of Neuroscience 15 (2): 1587–1604. PMID 7869120.

51. Subrata Ghosh, Satyajit Sahu, Anirban Bandyopadhyaya (2013). "Evidence of massive global synchronization and the consciousness: Comment on "Consciousness in the universe: A review of the ‘Orch OR’ theory" by Hameroff and Penrose". Physics of Life Reviews. doi:10.1016/j.plrev.2013.10.007

Dr, Datta-

I agree that this is an "important question for which there are protagonists...and antagonists", but many of your sources are not really related to it. Penrose has used Gödel's proof to demonstrate issues with treating cognition and consciousness using standard mathematical methods universal to the sciences. However, that argument, as well as many you cite, do not concern QM but non-computability or computability in computer science terms). Did you have some other points you were making by using these? Thanks.

"I agree that this is an "important question.."

But totally unanswerable, and probably meaningless. I don't see how something as complex and nebulous as mind, consciousness or will can be explained by something even more theological, like quantum theory.

Anthony, an outstanding primer would be 'The Physics of Consciousness" by Evan Harris Walker, then there are more advanced texts.

Never heard 'theological' applied to Quantum Physics, that's a first.

"Never heard 'theological' applied to Quantum Physics, that's a first"

Like theology, QP takes pleasure in difficult and insoluble (at least at present) problems, and suits those of a mystical disposition or who take delight in incomprehensible topics as a displacement activity.

@Anthony

I've read, I think, a pretty wide range of technical and popular (and sensationalist) approaches to modern physics, from monograph series to religious/spiritual books for the non-scientist, but with rare exception one does not find physicists writing books like

Polkinghorne, J. C. (2007). Quantum physics and theology: An unexpected kinship. Yale University Press.

And when they do, it is very clearly not intended to be taken seriously as physics literature (the only possible exception I know of off the top of my head is Amoroso, R. L., & Rauscher, E. A. (2009). The holographic anthropic multiverse: formalizing the complex geometry of reality (Vol. 43 of Series on Knots and Everything). World Scientific).

Nobody took pleasure in the appearance of quantum mechanics (or QED, QCD, QFT, etc.) One of its founders dedicated years to showing it couldn't be correct, culminating in the paper known as EPR (1935) in what was to be his most devastating critique (showing that QM entailed nonlocality and therefore, thought Einstein, was either incomplete or could not be a theory of reality). It is one of the most cited papers in all of physics because some 50 years later the logic underlying the argument was used to empirically demonstrate what Einstein thought impossible. Bohr was no better. He accepted QM as theory of physical reality in ways that Einstein would not, but he banished it to some netherworld from which our world of classical physics was forever free of and about which physicists could describe only in mathematical terms, thus "brainwash[ing] a whole generation of physicists into believing that" the measurement problem had been solved by basically retaining the language of classical physics and applying it to mathematical entities that dwell in Hilbert-space.

Statistical physics (along with statistics and much of mathematics in general) was developed in order to help model systems which were too complex, begrudgingly granting them epistemic indeterminacy but without yielding the Laplacian determinism by acknowledging any ontological indeterminacy. Quantum physics not only placed and absolute boundary in front of the positivism of the previous century (so aptly characterized by the advice von Jolly gave to Planck or Lord Kelvin's similar description of physics as basically settled/resolved), it required a mathematical structure to describe physical systems rather than physical structures motivating mathematical models. I've yet to meet or hear of a physics student who appreciated, after 4 years as an undergraduate studying mechanics in terms of the dynamics of systems represented in a one-to-one correspondence with whatever formal descriptions were used to describe any properties/processes of interest happy to find terms so familiar they pre-date university to mean something so alien. Suddenly one is using "system" to describe a mathematical function, "observable" to mean an unobservable mathematical operator that will give us a probability (namely, that the system prepared in whatever specified manner will yield a particular measurement), and an initial state that we "discover" after measurement (part of which is applying our unobservable "observable" operator to our physical system that dwells in an infinite-dimensional complex space with an inner product).

It is one thing to find buzzwords ripped from what scientific (empirical and quantitative) context they possessed and used to endorse what can at most be kindly described as metaphysics. Quantum physics is difficult in practice mainly because it is a statistical mechanics that deals with e.g., N-body problems in which there isn't necessarily any distinct N bodies (hence many-body problems). This is very different from the epistemological questions or issues that have remained while the modern world rests upon the success of QM. One may equate metaphysics and the philosophy of modern physics with some work in theology because there are similarities: many of the same methods are used (although in theology, they are used to justify conclusions already reached, while in philosophy they are used to reach conclusions). But equating quantum physics with theology is to make the very mistake theologians or new-age gurus do: mistake physics for metaphysics and use interpretations of the latter as if they were ontological descriptions of the former.

Nice post Andrew,

I would perhaps further comment that QP does not 'take pleasure', that QP is simply not difficult (just follow the math), and that indeed it's sometimes not straightforwardly soluble (as an example, we still cannot manage to explicitly write out the wave functions of most systems), but that is not a problem of QP per se, but a problem stemming from our limited math abilities (and a problem that crops up in many other pursuits than QP, such as e.g. the millennium problems etc.)

@H Chris Ransford

Thank you! And in my meandering post, if I failed to communicate a central notion (that QP does not, as you say, "take pleasure"), I was remiss. I would say, however, that "follow the math" is a great deal simpler to those who learned much of linear algebra/matrix algebra through physics notation, and did not (as mathematicians) have to learn and use it anew: "Mathematicians tend to despise Dirac notation, because it can prevent them from making important distinctions, but physicists love it, because they are always forgetting that such distinctions exist and the notation liberates them from having to remember"

(from footnote 32 of Mermin's lecture notes found here: http://people.cs.clemson.edu/~steve/CW/395/CS483-part1.pdf)

There are also two ways (I'm simplifying here) of following the math. One is that of Everett, who begat relative state interpretations and retired after the over-bearing influence of Wheeler and the reception of his thesis (and made millions). He did not coin the term "many-worlds" but his work was the foundation for the many-worlds interpretation. The other I have found expressed never so succinctly nor so powerfully as in Silverman's Silverman, M. P. (2008). Quantum superposition: counterintuitive consequences of coherence, entanglement, and interference (The Frontiers Collection): "What quantum mechanics ‘adds up to’ is that it is an irreducibly statistical theory, albeit unlike any necessitated simply by ‘incomplete knowledge’, with nonlocal features inexplicable from the perspective of classical physics. But something that is strange is not necessarily incomprehensible, although it may not be visualizable. Mathematicians, for example, may understand very well the principles of a 10-dimensional geometry even if no 10-dimensional figure can be drawn."

This would be roughly equivalent to the "shut-up and calculate" maxim in QM often attributed to Feynman. It seems that it wasn't Feynman, but the very N. David Mermin cited above: Could Feynman Have Said This?

(http://fisica.ciencias.uchile.cl/~emenendez/uploads/Cursos/callate-y-calcula.pdf)

Quantum physics has been among the few most successful theories (or theoretical frameworks) ever. We depend upon it in ways few know (even those who have had e.g., MRI scans). Heisenberg's uncertainty principle is too often expressed as a kind of general "we can't know what's going on" rather than what it is: a mathematically-based ratio that TELLS us how uncertain we are AND of what, not some mystic boundary to a quantum otherworld (although I am reminded of Susskind and another's published a multiverse interpretation that they argued was equivalent with the many-worlds and the correct interpretation; I found the paper interesting mainly because of the incorporation of an imitation of Galileo's dialogue not for the results). Quantum physicists do not revel in the insoluble but forever develop technologies (e.g., ion traps or NMR) to implement versions of Wheeler's delayed-choice and Schrödinger's cat thought experiments.

Short version: exactly what you said.

An interesting discussion, but is it twenty, thirty or even forty years out of date? Most of the people who have written on QM and consciousness have assumed that the quantised modes that might underlie phenomenal experience would need to be very special, perhaps involving 'hot' coherence of the sort normally found in condensates near absolute zero or of the Frohlich type, and that the link would be through some aspect of dynamics with no classical description. Yet to be much use biologically it would seem we want a classical description, at least in the sense of involving only real number values in Euclidean space and nothing tied too much to uncertainty - which would make behaviour unreliable (and be no help if you want free will).

But contemporary quantum field theory has a stack of modes that, being based on spin zero bosons, relate very readily to classical (real number) descriptions and tend to be the modes that explain the events of our daily lives, like sounds and the reflection of light off water, and when I was a boy, the music coming out of a crystal set radio. As I see it once one has appreciated the central message of Lie Group Theory and the Nambu-Goldstone theorem the relation of QFT to everyday life becomes much more straightforward and transparent. As I see it the modes we should be looking for in the brain to support phenomenal experience should be pretty unremarkable.

And I don't think QM should ever have been thought counterintuitive or 'difficult' anyway. As someone said, the basic maths is not hard. Once you have got used to it it becomes clear that a theory that has a discontinuous dynamic grain (i.e. is quantised) has to have these odd features like uncertainty and 'path integrals'. Moreover, there are very good reasons why the world must have a grain. I think it may be salutory that in the 1920s, before QM had got anywhere near to being a field theory of the sort Feynman played with, AN Whitehead laid out how he thought the world must be constituted, without reference even to QM, in a way that fits very neatly in with Feynman's picture (Joseph Rouse recently sent me a rather nice paper explaining this:

http://organicism.org/ojs/index.php/ajpt/article/viewFile/106/68). Whitehead had worked out the strange features of QFT from first principles, with some help from reading Leibniz. Nobody else could understand him because physics had got so dumbed down in the Rutherford era just before.

All dynamics are quantum dynamics so consciousness is quantum dynamics. Now we have everyday modes for everyday phenomena the sorts of complaints Max Tegmark made are I think just irrelevant. Time we got on with some ordinary quantum biology.

@ Dr. Edwards-

1) Nothing about QM as far as mathematics is concerned was ever counter-intuitive (well, I will mention again that those of us who learned the standard and more precise formal language of linear/matrix algebra before Dirac notation have found it frustrating, but not counter-intuitive just needless and inferior). There are not hundreds of volumes, monographs, papers, etc., on the problems with scalar or vector fields, Feynman never said "nobody understands the arithmetic of elliptic curves", and the reason why Hardy, Littlewood and Polya remains an invaluable reference on inequalities despite being published some 30 years before Bell's inequality is for quite the same reason Bell's work was ignored some 30 years after him (in Everitt, W. N. (Ed.). (1991). Inequalities: Fifty Years on from Hardy, Littlewood and Pólya; Proceedings of the International Conference, London Mathematical Society)- mathematically, it's of little import and hardly warrants any treatment. Yet people have written volumes upon volumes and paper after paper on the problems with quantum field theory, Feynman did say "nobody understands quantum mechanics", and Bell's inequality is among the most cited papers in the sciences (entire works are devoted to it, e.g., Bell's Theorem and Quantum Realism: Reassessment in Light of the Schrödinger Paradox (SpringerBriefs in Physics)).

2) In the world of mathematics, we can and do frequently make certain statements true simply by defining them to be so. Were quantum field theory straightforward, we would not care that for any PDE of some single "particle", or for simplicity an electron, Schrödinger's wavefunction cannot yield another particle as required by relativity. In fact, the entire starting point could be easily simplified but for one small problem: relativity is extraordinarily successful as a scientific model as is QM yet neither is particularly well suited when paired with the other unless we give up on any semblance of empirical bases for physics.

3) All dynamics are not quantum mechanics. That's one reason why quantum field theory exists, and QFT is NOT QM. Not only that, but modern physics remains without a suitable union of relativity and quantum mechanics, hence the plethora of unifying theories over the past few decades.

4) Neither the geometry of relativity nor the mathematical space of QM is Euclidean. The former, at least in terms of spacetime, is typically based on Minkowskian or Riemannian geometry and the latter is situated squarely in Hilbert space (which is typically infinite dimensional and complex). I'm sure you know this, which is why I don't understand your comment "Yet to be much use biologically it would seem we want a classical description, at least in the sense of involving only real number values in Euclidean space and nothing tied too much to uncertainty". If we want a classical description, then we have classical field theory. Tegmark, whom you state is simply complaining, objected to the idea of quantum processes significant to neuronal functioning because a central, basic, and absolutely fundamental aspect of quantum physics is decoherence (or collapse, or whatever model or interpretation one finds best supported from which classical reality is recovered from quantum physics). This is intrinsic to QM from a mathematical perspective: quantum processes unknown in our classical realm rapidly decohere as one moves away from the subatomic scales in which quantum physics alone is suitable for.

5) In a chapter in one of the sources I recommended, Alwyn C. Scott writes "Classical dynamics seems to imply that high-level brain processes can be reduced, in principle if not in practice, to a description that is based on the classical laws of physics and chemistry, leaving no room for the subjective experiences that we confirm in our daily lives. To avoid this unwelcome conclusion, it is asserted that quantum theory must be an essential component in the dynamics of biological brains, and various arguments are advanced to show that large-scale quantum states can indeed survive long enough to play functional roles in living organisms.

The primary aim of this chapter is to show that classical neuroscience cannot be reduced to fundamental descriptions; thus quantum theory is not needed to provide theoretical space for those phenomena that we know exist but don’t understand." Uncertainty is not recovered by some "classical description". Indeed, a main buzzword of popular science literature, nonlocality, is an aspect/component of classical physics. Laplacian determinism was never derived from empirical investigations nor indeed from theory but rather the notion of predictability crept in out of initial success in early modern science and worldviews/ideology. Whether Tegmark or his critics are right is an empirical matter settled hopefully both by an increased understanding of decoherence conditions/processes as well as neural dynamics.

6) Whitehead figured out nothing related to QFT. One might just as easily say that the bible predicts the big bang theory. Descriptions of the cosmos do not a theory make, no matter how analogous they may appear to the actual derivation of theories from inference and observation. Also, as quantum field theory simply an extension of classical field theory complicated by theory, not mathematics, I don't know why you would suggest that "Nobody else could understand him because physics had got so dumbed down in the Rutherford era just before" considering that Rutherford's work was contemporaneous with Whitehead and Whitehead's crowning achievement turned out to be flawed while Rutherford's work is integral to quantum physics. Plato "laid out how he thought the world must be constituted, without reference even to QM" and Whitehead remarked that the whole of Western philosophy was but a series of footnotes to Plato. Whitehead, brilliant though he was, achieved his accomplishments through logic and in philosophy, and was not required and never came close to laying out how the world IS constituted based on anything remotely resembling physical theory.

6) As quantum theories of neural dynamics remain as ill-grounded and poorly supported as parapsychology (and largely published in journals like NeuroQuantology designed specifically for the incorporation of research not publishable elsewhere) I wouldn't say the discussion is out of date. As there is no agreed upon definition to what consciousness is while the most broadly (in practice) accepted definition of quantum mechanics is that of a statistical theory, quantum theories of consciousness are mainly metaphysics and philosophy (as are all current theories of consciousness, but reliance upon a physical theory in which physical systems exist in a mathematical space is hardly bringing one closer to a testable, scientific theory of consciousness).

Dear Andrew,

Thank you for the comments, which I take as constructive. However, my points were perhaps intended at a different level of the debate. I will go through some of yours to try to see whether there is a real difference in opinion here.

I agree that the math of quantum physics (to be broad QP) is not counter-intuitive. What people complain about is the counter-intuitive nature of superposition. My point was that this is only counter-intuitive if one is still looking for a ‘visualisable’ account, maybe like Bohm. Leibniz understood why we should not look for a visualisable account and my reading of QP is that it ties in well with Leibniz’s insights of the sort of dynamics you have to have, especially if you have symmetries and quantization.

I realize that there are many technical problems with QFT and that progress has been hard won. I do not pretend to know what Feynman was intending when he made the famous ‘nobody understands’ remark. A simple answer would be that he was just saying that if you want to visualize QP then you will be disappointed however you try to produce an ‘ontological’ account. Whether or not Feynman understood why Leibniz had pointed out that this was expected I do not know. As I shall come to, very few people read Leibniz and related his ideas to QP until quite recently as far as I know. The second answer to Feynman’s point may relate to things like the content of his famous lecture on interference in reflection of thick glass plates. Even in practical terms his best shot did not seem to deal with the result. My understanding is that in the last ten years people have got much closer to making the results compatible with QFT using families of Bose modes based on other forms of symmetries.

The reason why Bell’s stuff was so much cited is, I assume, because it was a new and acid test of the non-visualisability of QP that took people’s imagination because it was seen as a struggle between the Titan’s of Bohr and Einstein. And the fact that Einstein did seem to want a visualisable reality is, I think, of key relevance. In some ways he seems like Newton, who got the equations but was much closer to intuitive realism than Leibniz on things like relative space etc.

One might ask why, if non-visualisability is to be expected, so few people seemed to have cottoned on to that (maybe including all of Bohm, Feynman and Einstein at different levels). And I think the simple answer is that it is tough. The fact that is tough is to my mind the best explanation for Leibniz’s work being regarded as daft for 300 years, with Kant being preferred because although he agrees with non-visualisability for us he provides the let out that the ‘thing in itself’ really would be visualisable if you were God. He misses the point of Leibniz and QP – even God could not visualize superposition, and we should never have expected to.

The problems of marrying relativity and quantum theory may be significant, but the physicists I have talked to tend to play it down. I am not myself a physicist but have tried to familiarize myself with the general structure of the theories from textbooks, with ‘tutorial’ help from among others, Basil Hiley and Michael Fisher. I am well aware that QM is not QFT but my statement was perfectly clear – ‘all dynamics are quantum dynamics’ implying whatever QP tool you want to use but involving the basic framework of quantization and superposition (or coherence if you like).

My reference to Euclidean space would I thought have been clear – it is the approximated metric that we find deals with all biology pretty much. True, some respiratory events require quantum level concepts, but the underpinning of conscious experience looks as if it will have to be at a bigger scale and, contrary to what became trendy, quantum level dynamic issues would seem to be a bad idea for efficient ‘thinking’. So the point is that we are looking for some dynamics that will cross the correspondence principle intact and translate into something like Hodgkin Huxley events, where Euclidean space will do. (So I’m a bit surprised you did not follow!) This may of course apply to lots of quantized modes but my understanding is that spin zero Bose modes of the Goldstone type yield real number based dynamics relatively directly.

As I indicate, I am well aware that superposition, or coherence is fundamental to QP. But acoustic type phononic modes are stable over many seconds at room temperature as we all know. I see no reason not to relate consciousness to these modes. The problem, I think is that everyone has got hooked on this odd idea that consciousness is something to do with a ‘collapse of a wavefunction’ (without being very clear which wavefunction that would be or even if it were formulable, or what a ‘wavefunction’ actually is, other than a descriptor of an ensemble). If you come at the problem from Whitehead’s or Leibniz’s angle or that of Ogrodnik

http://organicism.org/ojs/index.php/ajpt/article/viewFile/106/68 then all this Schrodinger cat stuff can be laid to rest.

I knew Alwyn, and read his book and miss his friendly wit. But he and I disagreed, amicably. Leibniz’s key contribution is to point out that we need indivisible points of view at the fundamental level. It does not matter what objects are – Mars can be Mars or two halves of Mars. But subjects must be indivisible and relational – like modes of excitation of quantized fields. Al’s arguments for the sum being greater than the parts in complex non-linear systems I did not buy. But Goldstone modes are more than just the fermions that they go with – they are true, extra, indivisibles (without any parts).

I don’t quite follow your comments on determinism but Leibniz also had that pretty well sorted I think. You dismiss Whitehead but I am not clear why. I agree fairly much with Ogrodnik. I think you would agree that although QFT extends classical field theory it does it in a very different context of unenvisualisable superposed quantized units. I am not at all sure that Whitehead’s work turned out to be any more flawed than the ‘solar system’ model that I was intending to imply when invoking Rutherford. Whitehead’s text is very difficult to interpret, I grant, but the general framework of ideas look to me to be very relevant to the empirical problem of the biophysical basis of experience.

I am well aware that almost all of the quantum theories of neural dynamics are rubbish - utter and complete nonsense. But that does not mean that they all have to be. Would you consider the paper by Heimburg and Jackson on axonal solitons in PNAS complete rubbish? These solitons are not going to explain experience but I see no reason why similar effects in dendrites should not. Defining consciousness in this context is not difficult or even very contentious – the issue at hand is what biophysical events are necessary and sufficient for the phenomenal experiences that most of us believe we have. I agree that QP is statistical but I think it reasonable to say that it is a statistical description of what are perhaps best described as individual modes of excitation of fields that we think exist as fundamental dynamic units.

My theory of the relation between quantized modes and experience is not intended to be either philosophy or metaphysics. It is intended to be just as hard biophysics as what I spent the last thirty years on in other areas of cell biology. I think maybe you are using some rather metaphysical arguments! Getting the maths of the dynamics right is how you solve cell biological problems. The dynamics can be in all sorts of forms at all sorts of levels but I see this is ordinary science, if admittedly challenging in practical terms.

My main point was why not think in terms of Goldstone modes? As fundamental dynamic indivisibles they fulfill Leibniz’s requirements for monadic units, they fit well with Whitehead’s actual occasions and they marry up nicely with known biophysical properties of cell membranes. People have been looking in weird nooks and crannies when what they are looking for may be in front of their noses.

Dear Dr. Edwards-

Thank you for the constructive (and enlightening) reply. I very much appreciate your more thorough take on the matter which I knew you must have but (given the medium) had barely expressed apart from a mere skimming over of your analysis (or analyses).

I have to say, before responding to anything else, that I could not possibly be more jealous and more intrigued that you knew Dr. Alywn Scott. As I have said already in response to this question, he's something of a hero of mine.

As for Bohm, I have to agree with what perhaps the most thorough reviewer of his works explicitly states (Dürr, D., & Teufel, S. (2009). Bohmian mechanics: the physics and mathematics of quantum theory. Springer.) Unlike his own works or even The Essential David Bohm, the above is a thorough review by physicists for physicists of Bohm's mechanics: "In books and seminars on quantum mechanics, there is so much talk about interpretation. One talks about interpretations of quantum mechanics: Copenhagen, many worlds, Bohmian , and so on. As if the laws of quantum mechanics were a Delphic oracle which required high priests to be deciphered. What is special about quantum mechanics as compared to Newtonian mechanics, where only a few scientists (influenced by quantum mechanics) would insist that Newtonian mechanics needed an interpretation? Newton certainly did not think this way, and nor did Leibniz (actually the equations in the form we are used to seeing them were written by Leibniz)"

Only according to the authors Bohmian mechanics isn't quantum physics. It is not an interpretations of quantum mechanics but an entirely different theory of physical reality. And Bohm's work is perhaps more misunderstood than that of any physicist of the modern era, as all anybody cares to hear is "deterministic" and fails to notice that this comes at the price of a nonlocality so complete it has been embraced by mystics as a holistic metaphysics of the cosmos and how all things are One.

Luckily, empiricism has provided us some instantiations of what were previously mere thought experiments. We don't just have Schrödinger cats, we have Schrödinger kittens: microscopic, mesoscopic, and macroscopic. Species of logical paradoxes: Dunningham, J., Rau, A., & Burnett, K. (2005); "From pedigree cats to fluffy-bunnies." Science, 307(5711), 872-875.); Gisin, N. (2006). "New additions to the Schrödinger cat family". Science, 312(5770), 63-64.. And Feynman? His delayed-choice experiment has also been implemented empirically just as Schrödinger fat cats have. A favorite of mine is Gerlich, S. et al. (2011). "Quantum interference of large organic molecules." Nature communications, 2, 263.

Nobody knows how physical systems described in any quantum physics, whether basic QM or QFT, QED, QCD, etc., corresponds to reality. It is as if a single particle is ontologically probabilistic and reality fundamentally statistical. As this is not physical theory, nobody quite knows what to make of it and most physicists just go with "it works if we treat physical reality as existing at the most fundamental level as probabilistic."

I'm not quite sure what you see in particle physics (fermions, bosons, etc.) given that these are more questionable than any physical system in quantum mechanics and quantum mechanics is treated as irreducibly statistical (and thus not a theory of reality).

I should probably cut-off before I blather onto more than is possible to respond to. However, I would recommend a text I have referred to before on this site regarding the dynamics of dendritic processes: Cuntz, Remme, & Torben-Nielsen (Eds.) (2014) The Computing Dendrite: From Structure to Function (Vol. 11 of Springer Series in Computational Neuroscience)

Dear Andrew,

I think we have established common ground and divergence. I will make a quick comment on the ?Dürr and Teufel quote and then raise what I think is the most interesting issue.

D & T: ‘What is special about quantum mechanics as compared to Newtonian mechanics, where only a few scientists … would insist that Newtonian mechanics needed an interpretation? Newton certainly did not think this way, and nor did Leibniz.’

If so, what is the Monadology? And the argument about relative and absolute space? Leibniz’s New System and beyond to Monadology is entirely ‘interpretation’ in the sense of being an account not of mathematics but of what reality we should understand the mathematics to reflect. Monadology has been forgotton until this tercentenary year but I’m darned if it is going to be for much longer. It is the key – literally the crib to what the signs on the map mean. Moreover, it points out that all the interpretations of QP go nowhere – they are a bit like physiological explanations in a bad nursing textbook.

You may disagree, but this is how I see it:

As Descartes pointed out, reality starts with experience. That is the one thing we know is real. Everything else could be a joke played by a demon. But he found that maths was very reliable, and even mathematical patterns in nature, so it seems that the way our real experiences shift with time follows some set of rules of regularity of change. The operation of those rules seems to be everywhere and that is what we call God or if we are atheistic, Nature.

So reality only implies two things: experience and a regularity in the way experience changes. This regularity is what physics studies. There is a constant tendency to think physics studies ‘stuff’ but Descartes, Newton and Leibniz all tell us that their physics is not about stuff in the intuitive sense, it is about the dynamic dispositional patterns that regulate our experiences. These patterns are defined purely mathematically, and as Leibniz argues, that implies statistical maths about uncertainty even if only at the smallest scale. Leibniz is much clearer in his ‘interpretation’ than Newton because, like Kant but unlike Locke and (probably) Newton he thinks that our ordinary ideas of space and time are purely illusory. There isn’t even any spacey space for stuff to be stuffy in. (Descartes’s space was nothing like intuitive space either.)

So to my mind a statistical or mathematical theory is all a physics theory will ever be – a theory of mathematical relations between experiences according to some agreed calibration via experiences of rulers and clocks. There is no other sense of ‘real physical’ once one has digested the Meditations – which I understand were intended as a primer in how to interpret physics for Sorbonne students. Unfortunately the teachers didn’t see the point.

Leibniz starts from this point and shows that once one has emerged from the other side of the metaphysical jungle of trying to find ‘stuff’ to the fresh mountain air of real changing experience (perception) all the basic structure of QP falls out effortlessly. Kant made the mistake of saying that there must after all be a ‘nether world’ of ‘things in themselves’ that we cannot see, and almost everyone slipped back into stuff-hunting. (I admit my account of 1910 physics was a bit distorted. Dear old JJ Thompson from my Alma Mater had some very non-stuff ideas about atoms but then got a bit stuffy with a plum pudding and lost the plot it seems.)

So we do know how QP corresponds to reality – it is a good account of the regularities in the changes of our experiences. Nothing more was ever on the menu!

Finally, two small points:

I don’t think there are particles, only modes of excitation. ‘Excitation’ is pretty meaningless, which may help to avoid billiard ball thinking, but at least it is a conception of activity or dynamics or instance of operation of change. As I understand it bosons and fermions are not things but increments of energy of Bose and Fermi modes, or to put it another way an s orbital is not occupied by an electron so much as just ‘in operation’.

I had access to the Computing Dendrite as a book review editor but could not afford the hard copy. Things are moving fast, particularly in the lab of Mike Hausser, whose new facilities are being built where my old office once was. Dendritic events are non-linear and temporally complex – that seems to be nailed. What I do not think is dealt with in that volume is how that can translate to experience – for the simple reason that hardly anybody thinks it would. But I think it has to. The story from there on is long and complicated but my thoughts are linked to my RG site.

Alwyn knew all the right questions. I just think he could not quite see how his insights led to the right answer. It needs collaboration between people with detailed QP expertise and neurobiologists who want to find an account of the proximal relations that determine experience that fits locality constraints (which I agree are subtle). To my mind the attempts so far have got caught up in some false assumptions, one of which even Leibniz suffered from.

I see recent studies on quantum cognition moving in the direction of the posed question. Look at my piblications on RG

Dear Dr. Edwards:

Re: what is Leibniz' La Monadologie if he thought mechanics required no interpretation:

Put simply, it's not concerned with mechanics. Recall that this is when mechanics was still linked to μηχανικά via e.g. the French translation "les mécaniques" Galileo's work during Leibniz' day- it described the motion of "bodies" (particles, planets, etc.). It was not metaphysics, as La Monadologie is, but quite fundamentally the ways in which gravity, work, energy, etc. (in general "forces" in the non-technical sense) caused things to move or not to move. Consider 34:

"C’est ainsi que chez les Mathématiciens, les théorèmes de spéculation et les canons de pratique sont réduits par l’analyse aux Définitions, Axiomes et Demandes."

Instead of equations of motion or the mathematical notation that Leibniz himself developed and the authors I quoted refer to, we find statement on mathematics and physics itself, a use of language to describe or speak of another "language" (metaphysics).

Quantum mechanics is, like it's classical counter-part, a theory of how things move. The reason it requires an interpretation, or seems to, is because it borrows the language of classical physics to describe the movement of things that, in classical mechanics, could not move in this way. More properly, these things did not exist, as "wave/particle" duality is a meaningful as "dead/live" duality to describe a cat that behaves both dead and alive. Only we do not describe a cat as acting both dead and alive, because this is nonsense. So too is the use of classical terminology to describe particle-like waves (dead-like living cats). Quantum mechanics speaks of the state of systems as a mathematical abstraction AND ONLY that, using a mathematical operator for an "observable" rather than observation. This is, again, akin to statistical mechanics but statistical mechanics does not describe the state of systems as ontologically statistical it describes systems statistically. Quantum mechanics does not. It combines the statistical or probabilistic terminology of statistical mechanics with the ontologically-based language of quantum mechanics. Put simply, it describes a physical system as BEING (ontology) probabilistically distributed, defined, and/or derived. But the motivation for the description is simply the borrowing of terminology. We refer to a system's state as it existed before we measured it based on how what we measured can then be somehow mathematically "observed" to project the value of measurement backwards onto the system's state. The problem is not that quantum mechanics is a statistical mechanics but that it is a completely deterministic mechanics. The Schrödinger wavefunction is entirely deterministic as are variations on it (other dynamical equations of motion in quantum physics). This is of necessity, as mathematics is well-defined. However, the statistical component comes from describing some systems as possessing a well-defined state after the application of a mathematical "observable" is applied to a value of measurement. Mathematical operators do not observe, and thus we get the state of our system deterministically via probability which, like a dead-cat behaving alive, is nonsensical.

The problem, then, is that while Newton, Leibniz, Laplace, Euler, all the way up to Planck and Einstein were all concerned with metaphysics but as a way of speaking about physics itself. Physics told us how things moved, ways to describe things (mass, trajectory, speed, velocity, etc.) that we could transcribe mathematically in a one-to-one fashion, and metaphysics was just that- the discussion of the meaning of what it was to speak of the motion of bodies and being, not the description of them. Quantum physics describes mathematical systems the way that classical physics described "physical systems", and thus no "metaphysics" of the type Leibniz wrote is possible to write regarding quantum mechanics because the "physics" is DEFINED, not DESCRIBED, through another language (that of mathematics) already.

We do certainly agree, though, that neither dendritic dynamics nor any current work in neuroscience can describe experience. There is in general a gap between computation models of neuronal dynamics and the higher level cognitive neuroscience relating to experiences. And while many speculate, we simply do not (and at the moment, given the limits of formal languages and formal models, cannot) use any mathematical model to render experiences into some complex nonlinear dynamics of neural spike train synchronization or what have you. We are limited to syntactical methods of explaining categories, which is clearly inadequate as these are conceptual. Most neuroscientists believe that the conceptual will somehow be derive from such syntactical manipulations, while the more philosophically oriented in the cognitive sciences tend to disagree, but regardless we are no closer to modeling the kind of conceptual representation and processing small mammalian brains are capable of than we were when early work on "latent learning' was done on rates in the 40s. This does not mean, however, that we can simply ignore the ways in which decoherence limits what we can say about the relevancy of quantum mechanics in neural dynamics or that we can casually disregard the need to explain how quantum physics is supposed to be responsible for explaining what classical physics cannot in ways consistent both with neuroscience and quantum physics.

Dear Andrew,

I am not convinced that Leibniz’s metaphysics is so different from ‘interpretation’ in the QP context. In Reflections on True Metaphysics he indicates that metaphysics is about being sure that we have a grasp of what we mean by substance (i.e. thing) or cause or action. New System and Monadology are in a sense a ‘hidden variables’ theory of collision mechanics that makes use of people like Hooke to argue that the dependency on elasticity shows that the ‘true atoms of nature’ are units of force, or better, entelechy, not smaller bodies within larger bodies. Interpretations of QP discuss whether the theory is complete and whether it describes particles or particles with pilot waves, or multiple worlds (I take the point that Bohmian mechanics and Everett’s thesis are not the same as the interpretations they spawned). I see Monadology as very similar – it indicates that the mechanics of the day was not complete and that what the maths was about was NOT 'things moving' but the way units of entelechy give rise, indirectly or directly, to perceptions of appearances of 'things moving'. My understanding is that QFT is not about ‘things moving’ either.

QP certainly introduces an overt statistical component to the ontology but Leibniz has indeterminacy built in to his ontology for reasons relating to the problem of what happens if you have discrete perceiving units progressing according to laws that are formulated as if everything was continuous and all dynamics infinitely divisible. I am not sure he gets it quite right, but he talks of the impossibility of pure determinacy. So I am sceptical about there being anything in QP Leibniz had not already cottoned on to.

To my mind the discussion about whether we are dealing with observables or observations only arises if we are still stuck in a degree of the naïve realism that Leibniz gets clear of. Bohr talked of the quantum system including the observation. But I don’t think Bohr’s metaphysics was very good - I think Pauli did a better job. The complexity and indirectness in the relation of dynamics to experience often gets glossed over, leading to confusion, but that can be teased out.

On a more practical and perhaps productive note, I wonder why you assume that experiences relate to ‘higher-level cognitive neuroscience’ whatever that might be! We certainly do not want to try to relate experience to spike train synchronization I would say. Von der Malsburg raised the hare of synchrony as a way of achieving ‘distributed binding’ but failed to mention that the mechanics of his theory was entirely local and so any binding associated with synchrony drawing on his arguments would have to be local to a single dendritic tree. That to my mind is fine. The relation of experience to the immediate dynamics that gives rise to it is one of incommensurability, so I agree that we have a new sort of problem. However, the number of degrees of freedom should correspond and relations of incompatibility (i.e. red and green at the same time) should be based on ‘sufficient dynamic reason’. The problem is just tough enough to be an interesting challenge once one has got bored with more tractable things like immunology!

I wouldn’t bother too much with what most neuroscientists believe in this area since in general they do not seem to understand the basic things like locality constraints – particularly temporal. Determinate events that occur in sequence cannot be bound into a single experience as far as I can see without raising an infinite regress in time that collapses the whole of physics. They may be no nearer to modeling representations than the 1940s but one does not have to follow the flock of sheep.

And as I said before, I do not think that decoherence is a problem. Goldstone modes are stable at room temperature. I don’t think decoherence is the limit of what we can say about the relevance of QP to experience – it only is if you stick to the sorts of theories that have been around for a while which to my mind make little sense. If we take the relevance of QP to be that it finally provides us with monadic dynamic units of the sort that could have experiences (while they are superposed, stably at room temperature, which for phononic modes is all a bit abstract but that is not the point) then all that matters is the nature of the mode to field of potentials relation has sufficient complexity, which for electromechanical photon-phonon coupling in a dendritic tree, it would seem to. My own model may be wrong but I think the route ahead is much more obvious than you suggest.

Dear Dr. Edwards

First I would like to thank you for the interesting discussion and your intriguing responses. Among other benefits, it helps me to clarify my answers (and all good teachers no that the more ways in which one can better answer a question is a mark of understanding).

Speaking of teaching, a lot of my income has been from tutoring and teaching (a minority, but that's just because one can teach/tutor many times and not make what one does in a single simple contract job). I am sorry to say that a great many students at a certain level in certain topics rightfully do (or should) regard me as inept or at least a poor teacher. This is I think mainly because I am overly concerned with simplifications that, as useful as they may be, are I feel too distant from actual theory/methods/concepts/etc. I have tried to supplement my failures by looking to popular texts, video courses, youtube clips, or iTunesU material that I can use because whatever simplifications are present in them are not of my own design.

I recall one I used to use (from iTunesU or YouTube probably) regarding quantum physics. I'm paraphrasing, but the lecturer (a specialist in this area) stated that there is nothing akin to quantum mechanics in 2 ways:

1) First, it diverges from all physics in that it incorporates the methods of statistical mechanics (which explicitly does not describe the deterministic evolution of any system) but uses the terminology of classical physics and thereby describes a deterministic system as BEING probabilistic (a contradiction in terms).

2) The most convincing argument for those who have not become accustomed, through years of experience using quantum mechanics in ion traps, NRM technologies, etc. around: we may be describing physical systems that are neither systems nor physical, but it works.

Leibniz would never have remarked that a we should interpret the state of some particle's trajectory by assuming it can exist in multiple or even infinitely many different ways and then that we define largely retroactively and through a measurement that measures nothing whatsoever. This is akin to asking Descartes, Newton, Leibniz, Laplace, etc., to accept that we can describe e.g,. the motion of a moon around the earth that we never see, that exists in more than one place at the same time and/or in infinitely many states at one time, but that it is a moon because when we use classical wavefunctions we are better able to predict tides if we assume this teleporting moon existing in some nebulous mathematical realm that we never detect in any way other than through a probabilistic effect on tides can be said to have an ontological instantiation we can determine as really existing in universes that vary depending upon how we look at waves.

That's what quantum physics does. Statistical mechanics exists for a reason. Most non-textbook problems are unsolvable but (hopefully) have some approximate solution. N-body problems can be easily mathematically intractable but just because there are a lot of e.g., celestial bodies or molecules in copper does not mean that our use of statistical mechanics implies or entails that copper molecules or planetary bodies have no defined trajectory, can teleport, can exist in potentially infinite states, etc. It just means that we have imperfect instruments to measure systems that are affected in ways we can't determine precisely.

Put simply, it means that we can't determine the precisely because we lack the ability to, while quantum physics asserts (on paper) that there is no determined precisions. Yet EVEN THIS would be fine were it not for the fact that QM is deterministic. It is a deterministic mechanics describing a statistical/probabilistic reality.

If you could show me that Leibniz so much as suggested that his own formal system for calculating things like motion assumed that the objects he described didn't exist or existed in multiple statistically predictable states, I would be grateful for the reference.

The very fact that Leibniz' model is indeterministic is why his work fails so utterly here. QM is deterministic, and accurately describes probabilistic/statistical systems. Hence the violations of the law of non-contradiction and the excluded middle in quantum logics. Physics is about the way things will happen (whether bodies in motion or some statistical mechanics applied to some network). Metaphysics is necessarily about the ways in which the whatever physics predicts or describes should be understood. More simply, if you said to Leibniz that, upon throwing a pebble in the air at x velocity with a-N other relevant variables that your function could demonstrate where the pebble would likely land, he would have agreed with most today that it LIKELY could. If you said that you mixed a bunch of sand together into an ensemble you dumped in a box, then called the sandpile a pebble, then launched the box into the air an hit it with a missile such that you could the find the grains of sand strewn across some region, and having found them said that their dispersion tells you about the state of the "pebble" that never existed as it was in the box before you blew it up he would have dismissed this as lunacy. That is QM.

There is not a single reference in Leibniz to the ways in which the values his own formal language can be used to derive describe the ontological reality of something that is never observed and logically contradictory. This the guy who, had he published his works, would have founded mathematical/symbolic logic.

As for synchrony and neuroscience, that's my field. Your locality constraints were given by Tegmark but you wrote him off. Neuroscientists are unfortunately too fixed upon an outmoded science for such a biologically oriented field (or set of fields). Nonlocality is ubiquitous within the physics, from QM to astrophysics.Neuronal models, complex systems, and the brain are my main research areas. "High-level cognitive processes" are things we can quite clearly identify through numerous neuroimaging methods. Explaining them is something else altogether. Likewise, population or single neural models can be very accurate, but we are as yet unable to relate them to the vastly more distributed, complex, and quite simply large regions of neural activity we refer to in neuroscience studies of cognitive processes. This does not mean we can simply assert that intracellular dynamics of neurons somehow results in the easily detected (and even nearly-zero lag time) synchrony of neural networks. When a neurons in certain cortical regions can connect to 100,000 others, to approach cognition (let alone consciousness) from the perspective that single neurons are somehow the brain's summation of parts is entirely bereft of empirical evidence, at least as meaningless in terms of "what we experience" as is the entirety of the brain, mathematically implausible, physically nearly impossible, and without any merit to subsequent these deficiencies such that we should entertain it. Synchronization is the norm nature. See Synchonization- A universal concept in nonlinear sciences.

Finally, decoherence is BY DEFINITTION the limit of what we can say about quantum processes. The entire point, from the various types of "Schrödinger cats" to entanglement, is to discover how the world we experience exists in any form whatsoever when quantum physics says it does not. It tells us that we can detect molecules of hundreds of atoms in 2 places at once and why we never see instantaneous effects between systems separated by 11 kilometers. The entire point is to figure out where the realm of quantum processes ceases to exist and under what circumstances. Were this trivial, we'd all be worried that at any moment an appendage would relocate to some region miles away or that we would feel the burn of a stove in a restaurant in another country than where we were. Decoherence is also the only way we can really investigate quantum systems as in order for them to be "quantum" they must cohere. As they decohere so rapidly at so short distances, much of quantum physics is concerned with how we can sustain quantum systems.

I have to be honest : never in the past I was able to find a so broken theory as quantum mechanics has been delineated in this question. Please , let me explain quantum mechanics has basic conceptual foundations that are very distant from it is here said. I intend that it is a difficult theory and we have in fact a course based on quantum cognition just devoted to students or scholars that have not great competence in physics or mathematics ( visit www.saistmp.com) but it is actually not to be accepted to delete a theory in such way. I have a number of papers posted on RG on applications of quantum mechanics in neuroscience and in psychology and I have also a published book with the same title. Before concluding without knowing why someone does not attempt almost to enter in some basic foundations?

Dear Elio,

If you want to contribute usefully to the discussion I think you need to make some specific points about what you think has been misdescribed. It is reasonable to point out that you have material on your site but people need to know why they should want to look at it!

Dear Andrew,

I am not sure we are going to converge. I am a bit disappointed this may be because you do not actually address the specific points I am making. For instance Tegmark does not seem to consider Goldstone modes. (Moreover, the most recent paper I have seen from him seems to indicate an embarrassing lack of understanding of neurodynamics, as someone else agreed on another thread.) Why not Goldstone modes? And your responses about ‘high level cognitive function’ appear to completely misunderstand what I was proposing: those on locality too.

You say that your field is synchrony and neuroscience yet you do not seem to recognize the points I have made about the originator of the synchrony fashion – Von der Malsburg. I cannot see any publications on this on your site so I am not sure what ‘your field’ amounts to. I do not doubt that you are committed to seeking the truth but some of the arguments you raise are non sequiturs that I have heard often before. I am not either a physicist or a neuroscientist but I have discussed my own approach with people who are – in physics including Basil Hiley and Michael Fisher, in neuroscience including Andrew Huxley and Horace Barlow (I assume those names are familiar). I do not claim any approval of my thoughts but at least I survived presenting my ideas without being told I was making technical errors. Can you say the same?

A maxim I have found useful over the years is that it is worthwhile to spend a lifetime on one question, but to spend a lifetime on one answer is to waste it. I worry you want to stick to one answer.

I agree that QP introduces a new take on the math but I am wondering just how much Leibniz you have read? He is happy that the math is deterministic but the ontology has to be statistical. As I said, I think his argument may be wrong. The maths of his mechanics of ‘bodies’ is as far as I know more or less the same as Newton but in New System and Monadology he makes it clear that ‘bodies’ are mere appearances due to our ‘confused perceptions’ (pretty much in line with modern neuropsychology). There are no moving things, just dynamic units that are better considered as ‘ideas’ rather than ‘things’. Many people have thought this was nuts but once one accepts just how contrived the view of reality our brains present us with is and goes back to first principles I think that he, like Descartes, is much further forward than most contemporary thinkers.

So it is not that Leibniz would never have allowed trajectories to be split into infinite ways – he just thinks the idea of a trajectory is naïve. It works at the appearance-physics level but is not reality. I would strongly recommend Dan Garber’s commentary of the development of Leibniz’s thought (Body, Substance, Monad). I do not deny that QP provides an explicit mathematical framework for dynamics at a level that Leibniz could only speculate about. But to me the continuing value of Leibniz is that he goes further and says how the conscious subject fits into the picture.

I have been careful to agree that locality is a complex and subtle business but there are still basic rules about what cannot happen – transmission of information without passage of time for instance. In these terms the idea that non-locality comes with complex systems sounds to me to be nonsense. And you cannot indentify high level cognitive processes with fMRI – as someone who trained in both basic and clinical neurology at least I am not having that wool pulled over my eyes. I look at fMRI images on a more or less weekly basis. (Your bits about single neurons and synchrony make no sense I am afraid – nothing to do with what I was referring to.) Synchrony may be common in nature, but so what? We actually need a causal story, not a haze of buzzwords I think.

I agree that superposition is crucial to QP, but what if it is ‘you’ that is superposed? The whole framework of QP has to be turned inside out. I am not clear that anyone in modern times has really explored how one could formulate that. My sense is that Leibniz tells us how it should be done. There are no Democritan ‘atom things’ in two places at once, but there may be a viewpoint that is distributed across, and perceives, a complex domain of potentials formed by an aggregate of other viewpoints. There are no quantum and classical realms. I suspect they are just the past and the present if they are anything.

Anyway, an interesting discussion.

Dear Dr. Edwards-

A central reason my list of publications is less than what I would like is that, in a stupendously idiotic move, I chose to bypass most of the projects that came along (other than to help in small ways, consult, or in a professional not academic capacity) to produce a response to quantum theories of mind/consciousness from a neurosciences & dynamical systems approach. As I mentioned early on here, this proved to be a fruitless mixture of dealing with the ways in which quantum physics couldn't answer basic questions required of a too theoretical approach within computational neuroscience (the only neuroscience approach in which quantum mechanics comes into play) regarding the role of neuronal dynamics in consciousness. This would be bad enough were it not for the fact that every time I tell myself to give up on the issue for now and produce something useful I ignore myself. However, that is my own stupidity and not exactly of note or relevance here.

I've read a great deal of Leibniz, although mostly some time ago. A project I did on the history of philosophy and its influence on modern cognitive science concerned in no small part his work in symbolic logic that Russell lamented remained unpublished and thus we had to wait for Frege when we need not have. Also, as the founding of science by those like he, Newton, Descartes, and other was intricately woven with philosophy and as I happen to read the languages they all wrote in this is not the first time I have addressed such issues, although never quite as they have been raised here. But I don't pretend to be an expert on Leibniz. However, your own description that his mechanics is like Newton's but his thoughts on what this means indicate something else just illustrate what I tried to: that is metaphysics, not physics. Probability, indeed, was a very thoroughly philosophical issue and in many ways remains so. I am not denying that Leibniz had much to say that is beyond the mathematics; quite the contrary. He did, as did Newton and Descartes before them both and Galileo before all three. Nor did this stop with Leibniz, but continued through Einstein whose objections to quantum physics were philosophical ("God does not play dice" and so forth). The problem I have with using such works to understand how quantum physics explains any mental or neural processes is that these are not issues of physics but metaphysics and philosophy. In order to have a model of consciousness or indeed a model of how quantum physics might play a role in consciousness requires the use of the actual physics and the actual brain, else we have left science behind.

I do, however, find it curious that you state "Von der Malsburg" is "the originator of the synchrony fashion" when the work on synchrony and biological systems in general and neurophysiology specifically came into its own in the late 60s. In his online chapter to Dynamical Systems in Neuroscience (http://www.izhikevich.org/publications/dsn.pdf#page=194) which is specific to synchronization EM Izhikevich gives a brief review of work dating back to 1914 and referring the reader to one book I believe I mentioned already as well as another of his own, yet in neither the most historically oriented of the three (Synchronization: A universal concept in nonlinear sciences) nor in the link provided is Malsburg so much as mentioned. His 1981 paper notwithstanding, synchronization in the neurosciences was a big deal some 20 years prior and is a consequence of neuronal models from the 40s.

With respect to Goldstone modes, I confess I am bemused by your reference to them, and in particular with your statement that non-locality cannot involve the transmission of information, as the only proposals I can recall offhand which involve these modes in neuronal dynamics are explicit in asserting that such constraints do not exist (see in particular Alfinito, E., & Vitiello, G. (2000). The dissipative quantum model of brain: how does memory localize in correlated neuronal domains. Information Sciences, 128(3), 217-229.) and we find "the non-locality of memory" suggested to be possible via NG boson modes.

This is not to say I disagree with you. Non-locality is indeed incredibly subtle and I think the vast majority of physicists would agree that superluminal information transfer is not possible. However, one of the reasons for this is purely theoretical- such transfers are thought to be violations of relativistic physics. Indeed, there are solutions to Einstein's GTR equations that allow closed timelike curves (CTCs) and therefore paradoxes, and relativistic quantum physics does naught but complicate such issues. This is, in fact, both related to your earlier remark about the oft ill-defined notion of "collapse" and the problem with any proposals of quantum theories of consciousness. It is true that in discussions of quantum mechanics, or at least with respect to any that involve interpretations, "collapse" is indeed ill-defined although the ensemble interpretation is an extension of Einstein's thoughts and is not generally accepted. However, it is a term we give to explain how an entirely deterministic, non-statistical mechanics end up being probabilistic. The inclusion of anything from QFT, M-theory, or any other component of quantum or theoretical physics simply removes us farther from an ability to determine what it is our mathematical descriptions relate to. A statistical mechanics does not purport to describe that which is as being statistical but is an admission that complex systems and our ability to control, measure, and model them is limited. Classical physics involves, in some ways, a more sophisticated and mathematically complex statistical physics than does quantum physics, as with the former we are dealing with the ways in which the one-to-one properties of a system's deterministic evolution are best approximated using statistical physics, while the latter is deterministic description of probabilistic dynamics. The statistical aspect may be contradictory, but it is at least built in.

As I said before, this is why quantum mechanics has metaphysics almost "built in". Newton, Leibniz, Euler, Hamilton, Maxwell, etc. did not describe bodies or even waves as something that has some nebulous mathematical representation we should use to determine the mathematical state of a mathematical system measured physically and mathematically. The descriptions of their systems, from those as simple as position and velocity to increasingly nuanced and complicated treatments of energy remained one-to-one. To do, as Leibniz and other both before and after did regularly, and discuss what implications something like a wave's propagation through a medium mean as to its ontological status were motivated by things like whether the physics (the maths) should be understood as describing an entity (a mechanical wave) or as a description of processes acting on entities and their answers were greatly simplified by the knowledge that such waves did not have any independent existence and were entirely encapsulated in the dynamics of physical systems in a one-to-one manner. There is nothing about classical wavefunctions that is, from a physics perspective, problematic. They are functions modelling forces acting on bodies or through media in a clear, unambiguous manner. They are no more ill-defined than velocity. Quantum wavefunctions offer no such clarity. What they describe is a system that has deterministic properties but only after we "collapse" this wavefunction to "recover" that deterministic state. This remains true, and if anything more so, in QFT. It's not that we have a statistical mechanics, but that we have a deterministic one we use to describe probabilistic systems and cannot explain this other than by references to notions such as collapse.

How, then, when we cannot so much as explain what a wavefunction is, can we expect to understand how so complex a system as the brain relies on such quantum dynamics for a functionally emergent property such as consciousness?

Dear Andrew,

I realize the situation is not directly analogous but compare the monad to the Higgs boson.

Leibniz proposes that mass is not the stuff of ‘mini-bodies’ but is the passive force component associated with indivisible dynamic relational units that have no size or shape and do not bump into each other. In fact this passive force is involved in a complex relation with other dynamic units such that it may seem to be ‘borrowed’ as ‘secondary matter’. In the end his model for mass does not work too well but it has some good features. In more general terms Leibniz gives no quantitative analysis of monads but gives a clear analysis of what he thinks their qualitative parameters must be. They are pretty much in line with the modes of excitation of QFT.

In comparison, Higgs proposes that mass is not a property intrinsic to familiar particles, but is a passive force component ‘borrowed’ through relation to another field, or arising from a relation to other particles (i.e. dynamic units). My understanding is that Higgs was not able to give a precise quantitative prediction for the units of this new field but gave sufficiently clear qualitative parameters for a semi-quantitative prediction to be made.

So was the Higgs theory just metaphysics? I think this an uninteresting distinction.

The key reason why I think Monadology helps as understand mental processes is that it links these issues of dynamic relation to the central problem for the study of mind – what is a ‘point of view’? How do we fit into a physical science framework something that can host a here and a now and have an idea of the universe. This is central to ‘actual physics’ and my model for Goldstone modes is actual physics with predictions about frequencies and domains and lots of grubby detail.

Sure, interest in synchrony goes back to Sherrington at least. But that was in terms of what processing dynamics would explain input-output rules for brains. This is an interesting area but I see it is separate from explanation of phenomenal experience. The hare that Von der Malburg raised was the idea that ‘the binding problem’ could be solved by invoking the role of synchrony in a distributed network. Unfortunately there are two binding problems and you cannot solve both with one mechanism (the Wikipedia entry on binding problem was at one stage written by me and covered this – not sure if it still does). Moreover, his model did NOT give a binding role for synchrony in networks, only in individual cells (in either sense). A host of others, including Francis Crick, picked up on this conflated theory and it is only just now with work from people like Tiesinga that sense is beginning to prevail.

Giuseppe Vitiello does not have a monopoly on Goldstone modes. Lieberman was talking of phonons about thirty years ago. Tuszynski has flirted with them. Giuseppe to my mind did great service by pointing out that these modes might be relevant but I find the models he has developed with Walter Freeman and others to be very hard to marry with neurology. Moreover, if he thinks there is supraluminal communication I think he must be wrong – apart from anything it would make nonsense of brain architecture – what are all those slow connectors for? So the objection here need not be purely theoretical – it wouldn’t make any sense.

You ask: “How, then, when we cannot so much as explain what a wavefunction is, can we expect to understand how so complex a system as the brain relies on such quantum dynamics for a functionally emergent property such as consciousness?” But who said consciousness was a functionally emergent property? Physics does not have such things, it has causal interactions and at a determinate level these obey locality fairly simply. Within a domain of superposition causality is distributed in such a way that it seems we cannot separate out component ‘events’ so locality has a more limited meaning relating to initial and final observable conditions. I am intrigued that you seem to have a concept of complex systems having ‘more than sum of parts’ behaviour that needs statistical treatment because the rules of parts are not enough. That actually sounds like Leibniz’s claim and I do not see it as in any way similar to the statistical nature of individual quantized modes, which I see as a necessary consequence of **simplicity**. Interesting!

I will try and explain in a nutshell why I think Leibniz and QFT are of interest to neurology. We need a physical event that can be an experience. It needs to be an event that involves a protagonist that is a ‘point of view’ or observing subject if all experiences are not to merge. Simultaneous determinate events in lots of different cells cannot host an experience because they have no immediate causal relation to each other (more than in other brains). They are separate events involving separate protagonists. And the fact that these cells are connected cannot be used as a way of making all the same protagonist because that makes their relation one of determinate events separated in time. The relations between cells are the only relevant relations the cells have so they cannot all be one protagonist relating to an environment – there is a contradiction. All the relations between cells are adequately covered by classical neuroscience and must be routes to experiences, not experiences. Complex systems with dynamic interacting parts cannot be venues for experiences. Outside the body everyone accepts that an experience cannot be in two places at once. Physics always predicts the observation at one particular place and time. A different place and a different time get different observations. We have no reason to think that this changes inside the skull. Unfortunately Gilbert Ryle persuaded everyone that experiences can only belong to whole people, not homunculi, but physics requires homunculi (in that sense). William James makes the same point in a different way.

James then points out that within a cell we have the same problem – the only protagonists in causal relations are atoms (in 1890 physics) and they are too small to get complex neural message patterns. But with Goldstone modes we have indivisible dynamic units that get involved in relations as protagonists that can be large, as long as they are associated with specific order asymmetries in the local distribution of other modes. These are quantised modes but all their relevant dynamics can be described classically, which gets rid of all the red herrings about free will. So there is no reason why modes associated with cell membranes should not host experiences. We would not want to include more than one cell because each cell is doing a different computational job generating an independent output from its own input, not that of another cell. Everyone assumes that experiences have to be spread across lots of cells but there is no reason. Experiencing seems to be widely distributed over the cortex but this need not mean that there is one big experience – that would be computationally very inefficient anyway. It is much more likely that there are millions of congruent experiences, all based on signals of the same significance radiating out to lots of cells in some sort of ‘global workspace’.

The arguments are much more complex but the gist is that we need an indivisible dynamic mode to host an experience and this cannot be either below or above cell level for reasons of basic neurology. All we need to do is find modes that correlate with influences of anaesthetics and which would fit into the standard neurobiological causal chain (with no supraluminal communication or strange QM collapse interpretations needed). As far as I can see electromechanically coupled acoustic modes are the most plausible, but I am keen to think of others.

Its all on my website, but there’s several hundred pages!

I retain that , before starting discussing about quantum mechanics , its advances and its application in nueroscience and psychology , one should at least know about a general theoretical framework what quantum mchenaical foundations are. I do not see here such necessary deeping!!!!!

Dear Dr. Edwards-

Thanks for the response and once more for continuing an interesting and enlightening conversation. After my last reply, I find myself somewhat distressed because I am not sure how much we actually diverge compared to how much it appears we do. Any social networking site, even one for researchers and academics, inevitably constrains and otherwise renders problematic communication to some degree. We are discussing simultaneously several complex, nuanced topics (quantum physics, neurophysiology, the mind, metaphysics, etc.), any one of which might pose problems even for communication in ideal arenas. We need look no farther than the infamous quips by eminent physicists e.g., Einstein’s “is the moon still there when you don’t look at?” (intended to be a scathingly dismissal of quantum physics’ counterfactual indefiniteness), Gell-Mann’s “Quantum mechanics, that mysterious, confusing discipline, which none of us really understands but which we know how to use”, and of course Feynman’s (a list of such quips/quotes may be found here: http://www.phy.davidson.edu/FacHome/thg/230s10_files/quantum-mechanics.pdf) and in-depth treatments on the problems all discussions of quantum physics faces such as

MacKinnon, E. M. (2012). Interpreting physics: Language and the classical/quantum divide (Vol. 289). Springer.

In light of such difficulties, I hope to make discussion easier by treating more thoroughly and carefully issues that you have emphasized in order to find, if not common ground, at least mutually understood divergent grounds. I proceed as follows:

First, I hope to clarify both what you mean by your reference to Goldstone modes and express more comprehensively than I have why I am having difficulty understanding how you intend these to be useful for understanding the mind. In doing so, I will touch on some relevant fundamentals of QFT and NG bosons in order to ensure we are both on the same page from a quantum physics standpoint.

Second, I will try to explain as concisely, clearly, yet nonetheless comprehensively as possible my understanding of Leibniz’ physics, philosophy, & metaphysics.

Finally, I hope to explain how neuroscientists with widely differing beliefs about the brain and the philosophy of science can nonetheless provide a superior theoretical framework and better basis for discussing brain functions (from movement to mind).

You state “with Goldstone modes we have indivisible dynamic units that get involved in relations as protagonists that can be large, as long as they are associated with specific order asymmetries in the local distribution of other modes. These are quantised modes but all their relevant dynamics can be described classically, which gets rid of all the red herrings about free will”. I hope you can help me by clarifying, but I’ll start with definition of “the Goldstone theorem, which states that, given a field theory which is Lorentz invariant, local, and has a Hilbert space with a positive definite scalar product, if a continuous global symmetry is spontaneously broken, then in the expansion around the symmetry-breaking vacuum there appears a massless particle for each generator that breaks the symmetry. This particle is called a Goldstone (or Nambu–Goldstone) particle.” (Maggiore, M. (2005). A modern introduction to quantum field theory (Vol. 27) OUP; p. 257). Granting that as a serviceable definition, I’m not sure how to understand NGBs as “dynamic units that get involved in relations as protagonists”. For one thing, NGBs live in a group coset space G/H. This is a complex space, and the “real number” version consists of two scalar fields that cannot exist in classical field theory. For another, we know next to nothing about how an actual systems’ dynamics yield NG excitations: “Indeed, the Goldstone boson after the spontaneous symmetry breaking was taken to be almost a mysterious object since there was no experiment which suggests any existence of the Godlstone boson. Instead, a wrong theory prevailed among physicists.” (http://arxiv.org/pdf/0806.2957.pdf). As for any classical description, I am unsure why you think this so simple, given the difficulties that even quasiclassical descriptions pose: “We have demonstrated that the quasiclassical suppression of quantum fluctuations of Nambu-Goldstone bosons is only possible for theories which either possess catastrophically unstable backgrounds or allow for superluminality. This finding supports the analysis performed before in [12,13].” (http://arxiv.org/pdf/1208.3647.pdf?origin=publication_detail ). Finally, there are quantum fields which largely do away with NGBs entirely, are highly critical of them, and/or point to the vast anomalous cases of spontaneous symmetry breaking. See e.g.,

Strocchi, F. (2005). Symmetry breaking (Vol. 643). Springer.

Fujita, T., Hiramoto, M., & Takahashi, H. (2009). Bosons after Symmetry Breaking in Quantum Field Theory. Nova Science.

http://arxiv.org/pdf/hep-th/0510151.pdf

http://arxiv.org/pdf/1302.4800.pdf

http://arxiv.org/pdf/1312.0916.pdf

If you could demonstrate or explain, in terms of QFT or many-body physics as well as field theory how NG modes/bosons can do what you describe that would help a great deal. I have in mind this statement: “my model for Goldstone modes is actual physics with predictions about frequencies and domains and lots of grubby detail.” I would be grateful for the “grubby detail” as it might clear up a lot of confusion I have.

In the meantime, and before I move onto Leibniz (a central part of this response), I think that it might be useful to clarify what exactly the issues are in terms of the role of quantum physic in the brain. However one approaches the ontology of quantum processes such as entanglement and superposition, that the possibility of such processes becomes vanishingly small as we move from the subatomic to the atomic realm is written into the formalisms of quantum physics. You referred, for example, to Fröhlich condensation. In Penrose & Hameroff’s Orch OR model of consciousness, Fröhlich condensation is proposed as the mechanism behind quantum coherence in the brain, yet “no mechanical source of energy can produce such a condensate, and that although intense radiation could facilitate its formation, the energies required preclude its production in biological media.” (http://www.pnas.org/content/106/11/4219.full).

Nor do we need to rely on cognitive models or synchrony of spike trains to rule out quantum physics as relevant to brain function: “Two key biophysical operations underlie information processing in the brain: chemical transmission across the synaptic cleft, and the generation of action potentials. These both involve thousands of ions and neurotransmitter molecules, coupled by diffusion or by the membrane potential that extends across tens of micrometres. Both processes will destroy any coherent quantum states. Thus, spiking neurons can only receive and send classical, rather than quantum, information.” (Koch, C., & Hepp, K. (2006). Quantum mechanics in the brain. Nature).

To bypass the issue of decoherence by ignoring most of what we know about the brain (e.g., action potentials) while relying on the mathematical production massless bosons from symmetry breaking when we know next to nothing about how this can happen (or what it means when or if it does), is, I feel, unjustified.

Before looking at neuroscience approaches, I’d like to touch upon Leibniz: “Tempus erat quo credebam, omnia Motuum Phaenomena principiis pure Geometricis explicari posse, nullis Metaphysicis propositionibus assumtis, et concursuum Leges ex solis motuum compositionibus pendere; sed hoc impossibile esse profundiori meditatione deprehendi; didicique veritatem tota mechanica potiorem, scilicet omnia quidem in natura explicari posse Mechanice, sed ipsa principia mechanica ex metaphysicis et quodammodo moralibus, id est contemplatione causae efficientis et finalis, Dei scilicet perfectissime operantis, dependere” [“I used to believe that all phenomena of motion could be explained on geometrical principals alone, assuming no metaphysical propositions, and that laws of the striking together of rest on the composition of motion alone. But I perceived this to be impossible through a more profound meditation, and I learned that a truth superior to all mechanics- I learned all things in nature can be explained by mechanics, but mechanics itself depends upon metaphysics and to a certain extent moral principles, it rests upon the contemplation of that efficient and final cause (God, obviously, the most perfect agent)”.] “Principia mechanica ex metaphysicis dependere”. Gottfried Wilhelm Leibniz. Sämtliche Schriften und Briefe. Sechste Reihe: Philosophische Schriften (4. Band, Teil C)

There are a few points I think important. First, notice that Leibniz is explicit in how he treats mechanics (physics) vs. metaphysics. Even when stating that the latter is necessary to really understand the former, it is not because natural laws require something more than mechanics but that mechanics itself requires higher knowledge- metaphysics. What purpose, then, in Leibniz’ thought do monads serve or what is their nature both alone and in contrast with whatever else there is? “[Monada] entelechiam primitivam seu Animam [et] materiam…completam” [“monads are completed by the primitive entelechy or soul and matter”]. Entelechy and matter are the first of Leibniz’s list of five components he regards (“Distinguo ergo….”) all nature to be made up of. The next is “secondary matter” (materiam secundam) or the “organic machine” (machinam organicam), followed lastly by the “animal seu substantiam corpoream” (the animal or corporeal substance) which THE monad of the innumerable subordinate monads (“innumerae…monades subordinatae”) all brought together for secondary matter makes into one. For most systems there is no élan vital, merely a conglomerate of lesser “forces”, but living systems (while made up of the same stuff as everything else) are distinct.

You do not mention this, but state “Leibniz proposes that mass is not the stuff of ‘mini-bodies’ but is the passive force component associated with indivisible dynamic relational units that have no size or shape and do not bump into each other”. Only Leibniz proposes no such thing. First, he is quite clear that an essential difference between living and non-living systems is the complexity of parts: "je definis l'Organisme, ou la Machine naturelle, que c'est une machine dont chaque partie machine et par consequent que la subtilité de son artifice va à l'infini…au lieu que les parties de nos machines artificielles ne sont point des machines." [“I define an organism, or natural machine, as that one machine wherein each part is a machine and consequently as one with a subtlety to its construction that extends infinitely...whereas the parts of artificial machines are not machines”]. This is an essential distinction (“C'est là difference essentielle”), but it is not his only one. Only living systems have a dominant monad that unifies and organizes it allowing it agency. Second, even if we are considering only living or only non-living systems the CONGLOMORATION of parts is central to Leibniz’ entire metaphysics (he has five categories to describe a sort of duality instead of two for a reason). Only by the composition of a kind of essential matter and a kind of essential force does Leibniz get to have his cake and eat it too. For with his god as the first cause he explains all of nature in terms of passive forces of non-living systems that have no machine parts nor dominant monad and the active agency of living systems that have both. You do not seem interested these distinctions, but without them you don’t have Leibniz’ physics, philosophy, or metaphysics.

Finally, a word on synchrony, neuroscience, and complex systems. Would it be fair to say that this describes the kind of solution to the binding problem you criticized (see in particular the last line)? “Under special conditions, coherent activity in a local cortical population is an inevitable consequence of shared presynaptic input [20–24]. Nevertheless, the mechanism for the emergence of correlation, synchronization, or even nearly zero-lag synchronization (ZLS) among two or more cortical areas which do not share the same input is one of the main enigmas in neuroscience [22–24]. It has been argued that nonlocal synchronization is a marker of binding activities in different cortical areas into one perceptual entity [23, 25–27].” Those four references in the paper (Kanter et al’s “Nonlocal mechanism for synchronization of time delay networks” (J Stat Phys (2011) 145:713–733) go back to

Eckhorn, R., Bauer, R., Jordan, W., Brosch, M., Kruse, W., Munk, M., & Reitboeck, H. J. (1988). Coherent oscillations: A mechanism of feature linking in the visual cortex?. Biological cybernetics

&

Gray, C. M., König, P., Engel, A. K., & Singer, W. (1989). Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Nature.

In other words, they aren’t particularly old from a historical point of view but are pretty far removed from modern approaches as Kanter et al. show. Same for Izhikevich. And if we look at what they cite, we find a diverse group of sources including von der Malsburg but also those that predated his work and on this issue. More importantly, the empirical evidence started mainly with the above two papers. I’m not quite sure why you feel von der Malsburg was THE impetus or main source for proposing synchrony as a solution to the binding problem, nor why it would matter if 1) there is empirical support and 2) it wouldn’t matter if it wasn’t a solution is synchronization were an important part of neuronal dynamics (and it is, as synchronization is ubiquitous in nonlinear systems). Also, even were it a dead end to the binding problem that such a problem exists is based upon assumptions that look for particular kinds of answers I think are better understood by divorcing from neuroscience outdated ideas inherited from classical cognitive science and borrowing from systems biology and complexity sciences. Synchronization hardly encapsulates what we’ve learned since Poincaré, Lorenz, etc.:

Di Ieva, A., et al. (2013). Fractals in the Neurosciences, Part I General Principles and Basic Neurosciences. The Neuroscientist.

Rubinov, M., & Sporns, O. (2010). Complex network measures of brain connectivity: uses and interpretations. Neuroimage

Bressler, S. L., & Menon, V. (2010). Large-scale brain networks in cognition: emerging methods and principles. Trends in cognitive sciences

Kozma et al. (2005). Phase transitions in the neuropercolation model of neural populations with mixed local and non-local interactions. Biological Cybernetics

Burger, J. R. (2013). Brain Theory from a Circuits and Systems Perspective: How Electrical Science Explains Neuro-circuits, Neuro-systems, and Qubits (Vol. 6). Springer.

ad infinitum. Sure, most are wrong, incorporate words like “emergence” or “complexity” or “dynamical” while rehashing work already done, entire journals are dedicated to what borders on pseudoscience, and nobody has a working model of how the brain processes concepts or categorizes information conceptually. However, while complexity sciences can point to the ways in which e.g., a fuzzy threshold gets us from a hundred or so ants walking around in circles until they die to a colony capable or unbelievably coordinated activity while quantum physics gets us a unity obtained mathematically that is neither in line with neuroscience nor physics. Sure, the formalisms of QM/QFT/QCD/etc. give us such unity, but before we relegate the brain to Hilbert space might it be prudent to understand ant colonies seemingly unitary action before deciding the brain is to reducible to explain unified experience? "For example, if 100 army ants are placed on a flat surface, they will walk around and around in never decreasing circles until they die of exhaustion. In extremely high numbers, however, it is a different story. A colony of 500,000 Eciton army ants can form a nest of their own bodies that will regulate temperature accurately within limits of plus or minus 1C" (Franks, N. R. (1989). Army ants: a collective intelligence. American Scientist). We still do not understand how swarm intelligence creates a seemingly singular organism out of the dynamics of "parts" we can observe and model. Nothing in quantum physics is particularly suited to observation in general and far less as a means of explaining biological phenomena. Apart from the quantum/classical divide, there is the issue of meaninglessness. You seem to dismiss notions like synchrony as viable options (at least to the binding problem), but how is adopting a mostly theoretical class of entities/modes that may or may not exist in this or that way, all to explain how they are involved in brain mechanisms in ways that violate the theoretical methods through which they result and to serve functionally in ways they cannot (so far as we know or predict)? There are a number of papers on quantum-like theories of consciousness/mind that use quantum formalisms to do more or less what you state: give us a unified, global “workspace”. However, they differ in that they make no reference to the need for actual quantum physics and thus are at worse as implausible as any quantum theory of mind from a biological perspective and don’t possibly violate known physics or postulate biophysical mechanisms based upon a conceptual approach to the formalisms if quantum physics. You might be interested in that literature.

Thanks again for the continued and comprehensive responses and I apologize for such a long reply so haphazardly thrown together.

Thank you, Andrew, these are indeed the key issues. Now we have the limits of each of our approaches in full view. You may be able to help me significantly on the NG modes. I need to put my case in your terms, which I think is now easier to judge. I don't buy systems biology. In immunology it goes nowhere and is mostly intellectual laziness. The success of my career rested on showing that a model with 55 steps and a dozen feedback loops, positive as well as negative, predicted a highly effective therapy that the systems people missed entirely. And meetings on systems biology are almost entirely people spouting strings of buzzwords designed to get funding from equally inane reviewers. You need the reductive turtles all the way down in practical biology and you can find them if you are prepared to put in the hard work. I've been there. Walter Freeman sort of tried to sit in both camps but I don't think it can work.

But if NG modes are no good then I might have to concede that we need to allow a new form of non-locality. That is why I asked Basil H and he could not be sure, so I agree that this is not set in stone. But I would add the caveat that the relation to neuron doctrine has to make sense and I haven't seen any sort of global systems model that will do that yet. So I need to answer you in terms of what a dynamic protagonist might be, in grubby detail. At least your interested! It may take a bit of time and more than I have tonight so I will send another post in due course.

Dear Andrew,

My understanding of Goldstone modes is that they are dynamic modes that exist where there is a limit to structural symmetry – at least in simple terms. I do not understand the detailed math because I find the formalism impenetrable. (In general where I have been led through the formalism I find quantum maths fairly easy to follow.) I use the general term because I do not want to miss options but my thought is that acoustic or phononic modes are the most likely to be of interest to consciousness.

In accordance with advice from tutors and textbooks I have assumed that a ‘phonon’ is not a particle in any intuitive sense but rather a potential increment or decrement of an instantiation of a mode, reflected in ‘energy content’. As I understand it phononic modes were proposed because they are needed to account for all the energy in a system in contexts like latent heat. To me that indicates that the modes are ‘real’ (being ‘energy-bearing’) just as much as mass-bearing modes like electron orbitals. The fact that this energy depends on an integer quantum number of ‘how many notional phonons there are’ but that this number is subject to the uncertainty principle suggests to me that it may be misleading to consider individual phonons as ‘real’ – as much as anything it seems unnecessary. This might fit with the comment that an NG boson would be a mysterious object never encountered as such. In contrast the modes are encountered through their contribution to total energy and acoustic modes are readily encountered. (I do not see any great puzzle about how these modes ‘arise from’ or perhaps better are co-entailed by the asymmetries – asymmetries provide for new ‘dynamic ways’ which seems to be all we ask for.)

So it is the mode I see as the dynamic unit involved in relations as a protagonist. By this I simply mean that the mode is an instance of a causal relation (we can only know about causal relations because only they can cause us to know) involving the energy bearing mode itself and the field of potentials within its domain. So on a Kronig-Penney type model a valence electron mode in a metal is a relation to an array of potentials. By protagonist I simply mean something that takes part in a relation.

But, to bring in Leibniz, I think that also requires that the protagonist really is a ‘something in itself’ – a ‘substance’. I don’t think London is a something in itself. There used to be a boundary for London, then Greater London and now they have given up. Similarly for a brain – there are no defined boundaries. These are aggregates defined from outside. A something in itself, to my mind, has to be ‘intrinsically informed of its own extent’ in some sense. If a Bose mode obeys a certain set of rules of progression in relation to a structural asymmetry I think we have to assume that in some way the mode is directly ‘informed’ (at least in the etymological sense of given form by) by the entire domain it occupies. Nothing of the sort is required in a brain where this sort of direct informing can occur piecemeal locally.

As I see it, Leibniz would have shared Descartes sense that our concepts of the material world with ‘things moving’ may be very confused. We know from neuropsychology that our sense of ‘things moving’ is due to some parts of our brain generating signs that other parts use to make survival-related decisions. These signs for the operation of causal relations in the world may be very misleading. Even Newton warns that our sense of space and time is not to be equated with these terms in his physics. So explaining things moving might be a false quest. And at least before we do that we do seem to need to explain our ideas of things moving. We are more sure we have the ideas than whether they are reliable ideas.

Ideas seem to be predictably related in a metric we call space and time and this gives rise to the notion that an idea of the world is from a viewpoint of a here and now. But for that to be the case whatever is having the idea would seem to need to be directly informed (in the etymological sense) of some domain from which it has its viewpoint. Aggregates given names by us, like brains and people, are no use here. That is why I think we need modes and Goldstone modes seem to have the desirable property that their domains of relation to a bounded field of potentials are co-entailed by their very existence.

The implications of the maths of NG modes are beyond me at present but my reading and tutorials have suggested two things. One is that for phonons it is much less clear what the equations provide us with in comparison to equations for electrons that seem to provide for deriving the ‘position or momentum of a particle’. The other is that the spin zero status in some way relates to the fact that such modes can appear to us as real classical (e.g. acoustic) waves in a way that traditional subatomic modes do not. This latter may be a confusion. However, all that would seem to matter from my perspective is that the way such modes interact with fields of potentials looks as if it can be treated in a classical fashion that would marry with neurobiology.

So, as an example of an NG mode ‘doing what I describe’ I have suggested a ‘sliding cuff’ longitudinal acoustic mode in the dendritic membrane (as has been observed in axons already) that is coupled through dipoles to the pattern of post synaptic electrical potentials PSPs. At the quantum level this is notionally a phonon-photon coupling of the sort seen in piezoelectricity but it can be treated in classical Hodgkin-Huxley dynamics too. I discussed this with Andrew Huxley before he died and his main concern was damping because at that time I was thinking of a transverse wave. In order for there to be interesting coupling with PSPs about 1 micron apart and taking into account the expected acoustic wave propagation velocity (known for axons) I made a rough estimate of the frequency of oscillation of 1-10MHz, although I may have made some significant false assumptions.

The significance of this to brain function might be rather similar to what I take to be the role of synchronous firing (there is an essay treatment of this on my site in relation to language ‘response to Poeppel and Embick’). I think synchrony allows triage by making use of finely tuned coupling to emergence from refractory period. I would suggest that the acoustic mode coupling to the pattern of PSPs might similarly guide responses through patterns that allow rapid genesis of resonance, leading to optimal early opening of ion gates at the soma. This also allows for more complex logical function than an integrate and fire AND gate – it can do IF…AND… THEN…

One aspect of this model that I do worry about is the assumption that the acoustic mode can ‘experience’ the entire pattern of PSPs in its dendritic domain. What if it is made of phonons, none of which live for long enough to do more than travel a nanometer? In other words, what are ‘path integrals’ for an acoustic mode? When I have tried to get an answer from physicists they have tended to evade the question. Maybe you can answer it? Every time I think about it I conclude that the mode **must** be informed by the entire pattern of PSPs in its domain because its very existence is contingent with being ‘given form by’ the whole domain. My suspicion is that thinking of individual ‘entangled particles’ is a red herring. I think that others may have assumed that the way to get ‘binding’ is to ‘entangle’ particles. But entanglement means correlation and if a mass of particles are all correlated then you only have one piece of information. The way to explain binding is to have one (protagonist) dynamic unit interacting with a rich field of independently varying potentials. A lot of people seem to hark back to Fröhlich and I think maybe he wanted entanglement. I am aware that his mode wouldn’t dominate is he hoped it would, but dominant acoustic modes are known to exist in neural membranes.

So I think Koch may be wrong in the 2006 quote about ruling out quantized modes as being involved in brain function. He was assuming a Fröhlich-type analysis but acoustic modes are there.

Your quote about ‘enigmatic’ nonlocal synchronization is not really relevant to my concerns about the interpretation of the relation synchrony to phenomenal integration. I think Melanie Boly’s studies indicate that this need not be very enigmatic. The problem is that all these comments tend to conflate binding of object features with phenomenal binding. The former is a segregation problem – how you get feature x to go with object P and feature y with object Q. The second is how you then get a **phenomenal** ‘scenario’ of Px next to Qy. You cannot use the same mechanism to separate x and y and to put them together. Feature binding is not really a big problem but is probably very nicely dealt with by synchrony of signal arrival with emergence from refractory period and triage by precession of refractory periods. Sending ‘P is x’ over to the left and ‘Q is y’ over to the right is easy. But phenomenal binding is a quite different issue of having some ‘real something’ to which a complex scene could be available (to ‘compute over’) or a rich field of potential with which some dynamic unit could have an indivisible direct relation. The only relevance of Von der Malsburg is that he tried to give an explicit justification of ‘distributed binding’ with a phenomenal implication in an early paper that was often used to legitimize others’ claims when in fact, as Shadlan and Movshon point out, his model does nothing of the sort.

I don’t have any great problem about a purely reductionistic explanation for the ants. I don’t see any need for ‘sum more than parts’ elements of the **dynamics** - these patterns are just what very complicated aggregates do. For me the puzzle is how you get a viewpoint that has an intrinsically defined domain. And there is no need for this to be a single global viewpoint in one brain. I foresee millions of them. The global workspace metaphor seems back to front to me. Sure there is probably a site in the brain that broadcasts the same data to millions of places but that does not mean there will be one **point of view** - there will be the millions of points of view on the same data at all the places reached. And that is what we should expect, contrary to our intuitions.

Dear Dr. Edwards:

I apologize for the delayed response, but alas I have of late been more occupied than usual. Also, I did not wish to treat casually so well-laid out and comprehensive a response, so I did not immediately reply even after I had time to read what you wrote. Rather, I forced myself to hold off until I had thought about it, read it again, and only then begin to draft a response. Hopefully, something of this latter aspect of the delayed reply is apparent.

You mentioned, if only in passing, the formalisms of physics in your latest contribution as well as in your first. For many reasons, I think that the issue of how we formally represent the properties, dynamics, states, etc., of physical systems merits a more focal treatment and one superior to any I have hitherto provided. The importance is not limited to obvious matters, but also more nuanced, subtle considerations. The first is how much we much we take for granted simply because we are so accustomed to representing “real” things, from price to protons, using formal (symbolic) languages. Even in a majority of historical accounts of mathematics one is likely to find modern notation that both did not exist during the period in question. Those like Leibniz were in a perfect position to appreciate how much the possession of formal apparati facilitated the development of the sciences, let alone mathematics. As a simple example, one has only to look to Greek mathematicians like Euclid who had to depend upon awkward use of grammatical constructions (e.g., regular verbs used irregularly including common verbs, a technical vocabulary that was technical only in context, the uncommon 3rd person imperative, and the use of the same verb differing only in tense/aspect to distinguish the statement of a proposition/theorem vs. declaration of proof). It required a fair amount of ingenuity for the Greeks (among others) to use normal language for relatively simple mathematics, and without symbolic notation much of modern mathematics could never have developed. Furthermore, long after such notation existed the lacked of uniformity in use and the systematic nature of a rich formal language ensured that even great minds struggled with symbols that they could not relate to sensory-perceptual experience (such as complex numbers, most of algebra, foundational concepts of analysis like limits, etc.). Leibniz and his contemporaries were used to symbolic notation but still lacked, for the most part, formal systems/languages. Today, 12-year-olds around the world are as likely to ask what “3” or “+” REALLY mean as they are to ask what a preposition does, but the lack of widespread formal systems made difficult such ready acceptance of symbols lacking concrete relations to real-world experience from Euclid to Weierstraß.

This has at least two relevant consequences for us. The first is how an early exposure to years of mathematics with little apparent application, not to mention the very the notion of “applied math”, has so thoroughly indoctrinated us that we are inclined to think of mathematical notations as meaningless symbols that acquire some abstract meaning through use. After years of using functions, manipulating algebraic expressions, the use of math to represent the properties, states, etc., of physical systems is just a more relatable use of mathematical representation. The second is how we approach modelling. Whereas for over millennia mathematicians struggled to express abstract operations, we have computers: physical ‘models’ of an abstract algebra. Few mathematical symbols in physics are unique to physics, and for e.g, the Dirac notation the uniqueness is in form only; the richer, more powerful language of linear/matrix algebra could replace it entirely. For Leibniz, how mathematics related to physics (and both of these to metaphysics) was of vital import: “to miscast his mathematics…is to misunderstand Leibniz, for in fact his "philosophical system" is positively awash in the consequences of an interplay between mathematics and metaphysics that occurs at the very center of his thought and produces several of its most defining features" (Levey, S. (1998). "Leibniz on mathematics and the actually infinite division of matter." The Philosophical Review). While this was not exactly unique, only Leibniz went so far as to attempt formalizing language with his “algebra of concepts” (formally equivalent to Boole’s algebraic set theory) and proto-predicate calculus. At the heart of all of this discussion of mathematics, formalism, representation, and so on, is one issue that remains at the heart of the sciences but is nowhere more vital than the application of quantum physics to models of consciousness and theories of the mind.

To illustrate more concretely, let us examine phonons. That they are “real” in some sense is not in doubt. The question for our purposes is whether they are real the way that e.g., speed and velocity are, or the way liquids are (a grossly simplified ontological distinction, I know). Simply put, phonons are siblings of photons. One finds them discussed and used mostly in condensed matter physics represented using the algebraic structure of lattices, as crystalline structures are everywhere in solid state physics and lattices are ideal mathematical representations of these. You quite rightly compare phonons to electrons, but I think you weaken the analogy by referring to “mass-bearing modes like electron orbitals”. First, phonons are quintessentially “mass-bearing” (if I understand your meaning). They are “units” of motion caused by sound waves. They are basically matter waves that propagate through a crystalline structure causing the “wave-like” (non-local) lattice vibration. More importantly, the representation of photons in QFT can be equivalent to the mathematical representation phononic excitation (i.e., a quantum harmonic oscillator), and like photons it is often necessary to treat phonons as “particle-like” by using the superposition principle (for e.g., thermodynamic excitation rather than acoustic). Second, in a field theory phonons are not “like” electron orbitals at all, but like any EM quanta: “We now throw away the mechanical props and embrace the unadorned quantum field theory! We do not ask what is waving, we simply postulate a field—such as φ—and quantize it. Its quanta of excitation are what we call particles—for example, photons in the electromagnetic case.” (Aitchison & Hey (2003). Gauge Theories in Particle Physics (Vol. I). IOP Publishing).

In other words, phonons are “wave packets” that, quantum mechanically, are as “real” as electrons, photons, magnons, plasmons, etc., and not particularly interesting (outside of nanotechnology, solid state or condensed matter physics, and similar more applied physics). It is also important to note that the number of phonons is both different from phonon types and almost unrelated to the uncertainty principle. However, you have mainly focused on Goldstone modes, which are interesting for a few reasons. In condensed matter physics such “massless modes” are called “soft modes”. Here again the issue of mathematical representation arises. Representing crystalline dynamics using lattices is intuitive as the mathematical structure is easily related to the physical. The conceptual leap is barely a step. Not all algebras have so intuitive a structure as those found in graph theory or ready analogues as does a lattice (and those that do are not limited to intuitive or relatable structures). Worse still, the language of modern physics is misleading here. There are exceptions, however, my favorite describing the dynamics of a Goldstone mode as a gauge boson fattened by eating a ghost. The reason for the description is the mathematical solution to the mathematical impetus for such an entity existing in a complex coset space to begin with. But before I get to that I’d like to give an example of what I mean by “misleading” language: “In principle it is indeed possible, though technically not so advantageous, to construct a quantum mechanical description of a spontaneously broken symmetry using a symmetric ground state. SSB [spontaneous symmetry breaking] is then manifested by long range correlations rather than nonzero vacuum expectation values” (Brauner, T. (2010). "Spontaneous symmetry breaking and Nambu–Goldstone bosons in quantum many-body systems." Symmetry.).

The “long range correlations” are characteristic of the kind of collective, unitary Goldstone mode you have referred to, but how do they suddenly “exist” if one is “to construct a quantum mechanical description” of SSB? For that matter, how is it “gauged away” (locally or globally) as the “ghost” the fattened gauge field “swallows”? First, note that even were we using some algebraic structure with clear physical analogues to describe Goldstone modes that are “global” we lose any intuitive pictures simply by virtue of the dimensions necessary. Goldstone modes cannot be produced (mathematically or otherwise) except in higher dimensions. As we live in a 3+1 dimensional world, we cannot possibly “observe” a boson that exists in n-dimensional space where n > 3.

Second, it is important to realize that Goldstone modes of the “unitary, collective”-type you describe are not just produced mathematically but exist as mathematical problems in a field theory: “Anomalies are of two types, anomalous global symmetries and anomalous gauge symmetries. In the case of anomalous global symmetries, the symmetry is not realized in the quantum theory…Quantum theoretically, since there is no symmetry, there is no Goldstone boson. In fact the quantum corrections generate a mass for the potential Goldstone boson.

Anomalies for a gauge symmetry can lead to unphysical results….Thus in a consistent physical theory there should be no anomaly for the gauge symmetries” (Nair, V. P. (2005). Quantum field theory: A modern perspective. Springer’s Graduate Texts in Contemporary Physics).

Third, they are “fixed” mathematically as well: “a question may arise as to why people obtained the massless [Goldstone] boson in the [Nambu and Jona-Lasinio model] model. Not only Nambu and Jona-Lasinio but also quite a few physicists found a massless boson in their boson mass calculation. Surprisingly, the reason why they found a massless boson is simple. They calculated the boson mass by summing up one loop Feynman diagrams, but their calculation is based on the perturbative vacuum state. However, after the spontaneous symmetry breaking, one finds the new vacuum which has the lower energy than the perturbative vacuum state. Therefore, the physical vacuum state is of course the new vacuum that breaks the chiral symmetry, and thus if one wishes to calculate any physical observables in field theory, then one must employ the formulation which is based on the physical vacuum state” (Fujita, Hiramoto, & Takahashi (2009). Bosons after Symmetry Breaking in Quantum Field Theory. Nova Science.)

There are several important points here. One is why a physical theory is made better by the existence of something “unphysical” (note that unphysical does not mean massless). Another is why one should be able to, let alone wish to, “calculate…observables in field theory.” We “observe”, whether through some sophisticated measurements or by sight, the “observables” of systems in classical physics. In quantum physics, we calculate them. For Goldstone modes, including those that act as a unified, collective entity the way you describe, we don’t even do that. We derive them using: Let g be a group element g on a symmetry broken ground state ψ, and let g =exp(SUMs{ φT}) suitably close to group identity where φ & T are understood has having indices a (φsub-a as being some set of expansion coefficients, and Tsub-a being our set of generators living in the Lie group). If φsub-a has a suitable profile (weakly spatially fluctuating), then the functional S gives us S[φ] /= 0 and the expansion of the S in terms of φ yields a soft mode. Fantastic. What does this mean? Well, for one S (or whatever one uses to denote the functionals in a field theory) is a functional in the functional analysis sense. In other words, the space in which a Goldstone boson resides is a “function space”- an abstract space in which functions rather than familiar coordinates are the “points” in that space suitably endowed with some sort of overall scheme or structure and typically infinite dimensional (it is VITAL to realize that infinite dimensional DOES NOT mean that the space is infinite, as the real number line R is an infinite space but is 1-dimensional; infinite dimensional may be regarded as a space that extends infinitely in infinite directions).

I believe at this point Leibniz would have a coronary. It’s one thing to represent a system in some phase space with dimensions greater than 3 because of a dynamical systems degrees of freedom and the ways in which multiple variables of interest can increase the phase space dimensionality. It’s another to have the space be non-Euclidean and the system not “represented” in that space but “living” in that space. How the dynamics you refer to describe anything that happens to a physical system is unknown and probably unknowable to the extent they exist/happen at all. Algebraic QFT was designed to try to rid QFT of infinities that were unacceptable in that the mathematical structures and descriptions could not be considered complete. However, as any quantum field theory in modern physics is an extension of quantum mechanics, and quantum mechanics is “complete” yet describes systems that also dwell in a function space H as well as systems with infinitely many states out of which the application of an observable FUNCTION tells us how our initial transcribed preparation yielded a retroactively applied “state”, completeness is at least as mathematical as it is descriptive of the physical reality that “physics” ostensibly deals with.

Alas, we are not done with roadblocks yet. This is because the Goldstone modes that are unitary, collective modes are acausal. In fact, the entire framework that describes such modes is acausal, and thus even if we weren’t describing entities in function spaces derived mostly via mathematical manipulations, we would not get any classical or quantum mode that acts as a “dynamic unit” causally “involved in relations” in any sense: “in causal theories the vanishing of the surface term is guaranteed as long as the operator Φ is localized to a finite domain of spacetime. (In practice, it is often even strictly local.) In acausal theories such as some nonrelativistic models with instantaneous interaction, the surface integral tends to zero in the infinite volume limit when the interaction is of finite range or decreases exponentially with distance. In case of long-range interactions, however, the disappearance of the surface term must be checked case by case.” (Brauner, T. (2010). "Spontaneous symmetry breaking and Nambu–Goldstone bosons in quantum many-body systems." Symmetry.)

Having gone over the issues of the formalism and its relation to anything real, as well as additional problems, how should we proceed if we wish to apply a quantum field theory involving Goldstone modes of a particular sort to the brain? It’s true that, as you say, there are classical (or at least mainly classical) phonons. The problem is that these are local vibrations of matter and are no more “real” than sound waves (which are mechanical vibrations of matter). Quantum mechanical phonons, on the other hand, are simply one among many quasiparticles and field particles that “act” in a unified, collective manner on or as a system that has no relation to any known physical reality but rather exists in a mathematical space that, at least for Goldstone modes, is necessarily impossible to reconcile with any classical description as it cannot exist in the space the brain does and we all do. So we are left with the concept that localized vibrations of quantized as units of mechanical vibration of particles (parts) of dendrites somehow are relevant for mental/conscious processes. Only that is less unified than weak synchrony and has no relation to the fundamental and universally agreed method of information transfer the brain uses (action potentials). It is also not the kind of mechanism you have described (so far as I can tell). Like path integration, nonlocality, superposition, etc., we have progressed in our understanding such that it seems no longer possible to describe such processes as merely statistical rather than reflecting actual non-classical dynamics, but we remain without any capacity to relate the “representation” of a quantum system with any physical system.

This, then, is perhaps the key point. The descriptions of “modes” (phononic, photonic, bosonic, whatever) in quantum physics, and in particular the way global, unified, collective “modes” are linguistically described along with the formal representation, do not exist in any known sense outside of a mathematical space we cannot relate to the brain. In fact, it is in general a truism of all quantum physics that however apparently simple the mathematical representation of a system it is not representing any physical system in any known way. This makes extremely problematic any application of such a system’s “dynamics” to any neuronal processes because we cannot say how the representation of physical systems without known physical correspondences apply to physical systems without any known quantum dynamics. Meanwhile, the classical counterparts of phononic excitations are localized and cannot produce the kind of dynamics you describe without clear violations of known physics. Just as importantly, the capacity for a dynamical systems approach to unified neuronal activity is not only better grounded in physics but also capable of explaining a more unified, collective brain state than any effects of acoustic waves. This does not mean, as you rightly note, that we can connect such collective behavior with “phenomenal binding”. That said, I do not understand how the fact that nonlocal nearly ZLS is an enigma is related to (or made irrelevant by) Dr. Boly’s work. She is not only the lead author of at least one (fairly) recently published paper on the difficulties in assessing neuronal states but has contributed to the literature on the kind of dynamics I have referred, so I am unsure what you mean or what study/studies you refer to. More importantly, feature binding is an extremely complex problem and the only way we can make it relatively simple is by making ir something it is not (i.e., comparing feature extraction algorithms that presuppose conceptual processing humans are able to “put into” and interpret the results “out of” some computational intelligence model/paradigm). In fact, the entirety of the “computational brain” is riddled with problematic assumptions based on metaphors from computer science even before computers that have consistently and wholly failed to reproduce the basic functions of brains. Also, empirical and formal models of dynamical properties of neural networks already go well beyond any mere integrate and fire model. The Hudkin-Huxley model of the 40s was a resonator not an integrator. I highly recommend (even if it is remedial for you) Dynamical Systems in Neuroscience by Izhikevich. The approach is very similar to Strogatz’ Nonlinear Dynamics And Chaos (an undergraduate level book that assumes a minimal amount of multivariate calculus and little else), but applied solely to neuroscience. Chapters 1, 8, and 10 are available online on his site.

Finally, I think it is a mistake to suppose that classical physics was definitively shown to be a some complete system that is entirely local, deterministic, and reductive (on this there is an interesting and pretty simple book Inconsistency, Asymmetry, and Non-locality: A philosophical investigation of classical electrodynamics by Mathias Frisch). I have no problem with a reductive model of a computational brain other than that after 60 years we have produced more of the same while we have empirically found that most of the nexus of different fields into the framework underlying the classical cognitive (neuro)sciences is without support. In that same period, the tremendous advances in nanotechnology, materials sciences, molecular chemistry, and a host of natural sciences have nothing close to comparable advancements in the life sciences. Schrödinger’s What is Life? is not far removed from Rosen’s work and the issue over the computability of living systems has no parallel in the natural/physical sciences. Yet even the study of non-living systems have revealed a complexity never imagined. “The athermal nature of granular media implies in turn that granular configurations cannot relax spontaneously in the absence of external perturbations. This leads typically to the generation of a large number of metastable configurations; it also results in hysteresis, since the sandpile carries forward a memory of its initial conditions.” (Mehta, A. (2007). Granular physics. Cambridge University Press). How do sandpiles carry “forward a memory” of their initial conditions? They don’t. It’s a way of saying that self-organized criticality and self-organization in general of properties of complex systems that we are, in non-living systems, able to describe in terms of known physical laws but cannot determine other than via some set of possible configuration states. The self-determination of living systems presents challenges that are unmatched by nonlinear systems in general. Let us also not forget that our fundamental approach to nonlinearity is to treat it as lines (which, locally, all curvature approximates; however, the higher the dimensional space the more arbitrarily small distances from an infinitesimal “point” make such approximations poor). You advised me against dogmatic or ideological dismissal of explanations, models, etc. I don’t dismiss quantum models, I simply prefer to not to assume that 19th century deterministic assumptions characterizes physics everywhere other than the quantum level and that we understand enough of complex systems to know we should look elsewhere to explain mental/conscious experiences.

Dear Andrew,

Thanks for the detailed analysis. I am familiar with more or less all of the issues you raise and in particular with Aitchison and Hey. The position you present is, ironically, similar in broad scope to that which I took at the start of all this. However, I still remember my first conversation with Michael Fisher about it, sitting in the shade of a jasmine bush in summer in a friends garden around ten years ago. Knowing that he was a physicist and wanting to pass the time of day, I posed the conundrum of conscious experience and raised the sort of objections you raise to acoustic modes being involved. (I assumed that would not work.) Michael replied gently but firmly, 'I think that may be wrong'. So I was converted from your position to the one I hold now by a man who has seen the whole of quantum theory unfold and who has no mean reputation in condensed matter physics. Michael may not buy my model but it was he who raised it in my mind as plausible. You say Leibniz would have a coronary but my reading of him is that he would be very happy.

You talk of things being 'physical' but I am not sure what that means. My explorations of the mechanisms of perception suggest that none of us really knows what we mean by it. What intrigues me is that many people only come to abandon the idea of the physical late on. Even Leibniz does not seem to abandon 'corporeal substances' entirely until his fifties, despite having worked out the frailty of the conception much earlier. I only came to see the full arguments in my mid fifties.

BEst wishes

Jo E

Dear Dr. Edwards:

While I can't offer a complete reply yet, I feel compelled to nod in agreement with something it seems you intimated. Namely, what is "physical"? How is a massless Goldstone boson "physical" in one mathematical representation that poses problems to theory yet is conveniently "unphysical" (and still massless) in a resolution? Along with the relation between formalisms and systems modern physics and modelling in general have turned out to be problematic at a quite fundamental level.

To simplify, "physical" is that which we can observe/measure and which is observable/measurable within a "complete" theoretical framework (by complete, I mean only in the sense that QM is complete while a QFT is not and different field theories have varied in how incomplete they are). We represent photons, phonons, electrons, etc., in identical or similar ways. However, in QM and to some extent extensions of it the representation may remain without a one-to-one correspondence to a physical systems (in the classical sense) but is nonetheless complete in that we are able to consistently use the same representations to produce the results predicted by the physical theory. Whatever problem exists with the representation does not prevent us from consistent usage.

You would (it seems) be in a far superior position than I when it comes to evaluating how Frisch, Scott, etc., would evaluate these matters. Leibniz, on this other hand, is another matter. I'm not sure if I can find evidence that his metaphysics suggests he would support your model. Obviously, this could merely be because I've missed important points he made, but you have not provided yet any pointers to such points.

Dear Andrew,

It seems I missed your last post. I think 'observable' and 'measurable' are rather slippery concepts, as has been discussed either on this thread or another. I will let that lie.

As to Leibniz's metaphysics, I can only quote from his 'last word', the Monadology. Leibniz tells us that what we think of as material is a well founded illusion based on the behaviour of aggregates of fundamental dynamic units, the monads. The monads themselves have no parts and no size or shape as such. They can only be created or annihilated, not built up or dismantled, since they have no parts. Their essence is a constant internal principle of 'force' or better 'entelechy' that may best be interpreted, as Heidegger did, as 'drive' or 'operating disposition to action'. Although this principle is constant the progression of the monad at any particular stage in its existence will be whatever harmonises with its environment (and at least trivially or indistinctly the whole universe). This principle of change is the same thing as what we call 'perception' (para #14), being the dynamic relation of the monad to the universe. The implication is that for the monad this relation is one of being 'informed' by the universe, which seems necessary for it to progress in harmony with it so that seems to make sense.

These and a variety of other details all seem to fit with the idea that a monad would now be regarded as a mode of excitation of a field. Some further points are interesting and I think worth considering int he context of, for instance, a p orbital in an atom, an electron mode in a metal (as in Kronig Penney) or a Goldstone mode. Each monad reflects and perceives most distinctly an associated 'body'. Body is an aggregation of monads. For the p orbital this would seem to be the aggreagate of quarks and gluons in the nucleus. For the electron mode in a metal coin, it would be the whole coin. For a Goldstone mode in a crystal it would be the crystal.

A further aspect of Leibniz's view is that he says that the dynamics of individual monads always runs in parallel with the dynamics of associated aggregates. The dynamics of monads are 'final causes' with implicit ends whereas the dynamics of aggregates are efficient causes without ends. He knows that these two types of description can be applied to light (shortest distance and straight line analyses) and I think he is essentially enunciating the Correspondence Principle. Although I have not seen this written by others explicitly the major Leibniz scholars I have talked to are sympathetic to the general approach (which I presented at the 300th anniversary monadology meeting this month). There are other issues but the more I look at monadology the more it seems to me that Leibniz had deduced the basic structure of quantum theory and its relation to perception.

I am not suggesting that Leibniz would have agreed with the specifics of my model because he had to fit his theory to certain religious beliefs he wanted to stick to. It may be true to say that Leibniz envisaged monads rather differently. However, I think it is also fair to say that it may be very dangerous to speculate at all about how Leibniz would have envisaged monads because it seems clear that he would have considered any attempt to envisage them as illusory and futile. For instance it is temptimg to think that Leibniz would have associated a person's soul monad with the whole body. Yet Leibniz makes it clear that the action of the monad would not explain the action of the body directly. It would provide the 'purpose' but the body's actual actions would derive from that through mechanical chains just as in a machine. So Leibniz might have been very happy for the direct action of the soul to be deep in the brain.

Does that give an idea of the evidence for Leibniz supporting a mode-based perception?