FQXi'ers - On the connection of my work to Joy Christian's (in parts because it's long)

Joy expressed Bell's analysis about whether there could exist a 'complete' 'local' theory that could replace Quantum Theory, as Bell considering functions of the form

A(n,l): R3 * L -> S0 (see eqn 1.1)

R3 is a co-ordinate based denotation of the flat Euclidean space E3 in which the 3-vector orientation n resides, the space L is a space of 'hidden' variables which gives 'complete' states and S0 is the function co-domain for the observable A. Joy identified that the function co-domain S0 is rather trivially wrong, it should be S2 sub S3 (see eqn 2) as the possible orientations of the 3-vector n define a 2-sphere. Quantum correlations follow from the topology of the spaces.

My work effectively addresses what is meant by 'hidden' variable and 'complete' states in physics, neither of which were sufficiently well-defined by Bell. There are effectively 2 different underlying meanings for 'complete'

1) mathematical completeness - every theorem in a formal system can be derived

2) scientific completeness - every observation can be predicted

Bell fails to specify which he means. This shortcoming can be viewed as originating with the original EPR paper which gives the meaning of 'complete' as: "every element of the physical reality must have a counterpart in the physical theory". But this isn't physics! It fails to specify how you would verify that this was true - namely by experiment. This is why I use 'physically-real' to specify a term in a theory that *directly* corresponds to an observable feature in reality (I took this term from a QT textbook discussion of Bell's theorem). Any mathematical term which does not have this 1-to-1 correspondence is a 'non-physically-real' term, eg. the wave-function denotes strictly countable numbers of electrons by the real-numbers, and since 0.5 of an electron is never measured in an experiment, the wave-function is a non-physically-real term.

There are also 2 possible meanings for 'hidden' and Bell fails to specify which

1) hidden from the subset A, B of observables considered in a correlation experiment - in which case the hidden variable could be found in the future by a new experiment

2) hidden from all possible observables - in which case it is a non-physically-real term!

Option 2 is what is implicitly meant by Bell, but how such a conspiracy of Nature could arise is not considered. The missing element is dynamics, which is because the physical space of the EPR scenario isn't just Euclidean space E3, but a Euclidian sub-space of Minkowski space-time M4. There are an infinite number of ways of picking out E3 from M4, parameterised by the velocity v of the reference frame, i.e. E3(v) sub M4. Joy didn't make this correction either, but it doesn't change his correlation results because they depend upon integrating over the space of the 'hidden' variable to get expectation values. This may suggest that the parameterisation E3(v) could just be dismissed. However, this would effectively amount to setting v=0 for all the reference frames of the scenario, but without any relative motion there is no dynamics and so nothing happens - thus setting v=0 is unphysical!

    In the archetypal EPR scenario, the interaction point is stationary and the two objects move in opposite directions:

    A(n, l): (E3(v>0) sub M4) * L -> S2 sub S3

    B(n, l): (E3(-v) sub M4) * L -> S2 sub S3

    The condition E3(v>0) sub M4 adds the minimum dynamics condition to Joy's analysis - and adds Relativity - where constraints on the expectation value integral (eqn 3.2 in Joy's book) or normalisation of the 'hidden' variable should make it possible to turn Bell's 'locality' condition of factorisation (eqn 4) into the space-time separation condition v<c (v parameterises E3 and c is in M4). My work predicts that this should be the case, because I identify a scenario with a suitable conspiracy of Nature that gives a hidden domain L.

    Any observable (A, B) is ultimately based upon some particle reaction which will take some minimum time t_min to occur, so if the local causation of the domain L occurs on times scales t<t_min then it will be hidden from all possible observation. This will be the case for a particle with a physical scale of the Planck length and internal dynamics that occur on a time-scale set by the Planck time - which is the case in my model where particles are Planck holes with radius of the Planck length. Furthermore, as every observation takes so long that very many cycles of the local dynamics on the time-scale of the hidden domain L occur within the measurement time-scale, the calculation of all observables *must* take an average over the domain L (such as eqns 5 and 6).

    However, for the hidden domain being that of a black hole particle on the Planck scale, the rotation causes a maximal ergo-region where the metric signature of Minkowski space-time M4 is reversed, ie. (-,+,+,+) -> (+,+,+,+). This means that there will be one more +1 or -1 issue in Joy's analysis, where the prediction of my work is that averaging over this metric reversal in the hidden domain L is the *source* of the illusion of non-locality in QT. I would expect that extending Joy's work by applying it to the correct physical space E3(v) sub M4 would explicitly show this - and in so doing snooker Joy's critics (even if they all don't register it). Being brutally accurate about the applicability of Bell's analysis to the spaces of physics would score him as 0 for 3.

    Joy's flatness condition on the topological spaces S3 and S7 is actually in agreement with my results - despite appearances given by previous discussion. The issue is that the flatness condition doesn't technically apply to empty space, as that would mean there were no particles in the EPR scenario - so nothing happened! EPR requires 2 particles to dynamically interact, and so the flatness condition applies to the space in the vicinity of the 2 particles - this is *not* the same thing as empty space. The particles of my work are topological defects in the structure of space, which necessarily will give a torsion in the space around them - torsions in space is how the particle forces arise in a Kaluza-Klein style theory. In my work, I show that the formalism of QT is an *approximation* that is required to get a scientifically complete theory because the physically-real classical physics theory is mathematically incomplete, and that the approximation *only* holds in the limit of point-like particles and flat space-time. This approximation limit effectively integrates over the region of space of the ergo-region and gravitational curvature, and this gives the origin of the hidden domain L.

    My flatness condition is a local condition - as in only applies in the local vicinity of particles - and not a global condition on all of space ie. the universe isn't required to be flat. Joy's flatness condition is also such a local condition that doesn't necessarily imply that the whole universe is flat - if it did that would imply teleparallel gravity. But as a local condition, it just implies that the particle forces are associated with torsions in space - which is the case in my work - and gravity is left being due to curvature of space. This distinction would naturally explain the difference between the forces of gravity (curvature) and particles (torsion).

    Hi Michael,

    You're talking my language now (or rather, the language of Nature) ...

    " ... the hidden domain being that of a black hole particle on the Planck scale, the rotation causes a maximal ergo-region where the metric signature of Minkowski space-time M4 is reversed, ie. (-,+,+,+) -> (+,+,+,+). This means that there will be one more +1 or -1 issue in Joy's analysis, where the prediction of my work is that averaging over this metric reversal in the hidden domain L is the *source* of the illusion of non-locality in QT."

    That's exactly what I mean by the source of all information from the point at infinity. I think this is well supported by Lamport's result (Buridan's principle) for all continuous measurement functions. No quantum entanglement, just the illusion, as Joy allows -- with orientability playing the key role. The point at infinity in Minkowski space is everywhere close to the observer, while the physical measurement is nondegenerate near the singularity.

    "I would expect that extending Joy's work by applying it to the correct physical space E3(v) sub M4 would explicitly show this - and in so doing snooker Joy's critics (even if they all don't register it)."

    I don't know. I think we're back into this question of measure space vs. physical space. My sentiment is still toward S^7 as a complete physical space, just as Joy has it. No compactification, octonionic degrees of freedom.

    " ... the universe isn't required to be flat. Joy's flatness condition is also such a local condition that doesn't necessarily imply that the whole universe is flat - if it did that would imply teleparallel gravity."

    Actually, I think that is what he means to imply. Flatness and curvature have to be relative for a fully relativistic theory consistent with your definitions of completeness (which are nice). As in ordinary geometry the straight line is a special case for the curve, topology renders the continuum in curved space.

    All best,

    Tom

    Hi Tom,

    The question of measure space vs. physical space is *precisely* the point to address, especially in the context of the distinction between local - as in the local vicinity of particles - and global structure. Both Joy's and my results regarding QT are local (vicinity) results about the description of measurements, i.e. conditions on measurement space which imply conditions on physical space, namely that it must be locally (vinicity) flat.

    Extending this result to the global structure of space and teleparallel gravity does seem to be Joy's intent (is stated in his book as such). My point is that this is not technically a *necessary* implication. Joy's results are fully compatible with a locally flat spatial structure and gravity being due to the curvature of space. It must be noted that the flatness condition coming from the condition of scientific completeness of the measurement space is restricted to the local vicinity of the particle interaction. Extending the result beyond this domain is technically an invalid induction.

    I was concentrating on Joy's work and missed your discussion where you mentioned compactification and Kaluza-Klein theories. Mine is only a KK-style theory as it explicitly does *not* assume a fixed size compactified dimension as in standard KK - which you quite rightly in my opinion object to as that was the problem I had with KK. I refer you my reply to Jonathan about the cosmological 'constant' being a naive error that is not correct in GR! My extended GR includes the correction for a *physical* GR theory and consequently contains a compactification-inflation see-saw - I *derive* both inflation and dimensional compactification as consequences of assuming that the 'fabric of space' is a real physical surface.

    A further consequence of the compactified S7 is that all scales are measured relative to them, and measuring the scale of S7 relative to itself gives the constant of 1. So the constant scale of the compactified dimensions is a total illusion, NOT an artificial assumption. This gives a non-trivial example of the sort of point Jonathan makes about measuring rods in his essay.

    Michael

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    • Post #85

    My be contradiction "global vs local" is wrong assumption?

    Greetings folks,

    I must say that reading the comments above brings the feeling of coming home, or finding myself unexpectedly in a familiar place. Reading your essay, Michael, brings with it a sense of being told things I already knew or believed, with the sense that an expert is telling you why it's finally OK to believe those things. The correct application of Gödel's theorem as opening up possibilities and choices, rather than closing things down, is most welcome.

    But a lot of what I read in your STUFT paper and the material discussed in Joy Christian's book put me in a geometrical playground of unlimited proportions, and let me have my favorite toys in the sandbox with me. I learn a lot through visualization. I take Alain Connes' recommendation to budding mathematicians seriously, by taking time to recline and reflect periodically when absorbing new concepts, and I find it serves me greatly.

    The thing is; it keeps me on track, because it is harder to visualize things - including abstract formulations in higher Math - that lead to impossibilities. This is why I find the work you and Joy are doing so exciting, because it jibes well with what my visualizations tell me, and it appears to lead to physically realistic possibilities. Of course, that doesn't mean that it IS what is real, but it could be.

    Regards,

    Jonathan

      Hi Jonathan,

      What you are saying is music to my ears. And I suspect it is music to Michael's ears too.

      However, while you, Rick, Michael, Tom, Fred, and others are trying to take these ideas further, I am engaged in addressing your very prudent caution: "...that doesn't mean that it IS what is real..."

      I want to make sure that it IS real before proceeding further. And in physics we do that by testing our hypotheses experimentally. Despite opposition, scepticism, detraction, and even scorn and derision, I am completely convinced by my theoretical analysis. What I am not sure about, however, is whether Nature prefers to side with me and Michael or with the quantum mystics. Only she can answer this question correctly, and I intend to get her answer.

      Joy

      My faith in rationalism agrees with Joy -- scientific results cannot be objective without a clear correspondence between the abstract description and the physical measurement.

      If this framework isn't true, then I have to agree with Einstein: "I would feel sorry for the dear Lord ..." There is no rule that says the world has to be rational; if it isn't, though, we've been doing science all wrong for 300 years. I can't imagine the alternative.

      Tom

      Hi Joy,

      Does my description of the connection of my work to yours seem correct to you?

      On the topic of experimental tests, would I be correct in thinking that the correlation inequalities for observables arising through gravitational interactions, i.e. astronomical observations, could provide a test for teleparallel gravity? As your work implies that this would be required for gravity to be quantied, is there a test here for whether gravity is quantised or not?

      Obviously I don't think it is - as QT is not fundamental and so Nature is under no obligation to comply with the prior beliefs of physicists and have quantised gravity - but an experimental test would nice.

      Michael

      Hi Michael,

      I look at it this way: Bell's theorem proves explicitly that quantum configuration space cannot be mapped onto physical space without a nonlocal model. To believers, this amounts to saying that there is no analytical explanation of locally real quantum correlations. One cannot logically extrapolate to that conclusion, however:

      Quantum configuration space requires us to assume a bounded set of perfect information (such is the source of quantum mysticism inherent in a probabilistic measure). The orientable topology, as Joy has it, requires only that Nature have a choice of output in every measurement function continuous from the initial condition. This necessarily eliminates support for nonlocal realism from all proofs based on the law of the excluded middle, which of course is all the nonconstructive proofs of Bell's theorem.

      Bell's theorem is then reduced to an existence proof for the inequality between local measure results and simultaneous results of nonlocal experiments not performed. Trivial -- because relativity already denies simultaneity of events.

      Best,

      Tom

      Hi Michael,

      I think your criticism of either Bell or EPR about their ideas of completeness and hidden variables is not justified. EPR, for example, were very cautious in stating that their condition of completeness is only a necessary condition (for their intended purposes), not a sufficient condition. Your understanding of what Bell meant by "hidden variables" is also incorrect. What Bell had in mind was what you write as option 1, not what you write as option 2. The issue of dynamics is also irrelevant for the analysis of both EPR and Bell. Given their premises, the argument of EPR is logically impeccable. Given the premises of Bell---which are based on the premises of EPR and the views of Einstein---his theorem too is both logically and mathematically impeccable. It does contain a massive blunder, however, in the very first equation of his famous paper, as I bring out in my work. Whether to call this a mathematical error or merely a wrong assumption is a matter of taste.

      Having said this, we are of course not required to adhere to either EPR's logic or Bell's mathematics beyond what is demanded by physics. So, in that respect, in the spirit of exploration and investigation, I fully endorse your efforts. In particular, the issue of dynamics should indeed be considered as you are considering, and you have some very insightful remarks in this regard. I myself have very different ideas about how to investigate the issue of dynamics, since my primary concern is basic quantum mechanics, not relativistic or gravitational physics.

      I also like your thoughts about the flatness condition and whether or not it should be extended to the universe as a whole. I largely agree with what you have written about this. But again I would not discount any options at this stage because neither of us have anything near a full theory of physics (in fact mine is not even a theory---I prefer to call it a mere "framework").

      As for the experimental test of my framework I do not have anything as exotic as teleparallel gravity or quantum gravity in mind. At the moment I am simply trying to test whether the topology of our physical space respects SU(2) symmetry in the macroscopic domain as I claim, or SO(3) symmetry. This may seem disappointing, but my entire framework depends on this distinction. If this test is successful, then I have some further ideas about how to test the S7 hypothesis.

      Finally, since I agree with the view that QT is not a fundamental theory, the question of quantizing gravity does not even arise. QT and GR are simply two epiphenomenal sides of a yet to be discovered perfect, one-sided coin.

      Best,

      Joy

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      • Post #92

      Hi Joy,

      Thanks for your feedback, it is much appreciated.

      My premise was implicitly moving beyond Bell - something that I didn't think was possible until I read your work! I did initially think that Bell's intended meaning of "hidden variables" was option 1, and this is the meaning I used in my essay. But it struck me that Bell's framework would also extend to option 2 as well, and that the spatial topological defects of my model actually give a realisation of option 2. These 2 meanings could lead to confusion in the usage of the term "hidden variables" - I see that I have inadvertently included both options.

      The potential ambiguity of the EPR usage of "complete" is not apparent in the EPR context because their usage is sufficient. But the relevance of Godel's incompleteness to physics requires the more careful distinction I give, otherwise the point that mathematical incompleteness of theories describing countable numbers of objects under certain physical conditions can be by-passed to give scientific completeness is missed, as are the consequences of the required change in mathematical representation (theories with some of the weird features of QT).

      The term "local" is another multi-meaning word that could lead to potential confusion, especially in the context of EPR and spatial topology:

      1) local vicinity - local structure as opposed to global structure

      2) local causation as captued by the fatorisation condition

      3) local time-like separations

      E.g. my metric reversal example confuses usages 2 and 3, and suggests the following "recipe" for the illusion of non-locality:

      1) Metric reveral in the hidden domain

      2) Average over paths of strictly local causation in the hidden domain

      3) Interpret the results as if there was no metric reversal in the hidden domain

      => apparent non-locality

      I understand your focus on the sort of tests you're considering; I was just wondering out loud how far tests within your framework could go.

      All the best,

      Michael

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      • Post #93

      weak reasoning ! it lacks a lot of generalities dear Badband in your reasoning and strategies.:)

      In fact you repeat always the same :) SO AND SO3 AND SO7 AND AFTER YOU SHALL INSERT THE SO8 AND AFTER THE SO11 and after what , a book sent for the so12. Let me laugh.

      I have pity in fact. You think what with your hate ? I forgive you all ahahah

      KK theory for the compactification and what after ? Mr Witten but what do you do there ? is it the businessmen around you which implies this kind of reasoning? If yes, I am understanding why this world does not turn correlctly. It is simply not universal these kind of comportments.The Planet, this earth merits more. Why these kind of systems decrease the velocity of evolution? instead of imrpoving it. Is it that? the earth ? I am shocked in fact simply in seeing these comportments. In fact Mr Witten,Mr Tegamrk and Mr Aguire are universal I am persuaded like Penrosqe and Hawking,and Sussking also.So why it exists these business around which implies a real probelm. It is not that the aim of this universal sphere. The Christianity is the torch of the universal love. The suit does not make the monk ! A goodband is universal. A bad band does not respect the real universalists. Their strategies are like an error in fact. They insist due to their lack of competences in ciences, so their only one solution is the business. These kind of persons like to be in team, because alone they cannot make concrete things. Their tools are simply the hate, the vanity and the envy. In fact I pray for their poor souls and I forgive them with love. Hope they shall understand one day what is the spherization theory invented by Mr Steve Dufourny, a young horticultor, humble in seeing the sky and its spheres. In fact, the usa has a responsability for this sphere, the earth.The imperialism american can optimizing the earth with India ,China,europa. Why a global commission above the bricks and the otan, having a lot of universal wisdom and consiousness, does not appear on this sphere? What are these high spheres so? who governs so this earth if it is not the Usa. China has a lot to give to the world, the india also. The prosperity can be implanted on earth, so why? It is not logic all this. I beleive that the corrupted systems must be stopped quickly . We cannot accept the unconsciousness and the corruptions. If the high spheres of this earth does not take its responsabilities quickly, we shall add chaotical global probelms and we shall reach several possible chaotical exponential. The prosperity can be global for all. The USA must take its responsabilities for the well of all. The capitalism can be liberated with more monney. The stock of Au(gold) or Pt or the financial products or this or that must be architecturated with a real universality. China and Usa And India and Europa must work together. The Africa ,it, is very weak, and must be helped with universality also. The prosperity like a torch of evidence. It permits to decrease the hate.

      The probelms of religions also can be optimized. The imperialism american has a pure universal responsability !!! It is essential for our future. I ask me if the high spheres are really universal. I say me that this monney sometimes implies a lot of problems. The system , global can be harmonized.Have you seen the increasing of humans.Have you seen the energetical probelm.Or the poverty, the sufferings everywhere.It is not acceptable for universalists and generalists. The sciences have the solutions. The competences, scientific, must be centralized for the well of all.Above the borders and frontiers and differences. We are all humans waiting for a better world. The prosperity is, like said a friend that I have knew when I was moderator of the group Africa on Xing, woman, Deborah Boyd, a catalyzer of peace. People are less nervous when they create,They are more in serenity with their minds. It is a simple evidence. The hour is serious dear scientists. The solutions exist. It is time to act concretally.

      Usa has a responsability !!! This country must showing the example.

      Regards

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      • Post #94

      If the Planck length not valid in 2D, because no, gravitation no G?

      See essay 1413

      See Wilczek articles

      http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits388.pdf

      http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits393.pdf

      http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits400.pdf

      Is trinity sacred?

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      • Post #95

      Sorry for broken links

      http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits388.pdf

      http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits393.pdf

      http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits400.pdf

      Is trinity sacred?

      4 days later

      Hi Michael,

      Let me introduce you to Jens Koeplinger's essay, in case you haven't seen it already. It is amusing and entertaining. His main work however is much more substantive. Parts of it is based on Rick Lockyer's approach to octonions. I thought you might benefit from it since it also takes the division algebras seriously.

      Joy

        Hi Joy,

        Thanks for the pointer. I can see where you, Rick Lockyer, Jens Koeplinger and others are hoping to go with the octonions.

        In contrast, I have gone to the very end of the line with Einstein: to his vision of physics unification in a purely geometric theory. I *conclude* S0, S1, S3, S7, I don't assume them, and arrive at the conditions of your framework. If you read my S10 Unified Field Theory paper you will see that it *is* a full theory based on 11D GR. I have checked your book carefully for any condition which specifies your favoured choice and rules out my realisation of Einstein's vision, and I cannot find one.

        Just as you said the credit had to go to Einstein, my STUF-Theory is the form of physics unification that Einstein envisaged it to be - purely geometric GR in which QT is *not* fundamental. The things to pin down were the number of dimensions, the separation of space dimensions from extra dimensions, and the way QT arises: the dimensions of the spheres add to 11D; a cosmological 'constant' for a closed space just isn't physics; and the origin of QT is with a mathematical representation change because Nature is *described* by Maths, Maths is *not* Nature. The distinction is actually the crux of it, which is why I made it the topic of my essay.

        Michael

        Dear Michael,

        ''The experimental observation of electrons passing through slits generating the wave characteristic of an interference pattern challenges this divide, although this is only really clear when the electron beam intensity is reduced to the point of a single electron passing through the slits at a time.''

        If we were to assume that we live in a universe which creates itself out of nothing, without any outside interference so particles have to create themselves, each other, then it seems logical to assume that particles and particle properties must be as much the product as the source of their interactions. If so, if particles in such universe only exist to each other if, as far and as long as they interact, exchange energy, with all particles within their interaction horizon, then the electron, on nearing the slits, would 'see' its world split into two slightly different worlds, worlds which from both sides of both slits interfere with its path.

        As to its wave character, the Uncertainty Principle (UP) is interpreted to say that virtual particles can appear by borrowing the energy to exist from the vacuum, for a time inversely proportional to their energy. This suggests that real particles can be thought of as virtual particles which by alternately borrowing and lending each other the energy to exist, force each other to reappear again and again after every disappearance, at about the same place. As in this view particles express and at the same time preserve each other's mass by continuously exchanging energy (the sign of which then alternates), the origin of mass is obvious, as is the equality of inertial and gravitational mass.

        The hidden variables Einstein wanted to exist to avoid indeterminism can be identified as the energy exchange by means of which particles express and preserve each other's properties. However, the unpredictability Einstein wished to eradicate remains if particles indeed are as much the effect as the cause of their interactions. It is because their exchange is unobservable as long as the particles are at equilibrium, because it serves to preserve the status quo, that we have been able to remain ignorant of it: because we've always assumed that particles only are cause of forces. Only when their equilibrium is disturbed so the frequencies they exchange energy at changes and net energy is emitted or absorbed, the effects of this exchange become observable. In the study I propose a mass definition based on the UP: the less indefinite the position of a particle (or mass center of an object) is, the greater its mass is, a definition which might make it possible to derive the equations of relativity from the UP. For other interesting features of a self-creating universe, see my essay or the more extended study at www.quantumgravity.nl (which also contains some remarks on (CTRL+F) 'Gödel).

        Regards, Anton

          Michael & Joy,

          "I have gone to the very end of the line with Einstein: to his vision of physics unification in a purely geometric theory."

          That's the way I think, too. Einstein did say that if algebra (quantum numbers) were going to contribute to the basis of a complete theory, the algebraic methods would have to be improved. With all the emphasis on octonion algebra, though, I still see the fundamental framework of physics as analytical, which I much better understand and which I htink most closely resembles experience. I think I have made the point before that if Hestenes were not able to explicitly translate his method to Minkowski space, I don't think it would hold my interest.

          It's still the property of orientability, however, by which the mathematical structure informs the physics, so we need that discrete part to make the whole thing work, don't we?

          Tom

          Hi Michael and Tom,

          If Albert was alive today and knew all the physics we know (which is orders of magnitude more than he could have hoped), then would he have accepted Michael's claim? That is the question I want to answer for myself. But to do that I will have to put in at least as much time and effort into Michael's theory as he has into my framework. I will try to read at least some of his papers---with serious intention to agree with him---and then we will see. For now I remain sceptical.

          Best,

          Joy