Q: If you quantize a complex adaptive system (...either the hard way - by summing over all the quantized subsystems... or the easy way - by looking at emergent system properties; invoking the principle of relativity in its broadest sense; and applying generalized Copenhagen operator axioms... ), I think you'll arrive at a quantum dynamic where an emergent field in system space is coupled with the QWF. I hope your grant that there might be a host of equivalent formulations of such physics... and lots of "discrepancies" among different formulations, might, after prodding, turn out to be logically equivalent.

A: Well, if they can predict the same things then they are equivalent. If you recall how Galileo's science came out of a whole bunch of ways of seeing things in the middle ages (I won't give names of little known thinkers then), what we are doing right now is in the same vein... and it may take quite a number of approaches (and years) to come up with one that sticks. At this point though experiments are primordial in increasing the number of "wiggles" by present science to the point of unbearability. So I bring out what will be observed *before* it is observed to show features of our world can be predicted through my approach. This is why I informed Dr Livio of the Hubble space telescope project about what he will see. Present physics for the past 50 years has been only *reacting* to new discoveries from dark matter to high Tc superconductors. Also, the Galileo approach won because it could produce practical things (Galileo was an engineer for the Venice prince after all). Here I point to microbiology where at last we could start predicting things instead of going exclusively the empirical ways of pre-scientific times. This is then where the different approaches become unequivalent...

On the "adaptive" aspect of the evolution, this could allude to the necessity for each of the realities to be able to "add up" to the set in order to continue the computation, and thus create their collective future, i.e. "survive" at each step of that computation (of course "uncomputable" with our finite machines!).

Q: In this "uncomputable" connexion I was trying to model a coupled (Quantum field/Quantum Wavefunction...) evolution as computationally equivalent to classes of Turing Machines with dense sets of cells on their tapes and finite tape speeds. There should be a whole hierarchy of such machines... all possibly reflected in our "universe at large."

A: There your thinking is similar to others in Computer Science. The P=NP intractability problem has triggered quite a number of thoughts on that matter. But we may be putting the cart before the horse here, and we may need to look at the mathematics behind this. My feeling is that we need to be bolder in our approach to come up with a breakthrough. The mathematics we know may not be adequate.

A: (Continuation from earlier answer) This condition of "adding up" ought to lead then to the known variational principles of both quantum and spatial systems. This is an area I have not expanded upon.

Q: Yes. Once you can prove the derivation, you add legitimacy to your ideas. Because science is a priesthood with Kuhnian evolution... you'll have to do that... derive 20th Century Physics as a special case. If you disregard the semiotics of the current worldview; you run the risk of being castigated forever.

A: The legitimacy of my preliminary study comes from experimental consequences of the logic I use. I do not disregard anything. I have tried to be as comprehensive as possible within the realm permitted at this point (the number of scientific fields I touch testifies to that!). If you recall Galileo, he showed how Aristotle was incorrect and how he was castigated about an hypothesis, not his fight with Aristotle using logic, and only practical consequences vindicated him (only in the long run). When it comes to deriving present Physics from a new broader position, not a single person can do it, a new mathematics needs to be worked out among other things. Galileo was inspired by Copernicus, and in turn needed Kepler, Newton and Descartes to obtain a complete work (even Descartes castigated him for not using the calculus!). But he did show the way, and this through a mainly conceptual (preliminary?) approach with practical consequences, such as the observation of the Jupiter satellites. I attempt to follow that path. My only hope is to make others think, others with capabilities I don't have, to fill the gaps such as the mathematics and the connection to the variational principles, as well as the experimental aspect. In the meantime my study is there to identify an outline of an approach which can be corroborated by experiments to lead us out of the theoretical box we are in. I don't attack QM and Relativity. My study is first and foremost to find the limitations of present theories. Right now the establishment has no idea where these limitations are. So I do not battle the establishment there at all, except for the big bang theory, which is a rather recent theory (an afterthought really), and this in order to reach the second goal. This second goal is to see how to connect QM and Relativity. There too the establishment is lost how to do that. So there also I don't fight the establishment, I merely try to help.

Q: People have a way of ignoring experimental evidence - or reinterpreting it in the reigning formalism. So if you're banking on "experimental" proof - they'll wriggle out of it... epicycles upon epicycles...

A: Of course, until practical consequences castigate them away... Already astronomers are very angry toward present theoreticians for their incapability in predicting things (see for example the failure of the dark matter hypothesis in the New Findings page) but again it takes time. When it comes to microbiology, there the world is accustomed to our incapability in predicting things. So I guess that the the breakthrough will have to come from astronomy. And then, instead of a theoretical void, the establishment through my study may have an out giving a broader vista, not a rejection of an entire system of ideas.

Q: If you look at the emergent QWF the field's interaction with it will occasionally cause collapse (...or decoherence - if you looked at it the hard way...).

A: Here I diverge (unless you understand "occasional" as "conditional"). In my approach collapses occur in systems that include nuclear elements, as their adaptive evolution emerges into *bounded* space manifolds connected to our space manifold.

Q: No divergence whatsoever... "occasional" only because in most situations the computation never gets to "here".

A: (Continuation from above) Whenever nuclear elements are involved in the EORs relations, such bounded evolutions (versus the unbounded ones from leptons) force a single reality to emerge at each step of the (non-local) computation by the EOR's. In other words the bounds begin to define separability and distinguishability. A system without nuclear forces has no collapse. I venture to point to one very close to us!

Q: But the cool thing is that the Born criterion no longer works (...because you have a deterministic physics of the collapse..) and the vacuum becomes accessible (...of course classical causality is also screwed...).

A: It's all deterministic in my approach since it is a giant computation! Even though non-local relations occur causality is maintained via the higher dimensionality of the systems' various relations. If you want to see it as Plato did, an evolving shadow has no cause for its movement and non-local transformations. Our world is the shadow of a higher dimensionality evolution (at the level of the EORs), so when we limit ourselves to the shadows we throw out causality. Such a wanton simplification is simply not physical.

Q: If the physical universe is a sufficiently complex adaptive object... this scenario might be valid on a cosmological scale...

A: Experiments I point to in my work address the cosmological scale, and not via "Quantum Cosmology," instead via the badly needed completion of General Relativity!

Preamble - More on the Axiom of Choice: As I say in my math page the independence of AOC from the other axioms of set theory was proved by Paul Cohen in 1963. AOC was also proved consistent with the other axioms of set theory by Kurt Goedel earlier (in the 1940s). I further quote here "The Nature and Growth of Modern Mathematics" by Edna E. Kramer -

p. 595: In 1963 "Cohen offered different substitutes for the AOC, just as the parallel postulate [of Euclid] is negated in different ways in Lobachevskian and Riemannian non-Euclidean geometries."

On the same page, Zermelo is quoted verbatim. His axiom states: "For any class of non-overlapping classes there exists at least one class which contains one representative element from each class of the aggregate of classes." This wording comes from an example clarifying what he means (given in the book I quote), but for me as a physicist, this wording does not relate to physical concepts. As I see it this is the main problem with AOC for its use both by physicists and mathematicians (Euclid's postulate wording was also the root of the problem).

Finally (p.597) (unidentified) mathematicians "proved the well-ordering theorem equivalent to the AOC." This is why I cannot put out an axiom stating the existence of a 1-1 mapping as this is equivalent to stating AOC!

What I do instead is introduce the notion of separability and give a constructive example of an unseparable set. This is the physicist in me speaking. I start from the real line which manifestly follows the AOC and build classes from it which are each not following AOC. Then I have a set which is unseparable, i.e. the AOC is indeed irrelevant to my set theory. In my point of view, very much as Cohen's view, the AOC is itself a matter of choice, a property of a set or a subset.

As a physicist seeing unseparability in the quantum giving out separable objects in certain circumstances I have to discard AOC and define what it means mathematically not to be able to separate things, thereby my definition, which is a lot more physical than Zermelo's. I must give a definition which is also constructive because I would not otherwise be able to talk about such unseparable sets. Note that the definition I give is fully compatible with what Galileo had in mind (see my quote of Galileo in one of the first sections of phase 1), i.e. in Nature "I cannot pick an element without picking an infinity of other ones," or something to that effect.

The very slow evolution within mathematics of the question of AOC (and its complete stall in the last 30 years) shows that mathematicians have not looked at physics to get beyond that point, unlike mathematicians of the 19th century about the 5th postulate of Euclid. My definition can be then seen as an input to mathematics, a hint how to go further in Set Theory. But as Einstein admitted in his famous quote "Do not worry about your difficulties in mathematics; I can assure you that mine are still greater," I am looking for a Riemann too... Einstein was just lucky that Riemann came before him and looked at the physics of his time instead of staying in his ivory tower. The mathematicians of our time have been fooled by the physicists being content with their formalism, failing to see the mockery this formalism was about representing reality. I squarely put the blame on Bohr. He stopped Science, both physics and mathematics.

A: Cohen in the 1960s was really the last one I know who extended the theory. But at the point Cohen brought set theory, someone in mathematics had to have an example of what a non-separable set could be in the physical world. The new math page summarizes this background on whom to blame... I have added the theory by Quine on that page as being the only one I know who has attempted to make sets not meeting AOC, and this dates from the 1940s prior to Cohen's work. Anything anterior to Quine would be even less relevant.

Q: Now, you have to spend a lot of time framing a rudimentary algebra of your big sets... The hard thing will be: can you say anything practically useful about a machine computation on G? Can you make it deterministic within G? Can such a computation tell you anything about the machine's output - the physical universe?

A: Without a mathematical development of unseparable sets I cannot go further than what I have right now in my math page.

Q: That's why I framed the machine (Q, PSI) (the combination of a postulated "space field" and quantum wave function field) which is derivable from an observer-based interpretation of QM without otherwise tweaking Copenhagen axioms...

A: That's a sure loser in my approach. I cannot physically start from the classical world to define the quantum. I can only do the reverse!

Q: (Continued from above) Such a machine demonstrates the incompleteness of QM by showing that the system isn't closed under (Q, PSI). This is a valid way of "bottom -up" extension of a mathematical system. It is sometimes more instructive to work this way... Thus the existence of the set of rationals can be surmised because the set of integers is not closed under division. Similarly... the existence of the Reals can be posited because certain operations, eg circle calculations and taking square roots seem to violate closure of the algebra of Rationals. Similarly the machine (Q, PSI) which seems to exist in observer-environment based QM violates any R^n manifold whatever the metric...

So while you're working top down - I'm working bottom-up; looking for suggestions from QM that will allow me to frame a workable algebraic system to house a 21st century physics...

A: I see that. I believe however that such an approach can only prove the limitations of present QM, but cannot get to features not covered by it. In other words, it cannot be a productive theory with experimental predictions, the key feature of any new theory.

Q: I think something like the system G = (R^n, 2^R, M) can work.... the problem now is to create an algebra of machines on such a system... an algebra that can say non-trivial things.

A: Your idea to present an algebraic system appears to be a meaningful base, with a minimum of hypotheses. I reflect this on my math page.

Q:This is a craft - a combination of mathematical skill & insight; knowledge of where we want our physics to go - and a sense of aesthetics - minimalizing algebraic complexity and maximizing mathematical "elegance".

A: Correct!

Q: You've started with directed graphs - maybe that's an approach... we should now explore all avenues... this takes a lot of creative work.

A: I do say so in my math page.

Q: You've seen the point I have tried to make: That we must try to look at evidence for the violation of the closure of separable set algebraic systems - and categorize them. It's substantial evidence and might point the way to the algebra of the huge sets that we're looking at. What's your opinion of this tack?

A: Sorry that I may have skipped answering fully your point. Here is more on the matter. The first evidence of the violation of the closure is Goedel's theorem, which amazingly enough needs not considering unseparable sets to demonstrate (but cannot be fully understood without considering unseparable sets). Other evidences will have to come from the algebraic study of the unseparable sets themselves which will lead to the existence of properties such as dimensionality, boundedness of certain subsets and common manifolds generation.

There is no doubt that if somone comes up with a definite method how to deal with unseparable sets, he will be our Newton. When it comes to mathematics, I am not even a Cavalieri, so I am not a good candidate for the job, and I never pretended to be. I have no idea how to deal with the unseparable algebraic sets beyond what I have presented on the new page at your request. I do say there that this is only an attempt at a start. I saw (and this is my opinion only) that you were trying to demonstrate the incompleteness of QM from within the present formalism by tacking the existence of space as interacting with the quantum, thereby possibly showing the incompleteness of the formalism to deal with space. I answered by saying that we can only hope that way to demonstrate the incompleteness, but certainly not come with new features due to the basic fact that the QM formalism assumes space as an arena. Referring to extending the rationals to the reals as an equivalent appears not founded. Non-separable sets are animals entirely different from the ones we know, they are not an extension of what we know, they are just different. We could not infer Einstein's mechanics from Newton's. The same here.

At this point I will add that trying to postulate something new within existing QM appears to be a dead-end. For example, gravitation was attempted to be represented in QM by gravitons. A long quarrel between Feynman and Wheeler appears to have occurred on that matter, ending up with Feynman quitting the quantum study of gravitation, a quarrel that left traces in at least one book by Wheeler. Feynman may have quit that field also when "ghosts" were found in the QED computation about gravitons, the formalism being then too weird (far out from reality) to continue in that path. In any case, I contend that this formal weirdness is a symptom of a formalism which is inadequate to allow a meaningful accountability of space within QM. A physical theory must make sense to our imagination, otherwise we will pay the price by having a sterile theory. QM assumes space as an arena, no amount of tweaking can change that.

Q: On the subject of Mathematics becoming an experimental science, merely looking for patterns and saying ooh! and ahh! like Chaitin does is perhaps not good enough now... or maybe that's the stage that 20th century science has to go through before it becomes 21st century science.

A: It appears that this stage must complete its course. The discovery by Goedel when combined with the discovery of the Quantum goes well beyond the 20th and the 21st centuries when it comes to our understanding of reality. So many centuries went by trying to use separable logic to understand reality... we are bound to have to "digest" the news for a long time. In my new page I humbly advance an alternate way of seeing what the Goedel discovery means, while my thesis at large does the same for the Quantum. The thrashing out of what to do with such discoveries may take 200 years until the obvious is finally seen... Hopefully experimental discoveries will speed up the process in the meantime. Right now there is not enough data known of our world to come up with a correct path. See for example the discoveries by Halton Arp in Astronomy about AGN's (in the other Q & A page) which don't fit in our official theoretical knowledge - they may fit my approach and allow to make it more precise in the "continuity equation" area of phase 1.

Q: When I read Chaitin's earlier randomness papers, back in the 70's was it?... I instinctively thought that he would go for a "bigger" set and put a computation there that would generate "random" streams... I thought that was the logical extension of the machine that was so complex that it was the only machine to run its computation.

A: In my Artificial Life period I was thinking that way. I thought that in order to bring complexity to the Tierra simulation, there could be an outside program that would supervise the Tierra program from without. The axioms of Tierra were not complete, thus the outside system would discover new properties of Tierra. Knowing them the outside system would then be able to add new axioms to the Tierra system and thus bring multicellularity at last. In other words, "the only machine to run its computation" was indeed contemplated in the AL field, but nothing came out of that. The properties that were discovered were found by human operators, not the supervising program.

Q: (Continued from above) The idea I had then was that the physical Universe was too complex to compute itself- ergo, it was the output of some other computation on a naturally much bigger set.

A: The idea of complexity (in algorithmic terms) for me is qualitatively different from unseparability. A system could be unseparable and yet not that complex. This is why I have not brought the idea of complex adaptive systems in my work. For me this complexity idea is now an unsupported speculation, especially from the fact the idea comes from classical separable sets. But I definitely see a related concept whereby only "successful" computations contribute to the future of our space manifold, thereby explaining the success of the Feynman path integral method which contains the variational principles of Classical Mechanics such as the Principle of Least Action. My math page reflects this possibility. For Mathematics now to confirm!

Q: I won't haggle on whether or not objective reality exists... but all this talk can be handled mathematically as a system of "compression" models of the universe by subsystems of the universe. Gerry Wolf is working on compression modelling. Do a search. That will lead you to a new math. In such a model, and when consistency constraints are strong... The Principle of Relativity holds.

A: And there is no reason for it not to hold. The EORs adaptive evolution results in such a principle, besides the variational principles mentioned earlier.

Q: This Principle, in a strong form, means that the dimensionality of a space (...even if it is a system space...) is an interesting thing. There remains no special fundamental "physical" space as we transform along those models. So the manifold that we humans find ouselves stuck in is (in part) related to our makeup.

A: There I strongly disagree (see my part 1 on this). The Principle of Relativity was not meant to deny existence in the first place. Another fellow (in my Correspondence page) said that space is an artifact of our senses. See my reply to him. Space is as real as fire and the other 3 elements of the Old Greeks! It is not because the shape of an object changes from the viewpoint you take that the "fundamental" object is not there. This object emerges from an adaptive computation as flowers bloom in a field! The screwy thing about space is that it is created by elements which compute all at the same maximum speed, the speed of all the EORs, even the ones which make us! That does not make it inexistent...My work takes Feynman's hypothesis that everything goes at the speed of light, and this fact needs a lot of pondering to realize its importance.

Q: We need to invoke processes that create information - and the relatively tiny sets on which we base our universe - from far larger universe(s) where information does not explicitly exist... because such things as the axiom of choice fail there.

A: Yep. These "processes that create information" are the processes that produce separability from unseparability as I mentioned earlier, and are laid out in part 1 of my work.

Q: Now I'm saying all these things and I haven't yet read your stuff... don't worry I will. At least I'll come to it with a different set of prejudices... and might be able to say useful things.

A: Thank you for your open-mindedness! My approach is of course incomplete, I won't deny that. For example I mention in phase 2 the apparent need for the EORs to form as large an association as possible. Such a need (the Groupish Monad) must come from an unknown principle defined at the level of the *set* of EORs, not at each EOR. It seems that unseparable and undistinguishable sets (where the axiom of choice is invalid) define their elements' behavior from the whole set, and not from the elements. This is only a guess on my part. An infinite unseparable element may be tricky in its behavior...

Q: You are right...the bigger set in which the generators of our manifold lie are inaccessible to modern analytical formalism. The resolute failure of the Axiom of Choice would result in Shannon information being absent globally. This is why I say you have to do two things: (1) Fix Set Theory; and (2) Look at the semiotics & axiomatics of the physical universe from Newton to today.

A: I agree. You are pointing to the formal ways that will in the end back up my approach. To get to there I started laying out the details of how to tackle both in my work, as you will find out. You and everybody else are of course eager to see the results. But Science does not move in one day. Let's first agree, via the *minimal hints* we can observe in the physical world, that the approach makes sense in the first place! The rest will come in due time.

Preamble: My initial guidance in biology, which I rejected later on, was Roger Penrose's The Emperor's New Mind and his subsequent Shadows of the Mind. The intractability of the emergence of spatial structures was pointed out by him, from a work by Markov in the 1940s and other work by him and Hartle in the mid-1980s. You may fool yourself if you think you can use our present axiomatic with a few changes only to get to the emergence of space manifolds... Certainly Roger Penrose is stumped right now, and I cannot say this is because of his ignorance.

Discussion:
Q: No, I'm not fooling myself. There is a steady progress of axiom addition and replacement since Newton... and it works just fine. WHY it should work... and why we should get useable empirical modeling of the Universe with such a simple axiom set is what Einstein marvelled about. Think hard Roger; you were at Santa Fe... why should a reasonable facsimile of a complex system (...the human-observable universe...) be able to be generated by a few paltry axioms? C'mon think.

A: I answer this below.

Q: And yes, I can say it's Penrose's ignorance that has landed him in the stew that he is in. He refuses to be flexible with his low-level paradigm. He keeps modifying at higher levels. If you're willing to invoke a set of cardinality 2^c or greater - and let your ordinary continous manifolds emerge thereof... and you can (...i think...) generate a such a set and manifolds from the interaction of a wavefunction and an emergent potential in system space - you can derive a 21st century physics that will generate the previous paradigm as a degenerate model. This relationship between superseding paradigm and preceding paradigm has been so since Newton... and there is a reason.

A: I suggest that you read at least my part 1 as there is there some history of the advances in my point of view, as well as the mathematical problem we are facing. As I said earlier we may be fooling ourselves about the mathematics physicists have access to right now...

Q: Will do. We need just a little more set theory and a way out to the universe at large by perhaps souping up the calculus of variations. But It's no coincidence that the wavefunction works... why should the essentially Maxwellian wavefunction work so well (...you can't deny the Quantum Mechanics has great predictive power...) when its introduction by Schrodinger WASN'T EVEN INTENDED TO DO THE THINGS IT EVENTUALLY DID??? If you're a gambler - what odds would you give that the mathematics of electromagnetic theory would work in QM??? None. Yet it did - remarkably well.

A: For me it is no marvel at all. QM deals with the quantum as a field too, and a field is a major classical sophism (remember Faraday!). Schroedinger was very uneasy as to why his formalism was working based on the Statistical Stance sophism he invented. He felt that it really was a mockery of Physics! He also expressed (as I mention in my study) his feeling that the works of a deity (the quantum) are unknowable by Man in his What is Life? set of lectures. The present QM formalism essentially gives up on tracking each EOR evolution and treats such evolutions as a statistical process. This fact is already an indication of the impossibility for mathematics using the axiom of choice to deal with unseparable sets. It HAS to treat them statistically within this kind of mathematics.

The formalism furthermore only looks at the result of infinite computations (the famous What is a Measurement? question...), i.e. the result of an adaptive evolution, so it is no marvel we find in it a variational principle. The odds are then very high indeed that such a formalism would work. With QM we just went one step higher in our ability to cope with reality, but it is still only half a step. The Statistical Stance sophism works as long as we can treat our space as an arena. When we try to look at the effects which result from space emerging from its content (from the continuously infinite computation we are glossing over), that sophism and the resulting formalism will be in trouble! I point to two very different areas where QM has the potential to fail, high redshift astronomy and the microbiological processes that are the key to Life. In one case we have not yet observed the effects, in the other we can't see what is glaring at us due to our lack of physical understanding.

Q: Before your formalise your theory you MUST address the above question. The Universe is defying the odds. Either "someone" is making it easy for us - OR there is an axiomatic degeneracy of the universe. If the latter case - why?

A: Well, I just did answer. When we neglect a process, it is no wonder we see things as defying the odds. The magician has tricks in his hat, let's look at the hat! The third alternative is that the universe is *finding* its future at each step of its computation, like when a machinist in a shop finds pieces that at last fit each other. He just finds the fit! You don't see all the pieces that have been discarded to find the fit...Adaptive evolution is of that sort. Nature in the crude classical evolution called Darwinism has discarded many pieces that did not fit. This is why we are marvelling now at its result, us for example! The fitting process I envision is an infinite parallel computation, infinitely faster than Darwin's classical evolution, which is a classical computation, thus the eons required to go through this last process. (Due to this slow pace, the start of evolution, the origin of Life, itself appears to have instead come from an infinitely parallel computational process involving the nature of space just to make it likely to occur. See my work, phase 2 on this.)

Q: Right...so I've gotten you to answer the question I have posed in a few of the letters: the axiomatic degeneracy of the universe - the easy fits have evolved because the "physical" universe itself is the "output" of an adaptive computation done in a set(s) that is very, very huge. You've answered Einstein's question. That's what I think too.

A: Watch out: The set is not so huge as it is unseparable! That's the clincher if you want to get at creativity.

Q: Now, forget physics for the moment...let's talk mathematics.. what do YOU think has to be done? Be honest now. I have my ideas... but I like the disagreement.

A: I have in fact given a lot of thoughts about this, but as Dirac did for his "function," I have merely given a description of how *physically* I see what is the goal (see phase 1). Out of the top of my head I would start back to where we invented calculus. Galileo had a feel that infinitesimals may not catch everything that the world was made out of (remember Cavalieri in the time of Galileo). If you read his Two New Sciences, you will read between the lines that the whole was preoccupying him more than the elements. Our present set theory is based upon infinitesimals. Cantor's diagonal method assumes each element as separable. Someone has to come up with a new method where you do *not* need to identify each element separately. The purpose of the whole will define each element's axioms. A top down view needs to be taken instead of a bottom up. Instead of a curve being defined by each of its points' coordinates it must be defined by what the curve *is* (bounded, unbounded, with cusps, crossings, a given total area, etc). Then you come up with the axioms defining where the points must be. This way each point has no identification, it is unseparated from the others. I may be totally out of whack there, or I may lack an enough broad imagination, but this is how far I can see. This is the kind of imagination that a real mathematician must have. And I don't have that kind of imagination. My math page is the maximum I can give at this point.

(i) while current QM only allows a quantum computer to solve exponential time problems in polynomial time... I think some classes of quantum computers will be able to solve Turing incomputable problems. This is because of the nature of the machine on a larger set that "computes" our manifold... our universe is the construct of a machine beyond this manifold.

A: There are many indications that this is true. An example is the way Penrose found the Penrose tiles through his imagination and later it was found they can be easily found through a simple higher dimension periodic arrangement. Minds appear to unconsciously operate in higher dimensions, so their physical support must be in higher dimensions too. Furthermore the creative aspect of minds shows that the quantum is involved, a "machine" cannot be creative as a classical object. That is my opinion, even though I cannot prove this experimentally at this point. We must first look at Life in a different light, with the experiments I propose.

Q: (ii) I disagree philosophically in the observer-universe dichotomy to which you apparently subscribe. But this, I think is cultural. However, I do not think it will substantially affect the mathematical equivalence.

A: You over-simplify my position. I discuss in phase 2 the properties of a non-separable system with no quantum collapse. The dichotomy appears there due to the classical records that this unseparable universe (a mind) connects to in its multiple-realities computation.

Q: (iii) Some classes of macroscopic quantum computers will defy normal thermodynamics... this is I think because a Strong (non Einstein) Principle of Relativity holds. I think can derive this from compressional modelling theory (..if I live long enough...).

A: I have no doubt that the very fact a non-local and non-collapsing system interacts with a collapsing one normal Thermodynamics cannot apply. I see such a system as able to get its "information" intantaneously from wherever it extends within the normal universe, although from the outside universe side for each piece of information causality won't be violated.

Q: (iv) The vacuum energy actively interacts with the conservation laws of this universe - accounting for a lot of unobserved mass and redshifting... I approach this through a derived violation of the Born Criterion.

A: This is where my approach may allow you a "shift" in your viewpoint which will bring you to an understanding of how the so-called dark matter is needed to explain galaxies dynamics. At that point you may realize that using dark matter as a concept is wrong, and infertile in its predictions. The evolution of space from its quantum make-up is the way to go beyond certain scales of the system so that predictions can be made in that area.

Q: (v) Certain aspects of "paranormal" phenomenon might be as a result of extra manifold physics. Strict causality is also violated.

A: I see this differently. A quantum system with no collapse and connected to our space in a non-local manner "knows" intantaneously events in our common space provided these events are located where the connections (sensors) of the system to our space are. This does not make the system "paranormal" (a notion which, I understand, considers action-at-a-distance). EPR experiments deal with holistic (non-local) phenomena, not action-at-a-distance phenomena in my view. Such holistic phenomena do require a higher dimensionality physics for our space to be understood.

Q: (vi) The current analytical formalism fails at this level. A formalism where the Axiom of Choice fails and where Russell & Set of all Set paradoxes are put to rest is needed.

A: Amen.

Q: I brought all these ideas up with a mathematical physicist back in '97 - he told me that he had withdrawn from Set Theory in frustration years before. His colleagues were aware of the difficulties with Set Theory but didn't see a resolution until mid- or late 21st Century. Yet he continued to try to demonstrate a lot of the above with inadequate mathematics.

A: Let's remember here that our present mathematics (as I describe in phase 1) is a product of our classical outlook of the world! Mathematicians need a lead from the physical world to go the extra mile needed here! (and what a mile!). I am faulting physicists for failing to keep the connection about what happened in the early part of the 20th century to our physical understanding, and to this day (70 years after) still failing to see how new and important the quantum discovery is for the future of mathematics. I explain this from the fact physicists felt satisfied with a bastard formalism based on classical concepts. They were wrong! There is no reason for mathematicians not to act, but physicists for this reason failed to identify what was really needed for math to act. I am trying to mend the gap in phase 1 the best I can at this point. Remember that for the small problem of the Dirac function it took over 15 years for mathematicians to act due to the divorce between math and physics.

Q: And I have been preaching (to non-one in particular) the inadequacies of modern mathematics for the past 20 years.

A: My preliminary approach should help you there through its resolutely experimental base. Theoretical work must connect to the real world in order to convince!