Hello George,

If you have the time and desire, might you respond to this (reproduced from a post at my essay site)?

While browsing *The Demon and the Quantum* by Robert Scully and Marlan Scully (good book - recommended)I came across (p. 148)a marvelous quote by George Ellis. Robert Scully relates that at a conference, Ellis was asked: "Do we need quantum mechanics to ensure free will?" Ellis is reported to have answered in a Zen koan-like manner: "On Monday, Wednesday and Friday, I think not. On Tuesday, Thursday and Saturday, I think so."

Scully used the quote to support his contention that nobody knows " ... is classical chaos enough to provide freedom of choice, i.e., free will?" I think he missed the point of George's reply (which I am going to ask George himself to confirm or deny, in this forum) for the following reason:

Just a short number of pages prior (pp 130-132), Scully had noted that the quantum eraser proposed by Marlan Scully and Kai Druhl that when published in 1982 'shook the physics community' in the words of Aharonov and Zubairy " ... underscores the statement (that) information is a physical quantity. That is, information is real and the utilization of information is what the quantum eraser is all about."

In his figure 9.6, p 131, Scully shows the wavelike correlation between erased potential and detected information (which corresponds to figure 2 in my essay).

That is the single message of classical chaos, Wheeler delayed choice, and the quantum eraser: Information is real. I think that the opportunity Scully missed is in realizing that George's comment could only have come from a physicist so steeped in relativity that no other answer than "yes" is possible. We need the continuous measurement function equally with discrete quantum detection to have complete information -- and objective knowledge -- of the evolving state. What do you think, George?

All best,

Tom

Hi Tom

I do like your figure 2. Very expressive. And of course you are right - why does nobody start with the dead cat? - because the flow of time is real and we just take it for granted. And just reassembling the components of any living being once they are dead will not by itself make them come alive. Something else is needed.

"Information is a physical quantity. That is, information is real": yes indeed, meaning by that it is physically effective and so must be recognised as real - else we will have uncaused events taking place.

"We need the continuous measurement function equally with discrete quantum detection to have complete information -- and objective knowledge -- of the evolving state" Exactly - and that is what we need for a classical world to emerge. And the one thing we do know for sure is that a classical world does indeed emerge. It also gives the flow of time and the arrow of time.

The issue about life and the brain is that it also gives uncertainty: a freedom from classical determinism. Please note my post of Oct. 2, 2012 @ 07:24 GMT. The Lagrangian formulation does somehow reach back into the past and choose the suitable initial data we need at present. It is not impossible that this is related to free will. Yes I now some hard nosed physicist swill just scoff at me for saying that. Well some of the founding fathers of quantum physics have thought along the same lines. (Just out if interest did you ever read the Jung-Pauli letters?)

best regards

George

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    • Post #449

    Hello George,

    On your comment "Actually rather than octonions I'd go for geometric algebra", perhaps you should read my essay; The Algebra of "Everything". I just squeaked in as a finalist at #33. You might change your mind about Octonion Algebra. You will see that Electrodynamics from potential functions through conservation equations are covered exactly as expected within an Octonion structure, as a subset of the presentation. The algebra demands this once you accept the simple fact that there is no preferred structure amongst the 16 ways to roll out a normed division algebra with consistent H subalgebras. This realization requires what I call algebraic invariance, and it not coincidence that all differential equations explaining physical observables are algebraically invariant when cast in an Octonion construction. This I call law without apology. This law demands the full set of entries in the Octonion equivalent of the stress-energy-momentum tensor divergence, nothing in the 14 pages it consumes when written out is inserted by hand, and nothing more is likely needed. The law with the proper form of differentiation I call the Ensemble Derivative demands the form of Lorentz covariance we all know and love with the simple requirement that both pieces of each EM field component velocity transform in kind.

    Me, I am not big on coincidences. If someone thinks all this might be, then as Ricky said to Lucy: "Lucy, you got some 'splaining to do".

    You do not get any of this from geometric algebra. I like the symmetry of multiplication and division, something else you do not get with geometric algebra which is not a division algebra.

    This all fits into your top-down premise. The Algebra drives the lower level from above.

    Rick

    George, you have good intuition. The Jung-Pauli letters (Atom & Archetype) is a book I have owned since it was first published here in the States, and though I have browsed it, I cannot say I have read it. I acquired it at a time when I thought that I was through with philosophy, and issues of free will and consciousness, forever. I had studied Damasio, and became convinced that Cartesian dualism is successfully falsified. I was impressed with Marvin Minsky, and reconciled to a belief that a computer made of meat is not the worst thing to be.

    Long ago -- I cannot remember where, nor all the details -- I read a story about Pauli who, when his death was imminent, got into a discussion with another prominent scientist about what lay ahead and whether a personal god might exist. At the end of the conversation, Pauli was convinced of the belief that he held prior -- no, no personal god -- yet unconvinced, IIRC, that the journey was over. As Einstein said at Godel's death, that "stubbornly persistent illusion" -- the one that seems to tell us that a life, and time itself, has an ordered beginning, middle and end -- has no real place in physics.

    If information is real, though, we're all already as dead as we're ever going to be, and consciousness cannot be excluded from physical reality. If "all physics is local" (Einstein) and if " ... life would not be possible without a well established local arrow of time" (Ellis) -- there is no dead physics either. "Do not send to ask for whom the bell tolls," as the great metaphysical poet John Donne put it.

    Thanks for the reference to your earlier post. I'm finding it hard to keep up. I think your summary paragraph is bang on:

    "One of the deepest questions underlying physics is 'Why variational principles?' If the dynamics is viewed as resulting from such a process of selection of a particular path from the set of all paths, there is a glimmer of hope for an explanation of this foundational feature, based in adaptive selection. This is one of the key forms of top-down action from the context to the local system, because selection takes place on the basis of some specific predetermined selection criterion, which is therefore (because it determined the outcome) at a higher causal level than that of the system behaviour being selected for."

    I very strongly agree. I think a whole lot of complex systems thinking is going this way, and most importantly, the result settles the question of local realism -- for a robust simply connected network does not require all of its elements to be "switched on" everywhere at once to be functional. Because a fully relativistic system is self limiting both locally and globally, local arrows of time are self similar to the global; there is no distinction, no boundary between self limiting topological networks (local behavior selected for) and "the experiment not done" described by Peres as nonlocal. There just can't be any nonlocal information in a fully relativistic theory; all measure results are metaphysically real. Probabilistic quantum theory that assigns value to nonlocality can only either 1) assume perfect information in a mystical way, or 2)refuse to deal with the issue at all and accept incompleteness.

    I have found a tremendous amount of meaning in Yaneer Bar-Yam's theory of multi-scale variety: "In considering the requirements of multi-scale variety more generally, we can state that for a system to be effective, it must be able to coordinate the right number of components to serve each task, while allowing the independence of other sets of components to perform their respective tasks without binding the actions of one such set to another." ("Multiscale Variety in Complex Systems." Complexity vol 9, no 4, pp 37-45 2004). Distributed control -- lateral information introduced into the system -- increases variety. Increased variety increases the coordination strength of the network, so vertical information (hierarchical up and down) isn't sufficient to overcome the problem of bounded rationality. If one might find it useful to the discussion, I covered these issues in a 2007 conference paper and powerpoint

    Do we need quantum mechanics to ensure free will?

    "On Monday, Wednesday and Friday, I think not. On Tuesday, Thursday and Saturday, I think so." How could it not be? Our brains process information discretely, yet we -- and the participating universe, as Wheeler says -- experience life continuously.

    Sorry for being so longwinded.

    Best wishes,

    Tom

    Correction: I should know by now not to trust my memory. Einstein's "stubbornly persistent illusion" remark was on the death of his friend Michele Besso, not Godel.

    Tom

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    • Post #453

    Is the quantum gravity problem or pseudoproblem?

    Dear George,

    After initially struggling with the idea, I've been thinking a bit about how your top-down causation idea might look from the perspective of nonmanifold models of fundamental spacetime structure that emphasize the role of causality. It seems that top-down causation might provide an interesting new perspective on such models. For definiteness and simplicity, I use Rafael Sorkin's causal sets approach as an example.

    Causal sets, as currently conceived, are by definition purely bottom-up at the classical level. Causality is modeled as an irreflexive, acyclic, interval-finite binary relation on a set, whose elements are explicitly identified as "events." Since causal structure alone is not sufficient to recover a metric, each element is assigned one fundamental volume unit. Sorkin abbreviates this with the phrase, "order plus number equals geometry." This is a special case of what I call the causal metric hypothesis.

    In the context of classical spacetime, top-down causation might be summarized by the statement, "causal relationships among subsets of spacetime are not completely reducible to causal relations among their constituent events." In this context, the abstract causal structure exists not at the level of spacetime itself, but at the level of the power set of classical spacetime, i.e., the set whose elements are subsets of spacetime. Discrete models very similar to causal sets may still be employed, with the exception that the elements would correspond not to events, but to families of events. Two-way relationships would also come into play.

    Initially this idea bothered me because of locality issues, but such a model need not violate conventional classical locality, provided that appropriate constraints involving high-level and low-level relations are satisfied.

    This idea is interesting to me for the following reasons:

    1. The arguments for top-down causation presented by you and others are rather convincing, and one would like to incorporate such considerations into approaches to "fundamental theories," particularly those emphasizing causality.

    2. One of the principal difficulties for "pure causal theories" is their parsimony; it is not clear that they contain enough structure to recover established physics. Top-down causation employed as I described (i.e. power-set relations) provides "extra structure" without "extra hypotheses" in the sense that one is still working with the same (or similar) abstract mathematical objects. It is the interpretation of the "elements" and "relations" that becomes more general. In particular, the causal metric hypothesis still applies, although not in the form "order plus number equals geometry."

    3. There is considerable precedent, at least in mathematics, for this type of generalization. For example, Grothendieck's approach to algebraic geometry involves "higher-dimensional points" corresponding to subvarieties of algebraic varieties, and the explicit consideration of these points gives the scheme structure, which has considerable advantages. In particular, the scheme structure is consistent with the variety structure but brings to light "hidden information." This is analogous to the manner in which higher-level causal structure is consistent with lower-level structure (e.g. it does not violate locality), but contains important information that might be essential in recovering established physics.

    4. As far as I know, this approach has not yet been explicitly developed.

    I'd appreciate any thoughts you might have on this. Take care,

    Ben

      Over on the Rationally Speaking blog, Massimo Pigliucci has an interesting posting: Essays on emergence, part I , including a link to a a very interesting paper by Robert Batterman.

      An ensuing interaction with Sean Carroll includes the following post by Carroll:

      "Sean CarrollOctober 11, 2012 4:46 PM

      I don't know what it would mean to "derived physical reductionism," nor do I think that qualitatively new emergent behavior is absent from Newton's laws (depending on definitions). The point is simply that Newton's laws, applied to a set of particles, gives you a closed set of equations. With appropriate initial conditions, the solutions are unique. There is no room for additional causal influence. The equations give unique answers; you can't get a different answer without violating the equations.

      There is an important and interesting discussion to be had about emergence, and it has nothing to do with being unable to predict behavior from component parts, nor with new "causal powers." "

      Pigliuicci's response (October 12, 2012 8:25 AM) includes, "I find that argument wholly unconvincing. First, Newtonian laws are known to be approximations, so clearly there *is* room, in a sense. Second, those laws tell you precisely nothing about all sorts of complex systems, like the temperature of phase transitions of water, or the functioning of ecosystems, so to claim (global) causal closure seems strange."

      He does not however make the points I make in Part 6 of my essay, including particularly the point I make in my posting here on Sep. 17, 2012 @ 18:15 GMT:

      " The mechanism of superconductivity cannot be derived in a purely bottom up way, as emphasized by Nobel Prize winner Bob Laughlin; see the Appendix to my essay for Laughlin's statement in this regard. The reason is that existence of the Cooper pairs necessary for superconductivity is contingent on the nature of the ion lattice, which is at a higher level of description than that of the pairs; they would not exist without this emergent structure."

      These arguments, it seems to me, completely undermine Sean's billiard ball point of view, based in Newtonian physics. They provide good reasons that top down causation can take place in computers and the brain without contradicting the underlying physics. And that is why the existence of computers such as the one you are using at this moment is possible, without invoking magic. It is the result of top down causation from the human mind into the physical world.

      George

        Tom,

        thanks for all that. I'll have to take time to digest it - I'm travelling at the moment (will be in Boston Sunday evening to Tuesday afternoon before flying home via New York) and have to do other stuff.

        But yes Bar Yam seems really interesting: much deeper than Per Bak, who tries to construct stuff in a purely bottom up way. There's a strict ceiling to what that can achieve. Sand piles, bird flocks, reaction-diffusion patterns, etc. are a step on the way but they are not the real thing.

        George

        Hi Ben

        I think that is an exciting possibility to pursue. Please note that it might relate also to my posting of Oct. 2, 2012 @ 07:24 GMT. I am a fan of Causal Set Theory, and trying to develop it the way you suggest would be a great project.

        Maybe there is a Wheeler-like dictum here: "Part from whole!"

        George

        Thanks, George. Perhaps you will find time to say hello to Bar-Yam yourself, while in Boston. And it's a particularly great time to be in New England -- the Fall leaves should be peaking in color about now.

        Have a pleasant flight.

        Tom

        Dear George Ellis,

        As the thermo-dynamics of universe prevents the universe from gravitational collapse, gravity is the causation that is descriptive in top-to-bottom approach, in that the thermo-dynamics of the matters of universe and the gravity of universe are in balance. This implies Homeomorphic segmental-fluctuations of universe in causality cycles and thus Holarchial clustering of matters is ascribed in Coherently-cyclic cluster-matter paradigm of universe. In this paradigm the flow of time that correlates the dynamics of matters of universe, is in references with the discrete-times that emerge from Eigen-rotational quanta of strings in the Holarchy of universe, in that the nature of reference-time is expressional as cyclic.

        With best wishes

        Jayakar

        I've contributed the following further comment over there:

        Sure the lattice emerges according to well defined bottom up principles. Once this has happened, it then exists as an entity at a higher level of scale than the particles out of which it is composed (you have to use quite different variables to describe this lattice structure than you do to describe the particles: these variables are not reducible to lower level variables). The key point is that until it has so emerged, no Cooper pairs are possible. Once it has emerged, they can come into existence. Thus it is the very existence of the higher level structure (the lattice) that enables the lower level constituent entities (the Cooper pairs) to come into being.

        Sure you can work out in a bottom up way what effects the Cooper pairs mediate. But they can't act in a bottom-up way to create any physical effects at all until they exist - and their existence is contingent on the detailed nature of the higher level structure. That's a clear case of the causal effects of context on lower levels - that is, by any reasonable definition, causation flowing downwards in the hierarchy of structure. But if you dislike the word "causation", just call it a contextual effect,

        It is because superconductivity depends on this mechanism that you can't derive it in a purely bottom up way. This is stated strongly by Laughlin in his Nobel Prize lecture as follows:

        "One of my favourite times in the academic year occurs in early spring when I give my class of extremely bright graduate students, who have mastered quantum mechanics but are otherwise unsuspecting and innocent, a take-home exam in which they are asked to deduce superfluidity from first principles. There is no doubt a very special place in hell being reserved for me at this very moment for this mean trick, for the task is impossible. Superfluidity, like the fractional Hall effect, is an emergent phenomenon - a low-energy collective effect of huge numbers of particles that cannot be deduced from the microscopic equations of motion in a rigorous way, and that disappears completely when the system is taken apart ... The students feel betrayed and hurt by this experience because they have been trained to think in reductionist terms and thus to believe that everything that is not amenable to such thinking is unimportant. But nature is much more heartless than I am, and those students who stay in physics long enough to seriously confront the experimental record eventually come to understand that the reductionist idea is wrong a great deal of the time, and perhaps always... The world is full of things for which one's understanding, i.e. one's ability to predict what will happen in an experiment, is degraded by taking the system apart, including most delightfully the standard model of elementary particles itself."

        [R B Laughlin (1999): `Fractional Quantisation'. Reviews of Modern Physics 71: 863-874]

        The same basic effect - lower level entities only exist by courtesy of the detailed nature of the higher level structure - occurs all over the place in biology, for example in symbiosis, in ecosystems, and in the case of say blood cells in the human body.

        George

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        • Post #461

        Prof. Ellis, are physics and causation fundamentally limited to vision or visual experience?

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          • Post #462

          Hi,

          Your local/global variable example is a really good illustration of a really good idea. Forgive me if I'm preaching to the choir: Your illustration reminds me specifically of plain old thread synchronization, where a child thread's code executes (or not) based on the state of some parent-owned (non-local) lock variable with atomic read/write operations. Adding in dozens or hundreds of child threads all sharing the same lock, and it reminds me of one giant, complicated dance between the parent thread and the child threads, where both top-down and bottom-up causation play a critically important role (the children not only read the lock, they write to it). It is unusual for me to catch someone reveling so much in such a thing, and so I thought I'd try to share -- this computer stuff is fun and wonderful when you look at it the right way.

          - Shawn

          If you want to understand what physics is about, you should read a basic textbook on the subject. I suggest Conceptual Physics by Paul Hewitt. The chapter headings will give you an idea what basic physics covers:

          1. Mechanics; 2. Properties of matter; 3. Heat; 4. Sound; 5: Electricity and magnetism; 6. Light; 7. Atomic and nuclear physics; 8. Relativity.

          A more advanced text would include chapters on statistical physics and quantum physics, as well as topics such as plasma physics. Specialised texts will deal with biophysics, which is relevant to vision, but it is a very small part of physics.

          In response to a post by Peter Bokulich over on Massimo's blog (see my post here of Oct. 13, 2012 @ 08:53 GMT), I've now posted the following response:

          Hi Peter,

          I appreciate your approach. The key issue for me is that you agree that there are real high-level causes. Good. I agree that given the lower level dispositions of states resulting from those higher causes, the lower level physics gives a complete causal account; but overall, the causal account is incomplete without taking into account the way higher level causes lead to those specific lower level dispositions. A good example is a digital computer, where an engineering computation is taking place because a) C++ has been loaded as the current high level software, b) simulation software incorporating the relevant finite element algorithms has also been loaded, and c) specific initial data to run the relevant algorithms has been entered via the keyboard. The outcome that occurs is then a unique result of the lower level electronic states resulting from a), b) and c). However there is no way that the numerical algorithms embodied in the patterns of lower level excited states can be derived in a purely bottom up way from the underlying physics. It's a category error to assume that purely physical processes can lead to existence of any such algorithms.

          Whether we agree on causation or not depends on the weight you put on the words "nothing but" in the phrase "are nothing but constrained, structured, microphysical causal features". I think the explanation above says it's a mistake to use the phrase "nothing but", because significant other causal effects are at work. Part of the problem for a true reductionist is that the electronic gate states are "nothing but" specific states of quarks and electrons; and these again are "nothing but" excitations of superstrings - if they exist, which may or may not be the case. Which level are you claiming is the true microphysical level? The embarrassment for a true reductionist is that we don't know what the lowest level structure is - we don't have any viable theory for the bottom-most physical states. Thus if we take your phrase at face value, all physics is "nothing but" we know not what. Why not leave those words out?

          As to quantum indeterminism: it plays two significant roles. Firstly, it ensures that outcomes on Earth today cannot have been uniquely determined by initial conditions in the early universe, inter alia because cosmic rays have altered our genetic history significantly, and emission of a cosmic ray photon is (assuming we believe standard quantum physics) an inherently indeterminate process. The complex structures that exist have come into existence through emergent processes with their own logic that is independent of the underlying physics. Secondly, the most important such process is adaptive selection, which is guided by selection effects operating in a specific ecological context; and that is an inherently top-down process (see "Natural Selection and Multi-Level Causation" by Martínez and Moya in Volume 3 (2011) of Philosophy and Theory in Biology, available from Massimo's website). In the example just given, quantum uncertainty plays a key role in providing the repertoire of variant states on which adaptive selection can operate (without the cosmic rays, there would have been fewer such states to choose from). The conjecture is that perhaps something similar might be true in the way the brain works. But that's very hypothetical.

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            • Post #465

            Hi George,

            i always enjoy your insightfull comments here. Your example with the digital computer is, as always, very interesting. Some years ago i answered to Florin Moldoveanu here at fqxi in the same way. The question was if nature is as deterministic as maths, should mean, if nature is strictly deterministic or not and if there is something like a proof for this strict determinism. I argued that a strict determinism is a closed system as for example the Godel's incompleteness theorem and therefore - if strict determinism is true - this system cannot be consistent in every detail. What follows from this is, that it is inconsistent to try to achieve a proof of strict determinism via strictly deterministic procedures (for example via maths).

            Florin replied that a computer - and therefore the underlying maths/logics has to be strictly deterministic. I replied that it isn't guaranteed at all that for the same input and output data of a computer the QM microdynamics that lead to the same macroscopic results must necessarily be the same.

            A programming language like C++ surely is a man-made construct. It is based on logic, implemented into the hardware of the PC, but without the possibility of humans to exist, there would be no computers and hence no example of top-down causation to consider here. If one argues this way, we arrive at the well known anthropocentric questions about wether there is some special, "unphysical", determinism-contradicting entity in nature that enables consciousness, free will and so on or not. the main point for me here seems to be that, again there is no way to prove in a strict and deterministic way that the fact that there are observers possible in nature is a result of a strict determinism in nature.

            What i assume to be fundamental, - as i outlined in my essay here - is, that those regularily re-appearing undecidabilities (determinism/indeterminism, free will/subjective lack of knowledge, completeness/consistence, which-way information/interference, non-locality/non-reality etc.) stem from a CLOSED SYSTEM itself. This system i have labeled with "logic of opposites" - it doesn't allow -due to its inherent rules- the possibility of another logic that isn't grounded on mutually exclusive possibilities. This logic of opposites (Boolean logic) doesn't allow to contrast it with something that hasn't mutually exclusive features. Because this would contradict that there are only mutually exclusive features possible at all. The "something" i spoke of is surely close to QM and its features like superposition. Mathematically spoken, it is simply the abandoning of completeness in favour of having consistence and truth as the fundamental features of reality. If one considers the problem of mutually exclusive possibilities concerning the scientific/philosphical questions raised above, then it is possible to gain an insight that nature has some top-down, acausal features. Because by giving up the completeness criterion, we at the same time give up the "strictly deterministic" criterion. This is possible not due to arbitrary wishes but due to the consideration of systems in maths, cognition, complexity theory and so on. It is always the same pattern there: By giving up the assumption of closed systems, we gain - as Godel has proven on a deterministic basis BUT with some considerations to the necessity and stronger meaning of consistence over completeness - consistence and truth must be more fundamental than completeness. Otherwise sience would state itself as an inconsistent system and all our lines of reasoning would be highly questionable right from the beginning. That the latter could be indeed true in nature, is at least in my opinion, very unlikely, because of the huge success in science, physics and the human mind to decipher nature.

            The counter-argument of a strict determinism then can only be one that assumes a huge "coincidence" out of a somewhat wild "chaos". I assume the former to be true - on the grounds of my essay's considerations, and the latter to be absurd, inconsistent and illogical from the very start.

            "Coincidences" for me are then just another term to explain that QM-dynamics is fundamentally about generating consistence in nature - a result that i consider as somewhat very fundamental and meaningfull.

            Best wishes,

            Stefan

            Hi Stefan

            Thanks for that. Well the deep issue you raise is, "Is the universe causally closed?" My answer is, if you mean only the physical universe, the answer is no! Ok hackles are rising and squeals of protest fill the air, but please hear me out.

            This depends on issues of ontology: What kinds of thing exist? I addressed this in my paper True Complexity and its Associated Ontology. As in my essay, I define something as existing if it either (i) is a material entity, or (ii) has an undeniable causal effect on material entities. You'll find various non-physical examples there, but the key one for present purposes is:

            Mathematics and logic: A Platonic world of (abstract) realities that are discovered by human investigation but are independent of human existence. They are not embodied in physical form, but can have causal effects in the physical world.

            Roger Penrose [The Large, The Small, and the Human Mind], Alain Connes, and many others have argued for such a Platonic world of mathematics, which is not invented but humans - its nature is discovered by them (e.g. we did not wish to discover that the square root of 2 is irrational: we were forced to acknowledge that this is a mathematical fact through a process of logical investigation). How does it have a causal influence in the physical world? Through the human mind, which uses calculus and facts such as the value of pi as the basis for engineering calculations.

            The relevance to my previous post is that there is also space of all possible logical algorithms out there, waiting to be discovered. This is the ultimate source of computer algorithms. They become causally effective once discovered and implemented, but their existence is independent of such discovery. They are independent of time and place and culture, and (like mathematical truths) can be discovered by any intelligent beings anywhere in the universe. Thus for example there is a finite number of ways to sort a column of letters or numbers into ascending order. Any algorithm you may employ for this purpose will necessarily be one of this finite set of algorithms (e.g. Quicksort). They have causal power in terms of events in the physical world, because they lead to printouts of sorted numbers (which cannot exist if one does not employ one of these algorithms).

            So the world of material entities is not causally closed: it can be causally affected by abstract entities, such as algorithms, which underlie all computer operation. This is an existence proof for causally effective non-physical entities. There are other kinds of such entities , e.g. human plans for building a Jumbo jet airliner. My paper cited above discusses them.

            George