DP and Me:

I found the article interesting and stimulating in its description of Digital Physics, a field that was outside of my awareness before, though the basic concepts are familiar.

The transition in the final two paragraphs, however, puzzles me. It would seem to me that this idea of God as programmer and the universe as his program leads me to a conclusion that is in opposition to that of the author. I, and all other people, as a part of that created universe, are merely subroutines of the master program. Where does free will come in?

The author responds: Both reviewers take from my essay that DP leads to the conclusion that "I, and all other people, [are] part of that created universe . . . merely subroutines of the master program." In the original draft, I incorrectly stated that I imagine myself as a "character" in God's virtual reality "game," and I can see that this does indeed imply that I see myself as part of the programming. Although this is one possible conjecture (and it is the metaphysical position implicit in the motion picture The Thirteenth Floor), it is not a necessary conclusion flowing from DP and it is not my view.

Using the metaphor of the computer simulation, I see myself as the user -- the person playing the game and interacting with, but not part of, the programming. In my judgment, the most persuasive interpretation of QM (referred to below) supports the conjecture that conscious beings (humans) are not part of the created universe -- at least, not in the same way as the sun, moon and stars. Accordingly, I have modified my essay to read, "I can look around and imagine myself as an interactive participant in the virtual reality simulation programmed by God," and I have added a paragraph which attempts to make explicit the correspondences of the metaphor. I see myself as the user, not the programming and not the machine, and I regret the confusion.

The scientific question is whether quantum mechanical systems are "collapsed" into a definite state by intrinsic qualities of the system itself; or whether the appearance of definiteness requires the intervention of something outside of the system. The speculations fall roughly into two categories: first, that some as-yet-undetected physical mechanism operates on the elements of our universe when the physical system reaches some undefined level of complexity. This supposes that the quantum effects we note on the sub-sub microscopic scale disappear at the macroscopic scale because of some unknown type of self-measurement going on within the system. The second category of speculation is that something outside of QM itself operates on the system to produce a result. It is the je ne sais quoi that turns mathematics into material upon measurement or observation, and it can be termed "consciousness" or "mind" or perhaps "soul".

The latter approach, which I favor, has been urged by Eugene Wigner[1] and John Wheeler,[2] who argue the experimental results and logic to conclude essentially that a QM "measurement" is not complete until it has been received by a conscious entity such as a human being. Others are decidedly skeptical, insisting that scale and complexity alone, or hidden variables within the system, or some other intrinsic mechanism, must suffice to produce the experimental results. John Polkinghorne is an example of one who is skeptical that humanness has any special place in the greater scheme of things.[3]

The scientific debate is unresolved, but the author is convinced by Wigner and Wheeler (and by proclivity) that QM is the program and consciousness is an attribute of the user. This conclusion is bolstered in the context of DP by Roger Penrose's argument that true consciousness cannot be achieved by a computational system.[4] This implies that human consciousness is not a part of the program, not generated as subroutines: we are "other". We exist independently of the program, probably in the same realm as the computer itself, perhaps in the realm of the programmer. In the same way that a video game player "measures" the space and landscapes and characters inhabiting a particular room by manipulating the joystick to bring it on screen -- thereby making that room appear as dots on the computer monitor (while all other rooms remain inchoate as programming on the CD-ROM which is not needed at the moment) -- so our consciousness "measures" the states of QM quantities which affect us and leaves undisturbed those which do not. By this interpretation, we humans are "players" and not "scenery" (and not scripted "characters").

The question of free will is answered in this analogy. Just as a game player/user has free will to turn left or turn right, to rescue or destroy an opponent, to act and seize the prize or hesitate and be destroyed, so the human has free will to operate within the universe created by God. Exercise of this free will must affect the outcome of the simulation for the individual player (for the individual human) and for those with whom the user comes into contact (think of networked, interactive, multi-user games). However, it cannot affect the game itself any more than the user can change the digits burned into the CD-ROM placed into the computer's drive. Nor can it impinge upon the prerogative of the programmer to dictate an ultimate conclusion by literal deus ex machina, nor even to substitute an improved game, version 2.01, as a new heaven and a new earth (Isa 65:17 and 66:22; 2Pet 3:13; Rev. 21:1).

Also, computer science has some interesting results regarding the limitations of computation, in particular, that there are well-defined problems for which there is provably no possible computer program for solving them. Doesn't this place a limit on God?

The author responds: While I am aware of some of the limits of computation, I do not agree that these might limit the programmer in any sense which affects the subjects of the simulation. Alan Turing initially defined certain problems that were not computable. The halting problem comes to mind. Also, there is Goedel's Incompleteness Theorem which appears to show that no computational system -- no formal system of propositions which is what a computer program is -- can be complete unto itself. (These are arguments used by Penrose to show that computers are incapable of innate consciousness.) However, Fredkin actually makes use of the halting problem to argue that DP can emulate quantum randomness (see comments to reviewer #2). Nor do I expect this material world to be perfect or complete in the way that God is perfect and complete.

If I am making music, I may be "limited" by the tools I choose. If I choose an oboe, there are certain sounds I will never produce; if I choose a piano, my range is extended but still limited; if I choose a computerized digital synthesizer, my range is extended further but still finite. However, I do not feel that these limitations of my choosing -- or even in what is at hand for me to choose -- define me as a musician. Similarly, I do not have any sense that God is a limited God because he chose to create a digital universe for his children, any more than if he had built them a tree fort.

I have not included any specific response to this concern in my revision, as it seems to call for a more detailed discussion than the short essay will bear and I do not feel I have any ready answer apart from the above. However, I have qualified the assertion that "nothing is impossible with God" by continuing, "just as nothing is impossible with the programmer who created and controls all things with respect to the subjects of the simulation."

And the computer program metaphor seems to argue against divine intervention rather than support it.

The author responds: The cellular automata computer architecture posited by DP indeed argues for the evolution of complexity in the material world by unattended operation of the rules, and against micro-management interventions at the level of commands for causing a mulberry tree to uproot itself and be planted in the sea (Lk 17:6). For this reason, I tend to side with the evolutionists and against Creationists on the question of whether God decided what he wanted humans to look like and then molded them since, in my view, the shape of the earthen vessel is completely beside the point. On the other hand, the large if not infinite possibilities of the digital computer itself supply endless varieties of programming techniques of which strict CA is only one -- a facility which makes the Fredkin Hypothesis "too easy" in the words of one reviewer. My own feeling is that there are other programming features at work not yet incorporated in state-of the-art cellular automata. However, I recognize that this is something of a punt on the question.

I have attempted to address this concern in my discussion of the Newtonian clockwork model, added toward the end of the essay.

So, though I think there is some value in thinking of God as a computer programmer, and this article sets the table for this, the last two paragraphs yank away the table cloth and bring the dishes crashing to the floor.

The author responds: I think that is a bit strong. I have revised these paragraphs somewhat, and I have included other qualifications throughout acknowledging that different views are possible within the basic DP hypothesis. However, the conclusion of the essay doesn't really purport to be anything but a personal credo, and I do not see that it is contradicted by anything that precedes it. If the basic problem stems from the regrettable reference to myself as "character" and the attendant misunderstanding about my views on free will, then perhaps the reviewer will be content to indulge me. Otherwise, I can only hope that the disagreement will provoke further comment such as the reviewers have provided.

Reviewer #2 (Physicist)

In this article, Ross Rhodes presents a thesis that the universe is basically a large computer program being run by God. While I am not opposed to the journal publishing such a view, I feel that this is really a very old concept hidden in the language of technology. Following Newton and the beginning of the scientific process of modeling the universe via differential equations the clockwork model of the universe was discussed and accepted by many. The idea was that the universe was created and then set in motion to run itself out like a predictable clockwork mechanism. Elaborate and complex mechanical models of the solar system, which would run to demonstrate eclipses and other phenomena were constructed. The view of the author is essentially this model with the twist that we have a "computer program" rather than a mechanical mechanism. The author has a slight variation in that it seems that God has more freedom to reprogram the system and provides a more active sustaining role for God than in the traditional clockwork model.

The author responds: This is a most difficult comment, and I must leave it to more general philosophers to exegete the nuances among world views. However, it seems to me that such distinctions as "a 'computer program' rather than a mechanical mechanism," and "God has [complete] freedom to reprogram the system" and "a more active sustaining role for God than in the traditional clockwork model" are by no means trivial. One might as well opine that Einstein's view of the universe was only a slight variation on the Newtonian model, incorporating Lorentz transformations of coordinate spaces and throwing in a few extra terms to account for the constancy of light speed. (I seem to recall reading comments along this line by quantum physicists arguing that their science is more revolutionary than general relativity.) For myself, imagining myself as a participant in God's computer simulation has an entirely different quality from imagining myself caught up in God's clockwork.

There are, as well, many more antecedents to the computer model. The dichotomy between the user and the programming recalls Bishop George Berkeley's 18th century reaction against the Newtonian clockwork model through a strict idealist vision of matter which exists only as a perception of mind -- a view which echoes in Christian Science doctrine. Note however that the computer simulation model does not insist that the programming is dependent on the mind for its existence, but only for its manifestation.

The DP hypothesis is consonant, in part, with many such world views, ancient and modern. It is an encompassing metaphor for the universe -- something that Schrödinger thought to be quite beyond reach -- and a satisfying explanation for why the universe appears to be fundamentally tied to mathematics in the same way that a computer program is tied to its algorithms. I do not see it as criticism that DP leads to a world view which recalls elements of earlier philosophical speculations, from Plato through the Principia and beyond. How could it do otherwise?

The best I can manage in my revision is to suggest some promising comparisons, including a very brief reference to the clockwork model and to Berkeley's idealism, which I have done in the new paragraphs of the essay.

The author responds: On the question of free will and the unwarranted implications of my original draft, see my remarks to reviewer #1.

With respect to the ease, I, too, find the model easier than any other proposed conception of quantum reality -- by several orders of magnitude. Having delved into the many worlds thesis, the mechanics of Bohm's hidden variables, and others, I find them not so much impossible as hideously contrived. The computer model, by contrast, is wonderfully simple and accessible. And although some approaches to programming an emulation of the universe might be as complex and contrived as any of the above, the CA model again brings us to simplicity itself. But simplicity and ease are not bad qualities for an answer. William of Occam first took his "razor" to the multiplication of souls proposed by Aquinas, and since that time the most elegant answer has generally been reckoned the most likely.

The author responds: In his seminal papers, Fredkin acknowledges that true randomness is impossible in a digital universe. To obtain a suitably isomorphic model of QM, Fredkin proposes an alternative involving "unknowable determinism." In brief, Fredkin describes the operations of a cellular automaton in which there is no slack in the computations. "Every part of space [every cell] is computing its future as fast [as] possible, while information pours in from every direction." The consequence is that there is no shortcut to obtaining the eventual result. Even in principle, and following a deterministic set of rules, a programmer would have no choice but to simulate the operations of the particular cellular automaton, input the initial conditions (which would be the "state" of every cell in the universe of the cellular automaton), and run the program to find out what happens. The result, according to Fredkin, is that randomness emerges as an apparently intrinsic quality of the system as far as any observer can discern. This may be seen as a computer science analog to a "hidden variables" approach to QM, incorporating the flavor of chaos theory to explain how deterministic rules can result in something that cannot be determined in advance, even in principle.

Other solutions have been discussed in the digital physics community[5] and there is not as yet any widespread consensus. This week's Science notes that a good form of randomness can be achieved by obtaining input from outside of the computer's programming, rather than from an algorithm.[6] So far as my original draft may have implied that computer science has already achieved a true emulation of QM, randomness and all, I have clarified the point in revision by substituting "simulate" for "reproduce" in the third paragraph, and "mimic" for "model" in the fourth paragraph. I have also added a brief reference to Fredkin's efforts to deal with the acknowledged limitations of digital computing, which were necessary before he could propose DP in the first instance.

The author responds: This comment ("a great number of other systems") suggests that there is a problem with CA of which I am not aware, and which I have not been able to discover. There are indeed many mathematical problems which can be more easily solved by other algorithms, but you can't create a universe by hard-wiring the solution to a quadratic equation. In general, CA seems well-suited to applications in quantum field theory. "In terms of structure as well as applications, [cellular automata] are the computer scientist's counterpart to the physicist's concept of a 'field' governed by 'field equations'."[7] CA also offers a potential model for the sum over histories approach of QED because information affecting all neighboring cells literally takes all paths to all destinations. Similarly, it offers a good conceptual basis for the thorny problem of QM's ubiquitous waves propagating without any medium.

Apart from the question of randomness (referred to above and inherent in any computer architecture including CA), the principal objection that I have found to CA as a quantum modeling tool seems to be that it does not easily lend itself to non-local effects. That is, if we accept the EPR paradox, Bell's Theorem, and the associated (and ongoing) experimental verifications of these, then we may have to accept some form of non-local interactions in our world. CA, on the other hand, is based fundamentally on local interactions -- the interplay of each cell with its immediate neighbors according to their programmed rules. As one person familiar with CA puts it, "The concept of a cell for each point in space interacting only with its neighbors pretty much precludes you from building a non-local model."[8]

Fredkin did not address non-locality in his exposition of a CA universe, and there does not appear to be a consensus about it in the DP community. Following on Fredkin's solution to the randomness problem, it may be that non-locality is an "emergent" characteristic, i.e., necessarily appearing to the user but actually incident to some other computational process. Analytically, the problems of randomness and non-locality have some overlap.

In any event, considering the fits that non-locality gives to every other variety of theoretical physicist, it seems unfair to hold this against DP's reliance on cellular automata. Generally speaking, the computer is a particularly good metaphor for the concept of non locality because, for example, two apparently independent and unrelated pixels at opposite sides of the monitor may be intricately connected in the programming. Bear in mind that CA is not really a collection of independent computers, but a single computer running a collection of identical subroutines. Since the "cells" are never truly independent (or, at least, are never more independent than the programmer wishes to make them), it would be possible in principle to allow for interactions with whatever other cells are called for, regardless of whether they are defined for purposes of the simulation as "neighbors." This would seem to mar the beautiful simplicity of the CA model which is its most appealing quality, but it is not forbidden.

I have not addressed these concerns in my revision, first, because I am not entirely sure that I understand the comment, and second, because the discussion seems a bit more technical than I had intended for the essay.

The author responds: The predominant attitude I have come across with respect to the wavefunction is that it is a mere calculational tool, and not an independent reality.[9]

Be that as it may, the question of reality becomes somewhat confused in the digital physics model and metaphor, because one must refer to perhaps six realms of experience, each with distinct attributes. These are 1) the physical world, which corresponds to the images projected on a computer screen; 2) the process that defines the physical world (the "wavefunction"), which corresponds to the underlying programming code; 3) the process of measurement governing the interpretation and projection of the data, which corresponds roughly to the user interface; 4) the non-corporeal existence of the conscious being (me), which corresponds to the realm of existence of the user when not engaged in the simulation (i.e., that which we would experience if the simulation terminated and we walked out of the arcade); 5) the realm of the universe-generating mechanism itself, which corresponds to the room and machinery of the ultimate computer (which may or may not be the same as the realm of the user); and 6) the realm of God, which corresponds to the existence of the programmer (and which, again, may or may not be the same as the realm of the user and/or the machinery).

In asking whether the subject under contemplation is "real," I tend to use a Cartesian touchstone: "Does it have separate and independent existence in the same way that I think and, therefore, am?" Employing this criterion, realms 1, 2, and 3 appear artificial and, to my way of thinking, do not constitute "reality"; realms 4, 5, and 6 have at least the same level of existence as my consciousness and, accordingly, I think of them as "real." This is not to say that the universe, with its underlying programming and processes, has no existence. The wavefunction certainly exists independently of me -- I cannot change it -- just as my computer's operating system and applications exist; however, it is plainly a different order of existence from that of the user. Perhaps it would be best to discard the distinction between real and unreal, and simply stick with the metaphor as parable.

In revision, I have qualified my thumbnail of the Copenhagen Interpretation to state that "there is no underlying physical existence associated with the fundamental units of our world." I have also added a paragraph in which I attempt to make explicit the correspondences of the metaphor.

The author responds: If I understand this comment correctly, the reviewer is saying two things: first, that "erasing" is not a good description of the effect of measuring one complementary property on its partner; and second, that measuring one property (which happens to have a complementary property) may have no effect whatsoever on other properties which are not complementary to that property.

To the first comment, my use of the word "erasing" was limited in a strict sense to the situation where the complementary properties being measured are quantized in an either/or relationship. Thus, I speak of measuring spin and thereby losing all definiteness regarding a previous measurement of angular momentum. If one has lost all definiteness regarding previously acquired knowledge, one must make a new measurement which will bear no relation to the previous measurement of the same property of the same quantum unit. This seems equivalent to erasure in the computer analogy, but perhaps there is a distinction to be made.[10] Discretion being the better part of valor, I have revised the essay to erase the reference to "erasing effect," substituting an allusion to "the inconstant qualities of computer variables." I hope this addresses the reviewer's concern.

To the second comment, I do not see any conflict between my reference to one aspect of QM (the measurement effect with respect to complementary properties), and an altogether different aspect (the lack of a measurement effect with respect to other properties). Perhaps the reviewer felt that my statement implied a broader application than intended. In any event, I hope that removing the reference to "erasing" will eliminate the controversy.

Notes

1. [Back]	E. Wigner, "Remarks on the Mind-body Question," in The Scientist Speculates, I.J. Good, ed. (Basic Books, New York 1961); also reprinted in J.A. Wheeler and W.H. Zurek, eds., below.
2. [Back]	J. Wheeler and W. Zurek, ed., Quantum theory and measurement (Princeton University Press, 1983).
3. [Back]	J.C. Polkinghorne, The Quantum World (Princeton Univ. Press 1984) at 64-67.
4. [Back]	R. Penrose, Shadows of the Mind (Oxford Univ. Press 1994).
5. [Back]	Tom Ostoma and Mike Trushyk, "Cellular Automata Theory and Physics: A New Paradigm For The Unification of Physics," Los Alamos National Laboratory e-Print archive (1999).
6. [Back]	"Pick a Number From 1 to 2^32," Science, vol. 289 no. 5476 (7 July 2000) at 7.
7. [Back]	T. Toffolli, "Non-Conventional Computers" in J. Webster, ed., Encyclopedia of Electrical and Electronics Engineering, John Wiley & Sons (New York 1998).
8. [Back]	Jim Calfas (comment in Digital Physics e-mail list, July 3, 2000). I am indebted to the members of the Digital Physics mailing list for their comments on this question.
9. [Back]	E.g., N. Bohr ("The entire formalism is to be regarded as a tool for deriving predictions, of definite or statistical character, as regards information obtainable under experimental conditions described in classical terms"), quoted in J.C. Polkinghorne, The Quantum World at 79 (citing M. Jammer, The Philosophy of Quantum Mechanics); N. Herbert, Quantum Reality at 95 ("Most physicists treat the wave function as a mere calculation device, not as a real wave located somewhere in space"); but see J.C. Polkinghorne, The Quantum World at 80-81 ("[I]t is . . . difficult to think of a wavefunction as a mere calculational device . . .. [The waveform] is certainly the object of quantum mechanical discourse and, for all the peculiarity of its collapse, its subtle essence may be the form that reality has to take on the atomic scale and below").
10. [Back]	My thinking on this owes much to the discussion by David Z. Albert in the first chapter of his book, Quantum Mechanics and Experience. If Mr. Albert has simplified the physics for the purpose of illustration, then I may well have simplified the concept in a way that is subtly different, perhaps even wrong. (Mr. Albert does not himself suggest erasure as an explanation.)