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Are We Living in The Matrix? The Quest for Non-Computable Physics(Part 1)

By JohnThomas Didymus
Posted Jun 30, 2012 in Science
The idea of Simulated Reality is based on a proposal of technical feasibility of implementing Virtual Reality indistinguishable from Reality. Not content with the proposal, some thinkers, such as Nick Bostrom, have gone as far as to suggest that our physical universe could actually be Simulated Reality. In pursuing arguments in favor of this radical suggestion, some thinkers insist on distinguishing the concept of "Virtual Reality" from "Simulated Reality," though in the final analysis, any Simulated Reality is Virtual Reality. In this way of thinking, Simulated Reality is distinguished from Virtual Reality by the criterion that participants in Simulated Reality cannot distinguish their world from Reality, even when they are aware that they are in a simulation, while participants in Virtual Reality would readily distinguish their world from Reality. The fact, however, is that Simulated Reality is perfection of Virtual Reality technology, for the power of any virtual reality system is essentially its ability to simulate Reality.
The question whether we could we be living in a Simulated Reality hinges on the assumption that there is Reality and that the notion of reality can be formally defined in distinction from simulation. But it becomes obvious, on careful consideration, that the criterion of "indistinguishability," in the context of the simulation argument, is inherently incoherent. If it is possible to implement Simulated Reality indistinguishable from Reality, in what sense then can it be said that the simulation is any less "real" than any other world we choose to confer with the status of Reality?
It seems that at the background of the concept of Simulated Reality is the assumption that there is an ontologically self-existent world or a reality that is not merely the output of computation or information processing as may be implemented on a computer machine. That this is true is questionable. With regard to our physical world in particular, we have not yet found any compelling reason to believe that it is not the output of computation being implemented on a machine. (On the contrary there are myriads of reasons to believe we may be living in a computed universe.) We would need to show that some aspects of the physics of our universe are non-computable to confidently assert that we are not living in Simulated Reality.
The physics of our universe is widely believed to be entirely computable (this argument is typically expressed in terms of Turing-computability which some thinkers consider falsifiable) and that, in principle, it is possible to implement, using a computer machine, a simulation of our world indistinguishable from our world itself. This assertion, however, comes with such qualifications (especially for Turing-type Machines as opposed to hypothetical hypercomputers) such as that computation need not be run in "real-time," and/or computation need not render simulations of events not being currently actively perceived.
The qualifications that computation need not be run in "real-time," and/or computation need not render simulations of events not being currently actively perceived would seem what obtains in our world with the Heisenberg Uncertainty Principle in which the state of a particle is undetermined until it is observed or measured. Proponents of the argument that our world is Simulated Reality often cite the Heisenberg Uncertainty Principle as evidence that our world is the output of a machine with limited computational power.
The physicist Bin-Guang Ma had, in 2005, attempted addressing the question whether we are living in Simulated Reality by generalizing from the relativity principle of physics. His proposal of "Relativity of Reality," states that we cannot define reality independent of an absolute reference and since there is no compelling reason to believe that there is an absolute reference, we may conclude that all realities have a potential to co-exist on equal grounds. What this means is that any reality that starts off, known to its participants as simulation of another given reality, may mature into a reality standing on equal grounds with its "parent reality" once the "indistinguishability" criterion is fulfilled.
Testing the hypothesis of Simulated Reality
The question whether we are living in a computational simulation turns, at final assessment of its merit, on our ability to determine whether our world is entirely computable or not. An entirely computable physical universe leaves wide open the possibility that we are living in Simulated Reality, and it is difficult to explain why an entirely computable universe shouldn't actually be a computed universe! (if it is a computable universe then it is a computed universe, seems a logically consistent maxim). The clinching evidence that our physical universe is not Simulated Reality would come if someone could suggest a model for non-computable physics and point to such physics in our physical environment. A model of non-computable physics which our world does not satisfy would suggest that we are living in Simulated Reality. A valid model of non-computable physics would also show the limitations of theoretical distinction between Virtual Reality and Simulated Reality for participants in any Simulated Reality will only need to show that the physics of their world is wholly computable to demote it from status of Simulated Reality to Virtual Reality.
If, however, we can, by any means, come to assured conclusion that non-computable physics is a non-feasible theoretical concept, then Bin-Guang Ma's "Relativity of Reality" hypothesis holds sway, for if all possible universes are wholly computable then any Simulated Reality stands on equal grounds with its "parent reality," as soon as the indistinguishability criterion is fulfilled and, thus, we must abandon the notion of Simulated Reality altogether and simply hold that realities, being computable, may reproduce themselves as biological systems do. We may note, in appreciating the full significance of this last statement, that the concept of reproduction is new and different from the concept of simulation. We don't consider a man simulation of his father but a reproduction whose reality stands on equal grounds with his father's. Without an established absolute reference, the notion of our world as Simulated Reality becomes inherently incoherent and we must replace the concept of reality simulation with the concept of reality reproduction and adopt the analogy of the biological process of reproduction to guide us in theoretical understanding.
What should the Physics of a "Real World" be Like?
We may approach the question whether we are living in Simulated Reality by first considering the question: If our universe were not Simulated Reality what should we look for to confirm the fact? I shall propose that a potentially valid approach to tackling this riddle begins with examination of the largely unexamined native intelligence assumptions we hold about the physics of our universe which arise from our assumption of its reality, but which, in development of scientific knowledge, turned out very mistaken. The validity of this approach hinges on the conviction that if we are looking to build up a picture of the physics of a real world as opposed to a simulation, we should not be looking for "glitches" or "bugs" in the physical world system, as some theorists have suggested, rather we should be carefully considering those aspects of the physics of our world, as revealed by science, that run so wildly counter-intuitional as to seem to us, from the perspective of our native intelligence assumptions, flaws in the reality system.
This approach hinges on the conviction that a worlds programmer constructing Simulated Reality in a hypothetical real world could be expected to attempt to contrive the world of Simulated Reality he is constructing with superficial appearances of the real world in which he is living. In a Simulated Reality system any worlds programmer would construct, superficial appearances would coincide with the body of unexamined assumptions about reality inmates of the simulation hold such that when they (inmates of the simulation) begin close-up scrutiny of superficial appearances of their world, they would be struck by how unlike their expectations of Reality their world turns out.
What are the revelations of modern physics with regard to our world which seem to us so counter-intuitive and run against our most basic native intelligence assumptions of what our physical universe should reveal of itself at close scrutiny?
The revelations of quantum physics about the structure of our world at the small-scale are the most unexpected revelations of science relative to our native intelligence assumptions about the largely unexamined concept of "Reality." Nature is not structured nor does it behave at the small-scale in the way we had expected, judging from the presentations of its reality in what is termed "classical physics." The last century of development in physics has been not only a struggle to come to terms with the "can of worms" unveiled with regard to constitution of our world at the small-scale but one of yet unresolved conflict between the physics of our world at the small-scale and the physics of our world at the large-scale. It would seem as though two separate sets of irreconcilable laws govern the realms of the large and small-scale of our world structure.
Psychologists say young children often report that culmination of an operation of fractional analysis on an object is "nothing": that is, if you continue dividing an object you would finally derive a fraction of the whole with magnitude zero ("nothing'"). The significance of the child's assumption is that the human intellect has a strong tendency to assume a continuum in extension of space and time, that is, a manifold which actually converges to a zero-point at the small-scale. And nothing in a child's experience of reality suggests otherwise. It would take an adult with knowledge of the arithmetical process of division and limits to pause in confusion and wonder whether space could so converge.
So strong is our tendency to assume a continuum with regard to extension of space and time that not even presentation of the Zeno paradoxes (c. 450 B.C) would convince mathematicians and physicists of a necessarily fragmented spacetime structure before the Planck constant was established as a fundamental property of "action" in physical spacetime. Einstein continued laboring till his death in the quest for a Unified Field Theory based on assumption of a spacetime continuum and spacetime singularities (zero point convergences of spacetime). It would seem that nature pre-equips us with native intelligence assumptions which hinge our convictions of reality of our world on assumption that its manifold is a continuum. So counter-intuitive is the notion that motion or transformation in our world is indistuguishable from motion or transformation in a Mickey Mouse cartoon animation that we still continue to resist working out the full philosophical implications to our naive materialistic-physicalist conviction that the physical universe is self-existent reality.
The Planck Unit of physical spacetime is the single property of our world which makes its physics computable. A reality with a real spacetime continuum would present us with non-computable physics. Our physical world simulates appearance of a continuum misleading us into believing that our intuitional notions of its ontological substantiality are actually fulfilled at the small-scale. Quantum Physics demonstrated to us otherwise, and opened up to scientific culture and thought, traditionally steeped in materialistic philosophy, new avenues of speculations on the possibility that our world might, after all, share more than we ever suspected in common with online Virtual Reality worlds.
This article is first in a series by JohnThomas Didymus published in Perpectives and Symbolism. You may read the entire illustrated series here.