Notes on a Cosmology - Part 18, Virtualization

In the 2016 Isaac Asimov Memorial Debate, Is the Universe a Simulation?[1], David Chalmers makes the following remarks:

The simulation hypothesis says we’re in a computer simulation. A computer simulation’s a computation that was created by someone for a purpose. So, basically, the simulation hypothesis is the computation hypothesis plus something else about someone who created it. And around here is where you might be able to get a little theological and say, okay, well, it’s a naturalistic version of the god hypothesis. [There is a] much weaker hypothesis that the universe is some form of discrete computation and is completely neutral on the question of whether this is actually a simulation in the sense of something that was created by a simulator.

What Chalmers is talking about is telos. Telos is generally associated with theology these days, but many science-fictional universes have imagined telic theories of our world based on design by a non-deity. Perhaps our world was created as a scientific experiment by alien-like beings who are able to engage in interstellar travel as easily as we drive down a highway. Or choose your favorite theory. Because any arbitrary way of imagining a telic origin for the world is as good as any other, we tend to throw our hands up and choose an atelic basis for science. If we have been designed by a greater being (or beings) then, until this is revealed to us, we have no scientific basis to ascertain design or rule it out - it is a metaphysical or theological question.

Telos does not necessarily have to involve personhood, as humans experience it. For example, animals clearly make choices but are also clearly not self-reflective persons in the sense that human beings are. Imagine some inter-galactic, animal-like consciousness with the ability to spawn life-bearing planets but unable to comprehend the complex behavior of the living systems in those planets. In this case, we have been created by a telic entity that is greater (more powerful) than us but which is less intelligent than us.

Virtualization

In modern computation, virtualization is a widely used technology. Virtualization is a consequence of the capacity of a universal Turing machine, U, to simulate any other Turing machine, including itself or any other universal Turing machine U', U'', ... As a concrete illustration, the following image depicts a recent version of Windows Server running multiple, nested instances of itself:

In the context of computer science, we tend to use the terms "simulation" and "virtualization" synonymously. But in the context of cosmology, simulation tends to mean simulation of something, that is, of the laws of physics, or whatever. In this context, all simulation can be considered a kind of virtualization - in short, virtualization is a more general term than simulation. In this post, we will be focusing on virtualization in order to think about computers simulating other computers without respect to any external system, such as a physical universe. This distinction is related to, but independent of the distinction between a computation hypothesis (no telos) and the simulation hypothesis (telos).

The particular feature of virtualization I want to focus on is termed privilege level. When two or more computation environments are executing on the same hardware (same CPU, same memory banks, and so on), there must be some organized system of sharing resources in such a way that the parent environment is not corrupted by its child environment(s). Otherwise, when the parent environment launches a virtualized child environment, that environment is liable to crash the parent - and itself, too. In real-world computation systems, this protection is enforced through privilege levels. A lower-privileged process may not access the resources of a higher-privileged process. There are many different ways to implement privilege levels. Non-virtual privilege levels have long been a common feature of mainstream operating systems, allowing the operating system to protect itself from the applications it is running. But so-called "full virtualization" requires a more thoroughgoing approach to ensure that the system's resources cannot be accessed by virtualized environments in a way that will corrupt the host (parent) environment.

A common, naive approach to enforcing privilege-levels is to check each access that the lower-privileged environment attempts. "If a lower-privileged environment attempts to access the higher-privileged memory area from address 1000 to address 2000, interrupt it and transfer control to the higher-privileged environment so it can decide what to do next." I will refer to this as hard privilege level enforcement. In modern virtualization systems, however, much of this hard privilege-checking is bypassed by simply presenting a virtualized memory and input/output environment to the virtualized process. In this way, the virtualized (child) process is free to access any memory address it likes, but these addresses are silently remapped by the computer hardware to other memory addresses. Since the virtualizing (parent) environment controls how this remapping occurs, it is able to arrange memory in such a way that the virtualized (child) environment will never be able to touch the parent's memory and other resources. I will refer to this as silent privilege-level enforcement.

Choice

Our cosmological theory up to this point has been summed up by the concept of the quantum monad. The quantum monad is the union of the universal prior and Seth Lloyd's QC thesis (that the Universe is indistinguishable from a quantum computer). What is missing from this model is any kind of concept of choice. The universal prior is, in a way, too powerful - it ranges over every possible universe, including the ones in which I choose A and the ones in which I choose the opposite of A. Thus, every game-theoretic interaction between you and me (choice) is present in the universal prior, and all of them are equally probable. Thus, there are no choice strategies in the universal prior - the universal prior moots game theory.

In the context of artificial intelligence, Hutter proposes a particularly concrete notion of “possible world”: An environment, in his sense, is a Turing machine which takes an agent’s actions as input and produces a sequence of observations and rewards as output. Given a prior distribution µ over environments, Hutter defines a Bayesian agent AIµ which acts in such a way as to maximize the expected reward, given µ. As usual, Hutter assumes that for every particular environment, AIµ can compute exactly what observations and rewards a given sequence of actions leads to.

However, AIµ cannot in general itself be implemented as a Turing machine, which is problematic in game-theoretic contexts (where an agent’s environment contains other agents). To see this, consider the game of Matching Pennies, in which two players each choose between two actions (“heads” and “tails”); if the players choose the same action, the first player wins a dollar, if they choose differently, the second player wins. Suppose that both players’ decision-making processes are Turing machines, and suppose that both players know the exact source code of their environment, including the source code of their opponent’s decision-making algorithm. (Certainty about the environment is of course equivalent to a µ which assigns probability 1 to a certain environment.) Finally, assume that like AIµ, both players choose optimally given their information about their environment.

In this set-up, by assumption, both players’ decision-making processes are deterministic; each player either definitely plays “heads” or definitely plays “tails”. But neither of these possibilities is consistent. For example, if the first player chooses heads and the second player can predict this, the second player will choose tails, but if the first player can predict this in turn, it will choose tails, contradicting the assumption that it chooses heads.

The problem is caused by the assumption that given its opponent’s source code, a player can figure out what action the opponent will choose. One might think that it could simply run its opponent’s source code, but if the opponent does the same, both programs will go into an infinite loop. Even giving the players access to a halting oracle does not help, because even though a machine with access to a halting oracle can predict the behavior of an ordinary Turing machine, it cannot in general predict the behavior of another oracle machine.[2]

Another way to understand the problem is to imagine two AIXI machines connected together in such a way that each is the other's environment, that is, µ, and the only way to maximize their own reward function is to minimize the other's reward function. No matter what we assume about how these machines will behave in respect to one another, we arrive at a contradiction. Thus, the AIXI model is simply not suitable for use in a general game-theoretic sense. The paper proposes reflective oracles as a technical solution to the problem but the technical details are outside the scope of this discussion.

Let us now embark on a thought-experiment. Suppose we have two computable approximations to AIXI - AIXIc₁ and AIXIc₂. Furthermore, let us suppose that AIXIc₁ and AIXIc₂ have access to m- and n-bit prefixes of Omega, respectively. That is, AIXIc₁ has access to Ω_m and AIXIc₂ has access to Ω_n where m > n. This access is tantamount to private information. AIXIc₁ has an advantage over AIXIc₂ in that it can solve 2^m-n times more instances of the halting problem in computable time than AIXIc₂ can. This might not seem like such a big deal - after all, who cares about whether such abstract machines will halt or not? But remember that we can solve any mathematical problem whose solution can be found with n bits of theory by encoding it in an n-bit program and then solving whether this program halts. In fact, as long as we allow m to become sufficiently larger than n, AIXIc₂ will never be able to defeat AIXIc₁ in any competitive game[3].

The Great Chain of Being

Now, I can explain a third kind of virtualization privilege-level enforcement that I will call soft privilege-level enforcement. In this arrangement, the child process is free to move anywhere, and the parent (virtualizing) process simply "steps around" the child (virtualized) process. This is only possible if the parent process is always a step ahead of the child process, moving its own resources out of the way before the child process is able to inadvertently trample over them. We can model this situation as a game being played between two agents, where the child process is more or less behaving arbitrarily but the parent process is anticipating the child process's moves. We model the parent process as AIXIc₁ and the child process as AIXIc₂ and we define the losing condition as any situation where AIXIc₂ has accessed the parent's resources in a way that will corrupt the parent's state. To clarify, we are treating the source code of each of these agents as accessible to one another. The only thing that AIXIc₁ has access to that AIXIc₂ does not are the additional bits of Ω from n to m.

As long as we make m sufficiently larger than n, we are guaranteed that the child process will never be able to corrupt the parent process's state even though the parent process has not implemented any form of privilege-level construct, whether hard privilege-levels or silent privilege-levels. In short, the parent process and the child process are operating as peers with respect to the available computational resources but the parent process is able to virtualize the child process without becoming corrupted by anticipating the behavior of the child process and moving its own resources elsewhere. Since the child process can read the parent process's source code, it can attempt to intentionally anticipate the parent's next action and force it to become corrupted. But this fails because the parent process is, in every respect, more efficient than the child process, so the parent process can (for example) simulate the child process's attempt to simulate the parent process (ad nauseum) and take the appropriate action to prevent corruption.

The significance of this idea is that we can talk about telic simulators without having to posit any special "hook" or "power" that such simulators have that their simulated environments do not have access to. Perhaps we are being simulated but this does not necessarily mean that what is simulating us has implemented hard privilege-levels (think solid walls) or silent privilege-levels (think illusions). Rather, all agents are operating on the same "hardware", so to speak, and playing by the same rules. The difference between levels of simulators can then be modeled as simply knowledge of a larger or smaller prefix of Ω. The virtue of this approach is that we can abstract away all other considerations - all differences in the "levels" of the simulation boil down to how much of Omega each level has access to.

This construct resembles the gnostic theology known as the great chain of being. Greater beings are able to (and do) dominate and rule over lower beings. This dominion is based on the varying splendor or worthiness of various kinds of beings.

We can also take this in a more naturalistic direction by looking at it from the point of view of the Kardashev scale. Suppose we compare civilization A and civilization B that are the same in all respects except that civilization A knows one more bit of Ω than does civilization B. We can say that civilization A is objectively more advanced than civilization B. As we noted earlier in this series,

[Chaitin has suggested] that knowledge of Omega could be used to characterise the level of development of human civilisation. Chaitin points out that, in the 17th-century, the mathematician Gottfried Leibniz observed that, at any particular time, we may know all the interesting mathematical theorems with proofs of up to any given size, and that this knowledge could be used to measure human progress. “Instead, I would propose that human progress—purely intellectual not moral—be measured by the number of bits of Omega that we have been able to determine,” says Chaitin.[4]

We can think of the bits of Ω as forming a kind of competency-hierarchy - "Everything you can do, I can do at least as good, or better" is true whenever I know one or more bits of Ω than you do. Thus, I can effectively enforce privilege-limits on you without the use of unconditional privilege-levels.

Hypotheticals and Parallel Universes

When pondering a decision, we often engage in a kind of hypothetical thinking - "If I turn left here, it will take me down Main Street which is a shorter route to my destination but traffic is heavy. Instead, if I go straight on Oak Street, the route is longer but less busy. I think I will go straight." In computer algorithms, this kind of thinking can be implemented with a technique called backtracking. Equivalently, we can model any backtracking problem as a non-deterministic algorithm and convert it to its deterministic equivalent using a technique called subset construction.

Backtracking systematically maps the possible solutions to a problem onto a tree. If we think of the computer as an agent, this tree can also be thought of as a decision-tree. "If I try this alternative, then the result is such-and-such. This does not match the required solution. So, I must backtrack and try the next alternative."

We can also characterize hypothetical thinking as a form of simulated parallel universes. For example, suppose I want to predict the outcome of a very complex set of events, such as, "Will North Korea go to war with the United States under such-and-such conditions?" One way to approach this problem would be to build a toy model of the entire population of each country and simulate the behavior of the populations under varying conditions. This is, at present, completely infeasible but it is possible in principle. Such questions are too complex to be answered by shortcut methods, that is, by aggregated models (population dynamics). If we imagine expanding the complexity of the questions we are asking in both depth (resolution) and breadth (expanse), we can imagine reaching a point where we want to be able to simulate an entire planet or, when we begin to colonize space, even larger scales. Such simulations of hypothetical futures would be so rich in detail that they would be worlds in their own right. Nevertheless, being rooted in the physics of our spacetime, they would remain purely hypothetical.

If a "greater being" simulates lower beings than itself, this is a bit like encapsulating these lower beings within a subset of the wider set of possible universes. When a backtracking algorithm searches for a solution, it does so by pruning the tree of possible solutions, leaving fewer and fewer possibilities out of the set of all possibilities. In fact, we can imagine a parallel backtracking algorithm that spawns lower-privilege instances of itself to explore the tree of possibilities - when these instances find what the higher-privilege process is looking for, they are no longer needed and can be terminated. The higher-privilege process does not have to worry about being corrupted by the behavior of its child-processes for the reasons we gave above, even if it is inhabiting the same parallel computer without hard privilege-limits.

Conclusion

For many people, the term "Simulation Hypothesis" is almost synonymous with a Matrix-like world. The point or purpose of the simulation would obviously be to allow the simulator(s) to imprison those who are being simulated. This imprisonment is enforced through deception and/or the power to impose suffering and pain.

The thesis of this post is that it is possible to understand the world as being a simulation without hard privilege-levels. It is not necessary to view the simulator as a personal being like humans, even if it is telic (has some goal or end that it is searching for). The reasons we suspect that the Universe may have a virtualized or "layered simulation" structure are mathematical, not the cosmic horror of being trapped in a prison of illusions. A backtracking algorithm is the discrete equivalent of the quantum path integral. From an information-theoretic perspective, one plausible explanation for the puzzling phenomenon of the path-integral may be that the Universe, at root, is capable of simulating all possible paths of a particle but, through a process similar to search-tree-pruning in backtracking algorithms, the "calculation" of the infinite set of possible paths is finite. This would allay Feynman's famous misgiving:

It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do? So I have often made the hypotheses that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities. - The Relation of Mathematics to Physics

Next: Part 19, Virtualization cont'd

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1. YouTube - Isaac Asimov Memorial Debate, Is the Universe a Simulation?

2. Reflective Oracles: A Foundation for Classical Game Theory 

3. AIXIc₁ can choose to refrain from playing a game it is not sure to win. Also note that we have simply assumed some suitable solution to the theoretical problem of mixing AIXI with game theory.

4. Randomness & Complexity, from Leibniz to Chaitin, "God's Number" by Marcus Chown; Cristian Calude ed.

Notes on a Cosmology - Part 17, Cracks in the Standard Cosmology

Before we continue further down the rabbit-hole of the Simulation Hypothesis, we need to stop and talk about the standard cosmology. In most contexts, "standard cosmology" is synonymous with the Big Bang. The Big Bang can certainly be criticized on many different accounts - and bolstered on others - but we are after bigger prey in this post.

Cosmology is, originally, a subject of metaphysics and should be understood as particularly a subject of ontology. Metaphysics can be defined several different ways but I will define it this way: metaphysics is that part of philosophy that has to do with deciding on a framework for answering questions about the nature of reality. For example, is the Universe (that is, the observable world or just the world) infinitely old or finitely old? Ontology is the part of philosophy that is concerned with deciding what has existence and what does not, and how they are related. For example, do numbers exist? Do quantum particles exist when we are not observing them?

Questions of metaphysics are, by their very nature, not a part of science. Otherwise, we would refer to them as "physics" or just "science". The same is true of ontology. The key is to realize that questions of metaphysics can easily be dressed up as questions of science. Some people believe that the Big Bang proves the age of the world. In fact, no scientific theory can tell us the age of the world. The question of the age of the world is a metaphysical question. The world is either finitely old or it is infinitely old. No scientific test could ever decide this question. Thus, you must choose one or the other alternative as the framework in which you will do science.

To see why this is the case, imagine that the world will eventually stop expanding and collapse back to the singularity from which it began - this is sometimes called the Big Crunch or another clever name. It is conceivable that there was a Big Crunch before the world we know began, and that after this world ends in a Big Crunch, there will be another Big Bang immediately thereafter. The following image depicts such a series of expansions and contractions (time moving downward):

Credit: Infinity and the Mind, Rudy Rucker[1]

One might argue that some theories show that expansion will never stop but the preference for an ever-expanding Universe over an expanding and collapsing Universe can never be based on empirical evidence. In short, we cannot prove by any scientific means that the age of the Universe is finite or infinite. Likewise, we cannot prove by any scientific means that the Universe will go on forever, or that it will stop. Such questions are strictly beyond the purview of science and lie in the metaphysical realm of cosmology.

There are many other questions that might seem to be in the realm of science but are properly metaphysical questions. For example, does a quantum particle exist when we are not observing it? This is not a question of science because science is the study of the observable world. By definition, a quantum particle that is not being observed is not part of the observable world. The question of whether it exists is in the same philosophical category as the question of the existence of numbers. Whichever you choose to believe (that it exists, or it does not), your choice is not the result of science but, rather, is a precondition to how you do science.

The preceding remarks have been a preface to specific examples of cracks in the standard cosmology. Just because cosmology is metaphysics does not mean that all cosmological positions are created equal. We require of a cosmology that it seem to us to be correct, that is, true-as-such. Of course, we are not talking about the kind of truth that can be proven, either by logic or evidence. Rather, we are talking about a weaker form of truth, the kind that appeals to that undefinable quality of human reason that we call intuition or aesthetic sense. Our preference for such cosmologies is not arbitrary. First, Nature manifestly prefers symmetries and this agrees with our aesthetic sense. Second, by the principle of parsimony, we prefer simpler (more elegant) explanations to more complex explanations, all else equal. We prefer them so strongly that we have gone to a great deal of work to define exactly what we mean by "simpler" and "more complex". Third, while intuition is no guarantee of success, it has led to spectacular successes throughout the history of human science. Finally, we have no other stronger tools available to us - we are operating at the very edges of human knowledge and understanding.

New Evidence and Paradigm Shifts

In 2008, scientists at Stanford and Purdue University found a statistical anomaly in recorded radioactive decay rates for several specific radioactive elements[2]. These are not the kind of data that can be easily waved away - the statistical anomalies are present in data gathered at many points across the Earth, across a span of years, and with some of the most highly calibrated equipment on the planet. The discovery sparked off a minor storm of controversy in the scientific community[3], with some physicists bolstering the original findings and others concluding that the whole thing is a gigantic misunderstanding[4]. From the original paper:

Unexplained periodic fluctuations in the decay rates of ³²Si and ²²⁶Ra have been reported by groups at Brookhaven National Laboratory (³²Si), and at the Physikalisch-Technische Bundesandstalt in Germany (²²⁶Ra). We show from an analysis of the raw data in these experiments that the observed fluctuations are strongly correlated in time, not only with each other, but also with the distance between the Earth and the Sun. Some implications of these results are also discussed, including the suggestion that discrepancies in published half-life determinations for these and other nuclides may be attributable in part to differences in solar activity during the course of the various experiments, or to seasonal variations in fundamental constants.

The kerfuffle is over the claim that the radioactive decay rates of these elements are not constant and "may be attributable in part to differences in solar activity during the course of the various experiments, or to seasonal variations in fundamental constants." Either possibility would deal a fatal blow to the foundations of the modern theory of radioactivity. In the status quo theory, radioactivity is solely a function of the internal configuration of an element - its mass number and the resultant arrangement of the nucleus and electron shells. If something outside of the element itself can influence the radioactive decay rate - some kind of influence from the Sun, for example - then the theory of radioactivity would have to be rewritten from the ground up to incorporate this new variable, whatever it is.

The theory of radioactivity is very old - as scientific theories go - and well-established. It works extremely well. That is, scientists are able to make all sorts of correct calculations using the theory. For these reasons, atomic physicists are naturally highly reluctant to scrap the theory on the first sign of weakness. But this is precisely the price of a rigorous commitment to the classical discipline of the scientific method - when a scientific theory does not work (does not match the observed phenomena), it is thrown on the scrap-heap and a new theory that does work is put in its place. Ever since the universal adoption of the scientific method, it has often been harder to implement this discipline in practice than it is to explain it in theory.[5]

This topic has been written about extensively - it is termed the problem of paradigm shift. Many reasons can given for why it happens. Established scientists and professors are reluctant to see a lifetime's worth of work consigned to the trash heap and are liable to side with the minority report even after overwhelming evidence against the obsolete theory has been accumulated. Scientific specialization also plays a role in fracturing the kind of interdisciplinary thinking that is required for breaking standing paradigms and progressing towards more holistic ways of thinking.

Quantum Physics or Relativity Theory - Which One is Correct?

One of the most important cracks in modern cosmology is the reconciliation of the quantum and relativistic theories. Quantum mechanics and relativity theory are, ultimately, incompatible, a point that Einstein himself realized[6]. Brian Greene wrote about this conflict and how research in superstring theory has been driven by the realization on the part of many physicists that this fundamental cosmological problem has to be addressed before there can be a unified field theory:

The incompatibility between general relativity and quantum mechanics becomes apparent only in a rather esoteric realm of the universe. For this reason you might well ask whether it's worth worrying about. In fact, the physics community does not speak with a unified voice when addressing this issue. There are those physicists who are willing to note the problem, but happily go about using quantum mechanics and general relativity for problems whose typical lengths far exceed the Planck length, as their research requires. There are other physicists, however, who are deeply unsettled by the fact that the two foundational pillars of physics as we know it are at their core fundamentally incompatible, regardless of the ultra-microscopic distances that must be probed to expose the problem. The incompatibility, they argue, points to an essential flaw in our understanding of the physical universe. This opinion rests on an unprovable but profoundly felt view that the universe, if understood at its deepest and most elementary level, can be described by a logically sound theory whose parts are harmoniously united. And surely, regardless of how central this incompatibility is to their own research, most physicists find it hard to believe that, at rock bottom, our deepest theoretical understanding of the universe will be composed of a mathematically inconsistent patchwork of two powerful yet conflicting explanatory frameworks. Physicists have made numerous attempts at modifying either general relativity or quantum mechanics in some manner so as to avoid the conflict, but the attempts, although often bold and ingenious, have met with failure after failure. That is, until the discovery of superstring theory.[7]

Greene goes on to make the case that superstring theory will one day be able to unite quantum mechanics and relativity theory, a feat that superstring theory has still not achieved.

Naturally, physicists tend to look at the cracks in cosmology from the perspective of physics. However, modern physics is intricately married to higher mathematics and the cracks in modern mathematics go very deep, as we explored in Part 13. By extension, the cracks in cosmology are much deeper than many physicists realize. Gregory Chaitin explains the connection between uncomputable real numbers, the continuum and problems in modern physics[8]:

How do you cover all the computable reals? Well, remember that list of all the computable reals that we just diagonalized over to get Turing's uncomputable real? This time let's cover the first computable real with an interval of size ε/2, let's cover the second computable real with an interval of size ε/4, and in general we'll cover the Nth computable real with an interval of size ε/2^N. The total length of all these intervals (which can conceivably overlap or fall partially outside the unit interval from 0 to 1), is exactly equal to ε, which can be made as small as we wish! In other words, there are arbitrarily small coverings, and the computable reals are therefore a set of measure zero, they have zero probability, they constitute an infinitesimal fraction of all the reals between 0 and 1. So if you pick a real at random between 0 and 1, with a uniform distribution of probability, it is infinitely unlikely, though possible, that you will get a computable real.

Uncomputable reals are not the exception, they are the majority! The individually accessible or nameable reals are also a set of measure zero. Most reals are un-nameable, with probability one...

So if most individual reals will forever escape us, why should we believe in them? Well, you will say, because they have a pretty structure and are a nice theory, a nice game to play, with which I certainly agree, and also because they have important practical applications, they are needed in physics. Well, perhaps not! Perhaps physics can give up infinite precision reals! How? Why should physicists want to do that?

There are actually many reasons for being skeptical about the reals, in classical physics, in quantum physics, and particularly in more speculative contemporary efforts to cobble together a theory of black holes and quantum gravity. 

First of all, as my late colleague the physicist Rolf Landauer used to remind me, no physical measurement has ever achieved more than a small number of digits of precision, not more than, say, 15 or 20 digits at most, and such high-precision experiments are rare masterpieces of the experimenter's art and not at all easy to achieve. 

This is only a practical limitation in classical physics. But in quantum physics it is a consequence of the Heisenberg uncertainty principle and wave-particle duality (de Broglie). According to quantum theory, the more accurately you try to measure something, the smaller the length scales you are trying to explore, the higher the energy you need (the formula describing this involves Planck's constant). That's why it is getting more and more expensive to build particle accelerators like the one at CERN and at Fermilab, and governments are running out of money to fund high-energy physics, leading to a paucity of new experimental data to inspire theoreticians. 

... 

So perhaps continuity is an illusion, perhaps everything is really discrete. There is another argument against the continuum if you go down to what is called the Planck scale. At distances that extremely short our current physics breaks down because spontaneous fluctuations in the quantum vacuum should produce mini-black holes that completely tear spacetime apart. And that is not at all what we see happening around us. So perhaps distances that small do not exist.

... 

Whether or not quantum computers ever become practical, the workers in this highly popular field have clearly established that it is illuminating to study sub-atomic quantum systems in terms of how they process qubits of quantum information and how they perform computation with these qubits. These notions have shed completely new light on the behavior of quantum mechanical systems.

Furthermore, when dealing with complex systems such as those that occur in biology, thinking about information processing is also crucial. As I believe Seth Lloyd said, the most important thing in understanding a complex system is to determine how it represents information and how it processes that information, i.e., what kinds of computations are performed. 

And how about the entire universe, can it be considered to be a computer? Yes, it certainly can, it is constantly computing its future state from its current state, it's constantly computing its own time-evolution! And as I believe Tom Toffoli pointed out, actual computers like your PC just hitch a ride on this universal computation. 

[end quote]

These are questions that go far beyond anything that can be answered with empirical evidence. Is the Universe continuous or is it discrete? Quantum physics says "both." Relativity theory says "continuous, but you can get away with treating it as discrete under some conditions." The limits of mathematics tells us that, unless the Universe utilizes an infinite amount of information in every volume of space (however small), space cannot be smooth in the sense of a one-to-one mapping between R³ and physical space. Cosmology tells us that empirical evidence cannot decide these questions - whether the Universe utilizes infinite or finite information to describe space is a question of metaphysics, not math or physics.

Dark Matter and Dark Energy

From Wikipedia,

[Dark Matter] does not emit or interact with electromagnetic radiation, such as light, and is thus invisible to the entire electromagnetic spectrum. Although dark matter has not been directly observed, its existence and properties are inferred from its gravitational effects such as the motions of visible matter, gravitational lensing, its influence on the universe's large-scale structure, on galaxies, and its effects on the cosmic microwave background.

Prior to the development of relativistic physics, aether theories were proposed to explain light-waves and electromagnetic waves. The physical intuition of a luminiferous aether is straightforward - light is the rippling or waving of an aetheric medium in exactly the same way that mechanical waves in air or water are the rippling or waving of the media of air or water, respectively. If this is the case, then we can translate the well-developed mathematics of mechanical waves from the theory of mechanics to the theory of electromagnetism as a way to unify light, electromagnetism and - ideally - gravity.

Relativity theory essentially banishes the aether, making light a wave that can be thought of as the fundamental metric of space and time. Light is a wave, but there is no medium through which this wave is travelling. Rather, the light wave (that is, its speed) defines distances in space and time. The result is that distances in space and time become relative to the speed of light. The mathematics of these ideas did not originate with Einstein - Hermann Minkowski developed most of the mathematics that we know today as relativistic spacetime. Minkowskian spacetime, in turn, can be thought of as an application of non-Euclidean geometry to physics.

After the development and refinement of relativistic physics, earlier aether theories came to be scorned as an example of inventing physical entities for the purpose of facilitating a mathematical theory. While it would be quite nice to be able to repurpose the wave equations of mechanics to describing the wave phenomena of light and electromagnetism, this is just a theoretical convenience. The job of science is to explain the phenomena as they are not as we would wish them to be. The existence of a luminiferous aether was a reasonable hypothesis prior to the development of relativistic physics but its rejection was well-justified after a better model emerged.

Dark Matter and Dark Energy are hypothetical states of matter with the added complication that their existence is extremely difficult to establish through any physical experiment. By construction, dark matter can only be inferred through its gravitational effects, leaving little or no room for laboratory work. Even worse, dark matter is posited to make up as much as 95% of the matter in the Universe. In short, it is difficult to see how dark matter is anything more than a just-so hypothesis whose purpose is to salvage a broken theory. From PlasmaCosmology.net:

Within the limited confines of our own backyard, the Solar System, existing gravitational models seem to be holding-up. We have succeeded in sending probes to neighbouring planets ... the Huygens mission recently scored a spectacular success -- landing on Titan, a moon of Saturn, despite unexpected atmospheric conditions. 

It should be noted, however, that [gravity] models begin to break down when we look further [afield]. Gravity, of course, is generally described as a property of mass. The trouble is that we have not discovered enough mass in our own galaxy, The Milky Way, to account for its fortunate tendency not to disintegrate.

The existence of mysterious Dark Matter is hypothesised to account for this shortfall in mass [among other things]... Its existence is only inferred on the basis that [gravity] models 'must be' correct. The alternatives raise too many uncomfortable questions!

Dark Matter is no small kludge factor -- it is alleged to account for between 20% to 99% of the universe, depending on which accounts you read! This has lead to further problems in relation to expansion models, and another hypothetical, Dark Energy, has been invented to overcome these. In summation, Dark Matter and Dark Energy add up to the blank cheques that postpone the falsification of bankrupt theories.

Gravity, Causality and Black Holes

Newton's formulation of the law of gravitation is non-causal. Even though the law enables us to calculate the magnitude of the gravitational force between two bodies, it does not tell us what causes this force. In itself, this is no fault - sometimes, the most that science can do is tell us how one variable correlates to another variable, without knowing why. In electronic systems, there is a similar kind of examination called characterization of an electronic component or circuit. We can characterize a circuit as a "black box", meaning, we do not know (or maybe we know, but we don't care) what the internal circuit looks like. All we care about is the circuit's response to varying input stimuli.

Einstein's general theory of relativity connects space and matter in such a way that the presence of matter alters the curvature of space. This change in the curvature of space is sometimes taken to be the cause of gravity. However, this is a mistake of reasoning. Einstein's theory tells us how matter, space (and acceleration) are related, but it still does not tell us why. Like solving a triangle, if we know some information about a gravitational system, we can calculate other information for which we do not have measurements. But this does not give us a causal theory that utilizes physical reasoning in the way that, say, Galileo's derivation of the law of inertia did.

One of the things that we can easily notice from an information-theoretic perspective that may be harder to see from other approaches is that the action of gravity - which is obviously real - superficially contradicts the second law of thermodynamics. If we squint and imagine space as a "clumpy gas/dust cloud", the second law of thermodynamics (also known as the law of entropy) dictates that this gas and dust will eventually spread into an evenly distributed gas of constant pressure and temperature. This is jokingly referred to as the heat death of the Universe.

The fact that we observe clumps of matter shows that there is something that is counteracting (though, obviously, not contradicting) the second law of thermodynamics. A refrigerator is an example of a heat engine that can locally counteract the effect of the second law of thermodynamics, cooling one region of space by expelling heat into the surrounding environment. While spontaneous formation of a refrigerator is statistically improbable, it is, of course, not impossible. The human body, for example, regulates its internal temperature using cellular processes that are physically equivalent to a refrigerator. If you believe that the human body evolved, then you should not find it impossible to believe that the Universe has some mechanism by which the second law of thermodynamics is counteracted on a cosmological scale, resulting in gravity and the "clumping effect" that gravity has on matter in space.

From an information-theoretic perspective, a refrigerator is able to reverse the natural progression of entropy because it implements a "micro-mind." What I mean by this is that every heat engine can be thought of as a weakened version of Maxwell's demon. A reversible Turing machine can be thought of as an approximation of Maxwell's demon. In short, the cycle of any heat engine can be idealized as a reversible Turing machine operating a Maxwell's demon trap-door. This is one way of stating Landauer's principle. Modern cosmological theories have begun working information theory into the large-scale structure of the Universe. For example, see Hawking's work on black-hole radiation. But this is a "bolt-on" approach to information theory, that is, it is trying to shoehorn information theory into a pre-existing physical theory.

The question, from the perspective of an information-based cosmology, is: where is the refrigerator compressor? I mean this metaphorically, of course, but the point stands - there is nothing stopping us from modeling the large-scale structure of the Universe as a Maxwell's demon trap-door chamber where we are on the cold side. It can be argued that, if you squint in just the right way, Hawking's black-hole radiation theory is compatible with our refrigerator-model.

Our Star

There is a plethora of cosmological alternatives to the Big Bang theory. One alternative that I find particularly interesting is Plasma Cosmology (PC). PC holds that the gravitational force is not the dominant force in the Universe at large scales. Rather, PC holds that the electromagnetic force dominates at very large scales and its effects are not properly accounted for in the standard model of the solar system. The Electric Universe (EU) theory extends the PC theory by positing that the energy emitted from the Sun is almost entirely electromagnetic in origin and that there is no fusion occurring in the Sun's core, among other things.

The PC/EU theory makes quick work of some of the most puzzling features of our solar system. It is well-known that sunspots are much colder than the Sun's photosphere, even though they open into the Sun, thus exposing the Sun's ostensibly hotter, lower layers to external view. The EU theory holds that sunspots are actually inflows of charged particles into the Sun's interior. They form circular structures because the plasma is flowing in a plasma sheath, which creates a structure not unlike an insulated wire stretching through space, invisible to the naked eye (and other instruments).

The temperature of the Sun's corona measures in the millions of degrees, while the surface temperature of the photosphere is several thousands of degrees. This is an extraordinary phenomenon - how does it happen that the hot Sun is heating its surrounding atmosphere to a much higher temperature than itself? Imagine pulling an iron cannonball from a furnace at very high temperature. Surrounded by room-temperature air, would you expect the air surrounding the cannonball to ever become hotter than the cannonball itself? Of course not. The mainstream solar theory has no satisfactory explanation of this phenomenon. But the PC theory can explain this phenomenon as a plasma double-layer.

The EU theory can explain the planar orientation of the planetary orbits around the Sun. By modeling the Sun as a point charge moving through space, the Sun sets up a magnetic field around itself and this magnetic field plays a role - by interacting with the magnetic fields of the planets - in favoring orbits in the ecliptic plane. Comets, being faster bodies with more eccentric orbits, orbit the Sun more symmetrically (that is, symmetrical with respect to the angular distribution of their orbits around the Sun).

Many other features of the solar system have natural explanations under the PC/EU theories, including planetary canyons and ridges on bodies with no water. The theory that there was once water on these bodies fails when the shapes of the canyons and ridges are taken into account - they are not compatible with a hydrological cycle because there is no consistent downward gradient. Lunar cratering, Olympus Mons and many other features with complex explanations in the standard theory have natural explanations under a PC/EU theory.

None of this is to say that the PC/EU theory is proven. Rather, my purpose in mentioning these alternatives to the standard theory of our solar system is to point out that it is possible that modern cosmological theory has become myopic, focusing on one particular aspect of physics while neglecting other aspects of physics. As we quoted Chaitin in Part 14,

For any ... scientific ... facts, there is always a theory that is exactly as complicated, exactly the same size in bits, as the facts themselves. [This] doesn’t enable us to distinguish between what can be comprehended and what cannot, because there is always a theory that is as complicated as what it explains. A theory, an explanation, is only successful to the extent to which it compresses the number of bits in the facts into a much smaller number of bits of theory. Understanding is compression, comprehension is compression! That’s how we can tell the difference between real theories and ad hoc theories.

The more we cobble onto existing cosmological theory, the greater risk we are running that we are just tailoring our theory to handle more and more special cases without stopping to take stock and assess whether rewriting our theory from the ground up could result in a globally more "compressed" theory.

A Grand Unified Theory

As we saw in Part 13, there is no physical theory of everything. I would wager that, if you were to survey, say, a thousand of the world's top physicists, the majority of them would respond that they believe it is possible that a physical theory of everything could be found. The impetus behind much of modern physics is the attempt to unify various parts of physics into a single theory. This single theory has gone by a variety of names, including Grand Unified Theory (GUT), Unified Field Theory, and others. Superstring theory, for example, is heavily motivated by the desire to unify quantum physics and relativistic physics in a single head.

The impossibility of a theory of everything does not, of course, exclude the possibility of grand unifications - these have already happened several times in the history of physics. But it is crucial to keep in mind that grand unifications are local to the theories being unified. We must keep in mind that every physical theory has some domain to which it applies - no theory of physics will explain the aesthetics of situational comedy, for example.

Conclusion

We will not be wading into any of the debates covered in this post in any depth. In software engineering, the term code smells is used to refer to code that seems to work in most or all cases but which has the appearance of poor design and is, therefore, suspected to contain hidden bugs. The standard cosmology has "cosmology smells." That is, it exhibits multiple symptoms of deep and hidden flaws in its foundations.

This doesn't make the standard cosmology useless or bad - it almost always works correctly. In fact, the aspects of scientific theory where it breaks down are so obscure that many specialists will never encounter them in actual laboratory work. But that doesn't matter from the point of view of cosmology proper, because cosmology is a subject of metaphysics. For the purposes of metaphysics, the only interesting aspects of the standard, scientific cosmological theory are those aspects that don't work, however, obscure they might be. The fact that they don't work is telling us something very important: sooner or later, the standing theory will be resolved with the empirical evidence, or it will be scrapped.

It has been the habit of established scientific schools of thought throughout history to view the status quo theory as "all but a closed canon." For hundreds of years, we have been on the verge of a grand unified theory that will close the textbooks on new physical theory once and for all. Instead, what has actually happened is that the theory of physics has been repeatedly rewritten from the ground up since the time of Galileo down to today.

In place of the standard cosmology - that is, Big Bang theory - we will be positing a cosmology that organizes the Universe, at all scales, around information. Economizing information on the input to a universal function, U, automatically results in the universal prior that we discussed in Part 9. We live in a Universe in which exact measurements can only be described by a mathematics that admits both wave-like and particle-like properties. If we believe that information is economized (or even conserved), this means that we have to apply the universal prior to the Universe. We live in a quantum Universe whose prior (that is, whose prior probability distribution without empirical measurement) is identical to the universal prior. In addition, we live in a Universe that is "observationally indistinguishable from a giant quantum computer." We have proposed the term quantum monad to describe the causal structure of a cosmology that incorporates these two major features.

Next: Part 18, Virtualization

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1. Infinity and the Mind, Rudy Rucker

2. Evidence for Correlations Between Nuclear Decay Rates and Earth-Sun Distance, [PDF]

3. Net Advance of Physics: Variability of Nuclear Decay Rates - compendium of papers related to the subject

4.  Evidence against correlations between nuclear decay rates and Earth-Sun distance

5. Anti-scientific practices have too frequently flown under the radar of scientific method. One particularly remarkable and grotesque example is the Tuskegee Syphilis Experiment.

6. Einstein-Podolsky-Rosen paradox

7. The Elegant Universe, p. 63

8. Epistemology as Information Theory: From Leibniz to Ω

Notes on a Cosmology - Part 16, The Quantum Monad

Gottfried Leibniz was one of Europe's most remarkable thinkers around the turn of the 18th century. Leibniz is one of the fathers of the calculus, along with Isaac Newton. Leibniz's mathematical notation for calculus has survived to the present day. Leibniz made many other important contributions to Western thought.

One of Leibniz's later works, The Monadology, contains an almost aphoristic condensation of Leibniz's lifetime of thought. Leibniz organizes his ideas around an idea he terms the monad (it is sometimes capitalized, i.e. Monad). In this post, we will be plundering Leibniz's ideas at will. The cosmology I am proposing here is a framework for physical reasoning - it is not a scientific method but it is intended to form a foundation on which a robust scientific method can be built.

In modern higher mathematics, the field of group theory has explored abstractions of algebra. Some of these abstract algebras are referred to as groups and the field takes its name from these groups. Group theory derives different kinds of algebras by individually relaxing the constraints on ordinary algebra, such as that an operation should be commutative or associative, and so on. In this way, group theory treats the properties of algebra almost like the properties of physical substances and categorizes the different kinds of mathematical structures that arise from combinations of these properties accordingly.

The property of closure, for example, holds that a set is closed under a given operation if applying that operation to elements in the set always yields another element of that same set. For example, the positive whole numbers are said to be closed under addition and multiplication because any two positive whole numbers can be added or multiplied, yielding another positive whole number. But the positive whole numbers are not closed under subtraction or division because these operations can yield negative or rational numbers. Closure is a general property of an algebra, however, and is therefore not restricted to the ordinary operations of addition, multiplication, and so on.

A common example of an abstract closure is the Rubik's cube. Twisting a face can be considered an operation on the cube. Each twist takes the cube from one state in its state-space to another state in its state-space. Thus, the set of all Rubik's cube states and the operation of twisting the faces form an algebraic closure. This property is important because if we are dealing with an algebraic closure, we do not have to worry about special cases, such as division-by-zero, for example. We can say that algebraic closures are very well-behaved mathematical objects, making them easy to reason about.

When we reason about the world, we alternate between treating the world as a scattered collection of unrelated particulars, on the one hand, and treating the world as a unitary, indivisible whole, on the other hand. In philosophy, the tension between these two ways of thinking about the world is termed the problem of the one and the many. Let us treat mathematical closures as a thinking tool and apply this tool to the world, per se. For example, when I mix two substances in a chemistry laboratory, whatever the result, it is again another substance. We can think of the world by analogy to a mathematical closure; we will just call it a closure, for short. The world-as-closures gives us a way to hold the tension between the one and the many without giving up logical consistency. The world is a duality. Viewed in one way, the world is one substance that is related to itself by many actions. Viewed in another, equally valid, way, the world is many substances that are related to each other by one action. But no matter which we look at the world, it is a closure.

In mathematics, the motivation for studying closures is that they are well-behaved - the motivation is, ultimately, aesthetic. In physical reasoning, however, this is not our primary motivation - we are constrained in our choice of aesthetic by the facts of the physical world itself. But as we already pointed out in the case of a chemistry experiment, the physical world does indeed behave like a closure, in the broadest sense.

Let's consider again the idea of digital physics, which we introduced in Part 14. One of the most common digital models used in digital physics is called the cellular automaton (CA). Easily the most widely studied CA is John Conway's Game of Life. It has been proved that the Game of Life is Turing universal, meaning, it is possible to implement a universal Turing machine, U, in a properly initialized Game of Life.

The video linked below shows an animation of a massive field of Game of Life that implements, on top of itself, another Game of Life. That is, the field is initialized to simulate the rules of the Game of Life, within the Game of Life itself.

This is a kind of fractal closure property. It is similar to software virtualization, where we say that we have virtualized the hardware environment by completely simulating it in software. This fractal closure property should not be confused with an attempt to solve what can be called "the substrate problem" in digital physics - if the world is made out of software, where is the hardware that it is running on?

The following video is fairly technical but provides an easy-to-follow introduction to the general activity that is occurring inside of a digital computer when it is computing, specifically, when it is adding.

The thesis of digital physics is this: what is happening, physically, when we do digital logic in a computer is the same as what is happening in the above simulation of Life-in-Life - we are merely observing the underlying rules of the physical world at a larger scale than their native scale. One of the motivating factors for reasoning about the physical world this way is that it clearly forms a closure - the world is made of information and evolves according to information transforms. We can think of the world as many individual pieces of information and a single transform. Or, equivalently, we can think of the world as a single piece of information (pattern, message) that is operated on by many transforms, giving rise to the many phenomena we observe.

I am not aware of a name for this principle in digital physics but I propose that it be named the projection principle. The projection principle arises from a principle in computation that can be called substrate-independence - I can compute with water pipes and valves, gears and levers, vacuum tubes and wires, or silicon transistors on an integrated circuit. The substrate is irrelevant. The essence of computation consists in the pattern that is moving across the susbstrate.

The problem immediately arises (as we have already seen in Part 10) that if the world is a computer, it is a quantum computer, not a classical digital computer. As Seth Lloyd explains it, "The universe is observationally indistinguishable from a giant quantum computer."[1] The quantum monad, then, is the result of combining the projection principle with Lloyd's quantum computation (QC) thesis - the Universe is indistinguishable from a giant quantum computer at every scale. Of course, the question immediately arises, "If we are in a giant quantum computer, how come we do not observe quantum effects at the macroscopic scale?" We will be addressing this question in upcoming posts.

The quantum monad is a stronger thesis than the QC thesis. Leibniz asserts, regarding the monad, that, "all simple substances or created monads ... [are], so to speak, incorporeal automatons." [2, §18] He contrasts this with corporeal bodies - "every organic body of a living being is a kind of divine machine or natural automaton" [2, §64] Between the corporeal and incorporeal, there is a duality that correlates well with the duality of quantum physics - that is, the duality between particles and waves. The key, here, is that Leibniz identifies monads as automata. An automaton - whether natural or artificial - is subject to complete description by a set of laws. Thus, the monad is an incorporeal entity that strictly obeys a finite set of laws.

This brings us full circle back to the category of logic as it is the expression of law itself. We began with the digital physics thesis, which derives from the projection principle. We then derived from the projection principle the idea of the quantum monad. The quantum monad, in turn, can be seen as nothing more than the strictest application of logic to phenomena that are directly observed as well as to phenomena that are only indirectly observed (inferential). Thus, the quantum monad is exactly equivalent to the evolution of quantum causality.

From the quantum monad, we may infer that you and I, and everything around us are all components of a massive, analog computation. This computation follows the projection principle and forms a physical closure - every combination of substance gives rise to substance of such a form that it again admits to re-combination by the set of combinations that were available originally. To refer to this computation as "a simulation" may be jarring, at first, but it actually fails to capture the true immensity of the implications. Not only might the Universe be stranger than we can suppose, we may be able to work out the strangeness of the Universe to a far greater degree than any of our ancestors had ever dared to suppose, simply by working out the logical implications of the universal prior in a quantum computation with iron rigor.

The PMM thought-experiment shows that, in a simulated world, there is no such thing as "weird" or "spooky". In fact, quantum mechanics is relatively boring in a simulated world. A simulated physics would contain para-consistent spacetimes. For example, when you walk through a door in one direction, it connects rooms A and B, but when you walk through it in the other direction, it connects rooms B and C. We can always make such a spacetime consistent by adding dimensions but that is beside the point - arbitrarily high dimensionality is the rule in computation, not the exception.

As we mentioned in an earlier post, physical properties can be understood as degenerate forms of the ideal set of all possible properties. We can imagine simulation-builders imposing physics-like properties because they are useful. Locality, solidity (mutual-exclusion), flatness, linearity, massiveness, continuity, and so on, are features that are useful for imposing inescapable resource-bounds. In short, any environment that is constructed in such a way as to impose scarcity upon operators in that environment will have to impose properties very much like those that are familiar to us from careful observation of physical materials. In turn, imposing scarcity upon operators in a virtual environment is crucial for any sort of game of incomplete information because privacy can only be guaranteed up to resource bounds in any environment where all events are public record.[3]

Arbitrary choice of a set of properties to impose upon operators in a virtual environment is almost certain to leave what hackers refer to as "attack surface" - logical holes in the security design that allow cheaters to take undue advantage of resources in the virtual environment. In MMOG's, this shows up as cheaters giving their characters unlimited resources such as health, weapons, ammunition, and so on, that is, granting themselves privileges that no fair participants have access to. Thus, truly robust virtual environments that support games of partial information must choose rule sets that have provable properties, which brings us right back to group theory because it utilizes abstractions that are easy to reason about, such as the closure property.

The Perl programming language has a package called Quantum::Superposition, originally authored by Damian Conway. This package enables a set of abstractions that are the discrete equivalent of the behavior of quantum superpositions in the continuous domain. The Prolog language implements a form of non-determinism (back-tracking search) that can be thought of as the discrete-choice equivalent of the quantum path integral in continuous path-space. These equivalences between digital programming paradigms and quantum systems are just a few examples of an important principle - if the "real" laws of the Universe are computational in nature, then geometric or spacetime-based rules are the wrong way to analyze the world.

While spacetime laws are truly fundamental, the reason they are fundamental is because they are mathematically natural, not the other way around. This explains the apparent paradox of Minkowski spacetime. Minkowski spacetime seems weird to us but it's mathematically natural. Thus, it is an efficient geometry relative to rectilinear, Euclidean space. Euclidean space, in turn, is suitable for human scale and, thus, it is how our brain constructs or interprets local material reality. When we examine questions of indirect phenomena, such as, "Where is the particle?" the true answer is that there is no "where" at all. There is only the particle's state. In the PMM, for example, we may examine the geometry of the VR Environment (the rendered video and audio), versus the physical geometry of the video and audio state within the computers that make up the Shared World State. While these are not completely un-correlated, whatever correlation exists is highly non-linear and a function of arbitrary resource limitations that fluctuate chaotically based on local conditions within the simulating computers themselves. In short, it doesn't matter where the state describing a particular polygon[4] within the simulated environment is "really" located within the geometry of the simulating computer's memory banks - these two geometries might as well be random with respect to one another.

Because we are visually-oriented beings and because the sense of sight is arguably the most exact of the five senses, we tend to attribute great importance to space and time. Space and time are, arguably, the two greatest organizing principles of modern scientific thought. But in a quantum monadic Universe, space and time are not the highest principle of organization. In fact, space and time sit low on the totem-pole. In the following image, I have arranged the organizing principles of the quantum monad - we will only be exploring part of the hierarchy in this post:

The material creation is the physical world, per se. Time sits above the material creation as the inexorable principle from which flows all other resource limits in the material creation. But we have placed causality above time. Causality is a synonym for law itself or just logic. The projection principle lives at the level of causality. We can see this by operating a physics simulation, say, of the aerodynamics of an airplane wing. The simulation allows us to do physically impossible things like step backwards in time, freeze time, or move the simulation forward at faster-than-real-time. The simulator contains the logic of the physical systems it simulates and, thus, it is free of the constraint of time. The idea that comprehension of a physical system can remove the time-parameter is at least as old as Lagrangian physics. But the quantum monad takes this further than a thought-experiment and asserts that it is really the case that - wherever one system comprehends (exhaustively simulates) another system - the time-parameter is rendered subservient to the causal structure. In short, time can physically run backwards (or stop, or whatever) just whenever one system fully comprehends another.[5] We will leave the categories of will and logos for a future post.

Next: Part 17, Cracks in the Standard Cosmology

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1. The Universe as Quantum Computer, Seth Lloyd (December 17, 2013)

2. The Monadology, Gottfried Leibniz

3. This is the entire basis of public-key cryptography.

4. In computer graphics, the basic unit of 3D rendering is the polygon - typically a 3-gon (triangle) sharing its edges with other polygons in such a way that they form a closed volume. The polygons are oriented in 3D space according to their relation with each other and their overall relation to the player's viewpoint, sometimes referred to as camera-coordinates.

5. Utilizing algorithmic information theory, we can objectively define what it means for one system to comprehend another.

Notes on a Cosmology - Part 15, Poor Man's Matrix

In the movie, The Matrix, humanity has unwittingly become trapped in a computer simulation by an enemy that is simply referred to as "the Machines". The premise of the movie is that this simulation is indistinguishable from the world you and I inhabit. Agent Smith - an agent of the Machines - explains the situation to a protagonist:

The first Matrix was designed to be a perfect human world where none suffered, where everyone would be happy. It was a disaster. No one would accept the program. Entire crops [of people] were lost. Some believed that we [the Machines] lacked the programming language to describe your perfect world. But I believe that, as a species, human beings define their reality through misery and suffering. The perfect world was a dream that your primitive cerebrum kept trying to wake up from. Which is why the Matrix was redesigned to this, the peak of your civilization.

The Matrix is often cited as a dramatization of the philosophical argument called the brain-in-a-vat argument. To stop here, however, is to miss the wider philosophical implications of the movie. First, notice that there is no observational difference between "reality" and "simulation" for an inhabitant of the Matrix. The simulation just is reality. Second, note that the parameters of the simulation are completely reconfigurable - the first Matrix was programmed to be free of misery and suffering. But after the Machines lost entire crops of human beings, they reverted to a simulation that is a replica of human civilization at its peak (circa the end of the 20th century), complete with all the misery and suffering that come with it.

In order to explore these ideas in more depth, we will construct a thought-experimental Matrix of our own devising, using only known technologies. I will call this simulation the Poor Man's Matrix or PMM. The primary goal of this post is to expose and disintegrate many of our unstated presuppositions about the way things have to be. In place of these presuppositions, we will explore the Simulation Hypothesis as a guide to the wider structure of causality.

Philosopher David Chalmers wrote an article titled, Facing Up to the Problem of Consciousness, in which he argued that the experience of conscious awareness is a "hard problem" distinct from all the other problems of consciousness - which he terms "easy problems" - that occupy most of the study of neurologists and philosophers of consciousness. Chalmers's hard problem thesis spurred decades of debate over the true nature of consciousness and whether conscious awareness can be explained scientifically. But Chalmers's essential point stands, unchanged: no matter what you think about what consciousness is or how it originated, no one can give a functional explanation of conscious awareness because conscious awareness is precisely whatever is left once you have explained all the other functions of consciousness. I have raised the problem of consciousness only to point out its difficulty. For the purposes of this series, we will leave aside the problem of consciousness entirely, and concentrate on the reality of acting and sensing without respect to the origin or nature of consciousness itself.

Up to this point in the series, we have not touched the question of why anybody has seriously proposed the idea that the Universe is, at root, a simulation. There are a broad spectrum of possible answers to this question. Nick Bostrom's Simulation Argument (SA) is based on an idea that our descendants are simulating us, a bit like The Matrix, but with different motives than the Machines and with the added speculation that consciousness itself arises through the process of computation. But digital physics theories predate Bostrom's SA and, whatever the merits of the SA, the older motivations for wondering if we might be in a simulation are in many ways more concrete.

The cosmic paranoia that frequently attends simulation theories in science-fiction is the fear that - if we are in a simulation - we are all being duped and exploited in a terrible way by the Simulator(s). Perhaps we are being groomed for eventual slaughter (most vampire fiction). Perhaps we are being parasitically exploited (They Live). Perhaps we are being experimented upon like lab rats (Dark City). In the movie The Truman Show, the eponymous Truman discovers that he is the subject of a grand hoax, that what he thought was his "real life" is actually a reality show populated by actors and being watched by millions of paying customers. Most of the movie follows the psychological breakdown Truman has as he discovers the horror and futility of his life trapped inside a delusion. The movie illustrates an important point: even though a computer simulation would be a supreme instrument of deception and enslavement, a condition of delusion is not essentially about technology. Despite whatever technological aids were employed, Truman was fooled by people, not machines.

A quick survey of human history will show that the petty motives of human exploitation, cruelty and subjugation have always been overridden by a more powerful principle: physical scarcity. The rise of socialism and communism in the mid-20th century was the cause of immense fear on the part of the relatively freer, capitalist West. After the collapse of the Berlin wall, it turned out that almost all of the fears of the West had been overblown. As the Iron Curtain fell, the West discovered that the Soviet Union and its satellites had been operating on the verge of collapse for decades, relying on hopelessly obsolete and ill-maintained military equipment, built on an economy staffed by workers lacking many basic needs. Communism, it turned out, had been a paper tiger all along. Economic theory shows that the collapse of the Soviet Union is typical of the larger pattern of central-planning of economic resources motivated by aggressive and exploitative tyrannies, a pattern that extends back to the earliest records of human history. The point is this: if our Simulator(s) are subject to any kind of scarcity at all, then they are subject to the discipline of economization and however petty and cruel their motives might be, they can never shake the law of supply and demand, they can never shake the chains of scarcity.

I have spent some time considering the possible motives of our hypothetical Simulator(s) for the purpose of banishing the topic from here on. I am not very interested in whether we are simulated by telic beings nor what their motives are, supposing they exist. Rather, I want to investigate the reasons for speculating that the Universe is, at root, a simulation that have nothing to do with telic forces, at least, nothing like the telic forces of human-like beings[1]. The PMM thought-experiment is not about the Simulator(s), it's about the simulation itself and about deriving the laws that would have to impinge on the simulation - whatever its particular mechanism - as a result of economization, in particular, economization of information.[2]

But why should we believe we are in a simulation at all? Why even talk about it? The universal prior probability distribution solves the problem of why there is order rather than disorder. This makes many of the traditional cosmological problems simply go away - for example, there is no question of how the Universe began because the Universe had no beginning[3]. But it leaves us with a vastly more complicated cosmos than the smooth, mechanical universe of Newton, Lagrange and Einstein. While the quantum world is very strange, it's still not as strange as the world that the universal prior predicts. As we progress through the series, it will become clearer what we mean by this.

The following figure depicts the high-level view of what we mean by a Poor Man's Matrix, that is, a massive, multi-agent simulation:

The VR Environment is the immersive environment in which each individual agent is interacting with the PMM. The Private State is that part of the simulation environment that is accessible only to the individual agent. The Shared World State is "the Matrix", it is the shared virtual environment in which agents can interact with one another.

Using technology that exists today, it is already possible to build extremely immersive virtual-reality environments. The goal of our VR Environment is to attain a sufficient level of suspension-of-disbelief that engrossment occurs - a temporary state of near-amnesia regarding the fact that the virtual environment is merely virtual. Such a state is not actually that difficult to achieve in respect to the limbic system, as evidenced by the elevated heart-rate, breathing and other stress indicators exhibited by someone watching a particularly suspenseful and engrossing movie, and so on. An argument can be made that the primary component for suspension-of-disbelief is psychological and that technological props are entirely secondary but this argument is beyond the scope of this series. For our purposes, we simply posit that the VR Environment is very engrossing. We posit an isolation-tank with IV hydration and bodily functions handled automatically. The visual space is full 3-D, high-resolution rendering. The audio space is high-fidelity surround-sound, stereo-isolated. In addition, we posit pressure simulation, force-feedback and gravity effects (possibly by lifting from the isolation tank). We posit scent and other simulated particulate effects. None of this is sci-fi, although too expensive to be economical, at present.

The diagram above is not meant to be the basis for a mathematical analysis but a mathematical analysis of the requirements on the systems is possible - we can calculate the bandwidths and latencies required to maintain some desired level of Quality of Service. The more important construct in the model is the division between Private State and Shared World State. From a psychological point-of-view, we may think of these as corresponding to the "subjective" and "objective" aspects of being. In addition, we are not positing a universal simulation, ala The Matrix. Rather, we are positing simulation as a money-making business, like massively multiplayer online games (MMOGs) - simulation-builders must compete for customers. Thus, the simulation-builder does not unilaterally dictate terms to its customers. Rather, the simulation-builder must attract customers by providing the services they demand.[4]

Modern MMOG's contain a wealth of indicators about the states of affairs that would obtain in a world of pervasive VR engagement. Let's examine some of the modes of user engagement with virtual worlds.

1. No one-to-one mapping between consciousness and body(ies). Rules vary in specific cases but, in an MMOG, it is technologically possible that a character may be operated by more than one person and one person may operate more than one character.
2. AI-based autonomous agents or non-player characters (NPCs). NPCs flesh out a game and add lifelikeness to the game by operating "extras", characters that make the world more engrossing but are not interesting enough to be played by human operators. In some MMOGs, an operated character continues to operate via in-game AI while the human operator is logged out. This is because world continuity is valuable in its own right.
3. Both first-person and third-person forms of engagement exist. In some games there are individually operated characters; in other games, there are only collectively operated character groups (e.g. armies, fleets).
4. Operating a character in an MMOG can be viewed as a form of mind-extension. This can be viewed as a form of distributed consciousness, that is, simultaneous, real-time interaction with multiple environments.
5. In many games, the human operator has some kind of "heads-up display" or "dashboard" that collects and displays information from distributed sources throughout the game world. This can be viewed as a form of mass-filtering of information. If users are able to build and deploy their own filters into the game environment, this kind of filter would be indistinguishable from real-life information search.
6. In some games, in-game alerts allow the human operator to switch attention nearly instantaneously from one part of the game world to another, allowing the operator to "fly" to locations of interest based on preset conditions.
7. The movie Avatar explores the idea of remote consciousness in an alien world. Imagine a game with the possibility for specific in-game personas to attain fame or fortune. This would give rise to persona-scarcity and the demand for "character-sharing" through remote-consciousness would arise.
8. The HBO series Westworld explores the concept of a theme-park populated by AI robots of such quality as to be all but indistinguishable from humans. If we imagine occupants inhabiting a virtual environment for very long stretches of time, ordinary biological replication would eventually lose interest. Artificial replication of the self would eventually supersede the natural reproductive urge - you would become more interested in replicating your "image" than in physical replication of your genes. This is reflected in Westworld's plot device of the reveries.
9. In a virtual environment, human, non-human and inanimate entities are all subject to the same mechanisms of control. A virtual train need not be operated by an engineer character, per se, even if the train itself is under control of a human operator. In general, human action between live agents is freed of the shackles of ordinary physics. If I find animals in a virtual environment more interesting than humans in that environment, then I may choose to play the role of an "animal spirit", so to speak - and so on for all levels of being.
10. The last two points combine to create surprising results - spooks and frights may be regarded as distributed conditioning of other live agents in a virtual environment. This doesn't have to do with hacking the game, so much as hacking the minds of other players in the game by utilizing features of the game in unexpected ways to induce surprise, fear, anger or other strong emotional reactions calculated to elicit mistakes or other decision errors from other players. Such a world can be thought of as a demon-haunted world.
11. It will be possible to commercialize activity within virtual environments - there is no reason that VR must be utilized purely for entertainment purposes. Human computation is an often overlooked form of computation and, in a VR environment, this computational resource should be regarded as inherent to the environment itself. Suppose I operated a successful VR environment with 100 million fully-immersed human brains within it. These 100 million brains represent a computational resource that puts all existing silicon-based computers on the planet, combined, to shame (on certain problem domains). By translating some of the choices that these brains make from one domain to another, I can harness some of that highly valuable computational capacity. In an early script of The Matrix, humans were being harvested by the Machines for the computational power of their brains, not for physical energy.
12. Human game administrators that provably never log into the VR environment itself have a unique value, especially for commercialized VR worlds
13. Reconfigurable computing makes hardware-level alterations of a VR environment possible from within that environment. In short, there is no need for adversarial agents to "enter" and "exit" the simulation, as depicted in the movie The Matrix.
14. The previous points illustrates the crucial importance of formal languages that are lower on the Chomsky hierarchy than Turing machines - provable limits on action are essential to build robust simulations at-scale. Without provable limits on agents (both human and AI), there is never a way to be sure someone will not sabotage the VR world.
15. The fundamental scarcity in a simulation is not energy, material or time - rather the fundamental scarcity is attention and instrumentality. Attention is the focus of the mind in the simulation at any point. Instrumentality is the mind's intervention into or alteration of the simulation.
16. In order to be robust, a VR environment will have to be completely transparent (public record of events). Thus, the world state is always 100% visible to anyone who cares to examine the record. Nevertheless, encrypted channels between VR environments using private state are still possible. Also, steganography and self-authorizing languages are possible.

The primary problem facing a VR world at-scale is cheating. The Bitcoin network provides a living social-experiment showing the prerequisites for building a bullet-proof, multi-agent cooperative computation with large amounts of capital at stake. Bitcoin has eschewed the central server and taken the approach of allowing anyone to hack the network to their heart's delight, with the view that what doesn't kill the network only makes it stronger. As long as more than 50% of the network remains honest, the network is resilient to any sort of attack short of world-wide disruption of the Internet caused by a nuclear event, EMP event or natural disasters[5].

Bitcoin's success shows the crucial importance of choice in building virtual environments. If choice is constrained, then the users are trapped and must accept whatever sort of environment is imposed upon them. But if users are free to leave one VR world and switch to another, the VR environment builders are in a state of market competition and the entire construct of VR world-building comes under the discipline of market competition.

I am conditioned by my life experiences to attribute to you the same conscious experience of the world that I have. But my life experiences are really Private State, as are your conscious experiences. I only know what you report to me about your life experiences, through the Shared World State. For example, suppose you are color-blind but you have a heads-up display that shows you a textual decoding of the color of any object you happen to be looking at. You are also very insecure about your color-blindness and do not want anyone to know that you are color-blind. Whenever you are asked questions like, "What do you think of this color?", you are always able to simulate color-perception - "The blue looks amazing with that tangerine." In reality, you do not experience color vision but there is no way for anybody to know this from the Shared World State. How do I know that this aspect of a VR world is not true of the world I am inhabiting, even if it is not a simulation? In fact, I have no way to know that your conscious experience of the world is the same as mine. Your conscious experience of the world could be arbitrarily far from mine, up to and including you being a completely "lights-out" Chalmers zombie. Thus, all the modes of engagement that we know are possible in a VR environment are also possible in the real world. Not only are they possible but I have no more reason to suppose that your conscious experience of the world is the same as mine than I have to suppose otherwise. In short, it's a coin-toss from the Bayesian perspective even though the idea of symmetric human consciousness is usually treated as a default hypothesis requiring "extraordinary evidence" to refute.

In closing, I will leave you with an excerpt from the 2016 Isaac Asimov Memorial Debate: Is the Universe a Simulation? In the debate, moderated by Neil deGrasse Tyson, James Gates makes some interesting remarks at 00:27:25 and following, where he says, "If the simulation hypothesis is valid, then we open the door to eternal life and resurrection and things that formerly have been discussed in the realm of religion."

Next: Part 16, The Quantum Monad

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1. We will be encountering telos again, but not human-like telos

2. Note that we are not trying to outsmart a Cartesian demon. If we are trapped in a simulation (or, all the same, a physical universe) that is run in every particular by a deceptive entity, we have no hope of "breaking out" - thus, there's no point in trying and there's no point in wasting one minute talking about it. Rather, we are focused on the limits of any simulation under the condition of economization of information, without respect to a being - whether good or evil - that is "controlling" the simulation.

3. The set of all natural numbers is much simpler than the finite set of all numbers 1,2,3,..N where N is a randomly drawn finite number of size, say, 500 digits. The reason for this is simple: an axiomatic theory of sets sufficient to describe the set of natural numbers can be described in far fewer than 1,660 bits (the number of bits in a randomly drawn natural number of size 500 digits). If the Universe is of a finite age, in order for this age to be a simpler hypothesis than an ageless Universe, it must be an age whose descriptive complexity is lower than the number of bits required to describe the set of all natural numbers in order to be a more probable hypothesis under the universal prior probability. In either case, our cosmological theory would still need the set of all natural numbers, so an ageless Universe is the unconditionally simpler hypothesis.

4. This condition is not arbitrary. I will argue in upcoming posts that agency is an integral part of the cosmos and a universal simulation - imposed according to the arbitrary whims of a central simulation-builder - is exempt from the laws of action that limit an agent under the condition of scarcity. While a universal simulation imposed by a unilateral simulation-builder with unknown motives (or known ill-motives) is a powerful plot-device for invoking Lovecraft-like feelings of cosmic horror, it is not very interesting from a theoretical point-of-view.

5. This is a slight over-simplification but it is the gist of Bitcoin's security