Wave-Particle Duality Because Why?

We know from experimental observation that particles and waves are fundamentally interchangeable and that the most basic building-blocks of the material world -- quantum particles -- are able to exhibit either wave-like or particle-like behavior. Quantum physics thoroughly explains many quantum phenomena. And while we know that quantum particles exhibit wave-particle duality, no one (to my knowledge) has provided any motivating reason for why quantum particles should behave this way rather than some other way. In a typical quantum physics textbook, wave-particle duality is presented as an axiom -- we describe quantum systems as having wave-particle duality because that is how they behave.

I recently read a Machine Learning (ML) paper titled, Wave Physics as an Analog Recurrent Neural Network (arXiv). The meat of the paper might be tedious for anyone who is not interested in the topic of ML, so I will skip it. Instead, I will provide an intuitive explanation of the result that is demonstrated in the paper.

To facilitate my explanation, consider the following images:

These images are the result of a wave-physics simulation run by the authors of the paper. Here's a rough description of what the images show. Imagine we are looking at a top-down view of a sound-proof room. In this sound-proof room are a speaker (the bright spot on the left-hand side of each image) and three microphones (the three dots on the right-hand side of each image). Between the speaker and the microphones is a porous membrane -- think of it like plastic, foam or some other solid that has been laser-cut into a very specific pattern (the contours traced by the white lines in the center of each image). The sound waves cannot pass directly from the speaker to the microphones but must, instead, reflect and reverberate off the complex interior surfaces of the membrane between the speaker and the microphones. By construction, the microphones do not need to be able to record a full spectrum of audio, they only need to be able to detect the presence or absence of sound power.

The speaker can play one of three vowel sounds -- the ay in "cape", the ee in "keep" or the a in "cap". The shape of the membrane has been learned by a novel type of neural network called a "neural ordinary differential equation" or "neural ODE". The NN has learned this shape by being trained with many different examples of the ay, ee and a vowels, respectively. The goal of the NN is to learn a membrane shape that will "steer" the sound power from the speaker to a specific microphone for a specific vowel. The simulations above show that the same membrane shape can steer many examples of ay, ee and a vowels that the NN never heard during training to the correct microphone.

This result is remarkable for a few reasons. First, the membrane is completely passive, that is, the membrane does not require any power to perform its job of correctly classifying vowels. The sound power is provided by the input itself (the sound waves from the speaker). Second, the membrane performs the classification task via simple wave propagation (as described by the classical wave equation). Third, the system is analog (continuous). This is in contrast to most neural networks used in machine learning today which are digital (discrete).

This result shows that wave physics -- a completely continuous domain -- is capable of performing machine learning tasks typically performed by discrete processors. While the example simulation performed in the paper is relatively simple, the techniques used can be generalized to a significant percentage of ML systems -- recurrent neural networks (RNNs) are one of the most common neural network architectures. The practical implications of this paper are that (a) we may be able to save enormous amounts of power in machine learning systems (factors of a million or more, depending on the application) and (b) we may be able to speed up complex tasks that incur significant processing delay in digital systems since a wave-physics system evolves at the speed of whatever wave is propagating through it (the speed of sound, speed of light, etc.) In other words, the processing time for a wave-physics system is just the time it requires for the input wave to travel through the system from input to output.

At this point, I am going to part ways with machine learning and the above paper. What is most remarkable to me about this paper's result is not discussed in the paper itself. This is my thesis: that the simulation performed in the paper above demonstrates a microcosm of physical wave-particle duality. On the left-hand side is the continuous (wave) domain. On the right-hand side is the discrete (particle) domain. (Note that I have slipped in two identities, here: (1) The identity between waves and continuous mathematics. (2) The identity between particles and discrete mathematics.)

It might not be obvious how this demonstrates the equivalence of waves and particles. Wave physics is time-reversible, that is, waves propagate according to exactly the same rules when moving forward or backward in time[1]. Given no other information, you cannot tell whether a movie depicting smooth wave phenomena is playing forward or backward. For this reason, we can see that if a sound impulse were to be produced at one of the places in the room where a microphone has been positioned, the sound that would come out on the left-hand side of the room would be something roughly like the vowel which corresponds to that microphone. Imagine striking a steel rod with a hammer at precisely the point where the microphone for the vowel ay is supposed to stand. Someone standing on the other side of the room - exactly where the speaker is supposed to stand, should hear the vowel ay, or something very close to it. The same goes for each of the other vowels. Since we can focus waves to discrete points (forward propagation through the membrane), and since we can produce waves from discrete points (backward propagation through the membrane), we can see that the shape of the membrane somehow "encodes" a duality, that is, an equivalence transform between these types of waves and a set of discrete points.

The existence of the equivalence I am pointing out is not a new insight. Information theory gives a unified framework for both continuous and discrete domains. There are well-defined transforms between the two domains. In digital-signal processing (DSP), these transforms are implemented as devices called ADCs (analog-to-digital converters) and DACs (digital-to-analog converters). But this new paper gives us a demonstration of an equivalence transform between continuous and discrete domains that can be built (or simulated) using only wave physics and which is entirely passive (requires no active power input). This makes the transform itself describable without having to posit two separate domains from the outset and without having to employ a clock to synchronize a sampling process. If we begin with waves-only physics, we can build a system in which there are waves and equivalent particles (which are discrete elements) in a very natural way. What makes it more "natural" than, say, ADCs and DACs is that it does not require sampling or discrete processing, and it does not require any input power.

To recap, my thesis is this: All discrete and continuous phenomena are related by some (possibly extremely complex) equivalence transform and this transform can, in principle, be "learned" by a sufficiently powerful neural net, perhaps implemented as a neural-ODE, as in the linked paper. This relation is sufficiently general that it includes physically discrete phenomena (such as particles) and physically continuous phenomena (such as waves). Thus, wave-particle duality is merely a byproduct of the existence of such equivalence transforms.

We might still wonder why a particular system is behaving in a wave-like or particle-like manner. How does Nature choose on which side of the membrane (equivalence transform) to stand? This question is very similar to the design problems faced by signal processing engineers. In some cases, a signal can be processed very power-efficiently and with high fidelity by a simple analog (continuous) circuit. In other cases, implementing a desired signal transform with analog circuitry would require a very complex, noisy circuit with poor fidelity and poor power-efficiency. In these cases, the signal-processing engineer will prefer to implement the transform in a digital signal processor (DSP).

It is not difficult to imagine that Nature is making a similar choice when choosing to maintain quantum state in either a continuous (analog) or discrete (digital) form. We observe that Nature is everywhere economical in her use of resources. So, she chooses that form which is most economical in respect to the well-known conservation principles (conservation of mass, energy, angular momentum, and so on). Like the design choices of a signal-processing engineer, Nature's choices are not arbitrary.

I find this this deep connection between information theory and Nature to be remarkable. In fact, there are many such connections and I hope to cover some of them in future posts. A consistently information-theoretic view of physics eliminates almost all of the paradoxes that arise from thinking about Nature using purely mechanical intuition and metaphors (for example, the billiard-ball model or wave-model). For example, the Heisenberg uncertainty principle has deep connections to time-frequency analysis and signal processing theory.


By thinking more deeply about this subject, I think we will find that endangered classical theories may eventually be preserved from extinction. Stephen Hawkings's work on black hole radiation, for example, has deep connections to information theory. Resolving the tension between the black-hole -- a "pure classical" object -- and quantum uncertainty may require modifications to quantum theory to limit the universality of quantum theory. Of course, theoretical work is already ongoing in this area (string theory, M-theory, topological quantum physics, etc.) But it is possible that the answer lies in going back to what came before, that is, in reinvigorating classical theories of physics.

[1] There is a caveat, here -- the waves must be mathematically "smooth", meaning, they cannot have discontinuities. Imagine a sheet waving gently in the breeze versus a sheet that has been ripped by gale force winds. The waves on the gently waving sheet are time-reversible, the waves on a sheet being ripped by forceful winds are not.

Simulation Argument Revisited

In my Notes on a Cosmology series, I laid out the foundations for an argument that we live in a simulation. However, I have not directly made the argument itself. I am still working on the concluding post for Notes on a Cosmology. However, the substance of my argument came together in my mind today with exceptional clarity, so I thought I would write a brief post outlining the basic sketch of the argument.

Bostrom's Simulation Argument is a well-known philosophical argument, a trilemma that can be taken to suggest that it is likely that we are living in a simulation. The argument suggests that, perhaps, our descendants became vastly more technologically advanced than we are, today. Out of curiosity, they began to simulate past histories and we happen to inhabit one of those simulations. One property of a computer simulation is that whoever controls the simulation has absolute control over time, so objections to Bostrom's argument based on the subjective passage of time are unconvincing.

This argument is very interesting and might even be convincing to some people. But I do not find the argument in itself convincing and I think that it fails to pierce through to the root issues.

When we talk about simulating the entire world (physics, the five senses, psychological effects, and so on), we run into two problems. The first problem is called the substrate problem -- if the observable world is a simulation running on a computer "somewhere else", what is simulating that other place? The term "base reality" is sometimes used to refer to some kind of "really real" world, but the moment we set sail on the roiling ocean of simulation theory, it's too late to wish we were back on the terra firma of "base reality." If our world is being simulated in a way that is so convincing that it cannot be distinguished from "base reality," then how could any conscious mind distinguish between being in a simulation and being in "base reality"? If we admit the possibility of simulation, then the idea of "base reality" must be jettisoned entirely.

The second problem is the problem of metaphysical contingency of the simulation. In plain language, physics feels convincing to us (in the sense of being "really real", not just a dream or illusion of some kind) because the laws of physics are, in some sense, inevitable, inexorable. The laws of physics seem to be logically necessary (non-contingent).

This point is closely related to the previous point. What we mean when we use a term like "base reality" is that which could not be any other way. In metaphysics, a world in which things could not be otherwise would be a logically necessary (non-contingent) world. It is generally held that necessary worlds are abstract (not concrete) and that the concrete world is inherently contingent (non-necessary). Part of what we mean when we say that the concrete world is real (not an illusion) is that it could be some other way than it is, that things could have unfolded some other way. It seems that there is some ineradicable element of indeterminacy to the physical world, and this indeterminacy is part and parcel of why the real world feels real. If we were trapped in some kind of immersive, scripted, movie-like illusion, we would be aware of its farcical nature, even if we were unable to escape it or do anything about it. Of course, the mere contemplation of such a dimension seems hellish to us and I will argue that this is one of the reasons that the simulation argument is so difficult to handle correctly.

So, what we're looking for is one or more principles that would explain (a) why the world must be a simulation and (b) why the simulation is convincing in all the ways that we mean that the observable physical world is convincing (does not seem to be an illusion, dream or farce).

The first principle that we are looking for is the substrate-independence of computation. What this means is that it does not matter what machinery you use to perform a computation, the computation itself can be performed by any suitable mechanism. Today, most computers are built from silicon transistors in integrated circuits but computers have been built from discrete transistors, electronic tubes, mechanical gearing systems, and so on. The determined hobbyist could construct any Boolean logic function from water, pipes and gravity -- a purely passive system, discounting the potential energy of the water in the reservoir.

The second principle that we are looking for is the universal utility of computation for making choices. Any mind -- even an artificial, non-cognitive mind -- will find that computation is useful for making choices. Our mammalian brains use vast amounts of physical computation to inform the choices that we make on a conscious level, even though we are almost completely unaware of all the real computation that our brains are performing. But even from a purely abstract perspective, we find that computation is the foundation for choice-making. Computation can allow an agent, even in a purely abstract game, such as Chess or Go, to recognize losing choices and identify choices that will bolster its own aims and ends.

The third principle that we are looking for is the universal summum bonum (henceforth SB.) In plain language, this means that we are looking for the goal or aim that any agent (that is, being capable of making choices) would have, or would tend to have. Philosophers have been arguing for thousands of years about what is the SB (Latin for "highest good") and we cannot solve that argument, here. However, we can provide a reasonable proxy for the SB that I think serves as a placeholder for whatever the actual SB might one day turn out to be when human philosophy has finally become sufficiently enlightened to agree on such matters.

What is this proxy SB, you ask? First, we must note that a SB that is "beyond reasonable argument" will have to be objective, since humans will always argue about any subjective point, whether out of obstinacy, devotion to the truth, or for some other reason. Second, this proxy SB must be sufficiently all-encompassing that no one could reasonably name something bigger or greater. I think we already have such a SB although the general awareness of this SB is still not very high.

Let us suppose, for a moment, that the famous P vs. NP problem will one day turn out, to everyone's shock and surprise, to resolve to P=NP. I'm not going to review the P vs. NP problem here, there are many good introductions to it. What I will do is quote an informal argument given by Scott Aaronson for why would should believe that P≠NP:

If P=NP, then the world would be a profoundly different place than we usually assume it to be. There would be no special value in “creative leaps,” no fundamental gap between solving a problem and recognizing the solution once it’s found. Everyone who could appreciate a symphony would be Mozart; everyone who could follow a step-by-step argument would be Gauss; everyone who could recognize a good investment strategy would be Warren Buffett. It’s possible to put the point in Darwinian terms: if this is the sort of universe we inhabited, why wouldn’t we already have evolved to take advantage of it?

On its face, Aaronson's point is very persuasive. Despite all the technical reasons to believe that P≠NP, this non-technical argument probably has the strongest appeal to anyone's intuition.

But...

Let us suppose that we really do live in a simulation. Then, it is possible that the conditions of the observable world have been tuned by the Simulators to make it seem, for whatever reason, that P≠NP. For the purpose of physics proper, such speculations are obviously useless. But for the purposes of metaphysics, such speculations are unavoidable... we're not doing real metaphysics if we simply shy away from contemplating inconvenient possibilities.

I intentionally capitalized "Simulators" in order to play on the common notion of simulation as some kind of computer-driven hall-of-mirrors. But I think this notion of simulation is deeply flawed and leads to all kinds of mistakes of reasoning about the simulation argument. At a very high level, the primary uses of computer simulation in the year 2020 are: science/technology, commerce, governance, warfare and entertainment. When we talk about world simulation, and we try to imagine generalizations of any of these contemporary uses of simulation to a universal scale, the consequences are invariably terrifying. A commerce-and-entertainment-driven simulation could lead to a dystopian world like that in Westworld or Ready, Player One. A warfare-driven simulation could lead to a dystopian nightmare like that depicted in the Terminator series or Source Code. A purely technological, machine-driven simulation could lead to a dystopian nightmare like that depicted in The Matrix series. And so on.

But all of these contemporary, human applications of computer simulation have a very contingent (non-necessary) flavor about them. For example, we need entertainment but it is not at all obvious that we need computerized entertainment. So, it is hard to imagine how there is anything truly universal about an entertainment-driven simulation. Similar arguments can be made for each of the major human interests that drive modern applications of computer simulation. Simply compare human uses of computation to natural ones (bearing in mind that all living systems, even viruses, are fundamentally computational systems.) In short, our contemporary applications of computer simulation are all distinctly anthropocentric, contingent, non-necessary.

What does this have to do with the P vs. NP problem? Well, there is one constraint that binds all living things in the observable world: scarcity. We live under the constraint of scarcity of space (mechanical mutual exclusion), scarcity of time (imminent bodily death), scarcity of energy, scarcity of mental capacity, memory, attention, and so on. All of these constraints prevent us from being the Mozart, Gauss or Buffett that Aaronson points out we would be if we lived in a world where P=NP. That we do not know how to escape these constraints does not, in itself, prove that these constraints are actually inescapable.

We earlier supposed, for the sake of argument, that P=NP. The point of this supposition is to present the following conundrum. Suppose that an unmistakably divine oracle or angelic messenger appeared to humanity and gave us the following message: "To all humanity: be it known that you will one day solve the problem of P vs. NP and you will succeed in proving that P=NP because this is the case. However, the arduous task of finding this proof has been left to you to discover. We look forward to you solving it and joining us in the Higher Realm." I think that basically every reasonable mathematician, scientist, computer scientist, engineer, and so on, would realize that the single most valuable goal of all human effort would be to discover the proof that P=NP. But the heavenly envoy already informed us that this task would be arduous -- the real question would then be, how arduous?

The most obvious, "dumb" method to solve the P vs. NP problem would be to apply a technique called proof-search. The basic idea is to just use blind search - write out every syntactically valid formal proof, in order, and check whether its conclusion is "P=NP". Since we have already been given the answer by the divine oracle, we know that this proof-search problem is decidable -- if we search long enough, eventually, our proof-search will halt and it will give us the proof that P=NP. Unfortunately, even knowing that P=NP, the question of how long we will have to search to find the proof is still undecidable. Given that mathematicians, as of yet, have no better ideas on how to prove that P=NP, it would be inexcusable not to devote all free computing resources to this monumental task. Perhaps with all free computing resources devoted to the task, globally, it will only take a few months or a year to find the solution.

But the problem could turn out to be much, much harder to solve. In this case, brute-force proof-search will not yield the answer, even after months or years of running. The next step is to design more intelligent proof-search. In this case, we would want to build better tools for mathematicians, tools that help convert their brains into "proof-search cores." Basically, we imagine the brains of all mathematicians on the planet as some kind of massively parallel, wetware computer that is driving search heuristics into our already-existing blind search proof-searcher. We want to accelerate this wetware computer as much as possible by building powerful assistive machines that handle all the intercommunication and processing tasks as seamlessly as possible. Between the massively parallel wetware computer comprised of the brains of human mathematicians, and the mechanical proof-searcher that they are guiding, we would have heuristic proof-search that is at least as intelligent as the most intelligent mathematician in the world and, hopefully, much more intelligent than that, collectively.

But the problem could turn out to be so hard that even this wetware-based heuristic proof-search machine fails to solve it. In this case, we would have to re-task the wetware proof-search machine. Rather than trying to directly solve the problem of P=NP, this proof-search machine would instead turn to solving a less ambitious problem that, hopefully, will help us solve the original problem as fast as possible. Notice that everything we have described about how to prove P=NP has been seat-of-the-pants. There is no a priori reason to believe that a wetware computer comprised of human brains interconnected by all the latest technology guiding a brute-force co-processor for proof-search will necessarily outperform just plain old proof-search. That is, it might turn out that such a computer is only as fast at finding the proof that P=NP as a plain old, unguided brute-force search would have been.

So, our new, less ambitious goal would turn to solving the general problem of proof-search acceleration for decidable problems. Since the best model we have of applied computation is the human brain, we would "cheat" off the brain itself, as an existing instance of a fast problem-solving machine. We would devote our wetware computer (and its associated co-processing machinery) to solving the brain and generalizing its capabilities for problem-solving in order to derive rigorous criteria for faster proof-search. The results of such investigations might be that the human brain can be significantly improved upon by making alterations to our DNA or making other tweaks to its operation. The result is that we would likely start redesigning ourselves to make improvements that would make us structurally more suited to solving any kind of proof-search problem, so that we will eventually find the proof that P=NP, as quickly as possible.

But once we start to engage in this self-referential process of tweaking our own makeup to enhance our ability to find the proof that P=NP, we will need to simulate the long-run effects of such tweaks. Because the human organism is made up of trillions of cells and because we are extremely complex dynamical systems, the amount of simulation required to calculate the long-run consequences of major changes to our brain and physiology is enormous. In fact, in order to do it properly, we would need to simulate a small, representative ecosystem, including air, water, microbes, radiation, and so on and so forth. We would need to construct simulations capable of exhaustively simulating the earth environment, at least to the scale of a small geographical region.

And here, at last, we have come full circle to the idea of a simulation which has some purpose that is not merely a generalization of narrow human interests, such as warfare, commerce, entertainment, and so on. Obviously, no angel has announced to us that P=NP. But if it is true that P=NP, it would be rational for the human species to devote an enormous amount of its available resources to discovering the proof of this. It's like we're ants living on top of a mountain of sugar, encased in bullet-proof steel. No matter how impossible it might seem to penetrate that steel armor, we are rational to devote almost all of our available resources to discovering any possible technique that would allow us to get through to that effectively infinite energy resource. 

In closing, let us return to Bostrom's original Simulation Argument. It is possible that we have always been living in a simulation and it is possible that the motivation of the Simulators is not curiosity about their origins but, rather, to find a proof that P=NP! Imagine that finding the proof that P=NP is so hard that our original cadre of wetware mathematician brains transformed themselves into something completely un-human-like: universe-spawning replicators that seed all available computational resources (including the natural environment of Earth) with viral computer code that hijacks whatever it comes in contact with and converts it into P=NP proof-searchers. It's like Gray Goo that doesn't kill you, it just makes you search for a proof that P=NP.

Bostrom's original Simulation Argument has no particular normative aspect to it. But it should be obvious that my tweak on his argument does. Specifically, if it is the case that we are in a simulation that has been spawned in the process of some kind of proof-search for the proof that P=NP, it would behoove us not to blindly thrash our available resources around according to whim or fancy but, rather, to try to perceive the template according to which the proof-search process is already unfolding and align ourselves with that template.

The reason for aligning is superrationality. While the idea of some kind of superior entity (or entities) capable of spawning a simulation on such a terrifying scale can lead to feelings of Lovecraftian horror, there is every reason to believe that a mind or minds that are searching for a proof that P=NP are basically aligned with human ethical values. Specifically, there is every reason to believe that such a mind or minds are predisposed to the principle of reciprocity -- if we approach the possible existence of such hypothetical Simulators with a charitable orientation (instead of a hostile orientation), then we can expect that they would hold themselves to have an equal obligation of charity towards us. If they were not also searching for the proof that P=NP, we might hold the reservation that we are simply being exploited as an animal resource or in some other way. But their mutual goal in finding a proof that P=NP means that they are subject to the constraint of scarcity which we also want to escape (if possible).

There is some interesting game theory that opens up if we posit the real existence of some kind of abstract agency or agencies. If we are in a simulation, then it is possible that the local rules of our observable universe are not truly universal and, in that case, it could be that the Simulators are interacting with us in ways that do not conform to our ordinary notions of the limits of agency. To cut to the chase, I specifically mean to invoke something like the pagan notion of "the gods", but without all the superstitious baggage they attributed to them. In other words, it could be the case that what our ancestors referred to as "the gods" were real, yet abstract, agents. These abstract agents could be nothing more than purely deterministic scripts coded into the simulation by the Simulators, something like the "bootstrap loader" used in digital computers to initialize and invoke the operating system software. But it is also possible that these agents are cognitive beings that are not limited by the laws of physics, as we understand them today. If this is the case, we might be able to leverage this fact to accelerate our alignment with the goal of the simulation, supposing that it is some kind of proof-search for P=NP, or a similar goal.

There is a lot of buzz surrounding quantum computation but there are also some jeremiad voices among leading quantum researchers. While we know that quantum computers are capable of solving large classes of interesting and useful problems faster than digital computers can, we do not know how cost-effective, scalable and practically useful quantum computers will be. It is not obvious that quantum computers are going to moot the constraints that I already mentioned in respect to the P vs. NP problem. Even if quantum computers turn out to be less immediately useful for applied computational problems than hoped, it is still very possible that they will play an important role in enabling the kind of extremely large-scale, detailed simulations mentioned above, simulations that will be required in order to make significant alterations to the human make-up. If the Simulators exist and if they are searching for a proof that P=NP, it is virtually certain that they are operating quantum computers.

The Universe is observationally indistinguishable from a quantum computer...
- Seth Lloyd (https://arxiv.org/pdf/1312.4455.pdf)

Divine Meditations - Part 3, Syncretism and Abstract Theology

The idea that Christianity has strayed from its roots has been improvised upon countless times. The apostolic succession churches (Roman Catholic, Eastern Orthodox and even a few Protestant churches) argue that Jesus established the Kingdom of God on Earth about 2,000 years ago. The Kingdom of God is not merely an idea, they argue, it is an actual kingdom. Instead of being built using earthly power like the kingdoms of men, this kingdom of Jesus has been built by descending from heaven in the hands of Jesus himself. This is what he meant when he told Pilate, "My kingdom is not from this world." In turn, Jesus handed over the keys to the kingdom to the apostles and, if the Church of Rome is to be believed in arguing its own case, specifically to Peter (see Matthew 16:18,19).

Most versions of ecumenism are heterodox. No matter how correct their criticisms of corruption within the church, the Protestants opened up Pandora's box by breaking away from the authority of the apostolic succession of Rome. One man's heretic is the next man's reformer and the splintering of the church in the West into countless denominations of varying levels of non-communion is the direct consequence of this fact.

The traditionalists, as always, are convinced that the resolution to the paradox of the status quo is to return to a long lost Golden Age, whether that be pre-Reformation Catholicism, pre-Constantinian Christianity or something else. However, short of Jesus personally descending from heaven in an orb of light and universally re-instituting some long lost Christian praxis, there are many insurmountable problems in the idea of returning to a past Golden Age. Time and history themselves are God's creation and it is an obvious mistake to dismiss the forward march of history as some kind of cosmic oversight on God's part, as though he fell asleep and lost track of things as the church veered off into destruction. Returning to the verse where Jesus promises to give the keys to the disciples, note that he first promises that "the gates of Hell will not prevail against [the church]", that is, the kingdom.

We cannot know what God has in mind for the future of the church on Earth. We know that the return of Christ is imminent, right around the corner. It is a mistake to become baffled by the amount of time that has passed since the Ascension. We are specifically commanded to "keep watch" and this is not an idle command. However, we must assess the works of God as they are, that is, we must use wisdom when asking what reasons God had in choosing to bring about the status quo.

The world is in a terrible mess and the church is no better off. This is beyond dispute. The sunny optimism of postmillenial eschatology suggests that the technological and economic progress of the last few centuries is leading us toward a future Golden Age when the saints will usher in the kingdom of God on Earth. This idea sounds attractive and plausible, in theory. Unfortunately, it directly contradicts the words of Jesus: "Then there will be great distress, unequaled from the beginning of the world until now—and never to be equaled again." (Matthew 24) Note that the Great Tribulation, as it is commonly known, is prophesied to be worse than anything that has ever happened from the creation of the world and never to be equaled again. This includes even the Flood of Noah. Elsewhere, Jesus prophesied that the earth and the heavens will pass away. The Bible is consistent in prophesying that the heavens and the earth will be completely destroyed by fire. If there will be a future Golden Age on earth, there stands between us and that age a terrible cataclysm and, afterwards, the total destruction of the world as we know it.

The central problem of the church -- today and throughout its entire history -- is its lack of true unity. The enemy, Jesus explained, is undivided (Matthew 12:24-28). The forces of wickedness march in lock-step. Their ranks are unbroken. Joel 2:1ff gives a picture of an invading army of locusts -- and the terror this brings -- as a picture of the looming judgment of God. This judgment is mediated not through a host of gentle saints but, rather, through an army of locusts that march in line, never swerving. These locusts are a picture of the spiritual forces of wickedness. Their immunity to fatigue and their unity is a picture of the assault of the "gates of Hell" and the undivided kingdom of Beelzebub that Jesus spoke about.

The church is not able to stand against the gates of Hell under its own power. It will always depend upon the power of God, of course, but it is not even able to form a unitary will, desire and purpose to stand against the gates of Hell by calling with one voice on the power of God for deliverance. Jesus explained to the disciples that this would be the defining mark of the church in its witness to the world.

My prayer is not for [the disciples] alone. I pray also for those who will believe in me through their message, that all of them may be one, Father, just as you are in me and I am in you. May they also be in us so that the world may believe that you have sent me. I have given them the glory that you gave me, that they may be one as we are one — I in them and you in me — so that they may be brought to complete unity. Then the world will know that you sent me and have loved them even as you have loved me. (John 17:20-23)

If there is one thing the church thoroughly understands, it is the call of the Gospel. The church yearns for those in the world to come to salvation through Jesus. But she stops short of following through to completion because she keeps looking to her own understanding rather than relying on the mind of Christ. Like Peter, she turns her eyes from Jesus and looks at the waves. "Who will stop the normalization of homosexuality in society? Who will save the children from being aborted in increasing numbers?" And so on. The answer given by Scripture is the same answer that Jesus gave to Pilate: the Kingdom is not from this world. If it were from this world, then Jesus would have us fight for the things of this world: the civic order, the political affairs, the cultural context. None of these things matter to the church. None of the things that pertain to this world matter to the church because they are all slated to be destroyed.

In case you might think that we are getting carried away, let's look at what the New Testament has to say:

Do not let anyone judge you by what you eat or drink, or with regard to a religious festival, a New Moon celebration or a Sabbath day. These are a shadow of the things that were to come; the reality, however, is found in Christ. Do not let anyone who delights in false humility and the worship of angels disqualify you. Such a person also goes into great detail about what they have seen; they are puffed up with idle notions by their unspiritual mind. They have lost connection with the head, from whom the whole body, supported and held together by its ligaments and sinews, grows as God causes it to grow.

Since you died with Christ to the elemental spiritual forces of this world, why, as though you still belonged to the world, do you submit to its rules: “Do not handle! Do not taste! Do not touch!”? These rules, which have to do with things that are all destined to perish with use, are based on merely human commands and teachings. Such regulations indeed have an appearance of wisdom, with their self-imposed worship, their false humility and their harsh treatment of the body, but they lack any value in restraining sensual indulgence. (Colossians 2:16-23)

How long should a woman's skirt be? Should her hair be put up or let down? Or perhaps her head should be covered just to be safe. These are the very kinds of questions that Paul is repudiating in Colossians 2. Whatever rules pertain to social decency are a sufficient guide for the believer. Honest, common sense needs no supplement with legalistic guidelines. This is why Paul was able to say in 1 Corinthians 9:

To the Jews I became like a Jew, to win the Jews. To those under the law I became like one under the law (though I myself am not under the law), so as to win those under the law. To those not having the law I became like one not having the law (though I am not free from God’s law but am under Christ’s law), so as to win those not having the law. To the weak I became weak, to win the weak. I have become all things to all people so that by all possible means I might save some.

The position of the church with respect to the eschaton is an exact parallel with the position of the people of Israel with respect to the Messiah. We look forward to Messiah's return exactly as they looked forward to the coming of the Redeemer. The Old Testament, then, should be read by us with intense scrutiny to find out the causes of the failures of the people of Israel to remain steadfast while awaiting the promised Redeemer. There are many causes but one theme stands well above all others and forms the central theme of the marital argument between unfaithful Israel and her faithful husband: idolatry.

As far as I know, no Christian church literally worships idols, despite the iconoclastic hyper-ventilation of the Protestants over Roman and Eastern iconography. However, the church is filled to the brim with idolatry of the heart, that is, idolatry involving the soul. Idolatry is more than just turning one's attention away from God, even though this is always involved in idolatry. Idolatry is a question of one's ultimate loyalty, one's root devotion and root motivation.

Why did the Israelites turn away? We can glibly answer, "because they were sinners", and this is true, but it misses the point. What were the specific reasons and motivations that drove them to turn away from devotion to God? A hint is given in the story of the eradication of the Mosaic judges from Israel in 1 Samuel 8. God says to Samuel, "They have rejected me as their king." They wanted a human king because their hearts were idolatrous. Throughout the Old Testament, God compares the people of Israel to an adulterous wife. She seeks other lovers because, in her heart, she has already despised her husband, she no longer values him in himself. This is why she is now vulnerable to the charms of others and she becomes dazzled by the pomp and bravado of her husband's competitors.

An example of contemporary spiritual idolatry in the church that is exactly parallel to the idolatry of the Israelites is Christian conservativism in the US. The Republicanization of Christianity is an exact analogue of the people of Israel turning away to serve other gods. Instead of relying on the power of God to deliver the church from the sweeping tide of secularization and the revival of ancient Greco-Roman social mores, the church has turned to human deliverers. To that extent, she has rejected Christ and has indulged in idolatrous devotion to the State and has become dazzled with its pomp and bravado, as though the State has within itself the power to change anything at all, and as though changing anything in this world matters to God who is going to bring everything in this world to final destruction in a great fire.

So, what is the alternative? The church, like the ancient Israelites, has become filled with hypocrites and idolators, a necrotic corpse seeking to preserve the status quo and/or revive some imagined Golden Age of the past. Yet Scripture conclusively informs us that the gates of Hell have not prevailed against the church because they cannot prevail against it. God himself preserves her, just as he preserved his chosen people in the age before Christ.

In this series, I am going to argue that there is a notional solution to the problem. This solution is useless in the sense that the Kingdom of Heaven is not a matter of words, but of action or power, (1 Corinthians 4:20). This is nothing but talk. But I hope that it finds some use in illuminating the narrow path that is the path to eternal life by casting the history of the church in the context of its origins and outcomes.

As I mentioned at the outset of this series, I will be treating Scripture and the church tradition as the basis of authority. Authority is not synonymous with truth, even though these never come into conflict within the kingdom of God. The difference between authority and truth is important to emphasize since I think this is a major cause of confusion within the church today and throughout its history. Truth has to do with that which cannot be any other way. Jesus said, "I am ... the Truth. No one comes to the Father but through me." That he is the Truth is the basis of his exclusivity. If he were merely speaking from authority, then there might be some other way that things could be. Just as 2 and 2 absolutely sum to 4, so there is no other way that things can be. Jesus is absolutely the only way to the Father, that is, the only way to Heaven.

Authority, on the other hand, pertains to that which could be some other way, but which has been decreed to be as it is. In the famous words of the King of Siam in Anna and the King: "So let it be written, so let it be done." The Scriptures, the testimony of the church fathers, the saints and the martyrs, as well as the received traditions and writings of the church in their many manifestations are the mechanism by which Jesus -- the head of the church -- has set down his decree. This is the authority which he claimed in Matthew 28:18 -- "All authority in heaven and on earth has been given to me." This is what John meant when he said of Jesus, "In the beginning was the Word." The Word is who the Word is and no man can alter him (Luke 16:17, Hebrews 13:8, etc.)

It is easy to overlook the most important aspect of divine authority in the life of the believer -- the testimony of the Holy Spirit. The Holy Spirit is the living testimony of God to the believer and he speaks as authoritatively today as he did to the prophets and the authors of Scripture. This has nothing to do with private interpretations of Scripture since the mind of God cannot contradict itself. Today, we can say with confidence that the Protestant Reformation accomplished at least one important change within the church: the growing recognition of the centrality of the Holy Spirit within the life of the individual believer.

God speaks to us authoritatively through the external witness of the Scriptures and the visible church, as well through the internal testimony of the Holy Spirit. But it is a mistake to think that God only speaks authoritatively. That God is the Creator shows that God is a divine artist and that our artistic ability is a reflection of God's artistry, stemming from the image of God within us. I assert that a preoccupation with God's authoritative speech can arise from idolatry within the heart, specifically, the worship of power. God's power deserves our worship but only God's power does. The idolator is preoccupied with power itself and idolatry within the church, therefore, often manifests in a preoccupation with authority. There can be no doubt that the ranks of Christian leaders in the many sects of Christian belief are filled to the brim with power-worshipers who don't otherwise give a damn about God.

If David is to be believed when he says in Psalm 19, "The heavens declare the glory of God, the skies proclaim the work of his hands", then perhaps we should wonder what exactly God is saying to us through these communiques. The lesson of Psalm 19 can be boiled down to a simple fact: God speaks through all things. After all, he is the creator of everything.

When the church becomes embroiled in heart idolatry and seeks to influence the world, she loses sight of the reality of God's boundless power. "Surely the nations are like a drop in a bucket [to Him]; they are regarded as dust on the scales; he weighs the islands as though they were fine dust." (Isaiah 40:15) In turn, she begins to regard the happenings of this world as though they must be lobbied for or against. And this, in turn, deafens and blinds her to God's voice which is the still, small whisper that pervades everything whatsoever. The happenings of this world are not something to be fought for or against. Rather, they are the movement of God's decree through history in this fallen age, nothing more and nothing less. If the gates of Hell cannot prevail against the church, then the "invasion of foreign culture" cannot prevail against her. If the gates of Hell cannot prevail against the church, then the resurgence of paganism in modern society cannot prevail against her. If the gates of Hell cannot prevail against the church, then modern science cannot prevail against her, heresy cannot prevail against her, the beliefs of other religions cannot prevail against her, and so on and so forth. There is nothing in this world that she has to fear and she is in exactly the same position as Peter walking upon the waves. She must keep her gaze fixed upon Jesus and she must ignore and despise the tempest.

The thesis of this series is that Christianity is inherently syncretic. Jesus came to bring salvation to the Jews (first) and also to the Gentiles (the whole world). That is the root of syncretism that the church has always feared to embrace out of fear of the tempest. If we concede that the wisdom of God can be found among the writings of Buddha, for example, then we are watering down the exclusivity of the Gospel and conceding that there is a tiny slot in the sheep-pen through which others can find another way (John 10:1).

But to conclude this is to take our eyes off the Savior and focus on the storm. Was not Jesus in complete control of the tempest, even as Peter began to slip under the waves? In another case when Jesus is sleeping in the midst of a storm, he gets up and rebukes it. Afterwards, the disciples were amazed and asked one another, "What sort of man is this? Even the wind and the waves obey him!" (Matthew 8:27) Is the encroaching spread of Islam more powerful than the one who commands the wind and the waves? Is the rise of secular atheism more powerful than the one who commands the wind and the waves? Is the marked increase of wickedness in this world -- the very thing that Jesus prophesied would come -- more powerful than the one who commands the wind and the waves? The church cannot be unified in voice and heart until she takes her eyes off the storm and looks to the Savior only. She cannot fulfill her mission to bring the message of the Gospel to the world and to cause everyone to see that Jesus has been sent by God, until she is one. That is, when we are one in brotherhood with each other, and one with God in Christ, then the world will know that the heavenly Father sent Jesus to earth to be the Messiah.

So, what exactly do I mean by the assertion that Christianity is syncretic? Wikipedia defines syncretism as,

... the combining of different beliefs, while blending practices of various schools of thought. Syncretism involves the merging or assimilation of several originally discrete traditions, especially in the theology and mythology of religion, thus asserting an underlying unity and allowing for an inclusive approach to other faiths. Syncretism also occurs commonly in expressions of arts and culture as well as politics.

The Protestant reformers strongly objected to the syncretic practices of the Roman church. Pagan holidays were sanitized and incorporated into the Christian calendar. Pagan mythological heroes and even gods were also sanitized and sometimes identified with saints or angels or inducted in as saints in their own right. Today, these past events are beyond correction short of Jesus descending from heaven in person and explaining where things went wrong and how we are to correct them. Rather, our mistake is in assuming that the tempest caught the head of the church off guard, that he erred in allowing these pagan influences to be syncretically absorbed into the canon of Christian tradition and orthodoxy. Should we not, rather, see the final outcome of the divine decree for what it is? He has said, "So let it be written, so let it be done."

The notional solution should be obvious by now. The nations of the world, their cultures and their mythologies are exactly those nations, cultures and mythologies which God has decreed to be. To wring our hands at the terrifying thought of the church overrun by Muslims, atheists and homosexuals is to be guilty of unbelief and to flatly deny the words of Jesus. The gates of Hell, we implicitly assert, can prevail against the church that Jesus built. Faith tells us that the church is indestructible. There is nothing that this world can throw against her which can destroy her. As followers of Christ, we can never take the carnality of the world into our hearts, because this is mutually exclusive with the Spirit, the ethereal light of salvation. But neither does the carnality of the world have any power to pollute us and we do well to repudiate its power.

Once again, it might be objected that we are getting carried away, but let's see what the New Testament has to say:

Since Christ suffered in his body, arm yourselves also with the same attitude, because whoever suffers in the body is done with sin. As a result, they do not live the rest of their earthly lives for evil human desires, but rather for the will of God. For you have spent enough time in the past doing what pagans choose to do—living in debauchery, lust, drunkenness, orgies, carousing and detestable idolatry...this is the reason the gospel was preached even to those who are now dead, so that they might be judged according to human standards in regard to the body, but live according to God in regard to the spirit. (1 Peter 4:1-6)

While sanctification is gradual, it must reach culmination. And it is the power of God alone that brings about the culmination of sanctification. The result is that the power of sin over us is broken entirely. This is the point and purpose of salvation. This is why Jesus admonished us, "Be perfect, therefore, as your heavenly Father is perfect." (Matthew 5:48)

To drive the point home, allow me to extend Paul's discussion of the church as the body of Christ in 1 Corinthians 12:12ff. Let us say that you have been bitten by a spider and the bite has become infected. Some of your body's cells are directly exposed to the spider's venom. They perform their role to protect the body by working to prevent the further spread of the venom. When everything works as it is designed to do, the body itself is preserved. We can think of this fallen world as a kind of infectious disease that has gotten in and corrupted our true, divine nature as creatures made in the image of God. This corruption will certainly be expelled at the end of the age. In the meantime, we must not shirk from doing the will of God here on earth even where it entails exposure to the filth and venom of this age. We must resist the fleshly urge to try to carve out a comfortably civilized corner of the world so that we can, like the lazy steward, bury the master's treasures to be repaid on his return, without interest.

The syncretic umbrella of Christianity should not be understood as some kind of synthesis of world religions or forced ecumenism whereby heretics, hypocrites and idolaters can avoid expulsion from the body. Rather, it is to be understood as an act of faith, leaving the shepherding to the Good Shepherd while keeping our eyes on him and off the tempest around us. As concerns any matter of spiritual authority that lies within the realm of external witness, it is Scripture and the received, orthodox traditions which inform the conscience, being themselves the outworking of the divine decree in history. For the rest, the internal testimony of the Holy Spirit is a sufficient authority.


In closing, I want to give a brief sketch of the direction that I want to take this series. Specifically, I am going to utilize a syncretic approach to appropriate from other cultures and other religious traditions outside of Christianity in order to inform our view of God's work in the world, in specific detail. In particular, I am going to present a generalized approach to theology that builds upon the logical approach of medieval, scholastic theology. I call this approach Abstract Theology. It is not intended to supplant but, rather, supplement the traditional approach to theology. Where traditional theology speaks authoritatively, Abstract Theology speaks deferentially. It prods us to use our God-given creativity to imagine, artistically, what God is like, what it means to have a relationship with Him, what it means to dwell with God in heaven, and so on.

Announcing my new blog, Machine Elegant

I'll be posting tech-related and technical articles on Machine Elegant. This will allow me to make each blog a little more focused -- CF will be focused on philosophical topics and ME will be focused on technical topics.

Why do people believe in conspiracy theories?

Conspiracy theories have played, and continue to play, a prominent role in American culture. Belief in UFOs, suspicions about the official account of the assassination of JFK or the destruction of the World Trade Center on 9/11 are just a few examples of the many kinds of outlandish beliefs that Americans -- and even some non-Americans -- hold.

The causes of belief in conspiracy theories can be broken down into two broad categories -- internal causes and external causes. There is a kaleidoscope of internal causes of belief in conspiracy theories. Many kinds of mental illness involve symptoms of conspiracy theory belief. Conspiracy theory belief can fuel narcissistic delusions of grandeur -- after all, I must be a very important person to be the target of such a grand conspiracy!

But it is not just mental illness that can cause people to believe in outlandish conspiracy theories. Humans are notoriously susceptible to obvious mistakes of reasoning (for example, the Baader-Meinhof effect). We are not even good at probabilistic reasoning. And some people just have a melancholic temperament -- they inhabit a world in which they imagine a villain hiding behind every corner, peeking out of every window and slinking along every alley-way. Mistakes of reasoning, cognitive biases, mental dysfunctions, mental illness, emotional dispositions -- the internal causes of conspiracy theory belief are numerous and diverse.

In addition to the internal causes of conspiracy theory belief are the external causes. Everyone agrees that there are real, criminal conspiracies -- there are even laws on the books to punish criminal conspiracies, such as the RICOH statute. Unfortunately, not all criminals are dumb. The smartest criminals are able to evade detection for arbitrarily long periods of time. They operate in offshore jurisdictions, split their operations across borders and take other counter-measures that moot ordinary police work. Newer forms of policing have been invented over the course of many decades, but the fact is that police methods are, and always have been, at least one step behind the latest methods of criminal activity. That one step is all that the most astute and well-organized criminals need to operate.

It's bad enough that there are criminals who are intelligent enough to evade capture by the police and operate highly organized systems of crime. But what happens to all the money that is generated by organized crime syndicates? Does it just get buried in the ground? Try as you might, you could never purchase a billion dollars' worth of Lamborghinis, so the untold billions of dollars captured by South American drug cartels -- as just one example -- can't all be going into luxury items. No, the bulk of the money is "laundered" (put through apparently legitimate channels, such as shipping or warehousing companies) and then put into ordinary business investments. In short, there is some unknown, non-negligible percentage of ordinary assets -- real estate, bonds, stocks, and so on -- that are actually the proceeds of organized crime.

But are organized crime syndicates really the apex of power and corruption in the world? Again and again, throughout history, we have seen the emergence of depraved, autocratic rulers hell-bent on one narcissistic adventure, or another, often trampling over the skulls of millions of their murder victims. By comparison, the damage that can be done by any one private criminal is quite limited in the grand scheme of things. To make a really big mess, you need a national government with domestic police, tanks, ships, bombs and armies. But to anyone who opposed corruption in, say, Nazi Germany, what were the Nazis except the grandest and most sinister of conspiracies?


Ordinary people really cannot comprehend what it means to be extremely wealthy or powerful so we underestimate the structural influence of power on our lives. We are used to managing almost all of the mundane details of our lives. When the light bill is due. Which brand of dog food to buy. How many miles since the last time the car had a tune-up. Very wealthy and powerful people do not have to waste time and energy on these kinds of concerns. They have paid staff to take care of these -- and many more -- details. When ordinary people think about a "grand conspiracy", they fail to imagine what is really possible because they cannot imagine how they themselves could orchestrate such complex events at such large scales. Given the amount of criminal cash flow that we know exists in the illegal drug trade alone, it is impossible to believe that major corruption scandals, such as the Enron corruption scandal, are as exceptional as we are led to believe. It would require a superhuman capacity for naivete in order to believe that large-scale, white-collar criminal conspiracies are not commonplace. In the words of Gordon Gekko: "Fund managers can't beat the S&P 500 ... because they're sheep, and sheep get slaughtered."

The Nazis reduced countless millions of people to destitution, internment and death. You cannot operate a vast, criminal conspiracy without creating a lot of victims. Victims of crimes that are connected to organized corruption become acutely aware of the fact of corruption when the ordinary means of remedy against crime -- such as reporting it to the police -- malfunction in ways that are inexplicable. Let us say that a local gang holds up your corner store. You call the police and they dispatch an officer to take the report. Unbeknownst to you, this officer happens to be corrupt and on the take from the very gang that has robbed you. You find that the officer is singularly unhelpful, maybe even rude and disrespectful or incredulous. Or, maybe he is gushingly apologetic and offers a lot of emotional sympathy, while offering to take the tapes in for "evidence". Such petty conspiracy is indisputably real and has happened countless times. But the pattern generalizes. And it is this gagging effect by which corrupt conspirators silence their victims -- or even reverse the situation and accuse their victims of criminal behavior, irrationality or mental illness.

It is true that many people hold conspiracy theory beliefs because of some internal cause, not because of any actual evidence of crime which they have witnessed or experienced. But, by the same token, it is also true that many people -- ordinary people -- have been victimized at the hands of real conspiracies. We can argue about the extent of the problem, but the fact of the problem is beyond reasonable dispute.

It is obvious that any real criminal conspirator wishes to remain concealed and always to misdirect attention off of himself or herself. This is true in the small, and it is true in the large. Thus, using logic, we can infer that the smartest, most well-organized and most well-resourced criminals will seek to utilize the methods of mass communication -- that is, propaganda -- to conceal the true nature of their activities. In particular, such individuals will be maximally interested in discrediting the very notion of sinister conspiracies. Pedestrian notions about how effective such individuals can be at influencing public opinion are likely to be mistaken because ordinary people do not really understand how things are done at such large scales. And once we understand that conspirators and their victims have opposite motivations in respect to what people believe about conspiracies, we see that finding out the truth is really a problem in game theory, that is, it's a really hard problem.

In closing, it is worth noting that there are two, equally mistaken positions that one can take on the question of the existence of conspiracies. On the one hand, there is the pollyannaish view that there no real conspiracies or, at least, no real, large-scale conspiracies. On the other hand, there is Lovecraftian horror, the sneaking suspicion that everything is a sinister conspiracy. As it was succinctly put on a viral conspiracy theory video: "Everything is a rich man's trick." Both of these views are symptoms of lazy thinking. They fail to honestly handle the thorny problem of how to think about the category of sinister, large-scale conspiracies. The truth of the matter is that it is not easy to know the truth about conspiracies precisely because the smartest, most well-organized and most well-resourced conspirators seek to corrupt knowledge itself. After all, the corruption of knowledge is just a variation on keeping double sets of books.

The Continuum and Super-Resolution

How many rocks are there in this jar?:

Of course, it's just a photograph of the jar, so you don't have enough information to answer the question. But if I were to give you a jar just like this, containing sand and rocks of various sizes, how would you count? What, exactly, is a rock? We don't ordinarily think of sand as being rocks but that's precisely what sand is, a whole lot of really small rocks. With enough patience, you could actually work through all the grains of sand in this jar, and give some definite answer. "There are XYZ rocks in this jar."

The point of this question is to think about relative scale and how this connects to the question of what is discrete and what is continuous. After all, we could grind the sand in this jar down into ever finer grit, so that the process of counting would become so laborious and time-consuming that you would give up. If we continue on grinding the sand down in this way, we know that we will eventually reach the point that we have broken the sand down into its molecular components, at which point, it will become impossible to keep it from dispersing into the air as an aerosol. Air, being continuous, is a gas and is not discrete -- it is continuous.

Let's consider for a moment the known mechanics of how the brain tells apart distinct objects. When we look at a photo containing two distinct objects, we know immediately whether they are different or the same:

This "visual pattern-recognition" ability of the brain is not magic. Neurons in the brain "fire" in patterns that enable the brain to decide what sort of thing the retina is seeing. The basic theory of neurons -- that they are involved in pattern-matching and other higher-order cognition tasks -- has been confirmed not only by empirical measurement of neurons in the laboratory, but also by mimicking the capabilities of neurons with artificial neural networks (ANNs). While ANNs do not exactly mimic neurons in the brain, they capture many of the essential properties of the neurons in the brain, especially the capacity of the brain to learn new patterns it has never seen and to do this only by "looking at examples" rather than being told a formula for how to recognize one pattern from another.

The point of the rocks in the jar is that rocks, pebbles and sand show how our naive confidence in our ability to number things breaks down when we encounter objects at the limits of our perception. We can easily tell a dog from a tree under virtually any condition except the complete absence of light or being so far away that we cannot distinguish any objects at all. But defining the difference between a rock and sand is hard. Unless we are very close to it, we perceive sand in a similar way to how we perceive water. It is virtually fluid and it might as well be a continuum, even though we can see, upon close inspection, that it is not. Sand stands at the cross-roads between the discrete (rocks) and the continuous (air, water, etc.) For anyone who has studied the calculus, this will seem very natural. If you cut something up finely enough (infinitely fine, in the limit), you will be able to find its precise length, area or volume, no matter how complicated that object may originally have been.

Some organisms have much more limited senses and pattern-recognition ability than we do. For example, there are simple underwater life forms that can move towards warmth and away from cold by detecting a temperature difference. There are some animals with only the ability to sense the presence of light (and its direction) but are otherwise completely blind. And so on. Such limited sense abilities are almost binary, like "ON" and "OFF". Even though our brains are much fancier neuronal systems, we are really utilizing the same physical mechanisms, just refined and extended to a much greater degree. In short, pattern-recognition -- whether simple or complex -- is the same phenomenon in all living things.

Let's consider the set of natural numbers, or counting numbers. They are 1, 2, 3, ... The ellipsis can be read "on and on" or "so on, and so forth." It's a stand-in for the simple idea that we can always extend this sequence by incrementing the last element. If the last element were 173, we could extend it by adding 1, giving 174. The same is true for any other number. And we all know who the winner is in the Name the Biggest Number game: infinity!

But what, exactly, is infinity? Nobody has ever seen, heard or thought anything that is infinite. Every particular fact of our world and ourselves is finite. While infinity is common in modern mathematics, some mathematicians reject the idea of infinity altogether - this view is called finitism. Some of them have a conceptual objection to the idea of infinity. Some of them have formal objections to the idea of infinity. The view I will espouse here is that infinity is as real and useful as any other sort of mathematical object.

Let me begin by pointing out that number and enumeration are themselves really a metaphorical construct, built on our capacity to recognize patterns. Consider the image above depicting a tree and a dog. We say "there is one tree and one dog in this image," as though this is a fundamental fact of reality. But look again at the image of the jar of rocks -- how many rocks are in that jar? Is there any fundamental fact of reality that would serve as a reasonable answer to the question "How many rocks are in the jar?" We might object that the question is ill-posed in the case of the jar of rocks but this is just pedantry. The reason there is no good answer to the question is because what we mean by "the number of things" is itself vague in many cases, and this happens to be one of them!

At the risk of belaboring the point, let us spell out what we mean by the question, "How many dogs or trees or rocks are there in this image?" What we really mean is what answer would an ordinary human give when given the image and the question[1]. So, we can reduce the question of numeration itself to an empirical test by simply giving images to people and querying them as to how many objects of such-and-such type are in the image. (In fact, we could just as well use physical objects or images.) So, when we say, "there is one tree in this image," what we really mean is that any ordinary person would agree that they see one tree in the image (and we ourselves, being an ordinary person, also see this).

But as I pointed out above, pattern-recognition is not magic, nor is it unique to humans. In other words, there is no inherent "number-ness" in the one tree or one dog in the image. For any practitioner of Machine Learning, this is embarrassingly obvious -- an image is a large, two-dimensional array of numerical values called "pixels" [2] and there is no obvious answer to the question, "how many objects are there in this array of pixels?" Our brains are so accustomed to visual recognition of objects that it seems to us automatic and so fundamental as to be beyond analysis. How many trees in the image? There just is one tree, it needs no further elucidation. But imagine trying to write a program that would answer the question "How many objects are there in this image?" for any image I choose to give you. It turns out that this problem is so hard that it is unlikely that any human could ever write a program to do it. Instead, we have turned to Machine Learning algorithms to solve the problem.

So far, I have not mentioned the continuum. The continuum is an important concept in mathematics. It has been heavily studied but there are still important, unresolved foundational questions surrounding it. What is the continuum? Well, there are several ways to think about it but perhaps the easiest intuition is to think of an ideal geometric line, in the same way that the Greeks thought about it. An ideal geometric line is an analytical object that extends an ordinary line we might draw on a sheet of paper by imagining a line that is perfectly straight, having zero width, having some non-zero length, and being "dense" in some sense that, no matter how far you zoom in, you can't find any "gaps" in the line. Such a line corresponds to the mathematical idea of continuity.

In non-mathematical language, what the Continuum Hypothesis (CH) is really asking is how many points are there on the line? A naive answer would be "infinitely many." One reason this question is so interesting to mathematicians is that it turns out that the naive answer is wrong! Suppose you attempt to map the natural numbers 1, 2, 3, ... to the geometric line in such a way as to leave no gaps. 20th-century mathematics has proved that it is impossible to pack the natural numbers on to the line so densely that it is impossible to find a gap between any two points, even though there are infinitely many of them! Even if we map the rational numbers (a/b for any natural numbers a and b) to the number line, there will not be enough of them to make sure there are no gaps on the line. Therefore, in some very fundamental sense, there are "more than infinitely many" points on the line. This is a surprising result.

This isn't quite the whole story on the CH. There is a set of numbers which is "infinitely larger" than the set of all natural numbers. This set can be formed by taking the power set of the set of all natural numbers. This set (called omega-1) is so dense that no gaps can be found between any two distinct points, which gives it a suspicious resemblance to the continuum. While no one has proved that omega-1 is coextensive with the continuum, the CH is the hypothetical position that this the case (even though it is commonly stated in different terms, as it is on Wikipedia). The other alternative is that the continuum maps to some higher infinity[3].

One of the reasons I find this topic interesting is that it has indirect implications for the material world. In quantum theory, we can recognize some loose correspondence between the continuum and waves (continuous phenomena), and between discrete sets (such as the natural numbers) and particles (discrete phenomena).

To pursue this connection further, let's return to the problem of trying to write a program that can recognize objects. Recent developments in Machine Learning have led to a technology called super-resolution. Super-resolution works a lot like the fictional depictions in movies where spy satellite images can "freeze and enhance!" It allows more detail to be added to a low-resolution image by training a neural net to interpolate or "hallucinate" the missing details. Obviously, this won't give you license-plate numbers from a grainy image of a vehicle on a distant horizon, but it will allow a significant -- perhaps massive -- reduction in the amount of bandwidth required to transmit images, movies, audio and other forms of data.

What does this have to do with either infinity or the continuum? Well, if we suppose that Nature is as frugal with information as she is with all other material resources, it seems impossible to believe that the world constructed by our perception actually corresponds to what we imagine it to be. Let me explain. Suppose you are sitting on a mountain-top on a clear day, surveying a wide valley beneath you. As your eyes scan across the horizon, there are countless details that they can perceive. In fact, I have experienced a slight feeling of vertigo when looking across a large landscape, not from fear of heights or anything like that, but from the sheer immensity of how much detail is visible. It's almost like the brain is struggling to take it all in, there's just so much. But the idea of super-resolution tells us that almost all of the photons striking the eye are wasted information! If I look at a tree, my brain can (and does) interpolate the details of the tree, to one extent or another[4]. When we look very closely at something (with the "high-resolution" part of the eye), there is obviously much less interpolation occurring but we do not know that it is zero. In any case, the fact remains that physical theories based on the extrapolation from subjective experience assert that all the photons reflected off every leaf of every tree and every pebble or grain of sand in your field of view... every single one of those photons is striking your retina and most of them simply cannot be resolved because you only have so many rods and cones in your retina (resolution limit).

In computer systems, we use a "query-and-response" system to manage large information stores. This is precisely how any search engine works. You do not download the entire search engine's index (this index would be many terabytes or even petabytes in size!) Rather, you send a query to the search engine saying, "This is the information I'm looking for", and the search engine responds with the information it has, relevant to your query. If we take the observer effect seriously, it is not difficult to imagine that our observation of the material world has the same effect upon it.

This might seem a little strange because it feels like we're saying, "There are no trees until you open your eyes and look at them." But I think that's an over-simplification that misses the mark. It's not that there are no trees until we look. It's that there is no visual information about the trees that are there, until we open our eyes and look. An astute reader will object again, "Ah, but there is visual information since the photons produce enough light by reflection that some of the light is going through the eyelids, even when closed." Once again, this misses the point - we could put on black-out goggles or go indoors and close the door, or whatever. The point is that no information is sent but that information which would make a difference. If there is no effect upon the observer, there is no information transmitted at all. In short, when the proverbial tree falls with no one around to hear, it really makes no sound.

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[1] Note that I am not trying to establish the supremacy of empirical methods over analytical methods. As I see it, both have a place in any well-developed system of investigation into truth, as such.

[2] Actually, there are three such arrays in the case of color images, one each for the red, green and blue channels.

[3] Georg Cantor discovered that there is actually a hierarchy of infinite sets and that this hierarchy is infinitely large. The most basic hierarchy of infinite sets are called the aleph numbers and are formed by taking successive power sets of the set of natural numbers, N. Aleph-0 is the cardinality (magnitude/size) of N. Aleph-1 is the cardinality of the power set of N which is denoted 2^aleph-0. Aleph-2 is the cardinality of the power set of aleph-1. And so on. This hierarchy is infinitely high but it does not exhaust infinite cardinals. There is a branch of mathematics that studies infinite cardinals beyond the alephs, it is called large cardinal theory.

[4] We know that it interpolates because of the way the peripheral vision works, especially the blind-spot.

Divine Meditations - Part 2, God and the Devil

When I was in my early teens, I would take a lawnmower around the neighborhood and mow lawns for $5 or $10, depending on the size of the lawn. I was once given the address and phone number for an older couple who needed their lawn mowed, but I wouldn't need to use my own mower because they had a mower. When I arrived, I went out to the shed and it was a pretty typical lawn shed except for one thing - it was plastered inside with nudie pictures. I was a little creeped out by this, not because I was repulsed by the photos -- at that age, I was quite interested in them, of course -- but because something felt deeply wrong. Having already gone into the shed, and having already anticipated the $20 I was about to earn, I hauled the mower out and mowed the unusually large back yard. Later that afternoon when I was finished, I got the payment, thanked the old man and his wife, got on my bike and pedaled home. Nothing bad happened but I never went back or called them again and I never told anybody about the photos.

Deep down inside of us, there is a part of us that knows that danger is real, that horrible things happen to people and that one of those horrible things could happen to us. This knowledge is why we have the capacity for fear. From a scriptural perspective, this is an aspect of the fallen world and this knowledge is the very thing that Adam and Eve did not have in the Garden of Eden, having not yet partaken of the tree of the knowledge of good and evil.

In the collective psyche of humanity, the negative potentialities of the human condition have tended to get associated with one another, and this association (like many things) has tended to get personified, anthropomorphized. This anthropomorphic personification of evil we call "the Devil" in English, but it has gone by many names and forms throughout history and across the globe.

In many world religions, it is held that the force for good (God or the gods) and the force for evil (the Devil or devils) are pitted against one another in a form of unending cosmic warfare. This invisible cosmic warfare is taken to be the explanation for evil in this world -- the good does not always win out because sometimes it is simply overpowered by the evil. Today, we might refer to this as Star Wars theology -- the Universe is pervaded by an impersonal force comprised of two, equal halves, each standing in opposition to one another. The "dark side" of the force acknowledges no moral limits and is invariably based on might-makes-right. The "light side" of the force holds to mutuality in relations, and has faith that the soft power of being right will never be completely obliterated by the hard power of might. While the details vary from one religion to another, the sketch outline is remarkably consistent.

This is not the orthodox Christian view of the battle between God and what Paul terms "spiritual wickedness in high places" (the heavens). It is not the view of ancient Judaism, of which Christianity is a sect. In fact, it is not obvious from the texts exactly what the Devil wants. God's goals are clearly spelled out, however. God's highest aim and end is to glorify himself. In John 12, Jesus is prophesying his death and he prays aloud, "Father, glorify your name!" Afterwards, there is a thunderous voice from heaven, audible to everyone around: "I have glorified it, and will glorify it again." In Isaiah 48, God says, "For my own sake, I [delay my wrath]. How can I let myself be defamed [by destroying you completely]? I will not yield my glory to another." The language is very clear, especially in the Old Testament. The imagery is that of the conquering king who, by annexing more and more territory (ultimately, the entire world), makes himself and his immense power famous.

So, the view of orthodox Christian theology is that the battle between good and evil is singularly unfair -- in the end, good wins, completely. It's not even a proper war, since the ending has been written ahead of time and will not fail to come about.

In this post, I want to delve a little deeper into understanding the Devil. I will start by looking at the Bible in reverse -- who the Devil is in Revelation, and then work back towards the beginning of the Bible.

In Revelation, the Devil is a Great, Red Dragon and this dragon is identified with the Serpent of Genesis (Revelation 12:9). Conveniently, this connects the endpoints of the Bible together so that we know that John is speaking of a syncretic character. That is, John is specifically referring to the Devil as a combination of all the ideas of the Devil that had come before him and are included in the text. This is the conception of the Devil that I will explore in this post.

In Revelation, John uses the phrase "the Devil and his angels", a phrase he borrowed from Jesus, in Matthew 25:41. This phrase is very important, because it sets up an antonymy between God (and his angels) versus the Devil (and his angels). This antonymy does not set up God and the Devil as equal-but-opposite -- it merely sets them up as opposites. However, it is symptomatic of an important structural antonymy that is present throughout the entire text, a topic I plan to explore further in future blog posts. For now, it suffices to point out that the Devil has angels and these angels stand in a relationship similar to (yet different than) the relationship between God and his angels.

So, what are the aims and ends of John's Devil? What is the war with God all about? Is he angry with God? Is he trying to build an empire and God is standing in the way? What is it that the Devil wants so badly that he is willing to hazard certain destruction in order to attempt to achieve it?

To answer this question, we are going to look at the main appearances of the Devil in the Bible. The first major appearance John alludes to in Revelation 12 -- the Serpent in the Garden of Eden. Here, the Devil has taken on the role of the Deceiver. The second major appearance is in the murder of Abel by Cain (I John 3:12). Here, the Devil has taken on the role of the Murderer. The third major appearance is in the possession of Judas (Luke 22:3). Here, the Devil has taken on the role of the Betrayer. And the last major appearance is in the book of Revelation, where the Devil is fully unmasked (no longer pretending to be the good guy), where he takes on the role of the Rebel. An important side-appearance of the Devil in the Bible is in the book of Job, where he plays a prominent role in the story. Here, the Devil takes on the role of Satan, that is the Accuser (see also Revelation 12:10).

These roles are very important in decoding what the Devil wants. To say that the Devil is a deceiver, a murderer, a betrayer, a rebel and an accuser is true enough, but it fails to penetrate through to the heart of the matter. What is the unifying theme that ties all these various activities together? What is the overriding motive that has driven the Devil to take on each role, by turns, of deceiver, murder, betrayer, and so on?

The answer is found by taking a longitudinal slice of the entire Bible and looking at its own big themes. It can be argued that the largest themes of the Bible are (a) the glory of God and (b) whole-hearted devotion to God (the rejection of idolatry). When the Bible presents God-in-himself, it does so in a way that consistently and persistently emphasizes the glory of God. And when the Bible considers the relation between God and man, it consistently and persistently emphasizes that a relation of utter devotion to God is the only relation that does not result in destruction.

They exchanged the truth about God for a lie, and worshiped and served created things rather than the Creator—who is forever praised. Amen. (Romans 1:25)

Here, Paul sets up the contrast between idolatry and devotion to God in the simplest and starkest terms. The alternatives are worshiping and serving the Creator (the true, original cause), on the one hand, or worshiping and serving things that are just another creature, like yourself. So, this is the fundamental aim of the Devil, who is a creature -- to cause men to turn their worship away from the Creator and onto any created thing besides. In 2 Thessalonians, Paul prophesies the coming of the anti-Christ and he refers to the Lie, the lie-of-lies:

The coming of the lawless one will be in accordance with how Satan works. He will use all sorts of displays of power through signs and wonders that serve the lie, and all the ways that wickedness deceives those who are perishing. They perish because they refused to love the truth and so be saved. For this reason God sends them a powerful delusion so that they will believe the lie and so that all will be condemned who have not believed the truth but have delighted in wickedness. (2 Thess. 2:9-12)

What use are "displays of power through signs and wonders (miracles)" if not to convince people to believe that the anti-Christ is a divine being, deserving worship? So, this is the lie, it's the lie that goes all the way back to the Garden of Eden when the Serpent first sowed the seeds of doubt into the minds of Adam and Eve -- "You will not certainly die" if you eat of the tree, he said. When Adam and Eve took the word of the Serpent over the word of God, they rejected God's worshipfulness and turned their worship to a created being, instead.

But it is a mistake to think that the Devil's ploy to turn human worship away from God and onto himself is merely one of imposture or some kind of chivalrous competition between gentlemen. When we look at the roles that the Devil has taken down through the ages in order to further his agenda, we can work out a very specific pattern of thought. Specifically, the Devil believes he is worthy of worship and utilizes deceipt, murder, betrayal and the like, because he is implicitly accusing God of utilizing the very same means to secure the worship of his creatures. The Devil's argument with God boils down to the most childish argument of all: "If you can do it, then so can I." If God can receive worship, then so can I. And if I can't receive worship, then God is evil because he has a double-standard in that he takes for himself what he denies to others. And since God has this double-standard, he is no more worthy of worship than any other being. In fact, God must be willing to use any means to achieve his ends (to glorify himself), so how am I any worse than God if I, too, utilize any means to achieve my ends, including murder, betrayal and, ultimately, knowing rebellion against my Creator?

But what of the Devil's angels? Where has the Devil collected this rotten band of minions? The best hint is found in Jesus's discourse with the Jewish leaders in John 8:

Jesus replied, "... I am telling you what I have seen in the Father’s presence, and you are doing what you have heard from your father."

"Abraham is our father," they answered.

"If you were Abraham’s children," said Jesus, "then you would do what Abraham did. As it is, you are looking for a way to kill me, a man who has told you the truth that I heard from God. Abraham did not do such things. You are doing the works of your own father."

"We are not illegitimate children," they protested. "The only Father we have is God himself."

Jesus said to them, "If God were your Father, you would love me, for I have come here from God. I have not come on my own; God sent me. Why is my language not clear to you? Because you are unable to hear what I say. You belong to your father, the devil, and you want to carry out your father’s desires. He was a murderer from the beginning, not holding to the truth, for there is no truth in him. When he lies, he speaks his native language, for he is a liar and the father of lies. Yet because I tell the truth, you do not believe me! Can any of you prove me guilty of sin? If I am telling the truth, why don’t you believe me? Whoever belongs to God hears what God says. The reason you do not hear is that you do not belong to God." (vv. 38ff)

Here we see that Jesus has identified these deceptive religious leaders as the children of the Devil. But note that Jesus is disputing with the Pharisees -- these are men of repute, these are the popes, priests, televangelists and rockstar missionaries of that time. Yet Jesus is calling them the children of the Devil. Not the Romans. Not the lepers, the demoniacs, the prostitutes or the swindlers. The influence of the Devil in the world is through the idolatry of the heart, and it is this idolatry that is the unifying, global force of the synagogue of Satan (Revelation 2:9). This idolatry is found in its purest, most crystalline form only among the ranks of the devoutly religious, especially the religious leaders.

The Devil has been frequently and variously depicted in literature, film and the arts. The Lucifer comic series by Neil Gaiman depicts something very close to the set of motives of John's syncretic devil, the Great, Red Dragon. In that series, Lucifer is depicted as mostly aloof and indifferent to human matters. As a being that was once first among God's creations, Lucifer has only one over-arching motive: to remain eternally separated from God. God is depicted in the series as having complete omnipotence, even over time itself (he has the power to un-create the entire material world). After obtaining the power to create matter (something he does not have at the beginning of the series), Lucifer creates a Garden of Eden of his own -- the only rule in this Paradise is that no one must worship anyone else. Gaiman is not really presenting a positive theology of God but he has perhaps accidentally depicted the conflict between the Devil and God in almost exact agreement with orthodoxy.

Lucifer's point-of-view in the comics is not so bizarre or irrational. After all, why should the glory of God matter to his creatures? I do not have to desire to displace or one-up God in order to ask this question in all honesty. The Bible's answer begins with God's transcendence. In Isaiah, God says of himself,

"My thoughts are not your thoughts,
Neither are your ways my ways,"
Declares the Lord.
"As the heavens are higher than the earth,
So are my ways higher than your ways
And my thoughts than your thoughts."

God's glory matters to us because he tells us it does. Because God is transcendent, we have no basis on which to meaningfully question his assessment. We think of small things and we work in small ways. God thinks of higher things, and he works in unimaginable ways. We could accuse God of having a double-standard -- "Do as I say, not as I do" -- but this ignores the fact that God sent his only Son to Earth in order to unify us with God himself, where he dwells (in heaven). There are questions whose answers we cannot understand. The Bible answers them this way: You cannot understand it now but, one day, you will understand it through the supernatural assistance of God himself. In the meantime, God asks you to love him and devote yourself completely to him alone, and no one else. This is your whole duty.

In the culmination of history, this will be the issue over which the battle-lines of Armageddon will be drawn. The kings of the Earth, the whore of Babylon, the Dragon, the Beast and the False Prophet will be gathered together for war against God's son. The angels will call out to gather the birds together for a great feast because the defeat of the Devil is certain. That it is certain is God's answer to the Serpent's deception in the Garden, "You will not certainly die," he said to Eve. Adam and Eve certainly did die. The fate of the Devil and his rebellion is also certain.

In the Gospels, Satan enters into Judas after dipping his hand into the bowl with Jesus. [This would likely have been a traditional Passover meal consisting of lamb, prepared as a stew or curry and eaten with an unleavened flatbread, somewhat like dipping crackers.] After this, Judas seeks an opportunity to betray Jesus to the authorities. He leads the Jewish authorities, along with a large band of men, to a place where Jesus went to pray, a place likely known only to Jesus and the twelve. There, Jesus is arrested and taken to be crucified.

Satan's participation in the crucifixion stands in contrast to God's faithfulness. John 3:16 says, "God so loved the world, that he gave up his only, begotten son". God has not created us in order to betray us and abandon us to fate. He has not wormed his way into our lives in order to lead us into a trap or see us destroyed. It is true that we suffer, sometimes bitterly. Rarely is our suffering the direct result of our own, personal sins. But God has not betrayed us. His faithfulness is proclaimed prolifically throughout the Old Testament. Psalm 119:90 says, "Your faithfulness continues through all generations; you established the earth, and it endures." The imagery in this passage is that God's loyalty to his creation is as enduring as the very earth upon which we stand.

The story of Cain and Abel is the story of the first murder and illustrates the direct fruits of Adam and Eve's choice to abandon God's protection and provision in the Garden. God warned them that to eat of the would bring death. And no sooner had they eaten, than death began to spread upon the earth. In I John 3:12, it says that Cain "belonged to the Evil One" which can be taken to mean he had been possessed by the Devil. Whether or not he was possessed, he was doing the Devil's work and, thus, belonged to the Devil. This is an important point because it shows how choice is the glue that holds together the Devil and his angels -- it is the choice to do the Devil's work that makes one a child of the devil, see John 8 above. This choice does not always appear evil (as murder always does). Matthew 23 contains Jesus's famous pronouncements of woe upon the Pharisees. He says,

Woe to you, teachers of the law and Pharisees, you hypocrites! You travel over land and sea to win a single convert, and when you have succeeded, you make them twice as much a child of hell as you are. (v. 15)

Here, we see that proselytizing is itself part of the Devil's work on the earth, and Jesus identifies the religious leaders of his day as the children of hell (literally Hades, god of the underworld) who perform this work.

In the Garden, God told Adam and Eve, "Of any tree of the Garden you may freely eat." Think for a moment what a blissful state-of-being that would be. No odious toil. No deadlines. No paperwork. No hustle and bustle. Just peaceful, quiet, harmonious abundance and comfort. Lest he be accused of imprisoning Adam and Eve in this Paradise, God also gave them the capacity for choice. "You must not eat of the Tree of Knowledge of Good and Evil, for when you eat from it you will surely die."

When the Serpent questioned this claim to Eve, he did so by planting the seed of doubt into her mind. "You will not certainly die," he said. The Serpent is a realist. Be reasonable, he is saying, no one can know the future with certainty, not even God!

God is completely honest about himself, his motives and his relationship to Adam and Eve. They know that God is their Creator. They know that his motive in creating is to bless them with perfect comfort and bounty, to see them multiply and fill the Earth, to have them rule over the birds, the fish and the land animals, and to tend the Garden and keep it. They know that God's relationship with them is open and mutual -- it says that God walked in the Garden in the cool of the day, indicating that this was his daily routine.

God is the Creator of everything in Heaven (including the angels) and Earth. Even the Devil is a creature, a creature that is in rebellion against God. God informs us that his knowledge of the future is exhaustive:

I make known the end from the beginning, from ancient times, what is still to come. I say, "My purpose will stand, and I will do all that I please." (Isaiah 46:10)

There is no possibility of confusion about who God is, what he wants from us, what he gives us, and what our relationship with him is. This was true of Adam and Eve and it is equally true of us.

The battle between God and the Devil is not a battle of equal-opposites. Rather, it is God's work to overcome the fallen world and to redeem it and bring it back to life, the life that it had before humankind rebelled against God and put the world under the power of death. It is the battle between God's truth and the lies of fallen creatures. It is the battle between God's life-sustenance and the murder of fallen creatures. It is the battle between God's faithfulness and the treachery of fallen creatures. It is the battle between God's rightful supremacy and the rebellion of fallen creatures.

The name "Satan", in Hebrew, literally means "accuser" and is the word that describes a prosecutor in a court case. In Job, Satan takes on the role of the accuser and claims that Job only serves God because God so bountifully blesses Job. God then turns Job over to Satan's power, to do as he wishes, except he is not to kill Job. This book captures the essential nature of human suffering. Suffering is not the result of random chance, as the modern doctrine asserts. Suffering can be a test, but it is glib to wave away everyone's suffering as a test -- is God testing the poor child who is dying of leukemia? Ultimately, suffering always serves some purpose and it is rarely obvious to the one who suffers what that purpose is. But it is the Accuser who drives the furnace of suffering because the accusation contains within itself the seed of doubt, the suspicion of ill-intent. To Eve, the Accuser says, "God does not really have your best interests at heart." And to God, the Accuser says, "Job is only devoted to you in return for all the good things he gets from you." In a future post, I plan to address the problem of evil and suffering in more depth.