This is a vague continuation of a post I published a few days ago entitled “Your Personal State Machine”. If you’d like a good idea of how I’m approaching these sorts of concepts, I’d recommend giving that a peek.
The disclaimer for that which I’ve written herein is as follows: the chance that any individual venturing onward through the wasteland that is this post, only to find that their belief system after completion differs in any way from when they started, is excrutiatingly slim. Such is the way with practically any singular discussion, paper, topic, or debate. Minds are changed through consistent exposure amongst trusted peers, and not generally through the ramblings of one individual. With that in mind, I still want to approach this topic a little deference, not for the sake of the supernatural but for my friends who are theists and are honest in their belief. So before I begin, I should probably mention that autonomy and freedom of thought are significant pillars of my own ethical worldview, and so the following should be read as though I’m merely explaining my thought process on the matter, rather than as an attempt to truly convince anyone of anything.
Good. So I want to break this down into two sections. In the first section, I’m going to tackle the likelihood of the the existence of an omnipotent creator at all. After that, I’m going to talk about epistemological certainty, and whether uncertainty is necessarily honest.
The Omnipotent Creator
If we’re going to tackle the topic of whether an omnipotent creator could exist in the first place, we ought to first tackle what me mean by the term. This is particularly important for this thought exercise, because there are certain assumptions that we’re going to make in order to simplify our informal proof, that will absolutely fail to apply to certain deviations (and I’ll go more into depth on this later). What I mean is as follows: an omnipotent creator is an entity, existing before all other “things” (a loose definition that I’m borrowing from theists that believe in such a deity), that is directly or indirectly responsible for creation (you, me, our loved ones, and our taxes), whether through a process such as creationism (which I won’t tackle here, as I hope that most folks reading this already discard this theory as nonsense) or through the process of evolution. So this note covers the god of Abrahamic religions and derivations thereof, the gods and goddesses of certain polytheist religions that serve as a sort of prime mover, and (to a lesser degree), the “god” of those pantheists to which agency is ascribed. We’re not including, in this discussion, superheroes. And by this I mean “extraordinarily powerful beings” that don’t necessarily have a stake in cosmological events at large, and I’ll elaborate on that further in a moment.
Again, I want to remind the reader that we’re looking at things through a naturalist’s lense because we want to approach this the way that good Bayesians do. Probabilities cannot be assigned to the supernatural, because the supernatural serves only as a catch-all bucket for those questions for which an explanation has been forged without proper scientific inquiry. Get sick before early-modern times? Demons, clearly. How would you go about testing the supernatural? Not with anything natural, and unfalsifiable theories do us no good as we explore the cosmos and the nature of reality. Therefore, we must treat the concept of an omnipotent creator as a natural phenomenon.
Good. So there are two concepts regarding this that I want to touch base on. One is widely trusted and used, and the other is a very silly idea. The first: probabilities. Quickly described, given two events with two distinct probabilities of occurrence, one can determine the likelihood that both events will occur simply by multiplying those probabilities:
And this makes perfect sense in practice. Say you have two equally-weighted coins, and you want to determine the probability of flipping “heads” on both at the same time. Well, you have a 50% chance of flipping heads on one coin. So, the probability that you flip “heads” on both ought to be 25%.
And you can see this explicitly with the following table:
| Coin no. 1 | Coin no. 2 |
|---|---|
| heads | heads |
| heads | tails |
| tails | heads |
| tails | tails |
Four entries, each with a one-fourth chance. But what you should take from this example is as follows: given two potential occurrences with probabilities no more than 1 and no less than 0 (as no event is likely to happen more than 100% of the time or less than 0% of the time), the products of those probabilities will at most the smallest probability:
And, in life it is very rare that any probability is exactly 100%, and you can therefore say that given two probabilities less than 1 (and no less than 0), the product of those probabilities will be necessarily less than both of the original probabilities. Therefore, if you have two events that are not absolutely guaranteed to happen, the likelihood that both events will happen is less than the likelihood that either event will happen individually. So, to show that it is extraordinarily unlikely that an omnipotent creator exists, all we need to do is establish that there are extraordinarily unlikely possibilities that are nevertheless more likely to occur than the creation of a universe by an omnipotent creator.
Let’s talk about Boltzmann brains. And, before I go on in this section, I really ought to note that I really don’t care all that much for poor representations of science as they are often conveyed by pop science, so if you are reading my writings herein, please consider reading papers and links that I drop in the passages. I’m not infallible and the source material is almost always better at technical accuracy than someone’s brain dump of a blog post. So as far as this section goes, I’m going to encourage you to take a look at an excellent paper by Andreas Albrecht and Lorenzo Sorbo out of the Department of Physics at UC Davis entitled “Can the universe afford inflation?”, wherein they recount some of the work done by Ludwig Boltzmann, a mathematician and theoretical physicist who, among other things, assisted in the development of statistical mechanics and invented a definition of entropy that is still used today. The paper recounts that Boltzmann once theorized that “the observed universe should be regarded as a rare fluctuation out of some equilibrium state” and then proceeds to comment as follows: “…the logical conclusion of this line of reasoning is utterly solipsistic.”
So we can elaborate on this and break it down a bit. Boltzmann, being an expert on statistical mechanics and entropy, was concerned that it may be more likely that the universe as we know it—complete with our memories of the universe, and the phenomena that we measure to determine the fundamental laws of nature, could have popped into existence as a quantum fluctuation and therefore be, essentially, a false record in its entirety. Now, I really ought to note here that there has been a lot of discourse about this but in most cases the entire notion is tossed out as something that ought not be taken seriously for the same reason that solipsists aren’t taken seriously by practically any serious philosopher or scientist.
“They fail the Monty Python test: Stop that! That’s too silly!” ~ Seth Lloyd on Boltzmann brains
The unspoken implication is that discourse on the matter is not (and has no potential of being) useful or falsifiable in any sense of the word. And I suppose that that is because both solipsism and Boltzmann brains would render any sort of discovery null and void, and yet the mere fact that experiments with repeatable results exist ought to give one a strong instinct that these are in fact quite silly notions.
But suppose that we still consider the notion possible, if unlikely. We could ask ourselves how likely it is that this universe is actually a Boltzmann brain (or, a Boltzmann universe, as one might call it). Even disregarding the nature of its generation—via quantum fluctuation, nucleation, or some other yet unknown mechanism—we must consider the notion extraordinarily unlikely. And that’s assuming the spherical cow, without any of the other caveats and restrictions imposed by other scientists that have thought about this problem much longer than I have.
Let be the probability that this universe is a Boltzmann brain. (Let’s brush aside the complications that arise from the anthropic principle, thank you very much.) Now let be the probability that an omnipotent entity exists. Unless there is some definitive proof of an omnipotent entity that confirms its existence, this must be some value less than 1. Now, keeping in mind the extraordinarily low , (the probability that there exists both an omnipotent entity and that the universe is a Boltzmann brain) is even lower than if the world were to pop into existence by itself. This effectively makes it quite reasonable to assume an extraordinarily low likelihood that a given universe is created by a god in accordance with a Creationist’s playbook. But, I’ll note, still not an exhaustive proof (which I’ll touch on under the next header).
“Now wait,” you say, “I believe in evolution, but it was God that kicked that off, and he planned everything out.” Okay, well take some third term and assign to it the likelihood that any omnipotent being, as we haven’t pegged them as good or evil, would guide the interactions perfectly—and you’ll find that (even if you argue that it is close to 1). Thus, is even less likely than .
There are obviously a few problems with the above that I still need to work out myself. Namely, it’s difficult to assign probabilities appropriately to the past of a universe in which you currently live, or to the set of all universes that may come about in the future (if that’s even a sensical phrase). Probability is often regarded as a measure of the degree of certainty you have with respect to a particular future outcome which makes retroactively evaluating a situation a little messy. Second, there are a lot of “what-abouts” that can be assigned by anyone with the appropriate theistic dogma, and I’m much too lazy to provide an argument for each and every one of them. Thirdly, as mentioned before, such things still do rely on any omnipotent deity being in herently natural—which does call into question whether such an entity could possibly exist in the first place if they too are at the whims of physical law (which obviously spits in the face of most theists’ apologetics). And fourthly, again as mentioned earlier, the aforementioned workflow does not consider superheroes or magic powers bestowed on an individual. Spiderman could be bitten by a radioactive spider both in a “normal” universe and in a Boltzmann brain.
Epistemological Certainty
Given the above, we can ask ourselves “when can we be sure of the lack of an omnipotent creator, if we have no exhaustive proof of such a thing?” The short answer to this is that one should consider the analogy of Russell’s teapot. A paragraph of interest in Bertrand Russel’s article entitled “Is There a God?” (and which is also included on the corresponding Wikipedia entry—yes, I’m a bit of a sucker for Wikipedia, but God gave you a middle mouse wheel to scroll to the links at the bottom of the page, no?) reads as follows:
Many orthodox people speak as though it were the business of skeptics to disprove received dogmas rather than of dogmatists to prove them. That is, of course, a mistake. If I were to suggest that between the Earth and Mars there is a china teapot revolving about the sun in an elliptical orbit, nobody would be able to disprove my assertion provided I were careful to add that the teapot is too small to be revealed by even our most powerful telescopes. But if I were to go on to say that, since my assertion cannot be disproved, it is intolerable presumption on the part of human reason to doubt it, I should rightly be thought to be talking nonsense. If however, the existence of such a teapot were affirmed in ancient books, taught as the sacred truth every Sunday, and instilled into the minds of children at school, hesitation to believe in its existence would become a mark of eccentricity and entitle the doubter to the attentions of the psychiatrist in an enlightened age or of the Inquisitor in an earlier time.
The above is excellent commentary on external interactions with others in terms of who ought to assume the burden of proof when making claims. However, it does very little to provide any assurance for the instrospective individual in terms of their potential identification as a gnostic (or agnostic) atheist. And here I’m using the term “gnostic” in a slightly different way than might be known in pop culture; I’m not referring to the Gnosticism of early Christian sects, but rather as a term indicating certainty in a particular fact. My argument here is that there are many things of which we are certain but don’t require exhaustive proofs, especially in terms of practicality, usefulness (there’s that motif again!), and every day life. In other words: the average individual has, with nigh absolute certainty, the belief that the sun will come up tomorrow. There is of course an extraordinarily small chance that there may be some phenomenon that causes its immediate extinction without warning, but the chances are extraordinarily small and frankly, not worth discussing (unless some significant evidence comes up that would otherwise lead the scientific community to some other conclusion). So with respect to all practical usefulness, folks are essentially absolutely certain that Earth will continue to rotate tomorrow.
A potentially more esoteric example would be that of interactive zero-knowledge proofs that require iteration to establish assurance. If you’ve never heard of ZKPs, I’d recommend quickly skimming over yet another Wikipedia entry, enjoy. But I’ll quickly go over my favorite conceptual overview, which is that of Ali Baba’s cave. It goes like this:
Peggy and Victor go on a trip to visit an odd-looking ring-shaped cave. They know that the path into this cave forks into two tunnels, each which meet back up further inside the mountain. But what’s special about these tunnels is that there is a door in the back of the cave that separates the threshold where the two tunnels meet back up. Anybody visiting the cave would need the magic word to get past the door. Peggy knows the magic word to this door and she’s very excited to go exploring so she runs ahead and darts down one of the tunnels without telling Victor which tunnel she went down. How can she prove to Victor that she knows the magic word without letting him know what it is?
┌────────────┐
│ ┌────────┐ │
──────┘ │ │ │
--> │ │▒│
──────┐ │ │ │
│ └────────┘ │
└────────────┘Victor can shout at her to come back through a particular tunnel. If she successfully returns through the correct tunnel, then there is a 50% chance that she needed to use the door to return. And if Victor and Peggy repeat this process a ton of times, then Victor can be reasonably certain that Peggy does, in fact, know the password to the door.
Why is this ZKP ramble relevant here? That’d be because for all intents and purposes, Victor knows with certainty that Peggy has the magic word, even though technically he could be wrong — the likelihood that he is mistaken would be , with being the number of iterations executed for assurance. And yet this is considered cryptographically secure, because certainty is not a measure of absolute correctness, but rather a measure of trust in something being correct.
Another relevant example would be applications in quantum information science in general. When you conduct a final measurement on Shor’s algorithm, there is a chance that your answer will be incorrect and yet, NIST has found it necessary to launch its PQC initiative.
Because of this, I tend to find it not entirely honest when folks profess agnosticism—not because I think that folks have any definitive exhaustive proof of a lack of a deity, but rather because the agnostic term (as it tends to be used by practical atheists) belongs in a different layer of abstraction epistemologically. Professing agnosticism is a lot like professing a lack of free will, or professing a lack of altruism. They are all technically correct at a more foundational level, the level of biochemistry. But they’re simply not useful at that level and thus it really makes no sense to adopt the terminology at all. We’ve already talked about free will a little in a past musing, where its usefulness lies in its sociological implications. Likewise, altrusim is really only useful to speak of at a psychological or sociological level as well. Agnosticism sort of belongs in that space, lacking any real practical meaning or even useful application at a more foundational level.
Wrap Up
As I mentioned earlier, I really don’t have any expectation of changing minds here. But for those that were vaguely interested, my hope is that I’ve provided a framework for establishing the extreme unlikeliness of an omnicient creator, and a foundation for being comfortable in asserting higher degrees of certainty. All in all, sometimes “good enough” is good enough, so long as we’re careful to define standards for what “good enough” actually means.