Jan. 2021

Richard Dawkins proposed a theism scale where 1 means you're sure a god exists, and 7 means you're sure no god exists.

Note: capitalizing "god" implies that one exists and is unique; and using the masculine pronoun implies that god is male. I assume neither, so I use lower case and "it".

Where do I stand on the Dawkins scale? Well, my belief system is based on two principles:

• I believe something only if there's objective evidence of it; the more evidence, the stronger my belief.
• Given two alternative explanations with equal evidence, the simpler one is more likely (this principle is called Occam's razor).

Humans have probed the universe in tremendous detail on a wide range of scales, and have never found any evidence of god (I explain below what I mean by this). And the absence of god is simpler than the existence of god. So when my friend Ray asked me where I am on the Dawkins scale, I said 6.999... This is a math-nerd joke: I didn't say 7 because of course you can't prove that a god doesn't exist. But 6.999... (six followed by infinitely many nines) is actually equal to 7.

Why people believe in god

There's no evidence of god, but many people believe it exists. I can think of various reasons for this:

• The human experience is wonderful. Everyone has moments that seem transcendent: the beauty of a sunset, the genius of Bach's music, a surge of joy. These moments are great, but they're not evidence of god - they're electrochemical processes in the brain. The existence of these process is the result of evolution; they convey some kind of advantage for survival. The more we learn about neuroscience, the more we understand these phenomena. They seem transcendent, but they're not.

• Psychological needs. People want to be happy, and feeling like our life has a meaning makes us happy. Theism provides a made-up meaning: we exist because god wants us to exist. Personally, I have a less contrived answer: the point of our existence is to share the fruits of human creativity as widely as possible.

• Intellectual needs. Humans have a strong drive to understand the universe, and in particular its origin. Science currently doesn't (and possibly never will) explain origins, so people fill the void by making up an explanation.

• Perpetuation of oligarchy. Civilization is a string of various types of oligarchy (government by the few): monarchies, class hierarchies, unregulated capitalism, and so on. These oligarchies all need a way to suppress revolt by the poor and powerless masses. Organized religion has been used for this purpose in variety of ways: the myth of afterlife and heaven, the claims to divine right of kings, etc.

• Conformity and mass hysteria. Organized religions have evolved by mutation and natural selection, just like organisms. Those with better indoctrination techniques (i.e. brainwashing) survive. Generally these exploit the human need to conform. We want the approval of our parents and other authority figures, so if they tell us to believe in god, we do - or at least we try to. And when people want to believe something, and they're surrounded by people who want to believe it, they end up believing it - the existence of god, the existence of witches, that Hillary Clinton is a vampiress, and so on. This phenomenon - which can be called "mass hysteria" - is explored by Carl Sagan and Ann Druyan in the wonderful book The Demon-Haunted World.

If you're less than 6.9 on the Dawkins scale, I respectfully suggest that it's because of one or more of the above reasons. If you disagree, please let me know.

The meaning of 'god'

But before we go any further, we need to decide what "god" and "exist" mean. It's pointless (and amusing) when two people argue about words that mean different things to each of them.

What attributes make something god-like? I think most people would include the following:

• Metaphysical: god is something that can't be described by equations (or more generally by a "formal system"; see below).
• Agency: god has some interaction with the Universe, either by having created it or by influencing its day-to-day operations. If god exists but has never done anything, what's the point?
• Intention: god has some reason for doing what it does. Many people ascribe other human qualities to god: consciousness, intelligence, perception, mercy, and so on. I think intention is the most basic of these.

A god must have all three attributes. For example, it's conceivable that some aspect of the universe can't be described by equations; but if that component has no intention, it's not god; it's just noise.

The agency of god

What can god do? It seems to me there are two possibilities.

• Creator: a god that created the Universe, and determined its physical laws. The idea of Creator god, it seems to me, runs aground immediately on the question of what created the Creator god. The possible answers are: 1) The Creator god has always existed. But in that case, why not just say that the Universe itself has always existed? Occam's Razor prefers the latter. 2) The Creator god was created by another "meta-Creator" god. This leads to the absurd "turtles all the way down" model. 3) The Creator god created itself (that doesn't quite make sense).

• Manager: a god that monitors the Universe and actively controls it in some way.

A god could be a Creator or Manager, or both. A Creator god could have created the Universe and then moved on to other things - perhaps creating other universes.

The multiplicity of gods

There could be - as the Greeks and Romans believed - multiple Manager gods. They could cooperate or compete, and they could have their own little human-like society. If you're going to make up something, why not make it interesting?

I suppose there could even be multiple Creator gods. Perhaps the universe was designed by committee.

The meaning of 'Metaphysical': formal systems and science

God - if it exists - is metaphysical, by which I mean it can't be described by science - not just current human science, but ANY science. Let me explain what I mean by this.

A 'formal system' starts with a set of symbols, which include the familiar symbols from math and logic (equality, and, or, quantifiers like "there exists" and "for all"), as well as constants and variables. The system defines syntactic rules for "statements", and it includes rules for logical deduction (inferring a statement from other statements). A "theory" is a set of "axioms" (statements assumed to be true) and all their logical consequences. For our purposes, theories must have two properties:

• Consistency: the axioms don't imply a contradiction.
• Finite description: the axioms can be written down on a (possibly very large) piece of paper: either by listing them explicitly, or by giving a finite set of rules that say what's an axiom and what's not (like the Zermelo-Frankl axioms of mathematics).

A theory is called "complete" if it includes every statement or its negation.

The idea of formal systems comes from mathematics. But it applies to physics too; physics is a formal system for describing the universe. Its constants and variables correspond to physical quantities (like mass and position) that can be measured in experiments. A statement S can be disproven by an experiment that shows the universe doesn't behave the way S says it does.

Physical theories can include randomness. For example, quantum mechanics says that when you observe a particle, the position you see is sampled from a random distribution. It's possible to define "random" in a rigorous way, so that the intent of a god can't hide inside it. Theories that include randomness aren't predictive: they don't uniquely determine how the universe unfolds.

Let's call a physical theory "complete" if it describes everything; i.e. it determines how the universe unfolds except for random processes (this is vague but I think it can be made precise).

Physics has developed a core theory that includes equations describing motion (F=MA), light and EM waves (Maxwell's equations), matter at a small scale (quantum mechanics), matter at a large scale (Einstein's theory of General Relativity) and so on.

The theory includes randomness, so it's not predictive. It's incomplete - it doesn't explain dark matter, it doesn't reconcile gravity and quantum mechanics, and so on. There are many theories - such as string theory - that extend the core theory, and are closer to being complete, but are not yet supported by experimental evidence.

The True Theory of Everything and the Formalism Gap

Current science is incomplete. But if we're discussing god, the relevant theory isn't current human science or any of its variants; it's what I'll call the True Theory of Everything (TTE). This is the formal theory that most closely approximates the universe. It's extremely unlikely that humans will ever know TTE. It's possible that writing down TTE would take more pages than there are particles in the universe. It's possible that TTE fails the "finitely describable" criterion for formal theories: maybe there's an infinite sequence of theories, each of which approximates the universe more closely than the last, and there's no finite description of their limit.

TTE may not be complete; it may not completely describe the universe. The aspects of the universe that aren't described by the TTE I call the Formalism Gap: the gap between reality and what can be described by formal systems.

Let me emphasize: the Formalism Gap isn't what's left unexplained by current human science, or by future human science, or by the science of the most advanced ET race ever. It's what can't be described by ANY formal system. That's a pretty strong criterion.

I consider it likely that the Formalism Gap is empty. Human science has existed for a very short time, but it has already figured out an astonishing amount. Science has been confronted with a series of mysteries, and one by one it figured them out. And there may be races far smarter than us.

Origins

Should we expect the TTE to explain the origin of the universe? No; I don't think we can expect an explanation that most people will find intuitive and satisfying. If the TTE says there was a singularity, and that there was no "time" before the singularity, that's good enough for me, but probably not for some people. Also, we can't expect the TTE to explain itself - why its particular equations and constants are what they are. But that's OK; a lack of self-explanation is not a Formalism Gap.

Mathematicians has discovered amazing things about formal systems. For example, Gödel's incompleteness theorem proves that no formal system can prove its own consistency. Intuitively: if you're inside a complex system, you can't know even the most basic properties of the system. It's a stretch, but I think that physical systems have an analogous property: from within them, you can't know their origin.

Does god exist?

Getting back to the question of how to define "god". I've reduced it two assertions that must both hold for a god to exist:

• The Formalism Gap is nonempty. God must have agency, and if the gap is empty there's no room for this agency.
• The Formalism Gap has 'intent'.

The first is more or less precise; the second is not. Neither assertion can be proved or disproved, ever. No evidence is actually evidence. A gaggle of angels could descend from the skies with rainbows around their heads, praising God Almighty. But if that event is explained by a formal model, it's not evidence of god.

All we can do is to debate the probabilities of the assertions, and the size of the error bar on these probabilities. It's not even a debate - it can't be more than sharing of intuitions. My intuition is that the Formalism Gap is empty with extremely high probability. And if it's not, I doubt that there's any intent in the gap.

Is our universe a computer simulation?

There are some other cosmologies to consider. One is that our universe is a program running on a computer in a meta-universe. The program simulates everything in our universe. The program and the computer were developed by "meta-beings", who are gods in a sense: they're metaphysical relative to our universe, but not relative to theirs. And they have intent.

Given the limitations of our own computer hardware and software, this seems absurd. But maybe it's not:

• The meta-universe could be (in fact must be) much richer and more complex than ours. Their notion of "computer" could be way beyond our comprehension. In particular, it might not be digital.
• There are physical theories in which everything (including time and space) is discrete, and might therefore be simulated on digital computers.

Is there a way we could test whether we're a simulation? People have come up with some ideas, like counting upward until we can't count any more; then we'd know that we'd exceeded the "memory size" of the host computer, and that we're in a simulation (this idea is clever but flawed).

If our universe is defined by software, we can contemplate interesting features that could be added to it.

Is our universe abstract?

Mathematicians reason about things - lines, points, and infinite sets - that don't and can't have a physical existence. There is a school of thought - Platonic realism - that asserts the existence of an abstract "Platonic universe" in which these things exist.

Math has its own version of the Formalism Gap. There is a formal theory of Mathematics - a finitely-describable set of "axioms" from which all currently known Math follows. There are different but equivalent formulations of this - for example, Zermelo-Fraenkel set theory. Unlike physics - where continually refine our formal model as we do experiments - the formal model of Math hasn't changed in about 100 years.

Kurt Godel proved that Math has a Formalism Gap: i.e. there are formal statements that can be neither proved nor disproved from the current axioms - or indeed ANY finitely-describable and consistent set of axioms. Some of these statements are sort of artificial, like a formal statement that says "I am unprovable", and is therefore true but unprovable. But some of them are completely natural, like the continuum hypothesis.

But I digress. If you believe Platonism, every statement of mathematics is true or false. The set T of true statements is complete and consistent, and the Platonic universe is an embodiment of T: it exists because T exists.

If we take this idea to its conclusion, we can posit that for EVERY complete and consistent formal system, there's a corresponding abstract universe that embodies the system. My son Noah proposed a cosmology based on this idea: namely, that the TTE exists and is complete, and our universe is simply the abstract realization of this theory. In fact, every complete physical theory has a corresponding abstract universe. This neatly sidesteps the issue of Origin: formal theories are just lists of statements, they don't have or need a creator. (Others have proposed this idea too.)