What is 453,634,563 + 2,688,222? You can calculate it in your head or use a calculator but the result is the same: 456,322,785. Since when is that the case? Did the result of this addition only start to exist after you calculated it? Of course not! Nor did anyone first have to invent 456,322,785 as the sum of 453,634,563 and 2,688,222, and even if no person or other intelligent being ever thought about adding these two numbers, the result already existed before we even asked the question. Addition, like all mathematical operations, is completely time-less.

In this article I will try to convince you that it is the same with life itself. In particular, one does not need to bother with the idea of a simulation that we live in. The mere idea or concept itself of our universe and the life resulting from it is already sufficient for it to exist. Just like the result of 453,634,563 + 2,688,222 existed before you calculated or even thought of it.

Refuting Simulation: Occam’s Razor

Imagine someone building a simulation. This could be John Conway inventing the rules of his famous Game of Life, or something more widely known like Minecraft or, well, Sims. Every simulation is defined, roughly, by an initial state and a “transition function”, which is a function that, for each possible state of the world, determines the next state or the next set of possible states if the simulation is non-deterministic. These two things together define the entire simulation. In practice, it is helpful to break these two concepts down further. For example the state of the world can be broken down into things that can change, such as the age of a character, and those that don’t, e.g., the terrain or landscape. The transition function is usually where all the complication resides and it is often structured in terms of things like rules of survival, resources, and the physics of the simulated world including what is possible and what isn’t.

In what we call the real world, these rules are the rules of physics, and even if not all of them are known to us yet, we live by them.

The conceived world

When does “life” in the conceived world start? Only once it has been implemented in a computer and the computer has started simulating, i.e., computing the sequence of events and states starting from the initial state? Which part of that simulation exists at that point, only the states computed so far? If you are inclined to say “yes”, then tell me: what if the creator had already thought through some of these events and states in their head. If they did, then these states have already been computed, and they exist, no computer simulation required, right? But what about the states that have not yet been computed? Do they not yet exist even though their existence is inevitable as the simulation continues? This brings us back to the question of the result of 453,634,563 + 2,688,222. Did that result only exist once it was computed for the first time by a person? Or was it sufficient for someone to conceive of the rules of math in order for its result to exist? We all know that it’s the latter. So conception is sufficient for the entire life of the simulation to exist in its entirety.

This is the moment where we leave time behind. As the simulator, we have full control over time and know quite well what will happen before it happens (in the simulation). So time is not holding us back.

Conception unnecessary

So if conception of a world with all its rules in one go creates the entire, simulated world, then what about that moment of conception? Does the world really only start existing once it has been conceived and the rules of the world have been “written down”? Or did the world already exist even before it was conceived? We’ve already established that time plays no role here, so perhaps the moment right after the world is conceived and the one right before it, do not actually differ regarding the existence of the simulated world?

Logic and Existence

If we are willing to accept this, then indeed we can make our claim.

Claim 1: Anything that is implied by any logically consistent theory exists.

Wait, you might say, how did “logically consistent” sneak into this claim? You are right, we have not yet talked about this requirement. It is indeed necessary though, because without consistency, the theory of the life being conceived (or even computed) would “break the thinker” and a “broken thinker” cannot think, and hence the theory they think through cannot be computed. In essence, the thinker “wouldn’t know what to think” if the logic is not consistent, i.e., is ambiguous. Not random or stochastic — more on that topic later — but actually ambiguous or contradictory: things could be true and false at the same time!

Math and Logic

It is important to recognize that math and logic were not invented by humans, they were discovered by humans. 1 + 1 = 2 even if you use different symbols. For instance, if you and your friend find two apples, then each of you can have one for themselves. For this outcome it is irrelevant whether you and your friend know what numbers are, or what addition and division is. Mathematical properties of numbers and operations hold in nature no matter how we call them, and they held true long before humans discovered them. They are time-less. And because it is timeless, math also existed before the Big Bang.

The laws of physics, which are the rules of the “simulation of life”, do consider time. In fact, time even plays a very important role in them. However, the math and logic behind these rules are independent of time as such. Just like a simulation is computed outside of the simulation itself, the rules of physics can be reasoned about and simulated independent of the timeline they represent. Hence, all of our worlds past, present, and future already exists in the space of all possible logical ramifications of these rules. And since biology and chemistry are ramifications of physics, and evolution is a ramification of biology, so do our past, present, and future already exist in the space of logical consequences of the laws of physics.

What then is existence?

The aspect most difficult to comprehend about this theory is the notion of existence itself. Simulations, such as computer simulations, are satisfying because some physical (electronic) representation exists (in some world) that can be observed in that same world. This gives the simulated world a form of materialization in the simulating world. This materialization property is not true for logical consequences without simulation. But logical consequences also exist, as we have seen in the addition example, independent of their representation and even independent of a “thinker”. So what then is existence?

Claim 1 states that existence = logical consequences. 456,322,785 exists, because 453,634,563 and 2,688,222 exist, the notion of addition exists, and, importantly, mathematical logic is consistent. The astute reader might ask, how do we know that 453,634,563 and 2,688,222 exist? The answer is, of course, that they, too can be derived from a basic axiomatization (set of rules) of numbers and addition, which itself is consistent.

Relativity of Existence

Much like Einstein’s relativity theory distinguished between an inside and an outside system, so does this thesis of life-as-logic benefit from such a distinction. Ironically, but perhaps not coincidentally, the distinct notion of time between inside and outside system is of particular interest. For passengers and clocks (theoretically) traveling at half the speed of light in a spaceship, time progresses more slowly than to the outside world, measured in the outside world. In our theory of life, time is a concept that is experienced in its linear, always-moving-forward form only in the inside system. The outside system itself, which is best to be thought of as a set of equations that govern the inside system, is completely time-less, just like addition in math is — at least in terms of the notion of time we experience on the inside. Clearly, if it so happens that the logic we live in is actually simulated/computed/materialized in the outside world, then the outside world could have its own notion of time, thereby establishing the certain relativity. But as we argued above, this is not required to explain the existence of our universe, i.e., the inside system.

The other distinction between inside and outside system that needs to be considered in our theory of life and Claim 1 in general, is that of materialization. Does something exist in the inside world only once it has been materialized, i.e., represented explicitly, in the outside world? This is perhaps the most central question of this entire exercise. This question does not seem to permit a clear yes/no answer, as it is more of a question how we want to define existence. However it does suggest the possibility of defining existence without the requirement of materialization. If this reminds you of Plato’s cave, then you are not alone.

Plato’s cave is a very useful metaphor here. If everything about the inside world that can ever be observed from the outside world in the inside’s past, present, or future can already be observed in a computation of that moment in inside-time computed in the outside world, then what more is there to existence? If we cannot find any information about the simulated world that would only appear once that world has been materialized in the outside world, e.g., in a computer simulation, or a pen-and-paper exercise, then it is really difficult to point to any meaningfully stronger notion of existence of the inside world than the mere logical consequences of all the rules necessary to compute any state of that world.

Many will find this hard to accept — us all just being a consequence in a possible logic, perhaps not even conceived by any other “being”, just possible. But the thing to keep in mind is that nothing changes on the inside world, i.e., in ours. Everything that has mattered before still matters. And everything is still just as real to us as it was before.

Before we consider the provability of Claim 1 we should discuss a possible counter argument: probability.

Randomness, or “Does God roll dice?”

It could be argued that it is in fact not possible to compute or determine all possible consequences of a theory because the theory itself involves randomness, e.g., about what happens. It is easy to conceive of a world where what happens next is decided at random. In such a world, the future is a result of all the random outcomes since the present. The question then becomes: is the source of randomness “accessible” only once that moment in the inside world has been reached or can it be access — can we draw random samples, or query outcomes — independent of the inside time.

In case it is accessible from the outside world at any (inside) time, then the counterargument is defeated, since we can, of course, still perform the same kind of computation/simulation as before, just involving a branching of timelines on random outcomes, which we can access/query from the outside world as necessary.

If it is not accessible, meaning that simulation up to that point in inside-time is necessary in order to even find out what the random outcome will be, then, by definition, the random outcome depends on everything that has happened before. But if it depends on that then, clearly, the outcome is determined (at least partially) by that past. Hence the part that depends on the past seems to, again, be a logical consequence of the rules of the inside world plus the current state of it (which encodes its entire past). In this context it might be useful to note that there are various kinds of uncertainty and may be confused for randomness, most prominently, epistemic uncertainty. Epistemic uncertainty is only an illusion of randomness, based on a lack of knowledge, specifically the lack of knowledge of the factors that determine the outcome. Flipping a coin is actually a version of this. IF you knew the force with which the coin would be accelerated into the air, the angle, the weight of the coin, the air resistance, the height from the ground, etc., then the result could be computed a-priori.

The only thing we are then left with along this line of reasoning is the possible existence of true randomness, not merely a lack of knowledge of the determining factors. If true randomness does exist, then, rather than one possible timeline, there are infinitely many possible timelines that all exist — simultaneously, but since we’ve determined that logic is timeless this addition is meaningless.

Provability

Can we prove Claim 1? I’m not sure that that question can be answered. I believe the main purpose of the claim is to question what existence really means. There is another question to ask about Claim 1 though: can it be refuted? This question on the other hand, seems like it does permit an answer: no! This means that it is definitely possible that everything that is logically implied by any consistent logic, does indeed exist. Any other explanation of what life is needs to, at least, include this explanation of logic controlling all of “life”. As such, Occam’s razor suggests this thesis to be more likely than any other, in particular the simulation thesis. Hence, the only aspect that is worth trying to prove is its minimality: Can there be any other theory of life/the universe that makes fewer assumptions and still explains all of it? Logically, the only way to disprove Claim 1 would be to either show that it isn’t minimal or that it doesn’t explain everything.

Note that Goedel’s incompleteness theorem does not contradict Claim 1, since it makes no claim of completeness or effective axiomatization (algorithm computability). It does seem to impose limits on what we’ll ever be able to understand about our world though.

Benefits

The primary benefit of this thesis, of course, is that the simulation thesis really just kicks the bucket “up the chain”, into the outside world. It is not a definitive answer. It immediately raises the question: what is the outside world in which that simulation runs, and how did that world come to be? Our thesis here does not suffer from this flaw, because logic and its consequences do not require materialization. They exist, “hold true”, even if never represented in anything that can be observed. As such, the outside world does not need to exist to explain the existence of the inside world. Logic transcends world boundaries, just like logic and math existed “before” the Big Bang and will still exist if our universe ever cedes to exist. Another way to put it is to say that “I can imagine a world like ours, therefore it exists” and that thought alone, according to Claim 1, proves our own existence and the reason this line if reasoning is not cyclic is because your thought was not required to create the world you imagined, you merely discovered its possible existence using logic.

Ramifications and Conclusions

Despite its beautiful simplicity, this thesis of life is surprisingly useless. It does not further our knowledge of the world and in fact proclaims that there is a definitive boundary that we will never be able to cross — there is no escape from logic! There are some ramifications though that might be interesting.

• Parallel universes do exist. Clearly, if Claim 1 is true, then there are infinitely many worlds — uncountable in fact —, each defined by a different set of rules and, if true randomness exists, random outcomes. And no, we absolutely cannot “travel” between them as some sci-fi authors imagined and hence it doesn’t really matter — to us in our world — that they even exist.

• Time does not exist outside of “life”. This means that our entire past, present, and future already exist, we are just “live through it”, because that’s what the rules of physics in our world dictate. To an hypothetical outside observer of our world, time is merely another dimension along which our world extends. This does not mean though that time and what we do with it is meaningless inside our world.

• Meaning of life: There is a “computational gap” between what the outside world is able to compute and what are able to compute. This gap could also be called the “materialization gap”, since, as we noted, once we knew all the rules of our universe, we could theoretically simulate its entire future (and past). But practically speaking, for us to actually do so, meaning reach a representation of the world state that we can actually observe, e.g., in a computer simulation, we would need a lot more compute power than we currently have on earth, and probably also a lot more power. One could consider deriving three possible purposes of life from this cap:

  1. finding all the rules as noted above,
  2. findings ways to first determine a lower bound on this materialization gap — i.e., seeing how close to “complete self simulation” our world could get, and
  3. reducing that gap up to that lower bound. The most limiting factor in this endeavor, is, of course, time, since it moves linearly forward for us as a set rate. The strongest counter-measure to time is logic itself, as we know of ways to reason about future outcomes in logic that so not require step-by-step forward simulation.

  Personally I find 2. the most intriguing, simply because the smaller we make this gap, the more “power” we hold about our own world. We may not be able to break free from it, but within the bounds of the logic that governs us, it would give us the greatest ability to optimize it for ourselves. To me, this is probably the ultimate motivation for science.