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Suppose the simulation hypothesis is correct, so that we are living in one node in a tree of simulated universes. At the root of the tree is base reality, then the child nodes of the root are universes being simulated by base reality, the child nodes of those nodes are the universes being simulated within those simulations, and so forth.

Assuming that computational resources in base reality are finite (but possibly very large), and simulation time in base reality is finite (but possibly very long), at some level this tree of universes must end. But most nodes in a balanced tree are leaf nodes---in a binary tree half the nodes are leaf nodes, and in trees with a higher branching factor the vast majority of nodes are leaf nodes. See, for example, the following image:

tree of realities

So, can we strengthen the anthropic reasoning used in the simulation argument, to say that if we live in a simulated reality, we probably live in a leaf reality beyond which no further simulations will occur?

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  • This seems to be primarily opinion-based. If we are in a simulation, we are in a leaf node already since we are not making these simulations. However, I find it doubtful, but others might not (this is where the opinion comes in), why we would want to create such simulations. So my opinion would be that we would remain in a leaf state. Sep 19 '19 at 16:35
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    I'm not sure the fact we aren't making simulations necessarily implies that we are in a leaf node. There could, for example, be a technologically advanced civilization in a distant galaxy performing simulations
    – Nick Alger
    Sep 19 '19 at 17:06
  • Why should we assume that there is a single base reality? Or that the laws of physics in it are anything like ours, and the notion of "resources" even applies? And we are, in fact, running simulations, the videogames. For that matter, if the reason for leafing out was running out of resources we'd be very aware of that directly, so the argument seems moot.
    – Conifold
    Sep 19 '19 at 18:16
  • The core reasoning is valid (although many people instinctively reject the very idea). The problem is that you need to assign probabilities in order to compute the probability... what is the likelihood that a base node would even have a leaf node? Since we have absolutely no idea what those probabilities are, we have no idea of the odds. We can't tell if it's horrendously unlikely or almost certain. Sep 20 '19 at 16:42
  • It is a fair question, not sure why it was closed. I would say that multiple factors (such as the fact that we don't do such simulations and the Fermi paradox) do strongly favour the fact that we are in a leaf node.
    – Rexcirus
    Sep 26 '20 at 23:07
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In my opinion it's a bad argument for the following reason.

The argument always starts along the lines of, "In 1980 we had Pong and today we have massive multiplayer games and therefore in the future our simulations will be indistinguishable from reality."

But that argument misses the fact that the players in Pong are not self-aware. Ms. PacMan does not have an inner life in which she experiences pleasure at eating white dots and terror at being gobbled up by monsters.

It's certainly likely that in the future we'll have virtual reality headsets or direct neural jacks in the base of our spines that allow us to experience and participate in an illusion indistinguishable from reality. Just as our nightly dreams seem real at the moment we're dreaming them. It's the question of whether I'm a man dreaming I'm a butterfly or vice versa. Simulation theory's a trendy new version of a very old doubt.

But who or what is it that has the experiences? It's our Cartesion "I". I think therefore I am. I experience therefore I am. I jack in therefore I am. [Tangentially, how weird is it that life has come to resemble a William Gibson novel from the 1980's?]

To make the anthropic argument work, we'd have to assume that not only the experience but also the experiencer are created by the computer. But we have no idea how to do that or if it's even possible. We don't know what consciousness is, let alone how to implement it; or for that matter, how we could even know that we have implemented it. I can't test to see whether my next door neighbor is self-aware. "Hi Fred." "Hi user4894. Looks like a nice day." "Yeah. See you later." "You too." I drive away thinking to myself, "What a sentient fellow. He must surely possess what Searle calls intentionality."

In short we don't know what consciousness is, how to detect it, or how to implement it. Therefore it is a wholly unwarranted assumption to imagine that someone has not only figured out how to do that, but has figured out how to implement self-awareness that can itself implement self-awareness ad infinitum."

So the assumption is wrong. Bottom line: In the future we'll have really terrific video games, flight trainers, virtual sex vacations, pr0n ... Oh just imagine the pr0n!

But implementing self awareness? Tell me how to do it once, and maybe I'll consider the hypothesis that it can be done recursively.

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    I don't think this really addresses the question. There are two possible cases to consider: either simulated brains are conscious, or they are not conscious. Obviously, determining which is true is very hard or perhaps impossible. But we can still consider each case independently, without knowing which is right. This question considers the case that they are conscious. This is what I mean by the first sentence, "suppose the simulation hypothesis is correct.."
    – Nick Alger
    Sep 20 '19 at 2:33
  • @NickAlger You're right, but one of the premises has no plausible basis in fact. It's true that if 2 + 2 = 5 then I am the Pope, but that puts me under no obligation to consider the possibility that 2 + 2 = 5. I do believe the simulation argument fails by virtue of ignoring the distinction I brought out.
    – user4894
    Sep 20 '19 at 7:01
  • This is not a fair analogy because we already know that 2+2=5 is false. A more apt analogy would be a very difficult conjecture, the result of which is unknown. There are, for example, many mathematical papers that start with a statement along the lines of "Assume the Riemann hypothesis holds" or "Suppose the the Riemann conjecture does not hold"
    – Nick Alger
    Sep 20 '19 at 7:43
  • @NickAlger For sake of discussion: As far as we know. creating consciousness by algorithmic means is just as false as 2 + 2 = 5. The Riemann hypothesis, on the other hand, is widely believed to be true. It's not a good analogy. Bear in mind that algorithms are highly restrictive. An algorithm can't generate the digits of any of the uncountably many noncomputable reals. An algorithm can't solve the Halting problem. Etc. Algorithms are highly constrained and are not likely to be the only thing the universe is capable of. Newtonian gravity, for example, is not computable.
    – user4894
    Sep 20 '19 at 18:23
  • "Tell me how to do it once, and maybe I'll consider the hypothesis that it can be done recursively." If you're conscious, then it's been done once. Sep 20 '19 at 19:39
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can we strengthen the anthropic reasoning used in the simulation argument, ...

The idea that we are simulated is a contradiction to the anthropic principle...

The anthropic principle is a philosophical consideration that observations of the universe must be compatible with the conscious and sapient life that observes it. https://en.wikipedia.org/wiki/Anthropic_principle

The idea that we are simulated is a contradiction to the anthropic principle because the most salient and incontrovertible fact about our own "conscious and sapient" life is that it is indeed conscious. Consciousness suffers no simulation, at least not in any sense of simulation I know of, and not for the kind of consciousness I am now subjectively experiencing.

Simulation 3. (Computer Science) a representation of a problem, situation, etc, in mathematical terms, esp. using a computer

Despite the mind-boggling progress of science, We are still unable to even begin to explain subjective experience in terms of what we think of as the physical world. Any simulation in the sense given above would be a non-starter. No such simulation could possibly simulate subjective experience.

Of course, this leaves open the suggestion that at least the physical world might be a simulation, and why not, but I don't see why my consciousness would be experiencing this simulation from the inside.

The simulation thesis is even less plausible than God. The infinite powers of an almighty God would at least have enough credibility as the cause to our consciousness as we subjectively experience it.

... to say that if we live in a simulated reality, we probably live in a leaf reality beyond which no further simulations will occur?

This reminds me of the logic of counterfactuals. Once you depart from empirical facts, anything becomes possible and when anything becomes possible, there are no probabilities any longer, because the foundation of probabilities is empirical facts.

The more plausible place for our world is at the root.

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  • This is a fair critique of the simulation hypothesis in general, but that's not what I'm trying to get at here. This question is about supposing the simulation hypothesis is true, and then considering the consequences
    – Nick Alger
    Sep 19 '19 at 21:04
  • See David Chalmers on the "hard problem" vs. the "easy problem" of consciousness, to "explain subjective experience in terms of what we think of as the physical world" would be the hard problem, but it is unnecessary to solve that to simulate a brain and body at the physical level so that it would behave just like the real thing (Chalmers' 'easy problem'). And there are plenty of philosophers who think there are good arguments that behaviorally identical systems would have the same subjective experiences (including Chalmers).
    – Hypnosifl
    Sep 19 '19 at 22:59
  • @Hypnosifl I don't think it is possible to solve the hard problem. Indeed, I think it is a false problem. - (2) Yes, I would agree that any difference in qualia may not make any difference for our brain and our body, although we don't know that. - (3) There are no good arguments for now that identical systems have the same qualia. All we can say is that different qualia may not make any physical difference. Further, it seems clear there could be different brains and yet the same behaviour. Sep 20 '19 at 10:02
  • @NickAlger "This question is about supposing the simulation hypothesis is true, and then considering the consequences" I did answer to that, see the bit at the end, on probability: anything becomes possible. Thus, too many possibilities to discuss. If we limited ourselves to your explicit assumptions, sure, we're more likely to be in a leaf-universe, but you're asking us to go further. I can imagine cases where we would be more likely in a node. Or indeed, at the root. What you are doing is broadly equivalent to metaphysics and to mathematics. Any premise whatever is acceptable in principle. Sep 20 '19 at 10:18
  • @Speakpigeon - There are no good arguments for now that identical systems have the same qualia Did you read the Chalmers paper I linked to? I think it makes a plausible case that if there is some kind of lawlike relationship between physical structure and qualia, and if those laws have some of the qualities of "elegance" that we see in physical law, we should expect qualia to respect some kind of principle of functional invariance, based on thought-experiments where neurons are gradually replaced by substitutes that have the same functional input-output relations.
    – Hypnosifl
    Sep 20 '19 at 13:46
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The limits to how many nodes can exist is Zeno's dichotomy paradox however you already granted that with your assumption: "This tree must end." However your ultimate question is concerning our specific reality. Argument granting that "Simulation theory is correct:"

First, the caveat here is that simulation theory is only useful in science fiction and has never itself been considered in actual philosophical discourse; because actual discourse must respect the current state of knowledge. In considering universes, much of that knowledge comes from cosmology and physics.

The question specifically asks if no simulations can be derived from the one we allegedly exist in. If we are, as the theory argues, a leaf reality.

Answering this requires some more rigid definitions or ambiguity will derail the process.

Let's start with what we know today: Time is not as important as we once thought. All science today using both General Relativity and quantum mechanics leads us to the conclusion that space and time are fundamentally one thing, they are inseparable, where warping space necessarily warps time and vice-versa. Einstein's field equations clearly show that time was created with the universe. Saying "what happened before the Big Bang" is like asking what you were doing during the Holy Crusades. For some people that's hard to get around, but the math works that way so I accept it, and it really isn't so hard to understand for anyone who plays F.E.A.R. and battles the Replicas. While you may wonder why your opponents are so smart, the real question is, "How can I be faster than them?" The answer is called "reflex time" by the game designers. Even though Replicas are very smart and powerful, time itself is controlled at the whim of the programmer, who exists outside that simulated universe. At some point, the world F.E.A.R. takes place in was created. But no matter how smart a Replica becomes inside that world, even looking at trees that seem to be decades old, they will never understand that their universe was created in 2007 in a timeline above their own. Here is an illustration of the problem of time:

F.E.A.R. Gameplay

To the simulated person the tree is 15 years old. But that tree didn't exist 15 years ago - in our time. The simulation has no way of calculating our time, and we can pause the game, go get lunch, and start it up again without them ever knowing time was stopped in their world.

Nick Bostrom's problem with causality: Bostrom argues that computer power may advance to a point where the simulated world equals or exceeds the "real" world (or the simulation above it). This cannot happen in any causality, at any node of the alleged simulation. In all cases, a cause must be BEFORE any effect it causes. This means the delay between a cause and an effect can never reach zero. No matter how sophisticated a computer becomes, it will never make an eye blink, for example, with zero delay between the time the program decids to blink, and the time the eye actually blinks. Some delay will always exist.

This means we can never be replaced by our creation inside some simulation, because the cause of every action within the simulated time (which we created), will always happen in OUR time (real time), and will always be before the action we cause.

Is it impossble to create another simulation after a leaf reality?

Absolutely. What the programmers of F.E.A.R. call reflex time proves that any simulation can be as fast or as slow as the parent reality decides it to be, so long as it obeys causality and has SOME positive value of time. In other words, we could theoretically play F.E.A.R. on an ancient 1mHz computer and the simulation would work exactly the same. It would be extremely slow and boring for us, but within the simulated world everything would move "normally" as they expect it to. A bullet might take 2 weeks to reach the wall in our time, but it is still too fast to dodge in their reality. Because they are all thinking at 1mHz!

We can extrapolate this further and allow the simulated persons inside F.E.A.R. to develop their own computer and create a reality. They will use what they think is a "obscenely fast" processor - 3 Hz - and create their own simulated people. In OUR time (2 nodes above them), an eye blink may take 10 years to us, but that doesn't matter.

This can go on indefinitely. There is no reason that computers need to advance or reach "hi fidelity" before simulation begins. The processes which govern causal actions are time-independent - meaning that they only need to have a cause before an effect, but the amount of time between cause and effect is not governed in any way, it simply cannot be zero or outside the causal light cone.

In summary, given the definitions provided for the simulation hypothesis and our current state of knowledge of reality, there can be any arbitrarily large number of layers of realities created by any simulated reality; and each layer of reality is created with its own space-time dimensions that do not need to be "fast" by any measure in relation to the parent reality. General relativity prohibits the existence of "leaf realities" and refutes that reality spawning can have any dimensional limits at all. The anthropic principle does not refute that child realities may be created; it states that consciences outside that reality (us) cannot be supported inside that created reality - only created consiences inside are compatible (I.e., TRON demonstrates a violation of the Anthropic principle).

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  • Bostrom argues that computer power may advance to a point where the simulated world equals or exceeds the "real" world Equals or exceeds in what sense? Computational complexity, or something else? Can you point to where in his writings Bostrom made such an argument? Also your argument about indefinite layers seems to be based on time, but you should also consider the simple issue of the number of one-bit computational steps are involved in each simulated history, if all sim worlds run for finite number of steps, doesn't each child necessarily have less steps then its parent?
    – Hypnosifl
    Sep 20 '19 at 23:28
  • From the OP link: "Bostrom's "ancestor simulations", on the grounds that every philosophical school of thought can agree that sufficiently high-tech neural ancestor simulation experiences would be indistinguishable from non-simulated experiences." Indistinguishable means equal.
    – Vogon Poet
    Sep 21 '19 at 0:25
  • There is no empirical reason to believe any reality has a finite number of steps. We create virtual memory on computers today where many more applications are queued up and running than can possibly be contained within the memory. Likewise; where are the "walls" that contain this reality if it is finite?
    – Vogon Poet
    Sep 21 '19 at 0:26
  • Bostrom's argument is that the ancestor simulations would equal ours in apparent subjective complexity, not that the whole universe would be equally complex, maybe a smaller region of the universe would be simulated in detail. Finite number of steps is plausible due to increasing entropy making further computing impossible at some point, but also OP seems to have assumed it, see comment simulation time in base reality is finite (but possibly very long). Every computer has a finite number of computational cycles per second so if the time is finite, number of steps performed is finite too.
    – Hypnosifl
    Sep 21 '19 at 0:35
  • This makes too many assumptions to be relevant. Time doesn't have to be finite within a simulated environment unless time in the alleged "base reality" is finite, and that is not a given. We only started thinking about limited time when we saw the universe expanding. Time can be arbitrarily increased up to the bounds of the base reality. All of this also neglects the possibility to multiply time through multithreading (many tasks simultaneously). This reality for example could be completed with only 6 billion parallel processors (one for each observer). This is a trivial amount of resources.
    – Vogon Poet
    Sep 21 '19 at 2:02

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