# Living in Avalon

…If you assume any rate of improvement at all, then the games will become indistinguishable from reality….given that we’re on a trajectory to have games that are indistinguishable from reality and those games could be played on a set up box or a pc or whatever, and there would probably billions of such computers or set top boxes…it would seem to follow that the odds that we’re in base reality is one in billions…tell me what’s wrong with that argument.

When I saw him answer the simulation question, I was immediately reminded of  the 2001 film, Avalon.

The simulation question has been talked about extensively in the last month or so, but I still haven’t seen any physicists chime in and it seems an argument from this perspective would be most appropriate for Musk (1). There was a response from a cognitive scientist and a philosopher here, but they seem to have missed the mark a bit, and they don’t seem to have understood what Musk may have meant by indistinguishable. I’m going to focus on this word, because it makes specific demands on the physics of the possible technologies involved.

Questions:

1. Is it possible to build a simulation “indistinguishable from reality?” Indistinguishable is critical here.
2. I expect the trajectory Musk describes will change. Where is the asymptote? I will have no chance of answering this one.
3. If it is possible to build such a simulation, does it matter?

Re: Question 1: Is it possible to build a simulation “indistinguishable from reality?”

[All Equivalent] I am going to assume, as Musk seems to, that by “reality” he means a world that operates with the same rules as ours appears to; that it has the same laws of physics. The distinction he is making is between “base” reality and simulated reality. They both behave exactly the same but one is an original. His argument seems to require all of the simulated realities operate under the same rules, so that our experiences here can carry implications about what’s possible in realities that simulate other realities.

[Computable] I think I have to assume further, also like Musk, that “reality” is computable. That all of the rules can be reduced to logically rigorous statements, also that there is nothing that doesn’t follow the rules, and therefore classical or quantum computations are sufficient to simulate reality (2).

It happens that our experiences here operate under quantum mechanical principles at the most fundamental level. We live in a universe that obeys Heisenberg Uncertainty, and there is a fundamental scale set by a constant of nature:

$\Delta x \Delta p\ge \dfrac{\hbar} {2}$

Any object we observe has a momentum ‘$p$‘ we associate with what Newton called a “quantity of motion”, and a position ‘$x$‘. This inequality is an assertion about the distributions of position and momentum. Roughly speaking, the uncertainty principle sets an absolute, fundamental limit on how well it is possible to know $x$ and $p$. This limit comes from the quantity $h$ – it is Planck’s constant. It is an incredibly small number measured in units of space and time we’re familiar with, but it is not zero, meaning it is impossible to know both the position and momentum of an object perfectly.

The less obvious consequence for our purpose: the uncertainty principle represents the limits in nature’s own detail. Once you know as much as uncertainty principle permits, there really is nothing else to know: nature itself carries no more information (3).

It shouldn’t seem plausible that a full fidelity (“indistinguishable”) simulation of a physical space could be housed in any volume less than or equal to that space, but I don’t know how to prove this. My intuition says the most parsimonious way to simulate a  physical space is to have that volume time evolve on its own. As Einstein put it, “God does not care about our mathematical difficulties. He integrates empirically.” There shouldn’t be any shortcuts, I think.

Some work on the limits of computation using uncertainty principle, general relativity  (GR) (and/or?)  the second law of thermodynamics has been done, producing theoretical limits regarding computation. This work is bit out of my depth but it seems GR is required for its limits on energy density (4). Anyway, these details should not interfere with reaching this implication: Because there are fundamental limits on computational power, and by [All Equivalent] these limits apply to a simulating reality, it is not possible to embed, as a subsystem, an indistinguishable simulation of a region within that region. There can’t physically be any substitute for proper reality.

Now, what about the plug-in Matrix kind, aka the dream or the video game? Maybe it is only necessary to fully simulate observed, or observable regions of space and time? And even then only to the limits of observational powers of the individual. I have been assuming that our “reality” fully obeys all the known laws of physics, even when we don’t directly test or observe them. I should just be able to say this kind can be rejected because it is solipsism – we are trying to use physics here and this would take all the bets off. But I think I can do better, especially since it was this kind Musk directly proposed, though I will have to offer inductive arguments.

1. This world is too shitty for too many people. Unless Musk somehow thinks this reality is his very own oyster and none of the rest of us are real, what reason would we have to simulate a reality like this with so much suffering?
2. All software has bugs. “Indistinguishable” is too strong a demand for any software to meet with, no matter how advanced its developer. Honestly I think bug-free software cannot exist. There would be dejavu’s and glitches.
3. This reality is definitely not a video game in its lack of lucidity. Why don’t we know it’s a simulation?
4. If we had this kind of computational power, we could do a lot better for a video game than this. It would literally make gods out of everyone. Just ask: are you living in the world you wish existed?

If an indistinguishable reality were possible, it would not be desirable. The truth is too hard. If people had unlimited power to create their own realities they would hide from base “reality” in ways that are more robust and complete than religion and technology  allow them currently.

I have one remaining physical argument. We know that some physical systems are described by models whose equations lead to algorithms that are “hard” in this sense: That the computation time needed to predict observables scales so greatly that the computer would effectively require the lifetime of a universe in base reality to integrate, violating our [computable] assumption (5). This argument is not without a certain subtle problem.

Re: Question 2: I expect the trajectory Musk describes will change. Where is the asymptote?

I should just give up on this one for now…I suspect the bound found by Seth Lloyd is too generous but I don’t know how to improve it:

$\text{Max Operations Per Second}$ $\sim \dfrac{mc^2}{h}$

The numerator is the most recognized formula in physics: the rest energy of Lloyd’s “ultimate laptop” from relativity. Planck’s constant has appeared again because this is a quantum computer, and the computation speed is limited by how quickly one state can “rotate” into another state that is sufficiently …distinguishable, again determined by Heisenberg uncertainty(6).

Re: Question 3: If it is possible to build such a simulation, does it matter?

When we ask for indistinguishability we are asking, by definition, for a reality that will never fail to satisfy any demand we might make of it. It is impossible to devise an experiment that would reveal that it is a simulation. I don’t know why Musk is unsatisfied with this (7). Again by definition, these doubts would persist for anyone living in base “reality.”

I think a minimal plea for sanity requires us to take our reality as it presents itself. Further, that we take it as simply as it presents itself, and imagine no hidden variables, mechanisms, Wizards of Oz, Dungeon Masters, Cartesian Demons, or code beyond nature’s capacity for information, i.e. its ability to distinguish.

It is a hardcore, base reality that what can’t be observed really isn’t there. A simulated reality and a base reality if indistinguishable must be one and the same. Nature itself can brook no hypotheses about the unobservable. We cannot allow ourselves superstition, or even agnosticism if we are going to move past barriers of imagination. We’ll have to be atheist. Nature is just too creative and extends too far beyond our ken to allow us any less.

Maybe we should be hopeful that we are living in a simulation…either we develop simulations that are indistinguishable from reality or civilization ceases to exist.

Avalon, the legendary land
The isle of apple-trees and mist
Avalon is the land of elves
Where the hero comes today

Avalon, the legendary land
The hero set out there

Avalon is the land of elves
Avalon is the heavenly isle of shadows
Enchanted isle
The ship set out to an unknown voyage
Avalon…

1. There are reasons for a good physicist (not me) to stay out of this discussion. The primary one I’m thinking of being that this notion is, at least at face, untestable. Please take all of the physics presented here with a grain of salt.
2. One thing I’m definitely not sure of: would this reality simulation require a theory of everything, so that all of the physical laws would have to be known?
3. It might be argued that nature does know more, but simply behaves in a way that prevents us from knowing or observing any more. I think all hypotheses of this kind can be equated to a “hidden variables” description of quantum mechanics, and I believe all such theories have been excluded by Bell’s Theorem and its experimental verification(here, and here).
4. There’s a whole literature on this that I won’t be able to go into. I neglect distinctions  made between limits on memory capacity, the longevity of a record, and what research in this area may imply about time itself, and any relationships between gravity and thermodynamics. In due time, I think the research on quantum computing will reveal much more about these questions.
5. Most of the research in this area is for Classical computation – where the states of computer are strictly binary, 1 or 0. The situation for quantum complexity is less clear, as this field is still fairly new and many quantum algorithms are still being developed.
6. There is an energy and time relation analogous to the one for momentum and position, though its interpretation is a bit more subtle.
7. Really I think he didn’t mean the full quantum mechanical notion of indistinguishable, but I needed an excuse to write this post.