In the PMM thought-experiment, we waved away these differences - being able to temporarily forget that you are in a simulation was good enough for our purposes, like the suspension-of-disbelief we experience when reading a good novel or watching an engrossing movie. But let's take the PMM thought-experiment one step further by invoking some sort of phlebotinum. Let us posit that this phlebotinum can be ingested, inhaled, topically applied, placed on the skin like crystals, or whatever. The effect of this phlebotinum is that the user can travel through the parallel universes we posited in Part 18. Specifically, the user of this substance can travel to a universe that corresponds more or less exactly to his or her inner-most wishes and desires. This travel is unrestricted by the bounds of time and space. The user is freed from the possibility of death, regardless of the hazards the user chooses to encounter. Further, we posit that this travel imposes no psychic toll on the user - it is effortless and painless.
The Twilight Zone episode, A Nice Place to Visit imagines a man who has found himself in a very similar situation, though it is framed in a supernatural context, instead of a naturalistic context, as we have done here.
"Henry Francis Valentine, ... calls himself 'Rocky', because that's the way his life has been – rocky and perilous and uphill at a dead run all the way. He's tired now, tired of running or wanting, of waiting for the breaks that come to others but never to him, never to Rocky Valentine. A scared, angry little man. He thinks it's all over now but he's wrong. For Rocky Valentine, it's just the beginning."
After robbing a pawn shop, Henry "Rocky" Valentine is shot by a police officer as he tries to flee. He wakes up to find himself seemingly unharmed by the encounter, as a genial elderly man named Pip greets him. Pip explains that he has been instructed to guide Rocky and give him whatever he desires. Rocky becomes suspicious, thinking that Pip is trying to swindle him, but Pip proves to have detailed information on Rocky's tastes and hobbies. Rocky demands that Pip hand over his wallet; Pip says that he does not carry one, but gives Rocky $700 directly from his pocket and says that he can provide as much money as Rocky wants.
Thinking that Pip is trying to entice him to commit a crime, Rocky holds him at gunpoint as the two travel to a luxurious apartment. Pip explains that the apartment and everything in it are free, and Rocky starts to relax. However, his suspicions rise again when a meal is brought in, and he demands that Pip taste it first to prove that it is not poisoned. When Pip demurs, claiming that he has not eaten for centuries, Rocky shoots him in the head, only for the bullets to have no effect on Pip at all. Rocky realizes that he is dead, and he believes that he is in Heaven and Pip is his guardian angel.
Rocky visits a casino, winning every bet he makes as beautiful girls gather around him, and enjoys being able to pick on a policeman after Pip shrinks him. Later, Rocky asks Pip if he can see some of his old friends who have also died, but Pip says that this world is for Rocky alone. Except for the two men, no one in it is real. When Rocky wonders what good deeds he could have done to gain entrance to Heaven, Pip takes him to visit the Hall of Records. Rocky looks through his own file and discovers that it only contains a list of his sins, but decides not to worry about it since God apparently has no problem with his being in Heaven.
One month later, Rocky has become thoroughly bored with having his whims instantly satisfied. He calls up Pip and asks for a challenge in which he might run the risk of losing. Pip offers to set up a bank robbery, but Rocky abandons the idea, saying that a pre-planned outcome would take the fun out of the crime. He tells Pip that he is tired of Heaven and wants to go to "the other place," to which Pip retorts, "Heaven? Whatever gave you the idea you were in Heaven, Mr. Valentine? This is the other place!" Horrified, Rocky tries in vain to open the now-locked apartment door and escape his "paradise" as Pip laughs malevolently at his torment.Narratives surrounding the subject of life-extension are becoming increasingly important in the modern world. We are able to extend our minds using technology in ways that make us, relative to our ancestors, nearly god-like. We are bumping up against the real possibility of indefinite life-extension - artificial eternal life, more or less.
But we really do not know the very long-run implications of our choices under these conditions. Let us suppose that our children or grand-children will be the first generation to reach escape velocity. Does it make sense for them to follow the "tried-and-true wisdom" of their ancestors that has laid out the template of a supposedly ideal life: get a degree, establish a career, buy a house, marry, have children and prepare for retirement? All of these choices may actually be sub-optimal. In fact, they may be positively detrimental to their actual, long-run well-being. By carefully following the prudential advice of their parents, they may inadvertently end up like the infernal Rocky Valentine; they may wake up to find themselves eternally living out the consequences of their sins without even the release of death which delivered our generation from any long-run negative consequences of our supposedly ideal life-pattern.
In Valentine's case, he had become imprisoned by the demonic being, Pip. But we do not have to invoke demons and ghouls to surmise that it is possible that we might inadvertently invent a terrifying future and then curse ourselves with endless life within that future. Some of the leading lights in the development of artificial intelligence are worried about the possibility that we are inadvertently building the agents of our own extinction. But extinction is not actually the worst possible outcome. Even worse, we might invent indefinite life-extension or make ourselves actually unable to die and then end up imprisoned by some hostile, supremely powerful telos[1].
We tend to associate happiness with getting what we want. Rocky Valentine is miserable despite being able to have anything he desires. There are two possible causes of his misery: (a) it's unconditionally impossible for him to attain happiness or (b) he needs to have access to a purpose (end) greater than any he can generate internally[2]. In Rocky's case, we know that it is case (a) because he is imprisoned by a demonic being. But if our children found themselves in a similar position in a hypothetical future world, they would not know whether it is (a) or (b). In this case, the only rational course of action is to attempt to determine if (b) is possible, that is, to find out whether it is possible to get access to a higher end than any we can generate internally.
What we are really talking about is how to avoid regret, in the most generic possible sense[3]. Rocky Valentine thought he was in heaven but, later, found out that he had been duped and was trapped in a hellish prison. At this point, Rocky presumably felt regret for all his past crimes. Given his newfound regret, we can safely guess that, if he had access to a time-machine, he would fly back to a time before he committed all the sins that landed him up in this hell and make different choices. Note that time-travel, in this context, is equivalent to the backtracking agent we discussed in Part 18.
The need to time-travel is the result of encountering a problem of some kind in the unfolding history. Any deficiency or unsatisfactoriness in the history of one's existence within our phlebotinum-fueled trip through the multiverse would result in the desire on the part of the partaker to backtrack and try over. This is not unlike the situation that many gamers are familiar with when they encounter a trap in a game level and realize - too late - that they should have made a better choice. "I wish I had gone up the stairs instead of turning to the right!"
Let us informally define a concept I will call regrettal in analogy to the surprisal of Shannon information-theory. Regrettal can be measured as the deviation between the actual length of the history path of a participant immersed in the simulation (with back-tracking) versus the length of the final path they have taken as measured without any back-tracking down regretted paths. There is a formal concept of external regret that is used in game theory[4].
The thesis of this post is that a rational actor would not partake of the phlebotinum unless he had in hand a proof (formal, physical) that partaking the substance is zero-regrettal. Prior to partaking of phlebotinum, he had no ability to travel through the multiverse so, after taking it, he will not be able to return to the moment prior to taking it (to "undo" the action). But it could turn out that, in the future, the only action the user wants to take is return to the moment prior to partaking of the phlebotinum!
But what does this have to do with virtualization?
In the last post, we concluded that it is possible for an agent that is higher on our Ω-based Kardashev scale to virtualize an agent that is lower on that scale without utilizing hard privilege-limits or silent privilege-limits. This means that the "hardware" that the universe is hypothetically running on could be egalitarian even if we are inside a simulation.
Let's extend the analysis to two agents that are on the same level - in other words, both agents know exactly the same prefix of Ω, Ωm. If one-way functions exist (an unsolved mathematical problem), our two agents would be able to generate useful randomness with the help of an environment, µ. The procedure is as follows: the environment asks each agent for a random number (this random number is not useful to the agent itself, since it generated it), then it applies a one-way function to each number and then it combines the result using modular arithmetic (e.g. modulo-2 addition). This randomness does not rely on either agent "helping" the other or giving the other agent any insight into its current behavior, choices or operation. Given useful randomness, the agents can interact with one another in unpredictable ways, even though neither agent has access to more bits of Ω. In other words, the interactions of these agents are not a trivially solved game (ala Tic-Tac-Toe). Even though the behavior of each agent is computable (algorithmic), the activity of each agent is unpredictable to the other.
We now have the properties of action (choice) and liveness (through useful randomness). The agents can interact in games of perfect information (like Chess) or games of imperfect information (like Poker). Between the two of them, they are always faced with the possibility of regret because it is possible that one agent has utilized its available resources in solving one kind of problem while the other agent has utilized its resources in solving another kind of problem; if one or the other utilization has turned out to be advantageous in a particular game, the game will go to the agent with the advantage. Unlike in the case of two agents on different rungs of the Ω-hierarchy, this cannot be foreseen or avoided. Both agents run the risk of losing (regret).
The next property we need to discuss is lock-in. So far, we have assumed that the agents are bound by the time-parameter - lock-in is a simple matter of alternating the move. However, real-time games (which is the class of games that most closely resembles the world-as-we-know-it) open up a new realm of possible strategies - timing strategies[5]. And this is where the Simulation Hypothesis begins to loom large - if we are in a simulation, then timing (simultaneity) is much more complicated than a simple, linear time-parameter. Timing, in the broadest possible sense, is a function of what is being computed and how good your best algorithm is at computing it.
The Internet[6] and Bitcoin, in particular, are a good place to start to understand the difference between time in a simulated environment and time in an idealized geometry. In an idealized geometry, we simply wave a hand and say, "At time t, all objects {o0, o1, o2, ...} are at locations {x0, x1, x2, ...}" Einsteinian relativity alters this Newtonian concept of simultaneity but still preserves idealized simultaneity relative to any given inertial frame. What I am asserting is that there is no algorithmically simple definition of simultaneity in a simulated physics in which there is more than one agent.
The reason that simultaneity is complicated is that there is no easy way to define trusted timestamps across a distributed set of computational resources (e.g. the Internet or, more broadly, the universe itself). The Bitcoin network can function as a trusted timestamp service[7]. A simulated universe with multiple agents would have to have a similarly bulletproof mechanism for verifying time-ordering in order to resolve timing disputes to the satisfaction of all agents with a stake in a particular event.
This is why, in Part 16, we placed time below causality in the hierarchy of the quantum monad. Time, in a simulated universe, is an emergent phenomenon. It is the result of the activity of the simulation, not something that stands above and governs the simulation. In a distributed computation, there is no central authority to wave his hand and make all events simultaneous by fiat. Simultaneity must be weakened from the idealized geometric sense (or even the Einsteinian sense of relativity to inertial frames). Simultaneity becomes, instead, whatever agents will accept as simultaneity.
Simultaneity is the basis of lock-in. Like publishing an embarrassing photo to facebook, you can't take back something you published to the record but it is simultaneity that defines what has actually been published and what has not! Lock-in, in turn, is the basis of regret. The desire to "take back" a choice arises from the irreversibility of the move.
Conclusion
We asserted that a rational agent would not partake of our genie-in-a-bottle phlebotinum - even though it can and will fulfill his every wish! - until he has a proof in hand that he will not regret partaking of it. We then delved into the topic of regret and found that regret is, indirectly, connected to the problem of one-way functions because we need one-way functions to construct useful randomness, giving rise to liveness and the possibility of simultaneous games (interactions).
Here's the kicker - we don't know how hard it is to solve the problem of the existence of one-way functions. It is possible that it is much harder to solve the problem of the existence of one-way functions than it is to simulate a human brain - or even every human being on the planet, simultaneously. If this is the case, we might find ourselves in a position where we are building more and more powerful simulators to solve the problem of one-way functions and begin to simulate humans, human societies - or even the entire planet - merely as a by-product of the search for the proof that one-way functions are possible, or impossible. If the Simulation Hypothesis is true, there are good reasons to suspect that the simulation will not make this any easier than brute-force[8].
In summary, Bostrom's Simulation Argument might have misidentified the motivation of the hypothetical simulators. Perhaps they are not motivated by mere curiosity about their ancestors; perhaps this is computational warfare.
Next: Part 20, The Five Ways
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1. This is probably the reasoning behind the removal of access to the Tree of Life, recorded in Genesis 3:22-24, "And the Lord God said, 'The man has now become like one of us, knowing good and evil. He must not be allowed to reach out his hand and take also from the Tree of Life and eat, and live forever.' ... [Afterward] he placed on the east side of the Garden of Eden cherubim and a flaming sword flashing back and forth to guard the way to the tree of life."
2. We know this because Rocky already has access to unlimited means to whatever end he happens to choose. If the problem is not the available means, then it must be the chosen end(s).
3. Learning, Regret minimization, and Equilibria [PDF], Multi-armed bandits
4. From External to Internal Regret [PDF]
5. In boxing, for example, feinting a punch is a kind of timing strategy.
6. Google spans entire planet with GPS-powered database
7. Bitcoin Wiki: Block timestamp
8. Say I am an enlightened being of some kind that operates countless universe simulations. I am entangled in a protracted war (or game, if you like) with a being similar to myself and the battlefield is my simulations. Any help I provide lower beings in solving a non-trivial computational problem might assist my enemy in fighting me simply by helping him compute.
Stimulating series so far. Looking forward to reading more.
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