How are they similar and how are they different, can both exist, does one have more basis than the other, why are they important?
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Simulation Hypothesis:
The simulation *hypothesis* (not theory) is a philosophical argument about the fundamental nature of our existence.
It goes something like this: given the rapid increase in scope and capability of our computing power, it seems plausible that at some point in the future we will be able to create simulations of our universe, following our laws of physics, at extremely high fidelity.
If you also believe that something like consciousness can exist whether the processes are performed by animal brains or computers, this implies that at some point we will be able to create genuinely conscious minds that reside in a simulation.
If you also believe that, in the future, we will want to run these detailed simulations of various points in the past (say you were interested in really exploring what would have happened if Hitler had been successfully assassinated at one of the various assassination attempts), then it’s likely that people in the future will *want* to host many of these highly detailed simulations that support the actual consciousness of entities within the simulations.
If you also believe that running these simulations will not require an inordinate amount of resources, then it’s likely that there will truly be many of them.
If you put all of these assumptions together, you can come to the conclusion that any given conscious entity is much more likely to exist in a simulation than in the single true universe. It is taken as a given that because the resources are there and because there is a desire, the people in the one true universe will create many simulations, and those simulations will encompass many more conscious entities than exist directly in the true universe. Hence, the reasoning goes, it’s more likely than not that you and I, right now, are simulated entities rather than “real” entities. I put “real” in quotes because if you say by definition that a simulation is detailed enough to actually implement consciousness, what does “real” even mean at that point?
To be fair to Nick Bostrom, both his initial argument and his more recent arguments do not say that we must be simulated beings. What they say is that if you accept a bunch of particular statements about what’s likely to be true, then it’s likely that we’re simulated beings. But there are many possible objections and he acknowledges that.
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Holographic principle/hypothesis:
The holographic principle/hypothesis is a principle that states it might be true, under certain assumptions, that a particular volume of space can be conceived of as either a four-dimensional volume containing matter and energy and evolving in time, or a three-dimensional surface which contains all of the information required to describe what’s happening in the four-dimensional volume.
First, it’s important to emphasize that when you have an equal sign in an equation, from a logical point of view that means genuine equality. That is, if I have a quantity X and I say X = 2, it is correct to interpret that as saying X *is* 2 and 2 *is* X. Many people, including many highly educated people, tend to think of some equations as an implication arrow that only points in one direction. That is, they say that one side or the other of the equation is the *true* nature of the equality. But that’s not what an equals sign means.
Anyway, the holographic principle entails the conclusion that thermodynamic entropy as understood in the context of chemical reactions and so on is in some sense equivalent to informational entropy as defined by considering arbitrary bits of data. This has led people to say things like “our universe is fundamentally built of information instead of matter and energy”. Which falls into the trap I mentioned above, where an equal sign is not treated as a true equality but as an arrow of implication that works only in one direction. Usually the physicists themselves do not fall into this trap, and it gets propagated in popular media instead.
In any case, the only connection between the two concepts is that people have interpreted the holographic principle as evidence that our universe is, in fact, a simulation. There is no necessary implication in that direction.
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