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Mathematics disproves Matrix theory, says reality isn’t simulation
(interestingengineering.com)
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Uh... that's literally what a simulation is.
But dreams aren't simulating reality as we observe it; they just kinda do their own thing. Your brain isn't consistently simulating quantum mechanics (or, hell, even simple things like clocks) while you're dreaming so this is a moot point.
People who are lucid dreaming simulate a full reality that's nearly indistinguishable from the one they find themselves in during waking time. If your brain can't tell the difference during this time, how can you be sure you're not dreaming right now reading this?
The scope of what a simulation is has always been limited by the technology we know. It is only a failing of imagination and knowledge to assume that algorithmic computation is the only valid form of simulation in the future, these have existed for barely 100 years, but even Plato's cave was talking about the larger philosophical problem
You're not describing a simulation, you're describing a perception. A person perceives that they're seeing an indistinguishable reality, but we know that people's brains do not have the computational power to simulate molecular motion in even a cubic centimeter of air.
Or, if they look at the stars, are they then simulating an infinite space with infinite mass and all of the associated interactions inside of their finite brain? Of course not, that would be impossible.
Dreams are perceptions, not simulations.
The mind while lucid dreaming is creating a whole environment, which for some people has incredible level of detail. Your "consciousness" is experiencing a whole video game or whatever, which must be simulated to be percieved. Imagine you had some kind of really advanced VR setup and body suit that could touch your senses very richly - something must be feeding that perception, a simulation
Our brains build a model of the world inside of our head, that’s what we experience.
Those same processes can generate output that isn’t there, we can hallucinate. This is what we’re doing when we’re dreaming. We’re not simulating a world it is computationally impossible.
To perfectly simulate a volume the size of your bedroom for even a few minutes would take millions of years of compute time. That is not happening inside your brain.