Thanks for writing this, I enjoyed learning more about the mathematical universe theory, and it at least seems I’ve gained a useful intuition. I’m not sure the intuition has practical uses, and I also think I disagree on what can be drawn from this.
Clearly, then, if G.O.D. were turned off for a billion years, and then reactivated at the point where it left off, we wouldn’t notice anything either.
When the simulation is stopped, later to be restarted, we experience no difference because nothing is changed in our simulation by the progression of time in the “larger universe”. Whether the “next step” of the simulation takes place, in that larger world, a femtosecond later, a year later, or a million years later, the state of our simulation rests in perfect stasis until the next step is taken. And as soon and to the extent the “next steps” are taken, our simulated existence continues. I think we agree on that.
Now what if the simulation is never continued, and the “next steps” are never taken? Just as we don’t expect to experience anything while not being simulated in the aforementioned gap in our simulation, we shouldn’t expect to experience anything when our simulation is turned off. You use the term “notice”, saying that we won’t notice either a gap in simulation or not being simulated at all. In the simulation gap, “not noticing” feels like we’re talking about some unobservable detail that, assuming no concern about the larger world, can be ignored, which is true. For the case of the simulation being turned off, it’s true we won’t “notice” the simulation has turned off, but we won’t “notice” ANYTHING past that point, ever again.
I’ve gained the intuition that consciousness or sentience is a property of a mathematical structure, but it still seems like computation is necessary in order to create/fully specify that mathematical structure. At least with my possibly naive view of physics/meta-physics/math, even for us to conceptualize a mathematical structure is to compute it in some way.
While I don’t agree with your intuition pump, I’m not convinced that the mathematical universe idea is false, and my point is primarily regarding that pump. Also in reference to a computer simulating us backwards, I can’t immediately guess what COMPUTING backwards would do, but I recall the idea that “when” time flows backwards, entropy decreases, light leaves our eyes and returns to light sources, and our neurons remove connections based on evidence as we “unlearn”. I.e. it is only possible to experience life in one direction, though it might flow in both.
I think the situation here can be resolved using an analogue of the limiting behavior of functions in mathematics. If, from the perspective of the beings simulated, nothing happens when the simulation turns off for an arbitrary amount of time (call this number n), then as n approaches infinity, the simulation beings’ consciousness will still continue. (If a function f(x) = c for all real x, then the limit of f(x) as x approaches infinity will also be c.)
Thanks for writing this, I enjoyed learning more about the mathematical universe theory, and it at least seems I’ve gained a useful intuition. I’m not sure the intuition has practical uses, and I also think I disagree on what can be drawn from this.
When the simulation is stopped, later to be restarted, we experience no difference because nothing is changed in our simulation by the progression of time in the “larger universe”. Whether the “next step” of the simulation takes place, in that larger world, a femtosecond later, a year later, or a million years later, the state of our simulation rests in perfect stasis until the next step is taken. And as soon and to the extent the “next steps” are taken, our simulated existence continues. I think we agree on that.
Now what if the simulation is never continued, and the “next steps” are never taken? Just as we don’t expect to experience anything while not being simulated in the aforementioned gap in our simulation, we shouldn’t expect to experience anything when our simulation is turned off. You use the term “notice”, saying that we won’t notice either a gap in simulation or not being simulated at all. In the simulation gap, “not noticing” feels like we’re talking about some unobservable detail that, assuming no concern about the larger world, can be ignored, which is true. For the case of the simulation being turned off, it’s true we won’t “notice” the simulation has turned off, but we won’t “notice” ANYTHING past that point, ever again.
I’ve gained the intuition that consciousness or sentience is a property of a mathematical structure, but it still seems like computation is necessary in order to create/fully specify that mathematical structure. At least with my possibly naive view of physics/meta-physics/math, even for us to conceptualize a mathematical structure is to compute it in some way.
While I don’t agree with your intuition pump, I’m not convinced that the mathematical universe idea is false, and my point is primarily regarding that pump. Also in reference to a computer simulating us backwards, I can’t immediately guess what COMPUTING backwards would do, but I recall the idea that “when” time flows backwards, entropy decreases, light leaves our eyes and returns to light sources, and our neurons remove connections based on evidence as we “unlearn”. I.e. it is only possible to experience life in one direction, though it might flow in both.
I think the situation here can be resolved using an analogue of the limiting behavior of functions in mathematics. If, from the perspective of the beings simulated, nothing happens when the simulation turns off for an arbitrary amount of time (call this number n), then as n approaches infinity, the simulation beings’ consciousness will still continue. (If a function f(x) = c for all real x, then the limit of f(x) as x approaches infinity will also be c.)