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First off, if you lived an infinite amount of time, then you would have spent infinite amounts of time in some or all parts of the universe (assuming a finite size for the universe). Thus, the idea of "flying anywhere in the universe" as you put it would seem to be not that impressive if you had already spent an infinite amount of time in that part of the universe.If you were talking about a universe of infinite size or an infinite multi-verse, then you still would have spent an infinite amount of time in some or all parts of the universe/multi-verse in many cases. The only exception that I can think of to this happening is if the sizes (i.e. Lebesgue measure) of the infinite time dimension versus the size of the infinite space dimension were different (with the size of the time dimension have a smaller Lebesgue measure) and you were constantly moving to new parts of the universe (with or without repeated visits to old parts of the universe). In this case, you would actually technically spend zero percent of your time in any one part of the universe, which I find equally disturbing.

Second, the idea of always learning new things has troubled me too. According to Physics, information is ultimately stored as a state of a subsystem or subsystems in the Physical universe and is transmitted via energy (i.e. photons). Therefore, as the amount of information stored in a given subsystem of the universe (let's say God's head) tends to increase, then shouldn't the energy density and the energy expenditure of that system also increase to a point where it's no longer physically possible to pack more energy into the subsystem? In other words, shouldn't there be an upper limit on the amount of things that you can learn, even given an infinite amount of time to learn them?

Let me put this another way. Let's suppose that we have a system composed of N particles in a quantum state defined by the variables a_1, a_2, ... a_n. According to my intuition (which may be off because we are talking about quantum mechanics here), the number of possible quantum states attainable by a particle in the ensemble should be finite. In other words, any one particle in the system should only be able to contain a finite amount of information. With that assumption in place then, as the information contained in the system increases, the number of particles in the system (the ensemble) should also ultimately have to increase as well. Therefore, since the size of the system is finite (i.e. God's head is contained in a finite space), the energy density of the system must also either a) reach a limit where there can be no more information contained in the system or b) continue to increase as more information is pushed into the system.

So, to make a long story short, if you kept trying to learn new things forever, wouldn't you either a) run out of room or b) have your head eventually explode (due to too high of energy density)?

Also note that there is demonstrably an infinite amount of information in the universe, so you can't make the argument that there is an upper limit to the amount of information.

Has anyone else ever thought about this?