Assuming the universe is infinite, is it theoretically possible to transform it into something finite?
Reason for asking: if this is possible, it would have important implications on infinite ethics and the value and potential trajectories of the far future.
Depends on what you mean by infinite precisely. Consider for example that the in some sense finite (0-1) interval can be transformed into the interval (0-inf) via e.g x → 1/(1-x)-1. Or whether the infinite in some sense size of the universe can be described by some finite process (like here writing a finite representation ‘inf’ for something infinite..
Given an infinite universe, an infinite number of Mac’s are stubbing their toes. Is it possible to alter/transform the universe such that only a finite number of Mac’s are stubbing their toes? If so, how?
I’m not sufficiently well versed in physics but it might be the case that there aren’t necessarily infinitely many Macs. There might only be one (for a suitable definition of what makes a person). There could be infinite variety. In that case there might still be a way to reduce that somehow but it might be more complicated than talking about merging all same elements.
Answering the question that’s asked instead of giving the answer that someone seeks can increase the clarity about the nature of the question that’s asked.
is it theoretically possible to transform it into something finite?
Sure. Choose a finite volume and forget everything else.
If this example doesn’t suit you, then I suggest there are other requirements you want such a transformation to conform.
“Infinite” is only well-defined as the precise limit of a finite process. When you say “infinite” in absolute, it’s a vague notion that is very hard to manipulate without making mistakes. One of my university-level maths teacher kept saying that speaking of “infinite” without having precise limit of something finite is equivalent to dividing by zero.
Assuming the universe is infinite, is it theoretically possible to transform it into something finite?
Reason for asking: if this is possible, it would have important implications on infinite ethics and the value and potential trajectories of the far future.
Depends on what you mean by infinite precisely. Consider for example that the in some sense finite (0-1) interval can be transformed into the interval (0-inf) via e.g x → 1/(1-x)-1. Or whether the infinite in some sense size of the universe can be described by some finite process (like here writing a finite representation ‘inf’ for something infinite..
Given an infinite universe, an infinite number of Mac’s are stubbing their toes. Is it possible to alter/transform the universe such that only a finite number of Mac’s are stubbing their toes? If so, how?
I’m not sufficiently well versed in physics but it might be the case that there aren’t necessarily infinitely many Macs. There might only be one (for a suitable definition of what makes a person). There could be infinite variety. In that case there might still be a way to reduce that somehow but it might be more complicated than talking about merging all same elements.
Ignore all but one Mac?
Yes. But please how do you bound these elements? Or asked differently: What makes Mac Mac?
You could also simply transform everything into “mu”.
But that isn’t bijective. You can’t recover the original structure.
He didn’t ask for it being bijective.
Well. I kind assume that the set of answers he intended with his question didn’t contain your answer either ;-)
Answering the question that’s asked instead of giving the answer that someone seeks can increase the clarity about the nature of the question that’s asked.
Granted.
Sure. Choose a finite volume and forget everything else. If this example doesn’t suit you, then I suggest there are other requirements you want such a transformation to conform.
“Infinite” is only well-defined as the precise limit of a finite process. When you say “infinite” in absolute, it’s a vague notion that is very hard to manipulate without making mistakes. One of my university-level maths teacher kept saying that speaking of “infinite” without having precise limit of something finite is equivalent to dividing by zero.