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1) We perceive time as such because the future determines the past but not vice-versa (H(t|t-1)>0 and H(t-1|t)=0 in terms of entropy) -- thus our brain can at a
by justinpombrio 13y ago
1) We perceive time as such because the future determines the past but not vice-versa (H(t|t-1)>0 and H(t-1|t)=0 in terms of entropy) -- thus our brain can at a given moment contain relatively complete information about past moments, but necessarily limited information about future moments. I think relativity gives a pretty good picture of the nature of time; it is a partial order. Quantum mechanics treats time very differently though, so there is almost certainly more to say. I think this is a good question to be asking.
2) There's something inside a block hole?
It's funny that you should use those two examples in your last question. The first one is true or false depending on the logic you use, and the second is physically false.
The first statement -- that (p or not p) is always true -- is true in Boolean logic but not always true in Constructive logic; in fact this is what separates these two forms of logic. My very rough understanding is that boolean logic best describes situations in which propositions like p are taken to mean "p is true", whereas in constructive logic p is taken to mean "p is provable".
The second statement -- that the ratio of a circle's circumference and diameter is equal to pi -- is false under general relativity. In fact, if you were to measure the circumference and diameter of a big circle around the sun, their ratio would be a little off due to the sun's gravity (I forget in which direction).
You ask whether the laws of logic are true in every possible universe. It depends entirely on what you mean by every possible universe. To really consider one possible universe, though (say the one where everything is made of cheese), we have to be able to reason about it. So if the laws of logic are not true in it (maybe the cheese is also not cheese), we can't really consider it to begin with. So yes, the laws of logic are true in every possible universe, though for a rather boring reason.
- eli_gottlieb 13y agoOr in other words, every universe we can possibly think of has to have some kind of internal logic, except maybe the Lovecraftian ones.
- lifeformed 13y agoBut do those internal logics have to be the same across universes?
- lifeformed 13y agoHmm. I've never read about constructive logic, it looks pretty interesting. Thanks for bringing it up, I'll look into it. Maybe those two examples I gave are bad. But in general, I guess that the question itself (of whether or not logic holds true in all universes) sounds like it is fundamentally unanswerable by using our logical system. Since the fundamentals are axioms, and presupposing an axiom to be false would always be contradictory, we could never prove such a universe to exist. What even is logic? The more I think about it, the less fundamental it seems, and the more it seems like just an aspect of our brains. It's like they are just descriptions of the internal consistency in how our brains are wired. What does it even mean for something to be true or false? Reality is just reality, and any "sense" we make of it is just a state of equilibrium in our brains. Is a mathematical statement in our minds (like 1+1=2) true because of the nature of reality, or true because the structure and rules of arithmetic that we've created happen to trigger some pleasurable sense of consistency in our minds? And perhaps the whole derivation of mathematics is just a discovery of how our brains perceive "correctness". Well, I'm rambling, I guess it's an unknowable thing, because we're always operating in the bias of our own minds.