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How can an arrow move if it needs to get halfway to wherever it going first? Lots of paradoxes you can construct with infinitite recursion or self reference in
by joveian 8y ago
How can an arrow move if it needs to get halfway to wherever it going first?
Lots of paradoxes you can construct with infinitite recursion or self reference in the absence of time.
In this case, interesting is fundamentally a temporal concept and there is only a paradox if you pretend that it isn't.
- mikeash 8y agoZeno’s Paradox is solved with real numbers and calculus. This paradox is explicitly on the natural numbers, meaning you have a well defined notion of “smallest” for any nonempty set of them. I don’t think the solution is related to time. Rather, it’s simply a matter of recognizing that it’s ok for something to be well defined that does not exist. The notion of an interesting natural number, such that it’s a binary property and being the smallest natural number, just doesn’t work. Thus we can conclude that there’s no such thing as “interesting” as defined like this. You can fix it by making interestingness a continuous value, or using a definition such that being the smallest number in a set isn’t enough to be interesting.
- joveian 8y agoThere are a bunch of ways to solve Zeno's Paradox involving time (and not necessarily involving real numbers and calculus), Wikipedia gives a quick overview of many. In the interesting number paradox a solution can be related to time (or recursion depth) such that, as the person you were responding to mentioned, the first few otherwise not interesting numbers can be considered interesting without considering all not otherwise listed numbers as interesting. The wikipedia page gives a different example solution involving time.