Hilbert's Curve: Is infinite math useful?
Space filling curves, turning visual information into audio information, and the connection between infinite and finite math (this is a reupload of an older video ...
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Let's talk about space-filling curves. They are incredibly fun to animate and they also give a chance to address a certain philosophical question. Math often deals with infinite quantities, sometimes so intimately that the very substance of a result only actually makes sense in an infinite world. So the question is, how can these results ever be useful in a finite context? As with all philosophizing, this is best left to discuss until after we look at the concrete case and the real math. So I'll begin by laying down an application of something called a "Hilbert Curve," followed by a description of some of its origins and infinite math. Let's say that you wanted to write some software that would enable people to see with their ears. It would take in data from a c...
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Let's talk about space-filling curves. They are incredibly fun to animate and they also give a chance to address a certain philosophical question. Math often deals with infinite quantities, sometimes so intimately that the very substance of a result only actually makes sense in an infinite world. So the question is, how can these results ever be useful in a finite context? As with all philosophizing, this is best left to discuss until after we look at the concrete case and the real math. So I'll begin by laying down an application of something called a "Hilbert Curve," followed by a description of some of its origins and infinite math. Let's say that you wanted to write some software that would enable people to see with their ears. It would take in data from a c...
