Comments by "Ginny Jolly" (@ginnyjollykidd) on "3Blue1Brown" channel.

  1. I'm so used to frequency and wavelength describing waves that "speeding up" and slowing down" have no meaning to me. And I pictured each as opposite what you called them. Higher frequency, to me, doesn't mean "slowing down." Truly though, fast and slow don't seem to have meaning except as bad analogies.
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  2. I saw this kind of "number bounce" line you made on on the graph in another context, the mapping of a fractal. The values of each iteration plot start off "simple" and then get chaotic around the "limit point as the plots get closer and closer to the limit, then when the limit is hit, the next point is a simple plot, until it again gets chaotic around a limit point. Instead of being a limit, could phi, pi, and other special numbers be somehow plotted in the fractal itself? That they not be limits but be actual plot points? Perhaps another form of an integral from zero to infinity or negative infinity to positive infinity? I have always been fascinated by mathematics of zero and infinity, and I was never quite satisfied with "a very large number divided by a very large number points to a number very close to zero, and other limits. Could fractal mapping provide a key to these special numbers? (and am I asking a significant question?)
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  3. Integrals and derivatives describe many factors in a situation. The first time I saw this was in connection with physical chemistry. I hadn't had the Calculus of partial differentials, but my understanding was enough to see that they described different interrelated and interacting vectors: pressure, temperature, and particle or mass content. PV =nRT has 4 dimensions; four variables to determine in a given small volume (vicinity, really) in which other factors can be ignored. (gravity, e.g.) Now that it has been shown that gravity waves exist and they affect matter, it can be yet another vector to be considered. In architecture, much can be done by treating a design as a series of cantilevers and points of rotation, but a skyscraper requires consideration of weather factors, forces of buffeting winds, earth movements, differential heating from the sun, and support inside and outside the building. The dynamics of water pressure. The air movement in the building, and electric components all affect the design one way or another. Each has its partial differential with respect to all the others. Fluid dynamics is concerned with flow —how fast fluid moves through a channel —and flux —the cross section of that flow through the channel. But it is also concerned with other dynamics like eddies and waves. These are affected by channel size, but also the gradient of that channel: what cross - section of channel do you need to minimize or maximize the presence of fluid anomalies. So Calculus can be thought of as a series of related factors that need to be solved with respect to one another. This goes beyond finding the gradient of a 3-D graph hill (which you can do with a pencil: place it where it doesn't roll off).
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