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Here's what I wonder: If somebody is hung up on complex numbers, will getting them over that hump get them any closer to understanding how or why complex number
by analog31 5y ago
Here's what I wonder: If somebody is hung up on complex numbers, will getting them over that hump get them any closer to understanding how or why complex numbers are used in physics or engineering?
- dataflow 5y agoI think they'll understand it if you get them to solve a few Fourier series/transforms with sinusoids, and then with complex exponentials, and observe the difference in difficulty.
- ganzuul 5y agoThe behavior of complex numbers under certain operations is seemingly the same mechanism as is seen in physical systems. The style of notation used in engineering usually denotes a periodic motion or a compound of many waves. Of interest for physics is that without the imaginary part, real numbers alone are a leaky abstraction. This structure extends to quaterions and octonions.
- analog31 5y agoIndeed, I'm a physicist with a background in electronics, so I'm fluent in that stuff. The question is whether explaining complex numbers to a non physicist is really going to bring them any closer to physics.
- ganzuul 5y agoConsidering complex numbers lead to group theory and group theory may model atomic structure, this metaphysical correlation is at least worthy of note. It is almost as if we are living in a distortion of truth.