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Why don't imaginary numbers ever show up "in real life" outside of STEM? It's interesting everyone seems to think they are fundamental to everything, but we do

Why don't imaginary numbers ever show up "in real life" outside of STEM? It's interesting everyone seems to think they are fundamental to everything, but we don't see them. In fact we only see plus/minus/times/divide before getting into "You'll probably use a computer for that, and you probably don't need to unless you're an engineer" stuff. Does anything ever happen outside of science that we could use imaginary numbers to understand? Are they just fundamentally outside ordinary experience, or do we not see them because we have workarounds that hide them? It would be interesting to read a SciFi novel where regular people commonly encounter imaginary numbers and other similarly far from everyday life stuff like calculus.

p_j_w 4y ago
Man, "outside of science" is doing a lot of work here. We also don't see quantum mechanics "outside of science," why would they also not be fundamental? The fact of the matter is that there are A LOT of things we can't explain without complex numbers or quantum mechanics, so people believe that they're fundamental. That's not weird.
- eternityforest 4y ago
  Yeah, it definitely is. I'm not denying that they're fundamental, I have no reason to doubt that, I just think it's odd that they are so deeply embedded into everything, simple enough to kind of understand the basic idea of, and yet totally separate from everyday experience. Like, a construction worker may know hundreds of techniques. A painter uses hundreds of colors. A while many people likely only use four operations on real numbers their whole lives. Math is everywhere, essential for engineering, but almost totally hidden from most people. Probably just a consequence of how we kind of jumped straight from "experience and guesswork" to "Hire a pro if you want to build a barn and let them use computers" though.
RugnirViking 4y ago
real things heating up and down (i.e not an idealized particle but a thing with volume), the motion of a pendulum, electricity flowing through basically anything (same as heating, when you consider actual volume), these are a few of the things I have worked with where I literally have no option but to use imaginary numbers to model them. Modelling here means predicting what a change would do, for example if I want to make a robot that can balance a stick upright on its hand like you might do with a broom, I use maths related to pendulums to predict the movement of the stick, which require imaginary numbers to show how moving in a certain direction will cause the pendulum to fall (in what direction & how fast). I must emphasise here that I have done these things with real robots, and they do indeed heat/electricity flows/balance as the maths predicts. Does this imply your brain is doing the same maths, imaginary numbers and all, when you balance a broom on your hand? Is there an alternate mathematical notation that doesn't include such strange unintuitive things? probably, thats for the mathematicians to figure out. But as an engineer, they definately do work.
ben_w 4y ago
We used them in the late 80s and early 90s for pretty fractals on home computers; but for SciFi world-building… it can be done, but I don't think you can really get into those worlds as a reader without already being somewhat familiar with the maths. Reason I think this is having listened to Greg Egan's Dichronauts, in which spacetime is ++-- with all the counterintuitive hyperbolic rotations that this implies. Other ways to get i into common use besides that, probably gives equally counterintuitive results if you don't already know the maths; for example, instead of a maximum debt you can take out based on your ability to repay, you get a region which, for certain interest and repayment rates, is the Mandelbrot set.

p_j_w 4y ago

Man, "outside of science" is doing a lot of work here. We also don't see quantum mechanics "outside of science," why would they also not be fundamental? The fact of the matter is that there are A LOT of things we can't explain without complex numbers or quantum mechanics, so people believe that they're fundamental. That's not weird.

eternityforest 4y ago
Yeah, it definitely is. I'm not denying that they're fundamental, I have no reason to doubt that, I just think it's odd that they are so deeply embedded into everything, simple enough to kind of understand the basic idea of, and yet totally separate from everyday experience. Like, a construction worker may know hundreds of techniques. A painter uses hundreds of colors. A while many people likely only use four operations on real numbers their whole lives. Math is everywhere, essential for engineering, but almost totally hidden from most people. Probably just a consequence of how we kind of jumped straight from "experience and guesswork" to "Hire a pro if you want to build a barn and let them use computers" though.

RugnirViking 4y ago

real things heating up and down (i.e not an idealized particle but a thing with volume), the motion of a pendulum, electricity flowing through basically anything (same as heating, when you consider actual volume), these are a few of the things I have worked with where I literally have no option but to use imaginary numbers to model them. Modelling here means predicting what a change would do, for example if I want to make a robot that can balance a stick upright on its hand like you might do with a broom, I use maths related to pendulums to predict the movement of the stick, which require imaginary numbers to show how moving in a certain direction will cause the pendulum to fall (in what direction & how fast). I must emphasise here that I have done these things with real robots, and they do indeed heat/electricity flows/balance as the maths predicts. Does this imply your brain is doing the same maths, imaginary numbers and all, when you balance a broom on your hand? Is there an alternate mathematical notation that doesn't include such strange unintuitive things? probably, thats for the mathematicians to figure out. But as an engineer, they definately do work.

ben_w 4y ago

We used them in the late 80s and early 90s for pretty fractals on home computers; but for SciFi world-building… it can be done, but I don't think you can really get into those worlds as a reader without already being somewhat familiar with the maths. Reason I think this is having listened to Greg Egan's Dichronauts, in which spacetime is ++-- with all the counterintuitive hyperbolic rotations that this implies. Other ways to get i into common use besides that, probably gives equally counterintuitive results if you don't already know the maths; for example, instead of a maximum debt you can take out based on your ability to repay, you get a region which, for certain interest and repayment rates, is the Mandelbrot set.