• eran_morad@lemmy.world
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    1 year ago

    Imaginary numbers are merely a poorly named mathematical construct used to reconcile the empirically observable phenomena of nature (e.g., summations of waves). They’re the means by which we achieve mathematical closure under exponentiation. You could call them whatever the F you want, so long as they could be used to represent vectors in the complex plane.

    What reason do you have to believe in anything outside of material nature?

    • monotrox@discuss.tchncs.de
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      1 year ago

      Up to the introduction of quantum mechanics imaginary numbers where only ever a theoretical tool and any calculation in electromagnetism, mechanics or even relativity can be done without them.

      Also, any measurement you can make will always result in real numbers because there is no logical interpretation for imaginary measurements (a speed of 2+i m/s doesnt really make sense)

        • monotrox@discuss.tchncs.de
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          1 year ago

          I said that any calculation in electrodynamics CAN be done without imaginary numbers, I never said that it would be the most common or convenient way of doing things.

          If you use a different form of solution to maxwells equations, electrical impedance can totally be expressed as just another real property. Fourier transform also is not necessary to solve maxwells equations or any other physical systems. It just might make it significantly easier and more convenient.

          Obviously imaginary numbers existed and where used way before quantum mechanics was a thing but they werent technically necessary in physics because they never appeared in the equations of fundamental theories (Maxwells equations, general relativity, newtonian mechanics)

          • eran_morad@lemmy.world
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            1 year ago

            Yes, and one CAN integrate by taking paper cuttings and dispense entirely with the idea of infinity.

            • monotrox@discuss.tchncs.de
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              1 year ago

              I was just trying to make an argument that imaginary numbers were technically not necessary and thus it makes historical sense that they werent seen as something ‘real’. Im not trying to get people to stop using them ;)

              • eran_morad@lemmy.world
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                1 year ago

                Eh, this is not worth your time or mine to argue about. Let’s move on. Also, I take your point.

          • ChaoticNeutralCzech@feddit.de
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            1 year ago

            Well, in AC circuits, having √3̅+√-̅1̅ A of current makes as much sense as having 2 amps with a 30° phase shift. It’s just easier notation for calculations - Cartesian coordinates for what would otherwise be polar.

            • jarfil@lemmy.world
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              1 year ago

              That’s BS notation. If you want Cartesian, just use 3i+1j, no need for some impossible √-1 that you then redefine some operations for, just so it becomes orthogonal to R.

              • dyen49k@kbin.socialOP
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                1 year ago

                You might want to look up geometric algebra for a better geometric interpretation of complex numbers than the complex plane with a “real” and “imaginary” axis

              • ChaoticNeutralCzech@feddit.de
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                1 year ago

                The nice thing about 𝑖 = √-̅1̅ is that you don’t need to redefine any operations for it, ℐ𝓂 is “automatically” orthogonal to ℛℯ.