“Quite like a sphere is a representation of a complex plane. The Complex plane does not exist, it is a mathematical abstraction for representing a sphere (mathematically) on a Descartes plane. It is very important to underline that the capability of an abstraction to solve certain physical problem does not make the abstraction real. It is just an information-manipulative, discovered reason for a physical truth for which a real reason is not found or is not easy to be found and in some rare cases a real reason might not exist (this happens in case of informational truths, which have no physical existence at all).”

One such representation is the Riemann Sphere:

I am curious if you have an opinion about why we need the complex number plane is necessary for the scientific mapping of the real. Indeed, as this podcast between Eric Weinstein and Roger Penrose note, it seems to be a feature of both quantum mechanics and general relativity, as opposed to classical mechanics. Below is a quote from Niels Bohr on this point that many folks found at least somewhat mysterious:

 

 

Love to get your take on this.