The fact that there are several distinct clusters with the same label means that there are several distinct recipes that go under the same name, which I think is interesting.

You mean the axes? They are simply the 1st and 2nd components. Not very useful, and quite ok to omit. Do you mean the cluster labels? They are useful enough, I think. It would have been useful to label it as a PCA plot, though.

I guess this is a PCA plot. Most people commenting clearly aren't familiar with the concept and therefore don't understand the plot. It's not the plot's fault, it's a perfectly good plot, and these plots have no meaningful units etc. Maybe a link to the wikipedia article about PCA would have helped those without a scientific background, which is unfortunately most of the world.

Excellent description. I’d maybe save quantum mechanics to last though, because many people have the same feeling of doubt about qm as op has about imaginary numbers. Let’s just say that periodic phenomena are much easier to describe using complex numbers. To give a sense of why that is you can say it’s because these need to shift energy back and forth between two different forms of energy, which is reflected in the two different kinds of numbers that make up a complex number - the real part and the imaginary part. A pendulum, for example, converts potential energy to kinetic energy and back again. Quantum mechanics is just one example of periodic phenomena.