Open to the outdoors, to let the fresh air in.

Thank you for adding some facts to my vague conflated memories.

Does this mean the concept of infinity requires an infinite number of infinities?

A circle has one edge/side, that is grade-school geometry. There is no reason to engender confusion by trying to make it into a polygon or introducing infinity. Your model of shapes does not seem to account for curved edges.

Consider a stereotypical pizza slice. One might plainly say that it is a “like a triangle but one edge is curved” without falling into a philosophical abyss. :)

Or zero…

Furthermore, it is meant to highlight the fact that people gleefully embrace the concept of infinity, but try their hardest to avoid and depreciate the concept of imaginary numbers. It would appear to me that the bias ought to be reversed.

I recall hearing a quote from the guy that coined the term “imaginary number”, and how he regretted that term because it conveys a conceptualization of fiction. IIRC, he would rather that they would have been called “orthogonal numbers” (in a different plane) and said that they were far more real that people tend to hold in their mind. I think he said “they are as real as negative numbers” along the same lines of one not being able to hold a negative quantity of apples, for example.

The stray shower thought (beyond simply juxtaposing the discordant terms of ‘imaginary’ and ‘real’) was that infinity by contrast is a much weaker and fantastic concept. It destroys meaningful operations it comes into contact with, and requires invisible and growing workarounds to maintain (e.g. “countably” infinite vs “uncountably” infinite) which smells of fantasy, philosophically speaking.