I think inverse square laws are so common because they apply to situations where the distance of one object from another (a one dimensional line) is used to calculate the force potentially felt at any point across the surface of a sphere (a TWO dimensional surface) at that distance.

But then you also have the strength of magnetic fields that follows an inverse CUBE relationship. The simple way I model this in my head is that magnetic dipole fields kind of fill a three dimensional volume with curved field lines, as opposed to gravity or electric charge where the “lines” go straight out, and at any specific distance the total strength of the omnidirectional field is spread throughout that two dimensional surface of a sphere of the same radius.

The Wikipedia page is a good start. In a nutshell:

Since the surface area of a sphere (which is 4πr2) is proportional to the square of the radius, as the emitted radiation gets farther from the source, it is spread out over an area that is increasing in proportion to the square of the distance from the source. Hence, the intensity of radiation passing through any unit area (directly facing the point source) is inversely proportional to the square of the distance from the point source.

There's a good visualisation of that explanation which is the banner picture on the Wikipedia page.

I don't have any better theories than the existing ones, for sure! But there is an underlying pattern that goes deeper even than that law - the principle that physical objects follow the path of least resistance links these laws and many many others.

It's the same for the beginnings of life. We know loads about the conditions before in happened and after it happened, but nothing about that all important instant when it happened.

Fur the big bang's genesis, I like the thinking that small pockets of potential started to form, since a pair of opposed charges is sort of the same as nothing. But that does go along the lines of "nature abhors a vacuum" type of thinking, which has been comprehensively proven wrong since it was popular. Also it doesn't explain one of physics greatest mysteries: why is there so much matter and no antimatter. If things came into existence in opposing pairs, we should see equal amounts of both

You ever wonder if human minds just biologically aren't equipped to understand or comprehend this stuff? Same way ants can't possibly fathom the existence of radio waves or apes can't understand trigonometry or how it works?

I'm disinclined to believe that if for no other reason than I'm sure similar things have been said many times throughout human history about any number of subjects that were then much more fully explored and understood. Anatomy, biology, genetics, etc. all seemed to be fields that were "mysteries too far beyond human comprehension"...until they weren't.

Absolutely. I am completely convinced of the fact that there is knowledge that we can never possess simply because our minds aren't capable of understanding it. I mean nobody understands quantum theory. Some people can do the maths and make the right predictions etc, but they have absolutely no idea what's really going on. I think that's at the boundary of our understanding. Which means there's other stuff being the boundary, and other stuff way way beyond the boundary. But, I think that in the same way you can explain general relativity to a child in simple terms, if we produce AI that can grasp higher concepts, it could explain it to us.

That's why it's interesting that inverse square is in electrostatic and gravitational forces only. Weak and strong force don't follow inverse square. And we don't see the highly complex organization inside the nucleus that we see outside it (otherwise we'd have stable orbits inside the nucleus as well)