Not a physicist, just a passionate layperson. AFAIK real practitioners choose their units such that a lot of things are unity: speed of light is 1 (hence E = M

Not a physicist, just a passionate layperson. AFAIK real practitioners choose their units such that a lot of things are unity: speed of light is 1 (hence E = M), h-bar is 1, etc. There are some numbers like the “fine structure constant” (which I think is tantalizingly close to 1/137) that do seem difficult if not impossible to derive from others. The pop-science explanation for this that a layperson like myself would know about is the “anthropic” principal, they are such because only in such regimes would anyone ask the question. I don’t know what real scientists think about this.