It seems I'm not making myself clear; let me try again ....

The explicit scope of this thread is the five questions I just posted; my response to your earlier post was in relation to an apparent inconsistency - observations are math-free (my paraphrase), or perhaps observations are theory-free; that there is a clear, clean line between "observations" and "theory".

It seems that you have accepted, at least implicitly, that this distinction is not, in fact, plausible (wrt today's astronomical observations), but have replaced your original dichotomy with a strawman.

Here's what I said (I added some bold): "CCDs or PMTs (photomultiplier tubes), or other gadgets which can only work by virtue of good physics and much math".

At a practical level, you don't need any 'math' to use any of these gadgets - simply dust off the instruction manual, point the telescope, turn on the power, and at the end of your 'run', remove the USB key containing all the observations.

However, if you want to make one of these gadgets, or calibrate one, or fix one, then you will need to at least assume some powerful physics ... and your work will involve at least arithmetic.

The (historical) path which lead to the manufacture of the PMT you used surely includes inspiration and ideas expressed in purely qualitative terms .... however, without the physics and the math, you won't have a PMT with which to make astronomical observations.