All the same, it evidently was not a very high priority; once we had the answer there were not front page headlines declaring, "Huge Centuries Old Scientific Mystery Solved!" Remember, it is not a big controversy if few people care OR know about it; if everyone knows but no one cares it is still a "meh" question. In the grand scheme, finding an elusive explanation why fundamental things do NOT happen ranks well below finding elusive explanations why fundamental things DO happen. If I am Newton, universal gravitation is a far more significant study than Olbers Paradox.

Whose side are you supporting? There are lots of paradoxes, sure, but the Moon itself (i.e. its existence) was never among them, and never unknown. It still took a lot of innovation and bootstrap levitation to GET there, and their incidental dividends were and are more than merely "incidental." Exploring any frontier produces novelty and innovation, by definition; the only variables are their number and magnitude. It is entirely possible resolving a paradox shifts no paradigms, as evidenced by your cited examples of such, but the larger and more enduring the paradox, the more likely its resolution DOES radically and fundamentally change things.

No doubt, but I am not Newton and my periodic efforts at autodidactic calculus have been far less successful than his. The issue is almost certainly discipline, but remember, I got high marks in honors math classes by overcoming sloppy carelessness with tenacious brute force: Work and check the problem until getting the same answer twice, at which point the law of averages says it is PROBABLY correct, since the likelihood of all the same mistakes (but no others) at all the same points is increasingly unlikely as complexity increases. Once we were tasked with finding the formula for three dimensional distance and visually presenting its proof; I figured out the formula AND proof for the whole class within a minute or two of receiving the assignment, but got the lowest grade because my presentation sucked out loud.

So it tends to be "slow and steady wins the race," and doubly so when there is no way to ask clarification. Maybe I should just plow in and hassle you, moondog and our old engineering friend with emails every time I have a question. I usually got better test scores than that engineer when we were in the same math classes, but he always finished before me—EVERYONE did.

Oh, I realize it has frequently worked—that is the PROBLEM. The approach is valid with your stated caveat, but over time the absence of counterevidence can and too often DOES become evidence of absent counterevidence. Especially when a theory is plausible and persistent enough people start building new ones upon it; then the second theory REQUIRES the firsts validity, and people can be resistant to conclusions 1) refuting something they consider so certain and basic they 2) spent years constructing their own work on its foundation.

Look at string theory, or GUTs in general, and proton decay in particular. Many models require proton decay, prompting their authors and acolytes to resist and/or rationalize away arguments against it—even though proton decay is highly unorthodox, purely hypothetical and lacks any supporting evidence (despite decades and billions of dollars spent seeking it.) People dislike having their babies killed, whoever the killer and however good the reason, and often treat setting fire to the crib as no more than an especially outrageous unjustifiable homicide.

So sure, as long as we recognize unconfirmed hypotheticals—however longstanding—as just that, rather than elevating them to sacred cows (or sacred Flying Spaghetti Monsters,) fine. We can build on that foundation with the understanding the construction is just as hypothetical, and if it keeps working (i.e. receiving ultimate experimental conversation) there is no need to re-invent the wheel. However, when we come to broken ground progress requires more than a wheel and lots of elbow grease, and as long as we restrict ourselves to fancy new variations of the wheel because it always worked before we cannot move forward even an inch.

Again, unsure we are saying different things. Relative energy is the issue relevant to Olbers, and if red shift is high enough it will take many photons for us to even notice. c limits red shift magnitude, but objects do not re-emit all energy absorbed either, and emission amounts fall as their motion (and so red (or blue) shifts) rises.

Define "disproportionate." Transferred energy is all we are considering, after all, and how much particles struck re-emit vs. assume as their own momentum. A mountain striking a pebble (alone) will not transfer all momentum and stop dead, but HOWEVER much it transfers is all that matters to WHATEVER the pebble does (whether re-emitting it as light, assuming it as momentum of its own or "other.") A relatively large amount of momentum transferred to a low mass high density pebble in a vacuum would become momentum of its own. That it could only absorb a relatively small amount of the mountains momentum (i.e. "cannot absorb or emit much energy in the first place") is just one reason. Having little stationary inertia to overcome or other nearby matter to absorb ITS momentum on collision are two more.

"Uniformly random"=/="random and uniform:" The adverb modifies the adjective; they do not both modify the noun. I wrote a long analysis of probability before concluding I am likely arguing semantics: Energy would be uniformly distributed among MATTER (because all matter would be in thermal equilibrium with itself,) but not SPACE (because matter would be randomly distributed.) There would be pockets of matter, and thus of energy (which would thus be nonuniformly distributed in the universe) but it could do no work on more rarefied matter anywhere else (or vice versa,) because in thermal equilibrium with it. Good enough? Or is the contention Kinetic Theory must eventually distribute matter uniformly? If so, fine, but that is nonrandom.

Yes, but the nice thing about "if a tree falls in the woods..." is it gives bulding engines to move things and make electricity MEANING (and thus motive, pardon the pun.) Before founding physics Aritotle himself declared, early in his Metaphysics, abstract knowledge the noblest kind, because "scientia gratia scientiae" rather than as means to end. Or in this context, Newtons inspiration for the law of universal gravitation was not an ambitious desire to journey to the moon, but simply seeing an apple fall to earth and demanding, "wtf did THAT happen?!"