Physicists and Philosophers Debate the Boundaries of Science

>It took 2040 years before science/math could answer Zeno's paradoxes.

And that's only if we assume calculus answered them. Which is not the absolute consensus of logicians/mathematicians.

Many seem to believe they are simply about limits and that's all, but they may also point to a more fundamental aspect of reality. E.g. from Wiki:

A suggested problem with using calculus to try to solve Zeno's paradoxes is that this only addresses the geometry of the situation, and not its dynamics. It has been argued that the core of Zeno's paradoxes is the idea that one cannot finish the act of sequentially going through an infinite sequence, and while calculus shows that the sum of an infinite number of terms can be finite, calculus does not explain how one is able to finish going through an infinite number of points, if one has to go through these points one by one. Zeno's paradox points out that in order for Achilles to catch up with the Tortoise, Achilles must first perform an infinite number of acts, which seems to be impossible in and of itself, independent of how much time such an act would require.

Another way of putting this is as follows: If Zeno's paradox would say that "adding an infinite number of time intervals together would amount to an infinite amount of time", then the calculus-solution is perfectly correct in pointing out that adding an infinite number of intervals can add up to a finite amount of time. However, any descriptions of Zeno's paradox that talk about time make the paradox into a straw man: a weak (and indeed invalid) caricature of the much stronger and much simpler inherent paradox that does not at all consider any quantifications of time. Rather, this much simpler paradox simply states that: "for Achilles to capture the tortoise will require him to go beyond, and hence to finish, going through a series that has no finish, which is logically impossible". The calculus-based solution offers no insight into this much simpler, much more stinging, paradox.

A thought experiment used against the calculus-based solution is as follows. Imagine that Achilles notes the position occupied by the tortoise, and calls it first; after reaching that position, he once again notes the position the turtle has moved to, calling it second, and so on. If he catches up with the turtle in finite time, the counting process will be complete, and we could ask Achilles what the greatest number he counted to was. Here we encounter another paradox: while there is no "largest" number in the sequence, as for every finite number the turtle is still ahead of Achilles, there must be such a number because Achilles did stop counting.

I think high level theory is wandering aimlessly through a field blindfolded with little guidance or where to look. This is because our current theories are so good, we have no idea where to look. So it begins conjecturing and conjecturing. What it ends up with is nonsensical garbage that does little to advance physics.

But yet, there isn't a crisis in physics at all since these theorists are so far removed from reality, I don't really care what they think. They don't really tell use anything useful or interesting so I tend to ignore them. Instead, I focus on things we do know exist but cannot explain, say astrophysical jets, pulsars, or supernovas. We know they exist and we can see them, yet we understand them very little. We have models that are getting better and better over time, but they all exist within the current understanding of physics. This is where physics really is. Whatever garbage the theorists put up on the arxiv can be ignored with little loss.

Instead, those of us "in the trenches" can continue our work trying to explain observed phenomena with our current theories. There is no need to add in extra dimensions or cohomology. Maybe, when we've done really understanding our current theories can we talk to those theorists again.

Incidentally, since I started my PhD in physics doing numerical relativity, my views on science have changed completely. I used to be interested in stuff like string theory, but actually sitting down and trying to do it left me feeling empty inside. Now that I work in an area that is very closely related to observations, I feel like I am actually learning something about the universe. It's hard to explain philosophically, but I really believe in experiments as the guiding principle of science. In my case, we see pulsars (2500+ of them) and we have yet to provide a full explanation of their nature. To me there is something more real and scientific about this then trying to explain multiverse theory but I don't know the words to describe it.

Science is born the day that Socrates says ""I know that I know nothing".

Science dies the moment things that are untestable becomes "a new kind of evidence".

If we can't test something because whatever reason, like we don't have enough energy, the fact that we know we can't test it is in fact valuable. We will have to find methods or ways to get there in the future.

Until that , we can't be sure. Fine. We know we don't know.

But falsifying this fact and believing in evidence that does not exist is believing we know things that are unknown to us.

This is dogma, religion, philosophy, but not science.

Nothing wrong about religion, or philosophy, but it is not science.

Actually, at least in the US, physics is funded because of things like the atomic bomb and the transistor, as GP points out. Observe the rhetoric of any congress member. They don't care if physics is "cool", any more than the general public probably does.

Football isn't funded by the federal government at all, so your point about national security is just silly.

Most physicists are experimentalists, who work on testable predictions. And most theorists work on easily testable systems, like solid state physics or nuclear physics. And even cosmologists and astrophysicists in are very aware of the problems of ascribing astrophysical phenomena to new physics, it just took 70 years after Zwicky's invention of dark matter before anybody took it seriously as a sign of new physics.

By contrast, the small bit work done on theories that have purely theoretical appeal is getting all the press, and in a way that needs to improve a lot before one could call it grossly misleading. Take for example the sentence,

    “The imprimatur of science should be awarded only to a theory that is
     testable,” Ellis and Silk wrote, thereby disqualifying most of the 
     leading theories of the past 40 years. 

Well, what is a leading theory supposed to be, 40 years ago the standard model was just that, a model that needed confirmation. The W and Z bosons were only discovered in 1983, the Top quark in 1994 and the Higgs two years ago. General relativity only had strong support in the high field regime with the discovery of the Hull-Taylor pulsar a year earlier. And as I said, most physicists did not work on fundamental physics in the last 40 years, but instead on stuff like the quantum Hall effect ( discovered by von Klitzing in the early 80ies) or the Giant Magneto-Resonance ( discovered in the late 80ies), both solid state effects with technological applications and Nobels in the last thirty years.