[hodwik]

We had a rush of scientific breakthroughs 100 years ago. I believe we will have more.

That experimentation in physics has slowed down to 18th century levels doesn't mean science is over, it just means the low-hanging fruit is over and we will have to continue slogging through theory before we discover new experiments.

Science has always relied on philosophy for its underlying direction, it's just obvious again. It took 2040 years before science/math could answer Zeno's paradoxes. If you can't handle the slog you're not really a scientist, you're a technician.

[noobermin]

No one is arguing whether science is over, they are arguing whether modern theoretical physics is science.

Another thing somewhat impacted by this issue that people don't think about is that we might not be able to keep up this pace in research for things like string theory for non-scientific reasons: specifically, science funding has flat-lined while the number of students entering the fundamental research fields is increasing. Really, particle physics is probably one of the most saturated fields in theoretical physics today.

There simply isn't enough room for everyone to study what they want. Therefore, given the "zero-sum game" situation we have, we need to decide where it's beneficial to spend our tax dollars and time researching...or most likely, governments who barely understand how to balance a budget will decide it for us. Given that string theory's only argument at this point is suspect amongst a plurality of traditional scientists, it seems like low-hanging fruit to be picked off the funding tree.

Regarding the "keep researching" line in higher level theory that the end of the article and you seem to be promoting...I think yes, you will always have people researching something out there, although honestly, the people who will be able to will most likely be at a certain number of institutions which can be enumerated on one or two hands. The rest of theoretical particle physics? I guess the sustainability of that program is dependent on the stress tolerance of physics graduate students and post-docs for the time going forward.

The other way out is to, you guessed it, work in research that is testable, and leads to fancy toys the beltway boys can appreciate.

[VeilEm]

> science funding has flat-lined while the number of students entering the fundamental research fields is increasing

This is probably not true. All kinds of money is being poured into physics research to create better batteries for example. It may be indirect, but there's a ton of money going into physics research.

[noobermin]

I might be restricting it to government funding, so this might be true. Considering this in the context of the rest of my post, I'd think this kind of money is restricted to practical, applied fields, not quantum gravity. I do suppose once in a blue moon, a wealthy benefactor might want to support a grad student doing string theory. Still, the exceedingly small number of rich people willing to pay out for esoteric physics guarantees it will go to researchers working in those finger-enumerable universities as I said. For the larger pool of physicists across the country that mainly would be paid by NSF grants and the like? They lose out to the condensed matter physicists making leaps and bounds in material science.

On second reading of your post, you may be implying it isn't zero sum due to more money going to the applied physicists, leaving some for the stringy guys. It might be true, my impression is that it isn't enough[0], but I could be wrong.

[0] This is somewhat out of my ass, but it is tempered by colloquia at my university I've attended where this comes up from time to time.

[dozzie]

It's not science research, it's technology research. And it's not fundamental thing, it's just bells and whistles to be developed. Better batteries are not critical to our understanding of the universe.

[wolfgke]

> This is probably not true. All kinds of money is being poured into physics research to create better batteries for example. It may be indirect, but there's a ton of money going into physics research.

This is not research (in particular not physics research) but engineering or development.

[pheroden]

So science 2.0 will be encumbered by patents... Great.

[VeilEm]

Educational research at universities often leads to patents. Universities like Standford own patents or have helped research performed at a University lead to patents. Government funding for research in the U.S at least has never been hostile to commercialization.

[narrator]

Science slowed down in the 50s right when government got involved in a massive way in the grant process. Eisenhower even bemoaned this fact, along with the military/industrial complex in his final speech:

"In this revolution, research has become central; it also becomes more formalized, complex, and costly. A steadily increasing share is conducted for, by, or at the direction of, the Federal government. Today, the solitary inventor, tinkering in his shop, has been overshadowed by task forces of scientists in laboratories and testing fields. In the same fashion, the free university, historically the fountainhead of free ideas and scientific discovery, has experienced a revolution in the conduct of research. Partly because of the huge costs involved, a government contract becomes virtually a substitute for intellectual curiosity. For every old blackboard there are now hundreds of new electronic computers. The prospect of domination of the nation's scholars by Federal employment, project allocations, and the power of money is ever present and is gravely to be regarded. Yet, in holding scientific research and discovery in respect, as we should, we must also be alert to the equal and opposite danger that public policy could itself become the captive of a scientifictechnological elite."

[eli_gottlieb]

>Yet, in holding scientific research and discovery in respect, as we should, we must also be alert to the equal and opposite danger that public policy could itself become the captive of a scientifictechnological elite.

Well, nice that we managed to heed one of Eisenhower's warnings.

[eternalban]

If we disambiguate the factual success of applied science from the theoretical aspirations and/or formulations of the past 100 years [1], we would note the substantial downturn in the latter compared to 19th century.

I further disagree regarding your take on the "underlying" basis of science. Science begs philosophy to explain its (irreducible) mathematical foundation, where the said foundation ("basis") has a few un-canny givens/axioms in its bag of tricks.

Empiricism was the line drawn a few centuries ago. And just like the 'magna carta', the latter day "sages" apparently have determined the ancient ones were in error ..

[post-comment-edit: 1] Roughly speaking. To set bounds, above would consider Einstien a good citizen of 19th century science.

[tim333]

I've got a hunch there will be some breakthroughs when AI can visualise some of the theoretical stuff that human brains struggle with. I've tried to read and understand some of the literature as to how you get gravity from a spin 2 quantum field and why it's hard to renormalize and my it's hard to get your head around. And I think that's not just for me but also real physicists. It seems quite possible to me that there's a real breakthrough waiting there but human brains are not quite up to it.

[coldtea]

>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.

[im2w1l]

>Imagine that Achilles notes the position ... and so on

If in logic you assume/imagine something, and reach a contradiction, then your reaction should be to reject that assumption.

In this case we reach the conclusion that Achilles cannot note all the positions.

[coldtea]

That's not adding anything new. The very idea of the thought experiment is that we reach a contradiction and that we therefore should reject the assumption.

The problem, and the whole point of the thought experiment, is that the assumption is tied to Achilles being able to make the distance, so we should ditch that too.

[hodwik]

To be honest, I don't actually think calculus solves Zeno's paradox either, I was just using it for the sake of the argument.

I'm of the opinion that Achilles and the Tortoise is solved by there being a smallest distance, a pixel (Not smallest measurable. Smallest period.)

I make amends with Achilles' Arrow by believing the universal clock is independent of the moments that it measures -- like the internal clock of a computer's being independent from a pixel arrow moving across a pixel screen.

[chrisdone]

But the point of Zeno's paradox is to show that our model of reality is purely definitional, rather than objective in any absolute sense.

[choosername]

doesn't quantum mechanics mean everything has a lowest resolution of discrete steps, ie. Plank-time and Plank-length. In that sense, calculus over finite terms is enough.

The paradox is illogical anyhow, it fails to equate simple v*t=s.

[coldtea]

>doesn't quantum mechanics mean everything has a lowest resolution of discrete steps, ie. Plank-time and Plank-length. In that sense, calculus over finite terms is enough.

That's one solution yes, but whether the universe is continuous or discreet is not a "solved" problem in physics in general. The lowest resolution could just be a "sampling restriction" (or quantum laws etc) and not the actual reality. There have been some experiments to discern between the two cases, but nothing conclusive IIRC.

>The paradox is illogical anyhow, it fails to equate simple vt=s.*

That's not being illogical. vt=s is not logic, is just a formula that we deduced and which matches what we see in everyday life (and in fact it's not absolute, e.g. when it comes close to the speed of light etc).

The paradox just checks whether vt=s is compatible with certain descriptions of the chain of events that look intuitive at first.

[justifier]

by answer zeno's paradoxes do you mean the solution that the paradox is simply ill stated and requires more information to bound the problem finitely for a finite answer?