Math is non-empirical. This is why no discovery in science has ever overturned a theorem. So, shouldn't you be asking about future physics, which is empirical, as opposed to mathematics, which is completely non-empirical?

As @LD Saunders notes, the quote has nothing to say about math. It is about empirical knowledge, which is in all cases circumscribed by available evidence. Here you have a rather dramatic example, but one can think of countless ordinary examples that illustrate the same point. How many coins do I have in my pockets right now? I can answer this question by taking them out and counting, while you have no way of knowing whether I even have pockets.

Speaking of cosmology and astronomy, our present situation is only relatively privileged. Yes, we can say with great confidence that there are other stars and galaxies and all sorts of other celestial bodies and structures. But as we probe further, our knowledge becomes less and less certain, until it dissolves into guessing. The large-scale topology of the universe; the universe "before" the Big Bang - we may never have more than speculative answers, and not because we are not clever enough, but because we just don't have the data necessary to test our theories.

I don't remember saying anything about whether math is empirical or not. I can get pro/con views on that subject just by googling. I realize the quote says nothing about math and my questions again dealt with whether or not an assumption I could make might be valid and what if it is. Hey, thanks for answering.

I heard Krauss say that, and it annoyed me. i’m sure they’ll eventually discover space is expanding and then put 2 and 2 together. There’s a lot of science you can do without looking at other galaxies. Physics is so mathematical that laws governing nuclear chemistry have cosmological implications.

Krauss should have said the average time to reach our scientific maturity will increase after x years (5 billion? sounds low) due to the paucity of empirical clues. The average chance of reaching maturity will drop, surely, but it won’t be 0. Big existential/universal fail for Krauss.

They will inevitably come to the wrong conclusion about the universe.

This should serve as a warning to scientists of today. What if we have it wrong? We could also be in a similar situation like those 5 billion years from now. The present state of the universe could be just a ''phase'' in its evolution and our habit retracing the steps to the so-called Big Bang could be faulty.

Thanks for the post. Very interesting.

They will inevitably come to the wrong conclusion about the universe.

This should serve as a warning to scientists of today. What if we have it wrong? We could also be in a similar situation like those 5 billion years from now. The present state of the universe could be just a ''phase'' in its evolution and our habit retracing the steps to the so-called Big Bang could be faulty. — TheMadFool

I have used this quote to argue with cosmologists over the years. We may live in a special time but how can you know if all the evidence of the universe's creation is still available? All it takes is one key component to be missing, yet you'd never know that it was.

It's nice to know we are more privileged, better informed and cleverer than future civilisations. We have already established that we are far smarter than any civilisations of the past. So I guess that makes us really top diggety-dog all round. And yet. And yet. I wonder.

I heard Krauss say that, and it annoyed me. i’m sure they’ll eventually discover space is expanding and then put 2 and 2 together. — Fool

How would they figure that out? Expanding space is validated by precisely the sort of astronomical observations that would not be available in that hypothetical future.

Physics is so mathematical that laws governing nuclear chemistry have cosmological implications. — Fool

Oh no they don't. You can have all of nuclear chemistry and a static universe, no problem.

I have used this quote to argue with cosmologists over the years. We may live in a special time but how can you know if all the evidence of the universe's creation is still available? — Codger

The universe may have popped into existence last Thursday, complete with all of the evidence that points to a much greater age. How would you ever know that this is not the case?

This is not cosmology, this is just sophomoric philosophy.

deleted - redundant

Just posted a civilized reply but it’s not here anymore. Am I being moderated?

This is not cosmology, this is just sophomoric philosophy. — SophistiCat

I feel justified saying what you practice is not philosophy, it's just an evolutionary quirk.

After a couple of near misses I collide head-on with Philosopher's Arrogance. Less than 10 comments in !!! Have no time for such garbage so I'll see you later. I'm out.

Mods: please remove me from member's list. I won't be back

Whatever, here's the short version.

@SophistiCat

How would they figure that out? Expanding space is validated by precisely the sort of astronomical observations that would not be available in that hypothetical future.

I'm suggesting this evidence may not be necessary. Even if we had to rely on red or blue-shifted light, Doppler Effects within our own galaxy may compel the same hypothesis - not that I'm convinced we could only discover the expansion of space through shifted light. The point is the mathematical nature of physics connects seemingly unrelated phenomena in unforeseeable ways, so it seems premature to rule out all possible evidence.

Oh no they don't. You can have all of nuclear chemistry and a static universe, no problem.

Maybe, maybe not, I don't know about that. At any rate, I never said that. I claimed that nuclear chemistry has cosmological implications. Our current theory of the fundamental forces tells us which structures/substances can exist, under what conditions they can come about and how long they would take to form. Combined with observations of stars of different classes and ages within our galaxy, that would give us a minimum age of the observable universe. So no, the current situation (observable galaxies or not) isn't consistent with the universe coming about last Thursday. I suspect other, more sophisticated hypotheses could also be ruled out.

@Codger A little tension in an internet forum is par for the course, man. There's still fun to be had.

I'm suggesting this evidence may not be necessary. Even if we had to rely on red or blue-shifted light, Doppler Effects within our own galaxy may compel the same hypothesis - not that I'm convinced we could only discover the expansion of space through shifted light. — Fool

The thing is, you need much larger scales in order to detect redshifting due to expanding space. On the scale of a galaxy gravitational attraction overcomes this effect. It's not just that the effect would be too minute to extract from the background (though it probably would), it is that gravity keeps objects within the galaxy together, so the effect is nonexistent.

The point is the mathematical nature of physics connects seemingly unrelated phenomena in unforeseeable ways, so it seems premature to rule out all possible evidence. — Fool

I think you are underestimating the underdetermination of theory by evidence in general, and the autonomy of physical theories at different scales/energies in particular.

From the perspective of theory, expanding space is just a parameter in Einstein's field equations. It is altogether absent in quantum physics, or any other theory that deals with scales much smaller than cosmological. Initially, when he didn't know any better, Einstein introduced his cosmological constant in order to make space static, rather than expanding. The constant was dropped, and then reintroduced again in response to further astronomical observations.

But what if such observations were not available? What form of the equations would we have ended up with? On the one hand, a static universe just seems like a simpler assumption. If it is not static, then is it expanding? Contracting? At what rate? On the other hand, equations would have been simpler without the constant. This dilemma aptly illustrates the difficulty of theory choice under insufficient evidence. Even if we are comfortable with using parsimony as a deciding factor, just how it should be applied isn't so obvious.

From the point of view of parsimony, we ended up with the worst of both worlds: we have the cosmological constant in the field equations, and the universe is expanding. Of course, plentiful evidence trumps parsimony, elegance, or any other such a priori considerations. But if we did not have this evidence, why would we have chosen such an inelegant, overcomplicated theory?

Our current theory of the fundamental forces tells us which structures/substances can exist, under what conditions they can come about and how long they would take to form. — Fool

Sure, theories at different scales (effective field theories) are not completely autonomous: they can constrain one another.

So no, the current situation (observable galaxies or not) isn't consistent with the universe coming about last Thursday. — Fool

Oh no, nothing can rule out Last Thursdayism :) This is where other, non-empirical considerations come in.

@SophistiCat

Hey, you’re making a lot of the same points I would make if I held your view. What’s your background?

The thing is, you need much larger scales in order to detect redshifting due to expanding space. On the scale of a galaxy gravitational attraction overcomes this effect.

It’s smart to distinguish frequency shifting from different sources. It’s standardly used to measure front-back motion within our own solar system, where inflation is negligible. The flip side is that the mechanics describing motion throughout the galaxy will entail increasingly precise frequency shifts. Seeing as we just observed gravity waves, I think it’s fair to suppose we’ll eventually measure EM waves precisely enough to notice a subtle climb in error for objects farther out with much longer orbital radii. Now, you’re right that the net effect of gravity is negative, meaning things fall back to us, whereas the Hubble data mostly concern galaxies in permanent recess, but that doesn’t mean the space in our galaxy isn’t expanding. The small but non-zero acceleration due to inflation may show up as error in our orbital mechanics. It does in principle, anyway. Adequate measurement is a technological question, and not one I feel we can confidently settle for all inquirers at all times.

I think you are underestimating the underdetermination of theory by evidence in general, and the autonomy of physical theories at different scales/energies in particular.

I have a deep appreciation for the Duhem-Quine Thesis and other literary hallmarks on this topic, so I get where you’re coming from. However, I think the success of science must come down to constraints imposed by the external world. A theory succeeds inasmuch as it conforms to nature, if I may risk sounding naive. So, while observation may not fix your theory, it will still reward theories that conform better to the world. In the case of inflation, I’m not saying other creatures would talk about it the way we do, but I’m not convinced they’ll fail to theorize around the same constraints.

I realize physical theory isn’t some grand, unified corpus with logical dominos from one end to the other. I’m just saying, I think rightly, that the reductive pattern in scientific progress tends to unify unrelated phenomena in unforseeable ways. Historical examples abound. I’m sure no one thought Mercury’s odd precession had anything to do with the effect of gravity on light.

You seem to understand this well enough. I guess I just find it more compelling. I think the trend will continue, and it seems immodest to rule out the possibility that scientific progress on the small scale will explain cosmological phenoma like inflation.

Oh no, nothing can rule out Last Thursdayism :) This is where other, non-empirical considerations come in.

Yeah, it’s basically a Cartesian demon. I don’t blame you for lashing out at it. Annoys me that it gets so much space still in the universities.

I have used this quote to argue with cosmologists over the years. We may live in a special time but how can you know if all the evidence of the universe's creation is still available? All it takes is one key component to be missing, yet you'd never know that it was. — Codger

Good point. Science could be wrong about it all. However, one redeeming quality of science is that it never claims infallibility. Theories are continually checked and rechecked. I don't know what the actual motivation is but that's a healthy system to base knowledge on.

What's the alternative though? Religion? May be there's truth in there people can't or don't want to see.

Hey, you’re making a lot of the same points I would make if I held your view. What’s your background? — Fool

Oh, my educational background is nothing spectacular. As far as physics, I only have a BA and some graduate courses from many years ago. So don't take my pronouncements too seriously ;)

It’s smart to distinguish frequency shifting from different sources. It’s standardly used to measure front-back motion within our own solar system, where inflation is negligible. The flip side is that the mechanics describing motion throughout the galaxy will entail increasingly precise frequency shifts. — Fool

Yes, we can and do observe redshift from peculiar motions of objects within our cosmic neighborhood. But that doesn't help with detecting cosmological redshift - on the contrary. Even ignoring the other issue to which I'll return in a moment, all this back-and-forth motion creates a background from which it would problematic to extract a tiny effect, even if it actually was systematic. (How would you distinguish a tiny systematic bias in the data from noise? Noise doesn't have to be perfectly unbiased!) But more to the point, bodies within our galaxy are gravitationally bound, and their free-fall towards each other counteracts metric expansion of space.

Could there be other ways by which we could predict and perhaps even detect expansion of space? Well, as I mentioned earlier, expansion was in Einstein's equations - in their (arguably) simpler, more natural form - right from the beginning, so that in order to remove that expansion, a term had to be added. So perhaps even without any observations to prompt it, the hypothesis would have already been on the table. And whether it would have been dismissed, as Einstein did before Hubble's discovery, or taken seriously, is a matter of historical speculation. To take another example from recent history, there is a sizable group of physicists that take the theoretical prediction of quantum "many worlds" seriously - simply because they seem to be right there in the equations, and it takes additional, non-empirical postulations to get rid of them. Some empirically inaccessible predictions of cosmological theories, such as "bubble universes," are also justified by the fact that they are inevitable consequences of a theory that is, or might be otherwise well-supported by observation.

Are there possible experimental ways of detecting metric expansion of space, other than through cosmological redshift? Perhaps you are right, and there could be alternative paths to discovery. But here I would rather defer to the experts. I don't think much about Krauss's philosophizing, but on this question he is undoubtedly an authority that ought to be taken seriously. He may be wrong, but it is far more likely for you or I to be wrong about this than it is for him.

So I'll meet you half-way: A civilization with no access to the same observations that we have might nevertheless entertain theories that predict those same observations, and might even in some cases find strong indirect support for such predictions. But this is by no means guaranteed. There is no good reason to think that scientific theories inevitably converge towards some fixed final shape. The less data we have in some area, the more uncertainty there is about theory choice. Moreover, observer selection effects can bias and lead us away from the "truth" (for lack of a better word).

(How would you distinguish a tiny systematic bias in the data from noise? Noise doesn't have to be perfectly unbiased!) — SophistiCat

Nice catch. I was going to say the bias is the giveaway. If the acceleration were independent of distance, it would make no difference, I agree. Maybe G would be slightly incorrect, but we’d never know. The acceleration is proportional to distance, though, so error would increase with distance. To increase accuracy beyond a certain point, we’d have to correct G for distance. Im imagining an elliptical orbit with constant acceleration (0 or >0) away from its barycenter. That path would look different from one where the accleration varies with distance. As someone with a lot of quantitative experience, I would look at patterned error as evidence that my model is fundamentally wrong. Obv, some models involve patterned error by definition, but I’m thinking of bias you can’t account for. Ultimately, this comes down to precision of measurement, where you seem very doubtful any inquirers could reach the necessary precision to notice the issue. The evidence is on your side here. I just hesitate to rule it out for all observers at all times.

I don't think much about Krauss's philosophizing, but on this question he is undoubtedly an authority that ought to be taken seriously. He may be wrong, but it is far more likely for you or I to be wrong about this than it is for him.

Yes. Just yes. It’s easy to impersonally challenge a worldwide name on an Internet forum. I would not want to publicly challenge him on scientific questions. The only thing that reassures me is his universal quantification over observers and times, at a moment when we still don’t know what our own science will eventually tell us.

There is no good reason to think that scientific theories inevitably converge towards some fixed final shape.

Not sure. I’d like to debate this sometime, after we get some definitions out of the way.

A civilization with no access to the same observations that we have might nevertheless entertain theories that predict those same observations, and might even in some cases find strong indirect support for such predictions.

Agree. I’m just saying I don’t think Krauss is right to rule it out so categorically. Of course, I accept that it’ll most likely happen way, way less often.

Math is non-empirical. This is why no discovery in science has ever overturned a theorem.

Eh, I suppose it depends on what you mean. I mean, we used to think the universe's geometry was Euclidean in nature but the adoption of Relativity seems to force us to accept a Non-Euclidean view given the curved space. "Disproof" is probably an inadequate term here. Something better might be "Science has shown the inapplicability of certain formalisms to certain tasks or even to reality itself".

Another example is possibly quantum mechanics. Classical logic essentially is a logic of individuals (everything has an identity), but this seems to be vitiated in quantum mechanics where there seem to be ontologically indistinguishable "non-individuals" who have no identity (hence inapplicability of the Law of Identity). So that may force us to adopt a quantum logic instead, so our logic and maths will follow our metaphysics and physics because the other logic may simply not be up to the task of constructing a theory of the appropriate kind. Math is not divorced from the empirical, depending on what exactly you mean.