[snet0]

You were talking about exactitude in space, rather than charge.

>Studying something that doesn't exist is unscientific

What about things that could exist, might exist, or even aren't expressly forbidden from existing? These have all been used as perfectly valid reasons for scientific inquiry, historically.

Asking "did some god create the universe" is unscientific by your reasoning so long as it is known that there is no in-universe trace or evidence that it was indeed created by a god. Proving that is proving a negative. I think it is not impossible for us to prove that the universe was created by a god, if we found some hidden message in subatomic particles or cosmic dust or something. It does certainly feel impossible that we will prove that the universe wasn't created by a god, though. The inquiry is deemed unscientific because we have no reason to go down that pathway, not because the question is fundamentally intractable.

Multiverse theory, on the other hand, would qualify as unscientific by your reasoning. If it were true, the different universes would be fundamentally inaccessible, according to our understanding. The model does not suggest that evidence could even possibly exist, as far as I understand.

A result being untestable doesn't, in my opinion, lead to it being unscientific. We cannot test whether black holes exist, except by looking for them. We cannot test whether wormholes exist, except by looking for them. These are predictions that we cannot "test" except by looking at the universe and seeing what we find, and even then we are not guaranteed a positive result, just because maybe it is the case that our model is correct but there was never the appropriate state of the universe to prove our prediction.

Of course if something was actually infinite, you wouldn't be able to measure it to be so, but if the model (that you have shown to be correct in other case) predicts an actual infinity and you keep counting more and more orders of magnitude, does it not make sense to assume your model is correct? Is that unscientific? Just like we assume that the charge on electrons is constant despite not actually measuring it always everywhere.

[tsimionescu]

I was talking about exactitude in general, as a requirement for a physical interpretation of the integers.

> I think it is not impossible for us to prove that the universe was created by a god, if we found some hidden message in subatomic particles or cosmic dust or something.

That's actually a good point, there could be scientific proof of some intelligent creator in principle. The fact that there is no reason a priori to believe that we will find such a proof is a problem, but I don't think it would be enough to deem the theory unscientific. Otherwise, many actually used theories would be unscientific - for example, there is no scientific reason to expect supersimmetry to exist, but that doesn't make the search for supersimmetry unscientific.

> Multiverse theory, on the other hand, would qualify as unscientific by your reasoning.

Yes, multiverse theory is unscientific by my definition. I don't believe speculation about a multiverse can be considered science in any meaningful sense. Just like simulation theory, it is using science-sounding terminology for idle speculation (though the universe being a simulation could similarly be proven by the same kind of evidence as the intelligent creator idea, to be fair).

> These are predictions that we cannot "test" except by looking at the universe and seeing what we find, and even then we are not guaranteed a positive result

But this is exactly the definition of a test. It's true that you can't prove that something doesn't exist in this way, but saying that something is untestable goes beyond that. An untestable hypothesis is one that by definition doesn't make any predictions about the universe. Multiverse theory is in this bucket - whether you believe it to be true or not, you won't expect to see anything different in the world.

> Of course if something was actually infinite, you wouldn't be able to measure it to be so, but if the model (that you have shown to be correct in other case) predicts an actual infinity and you keep counting more and more orders of magnitude, does it not make sense to assume your model is correct?

Of course it's OK to assume your model is correct, and infinity will likely be the simplest assumption in this case. However, any model that predicts an infinity can be replaced with an equivalent model that makes all the same measurable predictions but replaces the infinity with some arbitrarily large but finite number (or arbitrarily small but not infinitesimal). This second model may well be harder to work with and will contain an extra assumption (an explicit upper bound for the infinite quantity), so I wouldn't advocate for its use. But it would have to be accepted that it is not empirically distinguishable from the infinity based model.

[snet0]

Exactitude in general is impossible, though. We assume that the charge on an electron is a constant, but there are limits to the precision.

An infinite value is theoretically testable. It simply implies that for however long you make your ruler, the value is larger. That is a prediction. You may not reach a conclusion, as you said, in finite time, but that is still a prediction.

The problem with replacing an infinity in a model with an arbitrarily large number is that, given enough time and a long enough ruler, you'll surpass that number, meaning your model is incorrect. In defence of "science", you're adding an arbitrary number into a model that you expect to be incorrect. That's not how it should work.

If the model says there's a singularity, we don't then say "okay but well that clearly doesn't make sense, so put a limit on the formula that clamps the values to uh 10^45". That is unscientific.

[tsimionescu]

> Exactitude in general is impossible, though. We assume that the charge on an electron is a constant, but there are limits to the precision.

Yes, others have pointed that out and I am in fact conflicted right now.

> The problem with replacing an infinity in a model with an arbitrarily large number is that, given enough time and a long enough ruler, you'll surpass that number, meaning your model is incorrect. In defence of "science", you're adding an arbitrary number into a model that you expect to be incorrect. That's not how it should work.

I'm not against using infinities in scientific practice at all. I'm just pointing out that, when it comes down to it, that infinity is never necessary in the logical sense.

> If the model says there's a singularity, we don't then say "okay but well that clearly doesn't make sense, so put a limit on the formula that clamps the values to uh 10^45". That is unscientific.

Sure, picking some random big number would be unscientific. But saying "the model predicts a singularity or growing to infinity, so we're probably missing some piece of the picture that sets an upper bar" is not unscientific. It is in fact the common practice - just like no one believes that black holes or the early universe had an actual singularity at the center, we normally just believe the models break somewhere at those levels, and more powerful models (quantum gravity) will actually put a cap. Or how we keep saying that we know an upper bound for the possible mass of a photon, but don't actually know that it really is 0, and we keep trying to measure it.

[snet0]

I think we're not disagreeing, if we were before. Adding limits to functions without rationale other than avoiding infinities is arbitrary and unscientific. Given that we assume that the universe doesn't actually have the capacity for infinities (is this a scientifically grounded assumption, given the impossibility in measuring them?), finding them points us towards holes or limitations in the model, e.g. GR vs quantum gravity.