The idea isn’t so much that the sun rises only once, but rather that if you were to solve a differential equation for how the sun’s position in the sky varies over time, there would only be one possible solution (provided that you had sufficient initial conditions). The idea is that your equation is supposed to be a good model for reality and in non-quantum physics, only one thing can happen so either your equation has one solution or it is a bad model for reality.

Thank you, this helps. To my taste, jokes get better when they make more sense. :)

In a philosophical manner of speaking, that's true. You never step into the same river twice.

Well there are 3 fragments related to this, one likely fake. It is a way to wake you up in his crazy paradox.

There are books and articles and may be one can start with the key phrase What is same river

And the hidden issue is you. If you think it is unique every time frame ... what is same river and same you. Can One same you even step into the River

And if step into it and swim in parallel is the molecules mostly the same ...

Back to What is river? If it is keep on changing as any river that is not changing and moving is not a river, the sameness if you accept then you can step into the same river as many time as you like. But that is wrong per the statement. Hence what is “same river”.

Indeed. But the scientific approach is different -- it's all about finding patterns that do repeat and making predictions.

The original comment's "theorem" is funny, but unless you are doing a homework problem, you better have a good intuition for when to take a second look at a seemingly simple situation.

> the scientific approach is different -- it's all about finding patterns that do repeat and making predictions

Sure, but if you're scientifically looking to answer "where and when will the sun rise" you're only going to collect enough variables to answer that question, and within an acceptable margin of error, right? If you can measure with greater accuracy and collect more data, then you would probably realize that every sunrise is not strictly identical.

We're splitting hairs at this point but I wonder if the comment I replied to that stated that "it has never happened before and will never happen again" can't be argued to be actually true. In a philosophical sense it's more obvious, but in a scientific sense, the more precision you get in your analysis of a sunrise, the more data you would get that differentiates it from other sunrises, no? After all, our solar system isn't closed and constant and there are minor changes not only in smaller factors like weather on Earth, but also larger factors like the orbit of the earth and the drift of the different planetary bodies.

The funny thing is, besides this one you picked out, pretty much all the rest of these either are continuity assumptions or follow from continuity. I think that's because physicists tend to dismiss discontinuities and singularities as "unphysical," but it does make good intuitive sense.

I suspect that "all equations have one solution" is a lot easier to satisfy when all functions are continuous, or otherwise nice, as well.

That's mostly true -- however, physicists devote a lot of time to studying phase transitions and characterizing the kinds of discontinuities that are possible etc in that context.

Ah, yes, I forgot about phase transitions. Those are actually interesting discontinuities. It seems to me the uninteresting ones are the ones that have roughly the same behavior all around them (e.g. poles of complex functions are not that interesting).

Would you say that's an accurate characterization?

sorry don't have much more insight here. I think the goal is to generally make any approximation that isn't relevant to the physical behavior one is trying to model. if a pole sitting somewhere isn't related to the phenomenon you're trying to explore, ignore it!

Great point. There are a ton of good models that break down in certain regions (e.g. quantum mechanics and general relativity at large and small physical scales, respectively).