ZetaX

You really need to use better english. It is still a mystery what you actually want. And what is that index-x supposed to mean¿ What is a union or \cup supposed to be for functions¿

As I said: if you go that way, you won't end at star's brightness. The universe would heat up to infinity and everything will be infinitely hot and bright (whatever that actually means). Thus this assumption is moot. You could still have infinite time in the past, but at there were not always that many stars.

To quote you: That's where you assume both parts of spacetime to be infinite to get the brightness conclusion. Only one of them won't suffice. We can observe if the universe continues existing forever. We can also observe if space goes on forever by flying straight or just waiting for light from further away. Neither of them completely proves that something is truly infinite (it might just be larger/older than we know for sure). But that kind "does not prove" is the same as in "we cannot know for sure of gravity really exist, maybe it was all just a huge coinceidence so far". Science cannot make absolute statements; but it can say if something is very probable. In other words: the universe being infinite in space or existing for forever is something that can be tested. I am pretty sure I know how manifolds work On the very same. I am a working mathematician.

He and you are ignoring dust. Which I mentioned several times now. Maybe you can still conclude such a thing, but the argument would be less simple: but then the correct conclusion would be that most of the sky is of similiar brightness, but that brightness may be significantly below the sun's. Edit: and thinking about it, the stars being infinitely old would mean infinite energy everywhere, so that brightness I speak if is infinite and we are all gone by now. So now one should somehow account for stars being finite things while still allowing infinite time... So you are going with arguments from authority now? Can we please not go that low? This is (theoretical) science, where things are based on fact and argument, not on what somebody with a title says. And I still find the argument moot anyway because: You are always assuming that both space and time are infinite for your argument to work. It could very well be that only space is infinite while time is finite. That would still be an infinite universe, but we would obviously not have the brightness argument. So the "the stars did not shine before a certain time" part is fulfilled, i.e. nothing is contradicting what Hawking said. We could still have a universe that is, at this very moment, of infinite size in regard to space.

There is no outside. And yes, that's simply the answer. A more detailed elaboration can be found in some other threads (probably the one linked above). Umm.. it obviously does? At the very least: citation/argument needed.

So what? We can safely assume that every star absorbs all the light it gets hit by, so we cannot see more than one star in a given direction. And anyway, you ignored the part that finite means that both time and space are finite. I am not objecting to time having been finite in the past (and lets ignore the future). All those infinite light arguments become moot as soon as we consider a universe of finite age with a finite speed of light (i.e. the one we probably live in).

It makes perfect mathematical sense. Maybe we some day discover a law of nature that forbids it, but mathematics itself won't be the problem.

That would contradict the cosmological principle. You cannot have finite matter in infinite space while still having homogenity and isotropy.

a) The universe could still be infinite in either space or time. You are assuming that both are infinite, while being finite means that both are finite. That infinite brightness argument is wrong anyway. Just add a little bit of dust everwhere (and we know there is) and photon travel distances become finite on average. For time one might argue by Big Bang (yet there could be time before it), but we are lacking evidence for space being finite.

Sorry, but I have no idea what you want to say due to your english. Can you retry¿

Atoms have no definite borders. Your mind just imagines them like that. They have as much border as two magnets have one between them when repelling, i.e. none, just a force growing stronger when getting closer. The part that is real is the actual field itself, which is 3D.

There is a very relevant difference between actual 2d objects and imaginary 2d things we imagine. Equi-whatever surfaces/lines are an example of the latter.

If you read that thread carefully you will see that there was actually no good reason given why it should be finite.

My problem with that is not that it is highly hypothetical, but that I have no clue what this words try to convey. So you say time is (represented by) a line; so why isn't it just your usual one-dimensional time then¿ And how does this need for more dimensions arise¿ It sounds like a non-sequitur.

Sorry, I'm not sure I get what you want to say. Did you mean: consider every point in time as its own seperate thing¿ Well, that makes each of them three-dimensional, but they would also have no relation, so no "time" (and relativity renders it wrong anyway).

You might have missed that time runs forwards, which almost by definition makes it at least one-dimensional.

None but all those non-americans... The most natural one would actually be 2 pi i, where i is the imaginary unit (i² = -1). It comes into everything from circuits, functional analysis, complex analysis, number theory, algebra to all things Fourier by being the period of the exponential function exp(x) = e^x. But try convincing all those non-mathematicians and non-theoretical physicists that their beloved pi should be replaced by something that isn't even a real number, but a complex one. Some eletrical engineers may agree, but everything beyond will consider you crazy.

Only if you are one of those people that still think "middle, smallest, largest" is the obvious order of things like dates.

Falling through earth is a different setting (more akin to pendulums) where the orbit from the starting post is possible (assuming you clear the path). For the usual gravitational orbits (with the parent body at a focus) one needs to consider point masses or spheres (as long as one stays outside of them)

He could have been on the ISS... anyway, this is a horrible missuse of "staring at", so I would not blame anyone for missing this bad joke. (To quote the first definition of staring I found on the web: "To look at directly and fixedly"; note the "directly").

Must have been the latter then. The focal property follows purely formally/mathematically form Newton's laws. Or another reason: consider parabolas as degenerated ellipses (or hyperbolas); if there would be a parabola without the focal property, then (by some continuity argument) there must be an example with ellipses; but that contradict's Kepler.

No, it should also be restricted to the focus. The same goes for hyperbolas. But truly parabolic orbits (e=1) should, like circles (e=0), not exist.

AFAIK, "focuses" is also fine.

How is an unfounded post mostly composed of technobabble "learning something new"¿ For example, why is having "Bosian mass" (bosonic?) relevant, why not any other normal type of mass¿ What does it even mean for a planet to be composed of negative energy¿ And the post also claims that there then is only one apoapsis, so it surely cannot be that orbit anyway.

That's not how glasses work anyway. Sun damages cells required for vision (they can and often do regrow, but that depends); glasses (mostly) correct for deformations in the eyeball or lense that defocus your vision. And indeed, low light vision is one of the first things damaged by looking into too bright things for too long. If you only filter out the UV parts of light, most of the sun is not that likely to cause permanent damage (but still can, so I strongly recommend against trying): the damage by visible and infrared light often heals, but this can take several weeks. Getting back to glasses, people needing them are at significantly less risk for two reasons (but again: don't try either way): a) Their focus when looking at the sun might be less exact due to their glasses not being perfect. Some types of glass, e.g. the usual one for windows, filter most of UV. But as I said, you still should not try looking directly onto the sun unless using very strong and high quality filters. Most glasses use other types of glass (or just plastic), and even the IR part can do damage.