🎵 They're taking Hobbit-chan to Isengard! 🎵

Biyakugon!

The Trees fell during the First Age; the Downfall of Númenor and the Changing of the World happened towards the end of the Second Age, almost three thousand years later, and involved Sauron, not Morgoth, who'd been defeated and exiled from the world at the end of the First Age.

As for Legolas, he was a Sindarin elf born in the Third Age. He never saw the Trees, and had never been in Aman at the time of The Lord of the Rings.

The only named characters in The Lord of the Rings (other than ones mentioned in songs and legends) who had ever seen the trees were Galadriel, possibly Celeborn and Glorfindel, technically Gandalf and Saruman (provided the Istari count as the same people as the Maiar they were back in Aman), and, maybe, Tom Bombadil and Goldberry, but who knows, really, with those two. (I don't think Sauron ever was in Aman, at least during or after the time of the Trees).

So no they can use sign language to talk to someone on another planet of some other star?

Hmm. That should allow us to estimate the size of that world. The light of the trees must not be so bright as to cook everything in the vicinity; just make it nice and balmy. But, on the opposite side of the world, there must still be enough light to see. Having the occasional photon bounce back would eventually be enough to make out a static scene, but, apparently, it's possible to see things happening in real time, yes?

Does flat mean that we are talking about something like a simple disc here, or just that a beam of light travels parallel to the ground? The latter would imply a rather strange geometry, which I can't wrap my mind around. It would make more sense, though, as, obviously, we couldn't assume that light intensity diminishes with the {ETA:] square of the distance.

they could actually see things that were on the opposite side of the world.

But there's mountains and slopes and all.

Sounds like you need some anime eyes

It was a Minute Physics video. Only 2 minutes, and a great watch.

Legolas actually vibrates very very quickly and is therefore performing synthetic aperture Interferometry, multiplying the size of his effective optical aperture.

No, even without an atmosphere you have to contend with the diffraction-limited resolving power through an aperture (pupil), which is related to the diameter of the aperture and the wavelength of light.

A diffraction process is, mathematically, a fourier transform. A fundamental mathematical feature of a fourier transform is what's known as the uncertainty principle.

Side note: you've probably heard of the special case of an uncertainty principle encountered in quantum mechanics frequently misattributed to the head of the Nazi nuclear program (Heisenberg), but this mathematical principle was actually well known for centuries beforehand, and the misattribution is mostly because of Nazi propaganda. We see it anywhere a fourier transform is used, from optics to orbital dynamics to quantum particles. This mathematical phenomenon is frequently miscited as quantum "weirdness" even though there's nothing quantum (or all that weird) about it.

The pupil restricts the possible positions of incoming photons. A restriction in position increases the variance of momenta (for a photon, speed never changes, but the momentum vector can still change direction). A smaller pupil is more restrictive and causes the image to be blurrier as the incoming photons from each object you are trying to resolve. If you want to be able to resolve smaller angular sizes (small objects at large distances), you need a large aperture that reduces position restrictions on incoming photons and therefore diffraction-induced blurring due to momentum uncertainties.

Look up Airy diffraction for the special case of a circular aperture (e.g. a pupil or telescope).

Yes. The books are all carefully translated from elvish and would have accounted for unit conversions.

I remember asking my dad how far a league was when I first read the book, and then repeatedly questioning whether that could be right in the context of the writing.

I forgot that was the actor's name and for a second thought he'd gotten married.

A hypothesis is a theory, one that is being tested. It's got the same root word in both theory and thesis!

That would fall under “nonvisual” (meaning not light-based) perception.