The reason Legolas can see that far is because the curvature of Earth doesn’t exist for elves. It is the same reason they can sail off into the Undying Lands without circling back around.
I think vision would fall girly within the realms of physics. I don’t know if you can justifiably call it visual anymore when it incorporates magic
It’s like, if there’s magic bow that launches arrows at a far greater rate than it normally would, would you say that the energy comes from the buildup and release of tension in the wood? There’s another element there, which enhances the thing
Except that this problem doesn’t specify distance between horseman, so I think it’s a bit bogus — no need to resolve an individual person to be able to tell that they’re there. And for hair color, if you make assumptions about the clothes being worn, you could perhaps infer color of hair, even if the hair isn’t resolvable (a person being a “single pixel” would have a different hue depending).
So, a typical pupil is around 2 mm in diameter in bright conditions. With the Rayleigh limit that results in an angular resolution of 1.22 * 60010^-9 m / 210^-3 m = 3.66*10^-4 rad
At a distance of 5 x 3 mi = 15 mi = 24.1 km this corresponds to a point to point distance of
tan(a/2) = (d/2)/l
d = tan(a/2) * l * 2 = tan(3.66*10^-4) * 24100 * 2 = 8.8 m
So in conclusion, with regular, human-like eyes he could discern points that are at least 8.8 m apart in the best case scenario. Discerning hair color from the color of the clothes would need a much higher resolution, and the horsemen are probably not 10 m apart from each other either. And again, this is a theoretical limit, real-world resolution would probably be significantly lower.
That’s part of the “make appropriate estimates” bit. You can just pick any reasonable number for the angular resolution Legolas needs and answer the question using that. Provided you do the method right, you’ll get the marks.
The only way this would make sense is if the horsemen are all riding next to each other, which would allow him to estimate the count based on the average width of one riding horseman. As soon as one is even partially in front of another, the 105 number breaks.
If you get 50m above the ground and have nothing in the way, you can see 5 leagues away as well. Good luck counting individual people from that distance though. The anime eyes are a necessity
That, or he’s got absolutely bonkers retinas that have truly incredible sensory density, and an absurdly developed visual cortex to support it.
Argument basis: DSLRs. Compare the detail you can extract from a 1MP sensor to a 100MP sensor, shooting through the same optical setup at the same target.
I think the pupil size calculation is based on defraction, so it doesn’t matter how dense your retina is, if your pupils are smaller than that you still wont see enough detail. This is one of the reasons why we keep building bigger telescopes and especially telescope arrays. The bigger the effective apeture, the finer the detail it can resolve.
Honestly, I’m waiting with bated breath until we as a global society can get our shit together enough to create a massive system-wide observation cluster. The shit we’ll learn from that will undoubtedly be incredible. I want my fully automated post-scarcity hedonistic space communism society. But I guess we have to get through the Great Filter first :/
It’s neither, it’s the Will of Eru Illuvatar that determines whether you can travel the Straight Road or not. Ælfwine travelled the Straight Road and landed at Tol Eressëa in 869AD after fleeing the Danes, and he was a Man, not an Elf.
the world was flat until numenor made war on the undying lands. at that point, numenor sank and the world was made round and the undying lands were placed somehow outside them, so that elves could still sail west along the straight way and get there, but everyone else just sailed west around the globe.
later, tolkien changed his mind about a lot of this and played with it, trying to turn it into an always roundworld (scientifically accurate myth was his goal at this point) but couldnt really figure out how it’d work and he was old and then he died
How would that even work? Do time zones exist for everybody but elves? As the party travelled east, did Legolas start perceiving the sun to set later than it did for everybody else?
The sun was made from the last fruit of Laurelin (one of the two great trees) and is being shipped around the sky on a cart. Legolas has never seen the light of Valinor, i believe he was born after the trees died. It’s definitely not visible at all times to the elves, since even before the world was turned round it went below it out of sight at night-time. Presumably the elves still see the sun affect only parts of the world, they can just see beyond the horizon.
Edit: as an aside, the last remaining silmaril is the Evening star that shines in the west.
no, that’s not why. it’s because elves can just see better. it’s the same reason they can walk on top of snow. they are slightly outside the laws that apply to ordinary humans. even aragorn is a hair over the line.
The reason Legolas can see that far is because the curvature of Earth doesn’t exist for elves. It is the same reason they can sail off into the Undying Lands without circling back around.
even if you ignore curvature you have a resolution limit that depends on the aperture. Look up Rayleigh criterion for more info
But does it consider magic?
That would fall under “nonvisual perception”
What about magical visual perception?
I think vision would fall girly within the realms of physics. I don’t know if you can justifiably call it visual anymore when it incorporates magic
It’s like, if there’s magic bow that launches arrows at a far greater rate than it normally would, would you say that the energy comes from the buildup and release of tension in the wood? There’s another element there, which enhances the thing
Please don’t fix the typo.
Oh 😭 lmaooo
Except that this problem doesn’t specify distance between horseman, so I think it’s a bit bogus — no need to resolve an individual person to be able to tell that they’re there. And for hair color, if you make assumptions about the clothes being worn, you could perhaps infer color of hair, even if the hair isn’t resolvable (a person being a “single pixel” would have a different hue depending).
So, a typical pupil is around 2 mm in diameter in bright conditions. With the Rayleigh limit that results in an angular resolution of 1.22 * 60010^-9 m / 210^-3 m = 3.66*10^-4 rad
At a distance of 5 x 3 mi = 15 mi = 24.1 km this corresponds to a point to point distance of
tan(a/2) = (d/2)/l
d = tan(a/2) * l * 2 = tan(3.66*10^-4) * 24100 * 2 = 8.8 m
So in conclusion, with regular, human-like eyes he could discern points that are at least 8.8 m apart in the best case scenario. Discerning hair color from the color of the clothes would need a much higher resolution, and the horsemen are probably not 10 m apart from each other either. And again, this is a theoretical limit, real-world resolution would probably be significantly lower.
which is why legolas has huge anime eyes
That’s part of the “make appropriate estimates” bit. You can just pick any reasonable number for the angular resolution Legolas needs and answer the question using that. Provided you do the method right, you’ll get the marks.
The only way this would make sense is if the horsemen are all riding next to each other, which would allow him to estimate the count based on the average width of one riding horseman. As soon as one is even partially in front of another, the 105 number breaks.
If you get 50m above the ground and have nothing in the way, you can see 5 leagues away as well. Good luck counting individual people from that distance though. The anime eyes are a necessity
That, or he’s got absolutely bonkers retinas that have truly incredible sensory density, and an absurdly developed visual cortex to support it.
Argument basis: DSLRs. Compare the detail you can extract from a 1MP sensor to a 100MP sensor, shooting through the same optical setup at the same target.
I think the pupil size calculation is based on defraction, so it doesn’t matter how dense your retina is, if your pupils are smaller than that you still wont see enough detail. This is one of the reasons why we keep building bigger telescopes and especially telescope arrays. The bigger the effective apeture, the finer the detail it can resolve.
Honestly, I’m waiting with bated breath until we as a global society can get our shit together enough to create a massive system-wide observation cluster. The shit we’ll learn from that will undoubtedly be incredible. I want my fully automated post-scarcity hedonistic space communism society. But I guess we have to get through the Great Filter first :/
Didn’t Middle Earth lore say the Earth was flat, but was made spherical later? Had that happened by then?
Yes, but it’s not spherical for the elves, just the other races, which is why elven boats can sail to the undying lands, but human boats can’t.
Wait, is it the boat that ignores the spherical attribute or the entity that commands the boat?
Can an elf sail to the undying lands commanding a human built vessel?
It’s neither, it’s the Will of Eru Illuvatar that determines whether you can travel the Straight Road or not. Ælfwine travelled the Straight Road and landed at Tol Eressëa in 869AD after fleeing the Danes, and he was a Man, not an Elf.
Gimli and Frodo both also were able to sail to the undying lands
Yeah but Ælfwine got there by accident, and wasn’t escorted by elves.
I think you have to be an elf building a ship and convince each plank individually that the world is flat
Eru damn tangential elves flying off into space.
This gives strong “Lovecraft describing things he doesn’t understand as noneuclidian” vibes.
the world was flat until numenor made war on the undying lands. at that point, numenor sank and the world was made round and the undying lands were placed somehow outside them, so that elves could still sail west along the straight way and get there, but everyone else just sailed west around the globe.
later, tolkien changed his mind about a lot of this and played with it, trying to turn it into an always roundworld (scientifically accurate myth was his goal at this point) but couldnt really figure out how it’d work and he was old and then he died
so you’re saying flat earth killed tolkien?
You mean the curvature of middle earth, right? RIGHT?!
Middle Earth is canonically our Earth, in the past
Doesn’t it? Haven’t come across anything in Tolkien’s works that says this.
How would that even work? Do time zones exist for everybody but elves? As the party travelled east, did Legolas start perceiving the sun to set later than it did for everybody else?
If I remember correctly, the sun is the light of Valinor, so the sun actually never sets for Legolas (which is useful for seeing at night)
edit: it might be the remaining silmaril being paraded around? either way, should always be visible to elves
The sun was made from the last fruit of Laurelin (one of the two great trees) and is being shipped around the sky on a cart. Legolas has never seen the light of Valinor, i believe he was born after the trees died. It’s definitely not visible at all times to the elves, since even before the world was turned round it went below it out of sight at night-time. Presumably the elves still see the sun affect only parts of the world, they can just see beyond the horizon.
Edit: as an aside, the last remaining silmaril is the Evening star that shines in the west.
thanks!
I guess that means elves can’t go to space :(
Why not? They can’t go across, but they can certainly go up.
You’re saying television would just lie to me?
https://tvtropes.org/pmwiki/pmwiki.php/Main/SpaceElves
no, that’s not why. it’s because elves can just see better. it’s the same reason they can walk on top of snow. they are slightly outside the laws that apply to ordinary humans. even aragorn is a hair over the line.