Fun article, but I think the connection to Middle-Earth is tenuous at best. I had hopes that there was going to be some interaction between trolls and humans, but he ends up just using the tree-like beings.
The special rel just-so story I had got was night people and day people, and the night people had set true N to the north star, while the day people used the midpoint of sunrise and sunset for true N, so all their cardinal directions were rotated relative to each other.
They were then confused why their measurements of distances always agreed but of position always differed, until someone came up with the rotation equations that allowed one to map day to night and night to day.
Change normal trigonometric rotation to hyperbolic, and you've got most of special rel.
The way this describes two treefolk seeing each other both aging slower is the first time I've really understood how two parties relativistic effects are both able to see each other aging slower than themselves: the points at which they are seeing each other are not simultaneous.
The neighbor looks like it's aging more rapidly, not slower! Think if the neighbor tilts away from you, in the disk-by-disk play it will just look moving away disk by disk, the disks are elongated and the disks will end earlier.
And from the tilted neighbor's point of view it's similar.
Maybe it's easier to first think of two trees that both tilt away from each other.
The key observation is that there is no simultaneous. As in, an objective, observer independent, notion of simultaneous. Each observer carries its own notion of simultaneous and observers in different reference frames call different things simultaneous.
I've always liked this sort of interpretation. because it suggests that the entire universe might actually be a static object; and time itself a complete illusion.
Imagine a hyper-being that has a few more dimensions, looking down on us as we look down on Tao's treefolk. We might optimistically imagine that they see our little moment of conscious perception moving backwards and forwards in time like a motivated fish. We perceive it as one way though, because when our little window of perception moves backwards it enters a state where it cannot remember the future, and when it moves forward it enters a state where it has no reference of lingering unevenly at different past times.
I don't really understand why he didn't just use trolls (which, as he mentions don't move in the day) rather than invent a new tree folk.
It seems like he came up with the disk idea and then thought 'this looks like a tree' and back-solved Middle-Earth and then was like 'oops, this behaviour is actually trolls' when writing it up (rather adjusting his paper to use stone discs)
I can't imagine there's many people who both get past the opening and don't understand the concept sufficiently for the allegory to be useful.
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[ 4.3 ms ] story [ 44.3 ms ] threadThey were then confused why their measurements of distances always agreed but of position always differed, until someone came up with the rotation equations that allowed one to map day to night and night to day.
Change normal trigonometric rotation to hyperbolic, and you've got most of special rel.
And from the tilted neighbor's point of view it's similar.
Maybe it's easier to first think of two trees that both tilt away from each other.
Imagine a hyper-being that has a few more dimensions, looking down on us as we look down on Tao's treefolk. We might optimistically imagine that they see our little moment of conscious perception moving backwards and forwards in time like a motivated fish. We perceive it as one way though, because when our little window of perception moves backwards it enters a state where it cannot remember the future, and when it moves forward it enters a state where it has no reference of lingering unevenly at different past times.
Seems unlikely, but so does everything else.
However, he (and his successors) have had a great deal of trouble reconciling a static universe with quantum mechanics.
(a) as far as I know, "many worlds" is the closest anyone has yet come
(b) luckily there are very few physical problems involving scales that would invoke both GR and QM.
It seems like he came up with the disk idea and then thought 'this looks like a tree' and back-solved Middle-Earth and then was like 'oops, this behaviour is actually trolls' when writing it up (rather adjusting his paper to use stone discs)
I can't imagine there's many people who both get past the opening and don't understand the concept sufficiently for the allegory to be useful.