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> As there's a chance that the longest line isn't from a peak or plateau? Is there such a chance? I'm struggling to think what this could look like. If the fur

> As there's a chance that the longest line isn't from a peak or plateau? Is there such a chance? I'm struggling to think what this could look like. If the furthest point you can see is in a bowl or a valley, why can't you see all the way to the far side of the valley? I think we can rule out topographic ridiculousness like a mountain with a hole in it that you can see through. OK, instead of a peak or a plateau, perhaps the longest line could be from a ridge in a saddle. So it's a peak when approached from one orientation (say north/south) but a trough when looking east-west. You can't see the higher ground to the east and west because it's hidden behind some other mountain.

tombh 1y ago
I wonder if this is related to the so-called coastline paradox? https://en.wikipedia.org/wiki/Coastline_paradox https://en.wikipedia.org/wiki/Coastline_paradox In other words, what is the criteria for filtering out good and bad elevation candidates? Does it help imagining this on a tennis ball? Let's say we make 2 pyramid-like blobs of plasticine and put them on opposing sides of the tennis ball. Now we slowly move them closer to each other until they can both just see other. Is it not possible to form the pyramids in such a way, that the first point of visibility is the pyramids' bases, and not their peaks? For me it comes down to the fact that although it might seem obvious what a peak is when you see one, I don't think there's any meaningful way to geographically define one. They're always just _locally_ higher points. BTW this is exactly why I wrote the post, it's a fairly unique problem, and I'm sure I've made some problematic assumptions.
manwe150 1y ago
If you imagine having a very deep hole in the ground, the longest sight line would be from the lip to the bottom. If you then dig a small hole at the bottom, you wouldn’t be able to see the bottom of the second hole, but only some part of the wall Similar in reverse, if the pyramid had a false peak (a inflection place where topology changes from steep to less steep), it could obscure line of sight between the real peak, if the angle formed by the line of sight between the two distant peaks tries to intersect the intermediate inflection point
- dmurray 1y ago
  I can imagine some shapes like this in theory, I just think we can rule them out in practice. For the hole example, we know there aren't any holes 500 km deep. For the pyramids, we know the line of sight is very close to flat (it's at least 500 km long and less than 10 km in elevation change). If a false peak prevents you from seeing the real peak, the angle of the mountain above the false peak is shallow enough that you can call it a plateau.

tombh 1y ago

I wonder if this is related to the so-called coastline paradox? https://en.wikipedia.org/wiki/Coastline_paradox https://en.wikipedia.org/wiki/Coastline_paradox In other words, what is the criteria for filtering out good and bad elevation candidates? Does it help imagining this on a tennis ball? Let's say we make 2 pyramid-like blobs of plasticine and put them on opposing sides of the tennis ball. Now we slowly move them closer to each other until they can both just see other. Is it not possible to form the pyramids in such a way, that the first point of visibility is the pyramids' bases, and not their peaks? For me it comes down to the fact that although it might seem obvious what a peak is when you see one, I don't think there's any meaningful way to geographically define one. They're always just _locally_ higher points. BTW this is exactly why I wrote the post, it's a fairly unique problem, and I'm sure I've made some problematic assumptions.

manwe150 1y ago

If you imagine having a very deep hole in the ground, the longest sight line would be from the lip to the bottom. If you then dig a small hole at the bottom, you wouldn’t be able to see the bottom of the second hole, but only some part of the wall Similar in reverse, if the pyramid had a false peak (a inflection place where topology changes from steep to less steep), it could obscure line of sight between the real peak, if the angle formed by the line of sight between the two distant peaks tries to intersect the intermediate inflection point

dmurray 1y ago
I can imagine some shapes like this in theory, I just think we can rule them out in practice. For the hole example, we know there aren't any holes 500 km deep. For the pyramids, we know the line of sight is very close to flat (it's at least 500 km long and less than 10 km in elevation change). If a false peak prevents you from seeing the real peak, the angle of the mountain above the false peak is shallow enough that you can call it a plateau.