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something that keeps rummaging through my mind, is this. It always seems that the platform perspective has to be pointing straight forward at the center of the number line. Where as in the physical world to see the other points on the line you have to change that perspective. So I see other factors coming into play, like distance from train, distance from tracks, is the platform located even with train at start of measurement or end or is it arbitrary along the tracks ( or off ).
while I agree that light is a constant that we know, change it to single photons then throw out 1 at a time we can calculate our answer, Now we replace photon with baseball and then we come to the same answer just with speed of proton vs speed of baseball. Ratio’s will remain the same so the answer won’t change.
While I do understand that it would have no effect on Lorentz Contraction or the math at all to this point, I still can’t intuit that height is unaffected, when I look left and right along a highway with telephone poles along side. The farther they are from my perspective the smaller they appear. Now I know it won’t effect Lorentz contraction, but it seems to still be valid. I count proof in astronomical observations of red shift, let me explain. Go back to the light clock, up down up down, now imagine the red shift. The farther away the source photons originate the longer the frequency and the lower the amplitude as well. So in my mind that photon train not only slowed time it also shrunk in height. Maybe even to the point of no longer being detectable (Dark Energy?).
In the example that vexed me was a third perspective in the triangle. the other ones were linear, while this introduced to me another point that could be anywhere in space. and my mind went to all positions, towards train, behind me, farther down the track, so I could almost visualize a spot and single moment on the train when the slopes could be equal.