Ahhh! So now you're playing the "non-Euclidean geometry" card...I wondered how long it would be before you got THAT desperate.
I've asked you to demonstrate that the continuous rules of trigonometry and geometry apply to the real world on numerous occasions. You have yet to show that the perspective lines would actually continue approaching each other forever as Elucid predicted in his Euclidean geometry.
So you've given up with the other pathetic explanations? No more magic perspective?
My argument has been consistent. Questioning trigonometry's application to the real world is questioning Euclidean Geometry and Euclidean Space.
Well, I'm sorry - it doesn't help. If space is non-euclidean then ALL light rays are curved - including the ones that lead to the tree on the horizon. When the sunlight peeks between the leaves of the tree - that final path of light from tree and from sun have to be exactly the same.
What are you talking about? Curved? No one said anything about curving.
Also, any geometry that distorted the position of the sun by that much would also distort it's shape to a similar degree - so the sun couldn't possibly be circular when it was distorted enough to reach the horizon.
Where do you get that the sun would be distorted?
Space is non-euclidean in the sense that geometry of space is discrete in that the perspective lines merge to a finite point at 90 degrees and are not continuous. That is what I have been telling you for a while now.
There has been some confusion. Let me clear some things up here:
1. Space is non-euclidean in the sense that geometry of space is discrete. Perspective lines merge to a finite point at 90 degrees and are not continuous.
2. The nature of perspective changes the ORIENTATION of bodies around you. A change of the orientation means that there is a change to where bodies are positioned around you. If you had a super powerful rifle you would need to shoot at the degree to which they appear in reality, not the degree Elucid predicted with his ideas.
3. If you could shoot a bullet at the sun on the horizon, it will hit the sun. It does not mean that the bullet "curved upwards" or whatever crazy thing you are imaging in your head.
I simplified things and said that the sun is at 90 degrees. The visible sun is always technically at some small degree above the horizon, even when it is setting. If you were to aim at the sun, your bullet would travel upwards above the horizon at a slight angle, in a straight line.
4. To bring this in line with our mechanism for sunset, and to talk more specifically about what is at exactly 90 degrees, 90 degrees is technically in line with the waves and imperfections of the earth surface. While the perspective lines are perfect, the surface of the earth is not perfect and little waves and imperfections of the earth's surface will provide a barrier where the sun and other bodies can hide behind as they merge with the perspective lines of the earth, much like how a dime can obscure an elephant.
If you were to shoot a bullet (or a laser) at the horizon at exactly 90 degrees, it would bring the bullet to the surface of the earth.
5. The question now becomes how could the bullet/laser travel through space horizontally without dropping and hit the waves and imperfections of the earth; the answer to this query is that the positional orientation of objects is as we see it. We see the waves on the horizon and fire. The bullet travels straight to its target.
Under normal continuous Euclidean space it is impossible for a horizontal projectile to hit a wave below it; so it should travel forever. But the orienting nature of perspective (which is really just an allegory for how space presents itself to us) makes that wave appear in space at 90 degrees eye level, and so if you shoot at that angle that is where it will go.
The actual paths of these objects from a side view is immaterial. Your side view model is just a theoretical construct based on Euclidean space for how things *should* be positioned based on some continuous trigonometry rules. By pointing back to that model you and telling me that things are "curving" you are merely insisting that space operates according to Euclidean rules, when those continuous rules have never really been proven.
The entire scenario can be empirically described in terms of where things appear being where things are. What we see and what we experience is reality, and when we point at objects on the horizon we are really pointing at those objects, not into some void of infinity, and all of this trumps Elucid's hypothesis about a continuous universe.