You assume that large distance perspective follows the ancient rules of "simple trigonometry" which assumes a continuous universe model.
Yes, I do. But you characterize "simple trigonometry" as "ancient" and (by implication) old and outdated. But the proofs of what they said are still valid. Every logical step they take is still true. These are truths about mathematics - no some concept that can become outdated.
But I'm intrigued by your complaint that we're assuming a "continuous universe model".
This is not a clear-cut term. If you google it - you get arguments about the continuous universe as an alternative to Big Bang theory...and that the continuous universe model is outdated. So if THAT is what you're talking about, then (a) No, I'm not assuming that - the Big Bang seems a well-proven thing...and (b) I don't see how trigonometry and perspective and all of that relates in any way to whether you assume one or the other.
So I can only assume you assign some other meaning to the phrase. Deeper searching yields the possibility that you are talking about "discrete versus continuous" physics. But this is stuff about whether quantum theory is an artifact of a continuous underlying structure or one that is truly quantized...and again, I see nothing in either belief that changes my answers on trigonometry and perspective.
So in order for conversation to proceed - you'll need to explain what you mean by "continuous universe model" and in what ways discarding it helps your case.
That is called an assumption. A hypothesis. Something which has never been demonstrated. The Ancient Greeks never proved their perspective theories.
Euclid's "Optics" is the first serious mathematical treatment of perspective - and it most certainly does contain proofs. You can find a modern translation of it here:
http://philomatica.org/wp-content/uploads/2013/01/Optics-of-Euclid.pdfBut everything in it can be proven - and I have done so in at least two thread here - which you do not seem to have been able to follow. You just said something like "But that's just a diagram" and went back to talking about it in ways that double-dip on perspective by (in effect) applying it twice...which is simply an error.
You want us to make explanations based on a model you have not shown to be accurate.
There are many ways to show that it's accurate. One is to take the mathematics that I derive from nothing more than:
* a pinhole camera.
* straight light rays.
* the law of similar triangles.
This yields the equations:
x' = x k / z
y' = y k / z
(where x' and y' are the post-perspective coordinates, x,y,z are the real world coordinates and k is a constant related to the size of the camera versus the size of the image).
Using a computer (as I do, literally every day) to produce pictures of the world produces images that line up perfectly with real world photography. This is PROOF that the math is correct.
If you were challenged to show proof of the rules of the same model that two horizontal lines will approach each other for infinity but never touch, or that a body thousands of miles away will appear a certain number of degrees above the horizon, or that perspective behaves the same at all scales, you will be embarrassingly unable to do so.
I never said that "two horizontal lines will approach each other for infinity but never touch" - perhaps you mean "two parallel lines will never touch" (in the real world) or that with perspective "two parallel lines will touch at infinity". Those things can be proven from the definition of the word "parallel" and the equations above that I derived from pinhole camera/straight lines/similar triangles.
That "perspective behaves the same at all scales" is inevitable if light travels in straight lines and the law of similar triangles is true. You seem to agree that light travels in straight lines (although you "embarrassingly" are unable to write that thread you TWICE promised us in which you'd explain how photons get from the sun to the eye at sunset)...if you don't agree that the law of similar triangles is true - then I'd be happy to regurgitate the proof for you in small words that you'd understand.
Far *FAR* from being "embarrassingly unable" to prove those things - I HAVE proven them...many times and in many ways - you simply choose to simply dismiss or ignore all of my proofs.
Never once have you taken my careful step by step arguments and said..."HERE! Step 4 - that's not true because..." and explained precisely where my reasoning breaks down.
The reason you cannot is because my geometric arguments are 100% correct and either you can't follow them because you're poorly educated and don't understand high school geometry - or you willfully ignore them because you know they prove conclusively that there cannot be sunsets in a flat earth.
That a body some distance away will appear a certain number of degrees above the horizon is also proven in at least a couple of diagrams I posted and some posts which you basically ignored or dismissed as "just diagrams".
Unless you can substantiate the underlying assumptions of your challenge I see no reason why anyone should attempt an answer or take your questions seriously.
Ah - so after twice saying that you WOULD explain how those photons travel from sun to eye at sunset - you're now saying that you're not going to answer me.
The underlying assumptions of my arguments are CLEARLY stated...light travels in straight lines...pinhole cameras really do take good photos...the law of similar triangles is true.
The steps from that to "Here are the laws of perspective and they don't allow sunsets in FET" are laid out in at least two previous threads that you responded to and failed to follow up with your explanation.
OK - well that tells us a lot about your level of intellect and the weakness of your arguments. Would you prefer to be labelled ignorant or a liar?