[edby]

The response in all of the above is "but math says..."

But if we can't experiment on that concept of the infinite perspective lines how do we know that perspective plays by those rules? Numerous assumptions are being made about perspective.

Since it is widely admitted that we can't really experiment on such that matter, we are really just discussing a hypothesis.

No you misunderstand the nature of proof. A proof is valid in all cases, that is the whole point of it. Nor are we 'discussing a hypothesis'. A hypothesis is something put forward which needs to be tested by empirical investigation. A proof by contrast requires no hypothesis.

A hypothesis that you will need to prove wrong yourself, not demand proof for. It's already been proven experimentally over many different distances.

Again, the proof that perspective lines meet at a finite distance is a proof, not a hypothesis. You are giving too much away.

Nor is geometry 'proved experimentally'.

[Tom Bishop]

But if we can't experiment on that concept of the infinite perspective lines how do we know that the universe plays by those rules? Numerous assumptions are being made about perspective.

Since it is widely admitted that we can't really experiment on such things, we are really just discussing a hypothesis.

A hypothesis that you will need to prove wrong yourself, not demand proof for. It's already been proven experimentally over many different distances.

Tested over different distances, perhaps (based on what study and what exact results?), but the lines may eventually merge. Who showed that they continue infinitely and ad infinitum?

The response in all of the above is "but math says..."

But if we can't experiment on that concept of the infinite perspective lines how do we know that perspective plays by those rules? Numerous assumptions are being made about perspective.

Since it is widely admitted that we can't really experiment on such that matter, we are really just discussing a hypothesis.

No you misunderstand the nature of proof. A proof is valid in all cases, that is the whole point of it. Nor are we 'discussing a hypothesis'. A hypothesis is something put forward which needs to be tested by empirical investigation. A proof by contrast requires no hypothesis.

This statement just admits that the argument is weak house of cards and that you may be rationalizing your result rather than making an empirical conclusion.

[hexagon]

I don't think Euclid has ever defined parallelism in the view of perspective perception. It's completely unrelated. What we nowadays call 2d or 3d Euclidean spaces are two of many possible n dimensional geometrical spaces. They are defined by certain axioms. And because this are definitions, one has not to proof that one of the axioms is valid in a certain space. If e.g. the axiom of parallelism in Euclidean space would not be valid, the space would not be Euclidean, it would be a different space.

What you can try to proof is, if a certain real space is Euclidean or not. E.g. can our universe be described as an Euclidean space? Regarding to Einstein's general relativity theory we are living in a 4 dimensional non-Euclidean space where we describe points in this space by Gaussian coordinates. Nevertheless, regarding more down to the earth problems compared to general relativity, the space around us is Euclidean.       

[edby]

Tested over different distances, perhaps, but the lines may eventually merge. Who showed that they continue infinitely and ad infinitum?

Again, this confusion between parallel lines (which cannot meet, because defined as lines which never meet), and perspective lines (which are projections on a finite surface).

Tom, do we need an experiment to prove that no bachelor is married? Why? Is it a 'testable hypothesis' that no bachelor is married? Or that a bullock has no testicles?

The level of incomprehension here is staggering.

I don't think Euclid has ever defined parallelism in the view of perspective perception. It's completely unrelated. What we nowadays call 2d or 3d Euclidean spaces are two of many possible n dimensional geometrical spaces. They are defined by certain axioms. 

Euclid has definitions, axioms and postulates. Book I definition 23.

Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.

This is the same as defining a bachelor as an unmarried man. Tom will object 'have you tested all bachelors to make sure they are not married?'

[edby]

This statement just admits that your argument is weak house of cards and you are rationalizing your result rather than making an empirical conclusion.

My argument is a proof. Do you understand what a proof is? Certainly not a 'weak house of cards'.

[9 out of 10 doctors agree]

But if we can't experiment on that concept of the infinite perspective lines how do we know that the universe plays by those rules? Numerous assumptions are being made about perspective.

Since it is widely admitted that we can't really experiment on such things, we are really just discussing a hypothesis.

A hypothesis that you will need to prove wrong yourself, not demand proof for. It's already been proven experimentally over many different distances.

Tested over different distances, perhaps (based on what study and what exact results?), but the lines may eventually merge. Who showed that they continue infinitely and ad infinitum?

Nobody showed that they go on forever. However, since it works for near distances, you need to show that they don't continue infinitely.

[edby]

Nobody showed that they go on forever. However, since it works for near distances, you need to show that they don't continue infinitely.

Again, this is playing to Tom's strengths, such as they are.

Mathematics already proves this, even in the infinite case. Burden of proof not needed, proof already exists.

[Tom Bishop]

The conversation can go on many different ways form here.

- I can assert that it is not really me who claimed anything about infinite perspective lines being the cause, and so that is your burden to show.

- I can continue to ask for evidence of the admitted hypothesis

- I can point out the assumptions.

- I can argue by incredulity.

There are many ways for us to go on this, in my effort to show that a theory held as true for thousands of years can seem to wobble with the weakest of scrutiny.

It is not hard to argue on this side, and it encourages the production of evidence or supporting evidence. And isn't that more interesting than a forum full of dead threads and non responses?

Why hold up these interesting conversations based on the participation of a few people?

[edby]

I can assert that it is not really me who claimed anything about infinite perspective lines, and so that is your burden to show.

So you still don't understand the definition of 'perspective line'. What's the point in any discussion whatsoever if people (and that is not just Tom) fail to understand the meanings of the various terms used?

Count me out, although I voted yes. I will attempt not to return to this site. Completely crazy.

[Tom Bishop]

I can assert that it is not really me who claimed anything about infinite perspective lines, and so that is your burden to show.

So you still don't understand the definition of 'perspective line'. What's the point in any discussion whatsoever if people (and that is not just Tom) fail to understand the meanings of the various terms used?

Count me out, although I voted yes. I will attempt not to return to this site. Completely crazy.

This is a friendly debate. Even if your position is right, your posts also educates people in the audience to know the truth. We uncovered some interesting topics here. Maybe about some things people did not know before. And isn't spreading the truth what you came here to do?

[hexagon]

Perspective has in the first place nothing to do with geometry, its an optical effect due to imaging of 3D space onto a 2D plane via a diffracting medium. In this sense the merging of parallel lines at large distances has no physical reality. If I build a railway track and at every point I take care that at every point the tracks have the same distance, then this does not change suddenly if I look along the tracks and I have the impression they are merging.

And this has also nothing to do with Euclid. As I said before, the Euclidean space is self-consistently defined, if it holds the axioms it is Euclidean, if not, its non-euclidean.

[garygreen]

a theory held as true for thousands of years seems to wobble with the weakest of scrutiny.

you're not attacking anything held true for thousands of years.  you're attacking your misunderstanding of mathematics.  the thing you are attacking is not a thing anyone in physics or mathematics purports.

parallel lines are just a definition people invented.  for example, i can define parallel lines as two lines that maintain a constant distance from one another.  done.  i never had to use the word infinity.

more importantly, nothing about your perceptions requires anything to go to infinity.  there is a "smallest angle" your eye can resolve.  when stuff gets further away from you, then it subtends a smaller angle.  when it angle it subtends gets smaller than the "smallest angle" you can resolve, then you can't resolve it anymore.  again, no infinity required.  it's just angles and apertures and "how many rods and cones do you have."  or however eyeballs work.

[9 out of 10 doctors agree]

- I can continue to ask for evidence of the admitted hypothesis

Go ask an art teacher how far away the vanishing point is. There is also a model to show it on this very forum.

- I can point out the assumptions.

Again, you can't just assume that a working model for any distance you test will break down at a distance. Russel's teapot and Occam's razor both say no.

- I can argue by incredulity.

So could an art teacher. News flash: not everything makes sense.

[Max_Almond]

God only knows what Tom is even arguing here - Tom certainly doesn't.

The above really demonstrates, for me, why "arguing on the other side" probably won't work.

The only way to defend flat earth, at a certain stage, is to be intellectually dishonest.

I like to think we on the side of facts also have a sense of honesty and fair play about us.

Definitely, for me to even pretend to defend the flat earth with Tom's usual tactics would feel icky.

And also kind of boring too: how satisfying can it be to be backed into a corner over and over again and respond ad infinitum, "well have you tested every little aspect of that yourself?" or "yes, but Rowbotham says [derp derp]" or "perspective and optics and fairies and waves"?

Or, if none of that works, to just leave the room and come back later when a whole new group has arrived and start the whole thing over again?

[Tom Bishop]

If Rowbotham is wrong, then lets show and prove with some certainty that he is wrong.

One can argue that "math says and therefore" isn't really a good enough argument that certain rules are necessarily applied to something we can't really test the limits of.

I am not above saying that I was wrong. These debates explore the issue, and it is hard to deny that.

[Jura-Glenlivet]

I guess I’m with Gary, Max, Ed' and the others, I don’t say that that last argument wasn’t won by you because I need the RE to be true, it’s just that your assertion that “a theory held as true for thousands of years seems to wobble with the weakest of scrutiny”, using the Ancient Greek gambit, seems so weak, and I have tried to steer away from Incredulity arguments for the same reason.

I do like arguing and I admit I had to relearn a lot of stuff doing it here, but because I felt it was right to defend against this wave of anti-knowledge that floods the real stuff, I’m not sure I can do it with the same zeal if someone were to label me along with Dooby Doo or Sergeant.   

[hexagon]

One can come up with lots of follow up questions... e.g.:

If the earth is flat and mono-polar, its natural symmetry is cylindrical, so one should use cylindrical coordinates to define a place on the earth. One is the angle around the pole, the second is the distance to the pole and the third one the height above sea level. Why using spherical coordinates made for a sphere?

On a sphere, straight lines, defined as the shortest connection between two points, are part of great circles if the points are on the surface of the sphere. In this non-Euclidean spherical space this lines meat twice going around the sphere. How would you then define parallel or vanishing point, infinity and so on in such a 2D spherical space (the surface of sphere) opposed to a 2D Euclidean space?   

[Max_Almond]

If Rowbotham is wrong, then lets show and prove with some certainty that he is wrong.

We have. For those who have the eyes to see it.

I am not above saying I was wrong.

Can you remember three occasions when you've admitted to being wrong?

[hexagon]

God only knows what Tom is even arguing here - Tom certainly doesn't.

The above really demonstrates, for me, why "arguing on the other side" probably won't work.

The only way to defend flat earth, at a certain stage, is to be intellectually dishonest.

I like to think we on the side of facts also have a sense of honesty and fair play about us.

Definitely, for me to even pretend to defend the flat earth with Tom's usual tactics would feel icky.

And also kind of boring too: how satisfying can it be to be backed into a corner over and over again and respond ad infinitum, "well have you tested every little aspect of that yourself?" or "yes, but Rowbotham says [derp derp]" or "perspective and optics and fairies and waves"?

Or, if none of that works, to just leave the room and come back later when a whole new group has arrived and start the whole thing over again?

Of course you can, in principle, honestly discuss a flat-earth as kind of gedankenexperiment. So you can take the laws of physics and then assume a flat world. Then think of the consequences and design a model. You can even invent new laws of physics and use them in your model. That's all fine and honest.

The only problem is, that this would end up, if you keep your model self-consistent, in a very different world compared to the one we live in. This is the obvious problem of any flat-earth model. You can find alternative explanations for certain aspects, but you can never find a consistent model. Because you cannot, as any cartographer knows, without distortions transform a 3D space into a 2D one.   

[Tom Bishop]

I see some discussion on what would be necessary to successfully attempt a debate - no arguments by incredulity, and an effort in hypothesizing  physical laws or limits to optics.

Hexagon has the right idea. If you don't like my argument, why not open the door?

Why does does the theme of the forum need to be to be "debate the experts" then? Why hang up the debates on me or Thork to appear?

Why not hear more voices other than my own? Isn't that more interesting?