[Tom Bishop]

I have never ever said that. You are the one who keeps conflating parallel lines and perspective lines. They are NOT the same thing. Parallel lines will never meet. Fact.

According to "definitions," any "parallel" lines should never get closer to each other, either. But in a railroad perspective scene, they do.

Parallel lines will appear to meet in the eye due to the limits of perspective. Fact.

Meet in the eye? Do you have any evidence that this phenomenon is an effect of the eye? There are cameras without lenses which see perspective.

I showed you exactly how the math works in another thread.

The math you post is ancient greek continuous universe math we can throw right out the window until the fundamentals have been demonstrated otherwise.

[StinkyOne]

Tom - please explain your non-continuous universe and how it relates to FET. Much like perspective, no one knows exactly what you are talking about.

The ancients tried to apply their math and ideas about number lines, how they are infinitely long and infinitely discrete, in addition to other continuous mathematical concepts, to the real world. This is why, according to their math, the perspective lines never meet.

We challenge that assertion and would like to see more evidence than a mathematical hypothesis about how perspective would behave before concluding what should or should not happen with long perspective lines.

While the Greeks played a large role in math, they are hardly alone. Many other cultures contributed greatly to our understanding. Given how incredibly successful mathematics are for so many varied applications, your burden of proof is absurdly high.

I mentioned Max Planck and his work on a discrete universe that isn't infinitely divisible. The scales at which this has any effect are FAR too small to be noticed in the real world. The gaps between atoms in a table are far larger (by a massive amount), but that isn't relevant to what we see in the world. Number lines are infinitely long. You can N+1 for eternity and never run out of numbers. Seems a very weird bone of contention.

So, how exactly does any of this relate to perspective??

[inquisitive]

I have never ever said that. You are the one who keeps conflating parallel lines and perspective lines. They are NOT the same thing. Parallel lines will never meet. Fact.

According to "definitions," any "parallel" lines should never get closer to each other, either. But in a railroad perspective scene, they do.

Parallel lines will appear to meet in the eye due to the limits of perspective. Fact.

Meet in the eye? Do you have any evidence that this phenomenon is an effect of the eye? There are cameras without lenses which see perspective.

I showed you exactly how the math works in another thread.

The math you post is ancient greek continuous universe math we can throw right out the window until the fundamentals have been demonstrated otherwise.

What do you by scene.  We know we, yes we, have parallell tracks, it is just like they look to get closer simply because they are further away.

No need to reply as you know I am correct.

[Curious Squirrel]

I have never ever said that. You are the one who keeps conflating parallel lines and perspective lines. They are NOT the same thing. Parallel lines will never meet. Fact.

According to "definitions," any "parallel" lines should never get closer to each other, either. But in a railroad perspective scene, they do.

Parallel lines will appear to meet in the eye due to the limits of perspective. Fact.

Meet in the eye? Do you have any evidence that this phenomenon is an effect of the eye? There are cameras without lenses which see perspective.

I showed you exactly how the math works in another thread.

The math you post is ancient greek continuous universe math we can throw right out the window until the fundamentals have been demonstrated otherwise.

There you go using perspective in the wrong context again. The perspective effect is due to light traveling in straight lines, and a few other things as explained by 3D above. *Where* they appear to meet is a function of the eye, or whatever happens to be 'focusing' the light rays.

Once again. Parallel lines =/= perspective lines. Perspective lines are a construct of art, not math. Math CAN however still tell us how things will look, once again explained by 3D above in greater detail. If math couldn't you would never have a computer generated image that looked 'true to life' such as can be seen in any modern video game.

'Continuous universe' is another nonsense term at the moment, as neither standard definition has anything to do on the scales we are talking about. The fundamentals of trig have been demonstrated to work for buildings and more for a few thousand years by now, so your claim is without merit.

Once again. We claim math works, and we can show it reflects reality at any measurable distance. There is no inherent reason to think it stops working past those distances. You claim it does. What is your proof?
"We can see railroad tracks meeting"? Yeah, and the math shows us where/how/why and can be used to accurately model this in a computer. So this isn't proof. Try again.

[Tom Bishop]

While the Greeks played a large role in math, they are hardly alone. Many other cultures contributed greatly to our understanding. Given how incredibly successful mathematics are for so many varied applications, your burden of proof is absurdly high.

What do you mean incredibly successful? That math can't even explain how a rabbit could overcome a tortoise in a race.

I mentioned Max Planck and his work on a discrete universe that isn't infinitely divisible.

Yes, that is a good example. Zeno was right in that the universe is non-continuous. The ancients got it wrong.

That's one of the big problems with finding a Grand Unified Theory. Quantum Mechanics says that the universe is discrete, and that there are discrete units of space and time, while General Relativity says that the universe is continuous in space and time. The concepts are not compatible.

[inquisitive]

While the Greeks played a large role in math, they are hardly alone. Many other cultures contributed greatly to our understanding. Given how incredibly successful mathematics are for so many varied applications, your burden of proof is absurdly high.

What do you mean incredibly successful? That math can't even explain how a rabbit could overcome a tortoise in a race.

I mentioned Max Planck and his work on a discrete universe that isn't infinitely divisible.

Yes, that is a good example. Zeno was right in that the universe is non-continuous. The ancients got it wrong.

That's one of the big problems with finding a Grand Unified Theory. Quantum Mechanics says that the universe is discrete, and that there are discrete units of space and time, while General Relativity says that the universe is continuous in space and time. The concepts are not really that compatible and there are issues in translation.

Which is not relevant when discussing distances of several thousand miles.

[3DGeek]

What do you mean incredibly successful? That math can't even explain how a rabbit could overcome a tortoise in a race.

Oh good grief.  Even Zeno didn't believe Zeno's paradox.

You seriously think math can't sum an infinite series?   Good grief - you really didn't pay attention in high school math class did you?   This is literally child's play.

OK - so firstly you got the story wrong it wasn't a "hare" or a "rabbit" - it was Achilles.

Achilles gives the tortoise a head start of (say) 100 feet.  Achilles runs at 10 feet per second and the tortoise runs one foot per second.   So Zeno says - that in the time it takes Achilles to run 100 feet (10 seconds), the tortoise has covered 10 feet.  Achilles hasn't reached the tortoise, he runs 10 feet in one second and by then the tortoise has covered another foot...Achilles runs another foot in 1/10th of a second and by then the tortoise has covered a 1/10th of a foot...and so on.

Since at each step of the process - the amount of time we're considering halves - if we want to know how much time it takes for Achilles to catch up with the tortoise we have to sum an infinite series of time steps:

   10 + 1 + 0.1 + 0.01 + ...

Well - I think I can do that sum in my head - its  11.11111111....recurring.   No matter how many 1's you add after the decimal point, after 11.2 seconds - Achilles has definitely passed the tortoise.

If you want to know the distance at which he passes the lumbering beast:

  100' + 10' + 1' + 0.1' + 0.01' + ...

Same deal - it happens at 111.1111... feet.   So the tortoise is definitely overtaken before he can cross the 112' mark.

This is child's play math Tom.   Do you SERIOUSLY think we can't solve it in this modern world?   It's ridiculously easy.

There are some infinite series that are harder to sum (pi, for example) - and some which "blow up in your face" and sum to infinity or something like that - and even some that have no definite answer   (eg: 1-1+1-1+1-1....).

But Zeno's paradox isn't a paradox at all, it's simple math problem.

[Curious Squirrel]

What do you mean incredibly successful? That math can't even explain how a rabbit could overcome a tortoise in a race.

Does anyone else find it ironic that Tom trots out Zeno's paradox as an unsolvable problem for the math, by linking to a site that shows how we can solve the problem with math? Although irony might not be quite the right word I feel it's close enough.

Thanks for laying it out here for everyone though 3D. I found the whole thing actually quite fascinating when I came across it in an earlier thread. I love math but have never delved into the slightly more peculiar corners of it.

[3DGeek]

The ancients tried to apply their math and ideas about number lines, how they are infinitely long and infinitely discrete, in addition to other continuous mathematical concepts, to the real world. This is why, according to their math, the perspective lines never meet.

We challenge that assertion and would like to see more evidence than a mathematical hypothesis about how perspective would behave before concluding what should or should not happen with long perspective lines.

Be careful:  Parallel lines don't meet in the real world.  That's the definition of the word "parallel".

We know the math for perspective - I mentioned it before:   x' = x k / z  and y' = y k / z  (and incidentally z' = z k / z...not that we necessarily care)...we can choose a camera where the constant 'k' is 1.0 to make life easier.

x' and y' are the locations of the point (x,y,z) in your two-dimensional image.  z'=k ...so the image is located on the back of the camera.

I'm using x-is-right, y-is-up and z is distance away from the camera...which is conventional in 3D graphics.

So if we take two parallel lines - like railroad tracks - that are two units apart.  They are one unit below the camera and start one unit in front of the camera and end up at infinity: In the real world (x,y,z) the left rail runs from (-1,-1,1) to (-1,-1,infinity) and the right rail runs from (1,-1,1) to (1,-1,infinity).

So in our image, the lefthand rail goes from x' = -1/1 = -1 units to x' = -1/infinity = 0 units.  The righthand rail goes from x'= +1/1 = 1 units to x'= 1/infinity = 0 units.   y' is -1/1 to -1/infinity for both rails.

So the coordinates of the ends of the two rails in our image is:  (-1,-1) to (0,0)  and (+1,-1) to (0,0).    Hence both rails meet IN THE IMAGE at (0,0)...which is where you'd expect them to meet in a flat earth world with an infinite horizon.   In the round earth, the rails curve over the horizon and disappear before they can meet...however, they might get VERY close and require high magnification to actually see the gap between them as the go over the horizon.

So - that proves what math and actual perspective says.

All you have left to complain about is my equations (x'= x k / z, etc)

Those I proved for you in another post - and are self evident from the principles of a pinhole camera, straight light rays and similar triangles.  If you'd like me to re-post that proof, I'd be happy to do so.

You see the things that are claimed are childishly easy to prove.   Your claims that we CAN'T prove them are founded entirely on your own lack of knowledge.

[Tom Bishop]

What do you mean incredibly successful? That math can't even explain how a rabbit could overcome a tortoise in a race.

Oh good grief.  Even Zeno didn't believe Zeno's paradox.

You seriously think math can't sum an infinite series?   Good grief - you really didn't pay attention in high school math class did you?   This is literally child's play.

OK - so firstly you got the story wrong it wasn't a "hare" or a "rabbit" - it was Achilles.

Achilles gives the tortoise a head start of (say) 100 feet.  Achilles runs at 10 feet per second and the tortoise runs one foot per second.   So Zeno says - that in the time it takes Achilles to run 100 feet (10 seconds), the tortoise has covered 10 feet.  Achilles hasn't reached the tortoise, he runs 10 feet in one second and by then the tortoise has covered another foot...Achilles runs another foot in 1/10th of a second and by then the tortoise has covered a 1/10th of a foot...and so on.

Since at each step of the process - the amount of time we're considering halves - if we want to know how much time it takes for Achilles to catch up with the tortoise we have to sum an infinite series of time steps:

   10 + 1 + 0.1 + 0.01 + ...

Well - I think I can do that sum in my head - its  11.11111111....recurring.   No matter how many 1's you add after the decimal point, after 11.2 seconds - Achilles has definitely passed the tortoise.

You can't ever get to 11.2 seconds because the Greeks believed that time is continuous and infinitely divisible too. It's not just space. Achilles and the tortoise would continue to exchange positions, getting into smaller and smaller fractions of space and time, without being able to get to a final discrete unit of time and space to progress further.

But Zeno's paradox isn't a paradox at all, it's simple math problem.

You did not solve Zeno's Paradox. The only way to solve it is to decide that space and time are discrete; which pretty much admits that the Ancient Greeks were wrong and the universe is not continuous.

[inquisitive]

Tom finding my points too difficult for them to answer?

[Tom Bishop]

The ancients tried to apply their math and ideas about number lines, how they are infinitely long and infinitely discrete, in addition to other continuous mathematical concepts, to the real world. This is why, according to their math, the perspective lines never meet.

We challenge that assertion and would like to see more evidence than a mathematical hypothesis about how perspective would behave before concluding what should or should not happen with long perspective lines.

Be careful:  Parallel lines don't meet in the real world.  That's the definition of the word "parallel".

We know the math for perspective - I mentioned it before:   x' = x k / z  and y' = y k / z  (and incidentally z' = z k / z...not that we necessarily care)...we can choose a camera where the constant 'k' is 1.0 to make life easier.

x' and y' are the locations of the point (x,y,z) in your two-dimensional image.  z'=k ...so the image is located on the back of the camera.

I'm using x-is-right, y-is-up and z is distance away from the camera...which is conventional in 3D graphics.

So if we take two parallel lines - like railroad tracks - that are two units apart.  They are one unit below the camera and start one unit in front of the camera and end up at infinity: In the real world (x,y,z) the left rail runs from (-1,-1,1) to (-1,-1,infinity) and the right rail runs from (1,-1,1) to (1,-1,infinity).

So in our image, the lefthand rail goes from x' = -1/1 = -1 units to x' = -1/infinity = 0 units.  The righthand rail goes from x'= +1/1 = 1 units to x'= 1/infinity = 0 units.   y' is -1/1 to -1/infinity for both rails.

So the coordinates of the ends of the two rails in our image is:  (-1,-1) to (0,0)  and (+1,-1) to (0,0).    Hence both rails meet IN THE IMAGE at (0,0)...which is where you'd expect them to meet in a flat earth world with an infinite horizon.   In the round earth, the rails curve over the horizon and disappear before they can meet...however, they might get VERY close and require high magnification to actually see the gap between them as the go over the horizon.

So - that proves what math and actual perspective says.

All you have left to complain about is my equations (x'= x k / z, etc)

Those I proved for you in another post - and are self evident from the principles of a pinhole camera, straight light rays and similar triangles.  If you'd like me to re-post that proof, I'd be happy to do so.

You see the things that are claimed are childishly easy to prove.   Your claims that we CAN'T prove them are founded entirely on your own lack of knowledge.

I just see a thought experiment here.

[3DGeek]

You can't ever get to 11.2 seconds because the Greeks believed that time is continuous and infinitely divisible too. It's not just space. Achilles and the tortoise would continue to exchange positions, getting into smaller and smaller fractions of space and time, without being able to get to a final discrete unit of time and space to progress further.

So does time somehow cease at 11.111... seconds?  As far as I'm aware it does not.  My math is unassailable.

What you're talking about is a deeper proposition that an infinite number of TASKS must be completed before Achilles can overtake the tortoise - but the concept of "completing a task" isn't any kind of real world requirement here.   So long as the muscles in Achilles' legs are functioning - he'll overtake the tortoise.

Sure the greeks liked to argue about this stuff - but it doesn't mean that mathematics cannot solve it...as indeed, they so clearly do.   If you ran that race, I guarantee that Achilles would overtake the tortoise a moment before 11.11112 seconds.

What worries most people is that the number has an infinite number of digits - but that's just an issue of the units you happen to choose.  If I measure time in units of 1/9th of a second - then Achilles reaches the tortoise in exactly 100 time units.

You did not solve Zeno's Paradox. The only way to solve it is to decide that space and time are discrete; which pretty much admits that the Ancient Greeks were wrong and the universe is not continuous.

You didn't ask me to solve a philosophical debate about whether an infinite number of "tasks" can be performed (clearly they can because people win races).

You said "That math can't even explain how a rabbit could overcome a tortoise in a race."...which it most certainly can - and without hardly breaking a sweat.

A true zetetic would have no truck with philosophers...I see that people can win races...I see that we can sum infinite series...QED.

[Tom Bishop]

So does time somehow cease at 11.111... seconds?  As far as I'm aware it does not.  My math is unassailable.

You can only progress time further if you assume that time is discrete.

Sure the greeks liked to argue about this stuff - but it doesn't mean that mathematics cannot solve it...as indeed, they so clearly do.   If you ran that race, I guarantee that Achilles would overtake the tortoise a moment before 11.11112 seconds.

In a real race Achilles would overtake the tortoise, but that says nothing about whether the continuous universe math of the Ancient Greeks is correct.

What worries most people is that the number has an infinite number of digits - but that's just an issue of the units you happen to choose.  If I measure time in units of 1/9th of a second - then Achilles reaches the tortoise in exactly 100 time units.

If you measure time in 1/9th of a second you have decided that the universe is discrete and that we do not live in a continuous universe like the Ancient Greeks said we did, and which almost all math is founded upon.

You didn't ask me to solve a philosophical debate about whether an infinite number of "tasks" can be performed (clearly they can because people win races).

Yes I did. This whole discussion is about whether the universe is continuous or not.

You said "That math can't even explain how a rabbit could overcome a tortoise in a race."...which it most certainly can - and without hardly breaking a sweat.

A true zetetic would have no truck with philosophers...I see that people can win races...I see that we can sum infinite series...QED.

A true experiment showing people winning races would be empirical evidence that space and time are discrete; and would act as a disprove against a continuous universe, therefore showing that continuous math is fallacious and not translatable to the real world.

All of this strengthens our questioning of the math which predicts infinitely approaching perspective lines.

[3DGeek]

I just see a thought experiment here.

No you see the answer to your typically ill-informed question:

The ancients tried to apply their math and ideas about number lines, how they are infinitely long and infinitely discrete, in addition to other continuous mathematical concepts, to the real world. This is why, according to their math, the perspective lines never meet.

I pointed out that "according to their math" - the perspective lines most certainly DO meet.

I answered the thing that you said was impossible.

We challenge that assertion and would like to see more evidence than a mathematical hypothesis about how perspective would behave before concluding what should or should not happen with long perspective lines.

So now you ask for more than "a mathematical hypothesis".   Well mathematics doesn't deal with "hypotheses" - there are axioms and there are theorems.  I lay out my axioms and then I prove a theorem.  If the axioms are correct and if there are no errors in the steps leading to the theorem - then the theorem is true.

The problem for you is that you HAVE NO MATH for your magic perspective (which is indeed a "hypothesis" - you can't explain why it happens or even prove that it does).

So you know that you can't allow math to enter into the debate because the moment it does - it proves you wrong...and I do mean "proves".   A mathematical proof is unassailable.  You can only deny the axioms - which in this case means denying that light travels in straight lines - or denying that similar triangles have sides with identical ratios...which in turn requires denying Euclid's theorems - which in turn denies basic geometrical precepts such as the definition of a line.

That is a bear trap from which there is no escape.

Instead you childishly demand to see parallel lines of infinite length - when YOUR concept will fall apart for parallel lines of FINITE length - so I merely have to stand on a long straight railroad track and pull out a pair of binoculars.

So rather than try to produce empirical evidence to disprove the impossible - let's just disprove what you believe to be possible.  That's vastly simpler and directly
demolishes your crazy thinking rather than leading to more infinite regress.

So...I repeat: TELL US HOW PHOTONS TRAVEL FROM THE SUN TO YOUR EYE AT SUNSET.

You know you can't...if you could - you'd have done it already - as you twice rashly promised you would - right before you (presumably) realised that you can't.

[3DGeek]

You can only progress time further if you assume that time is discrete.

Not at all - I don't have to use whole numbers - we have decimals!   I can express time (and the race) either way - the result is the same.

I work in computer graphics - we have "discrete time" - everything happens in steps of 1/60th of a second (one video frame).  We can simulate races just as easily in discrete steps.

You wind up with Achilles being some short distance behind the tortoise - and you advance the distance of each one by it's speed multiplied by the time step - and in the next time step Achilles is ahead of the tortoise.

The discontinuous "jumps" are equally spaced - and not exponentially smaller chunks of time - so there still is no paradox.

To propose that Achilles can't beat the tortoise REQUIRES that you discretize time into smaller and smaller steps...which if "real" would mean it would indeed take an infinite number of steps.   But the real world (even if discrete) can't work that way because there are multiple events (different races, if you like) where the time steps would have to be different in order for those races to exhibit the same paradox.  The universe can't be jumping around in different length time steps because then you couldn't have interactions between events.

So - you want a discretized time...fine - no problem.   You want discretized space too...well that implies discretized energy - and therefore mass.  But that's not a problem.

You can formulate any of the things we've been discussing in either continuous or discrete forms...the answer comes out the same.

In a real race Achilles would overtake the tortoise, but that says nothing about whether the continuous universe math of the Ancient Greeks is correct.

Indeed.

If you measure time in 1/9th of a second you have decided that the universe is discrete and that we do not live in a continuous universe like the Ancient Greeks said we did, and which almost all math is founded upon.

I didn't say "integer numbers of 1/9th seconds" - you can still have fractions of 1/9th.  It's no different than measuring distances in centimeters instead of inches to get nice round numbers.

You didn't ask me to solve a philosophical debate about whether an infinite number of "tasks" can be performed (clearly they can because people win races).

Yes I did. This whole discussion is about whether the universe is continuous or not.

Well, you may have intended that - but it's not what you said.   You said that math can't do this or that or the other...and I show that it most certainly can.  I happened to use a continuous model - but the results come out exactly the same either way.

You said "That math can't even explain how a rabbit could overcome a tortoise in a race."...which it most certainly can - and without hardly breaking a sweat.

A true zetetic would have no truck with philosophers...I see that people can win races...I see that we can sum infinite series...QED.

A true experiment showing people winning races would be empirical evidence that space and time are discrete; and would act as a disprove against a continuous universe, therefore showing that continuous math is fallacious and not translatable to the real world.

Woooaaah...that's one step beyond what you're arguing.

I showed that math can demonstrate how people can win races using repeated addition of a series of steps...summing an infinite series.  That was a "discrete" solution to Zeno's paradox.   The "continuous" solution would be to write an equation for the position of the tortoise against time - and another one for Achilles - to solve those two simultaneous equations - and get the time (or distance) at which Achilles overtakes the tortoise from that.

The answer comes out EXACTLY the same - and math works in both approaches.

Your idea that math can't solve problems in a discrete universe is CLEARLY bullshit because math works great for making video games where the computer has only 64 bits in a word and can only display images once every 1/60th of a second.   That's all math - and it works SUPERBLY WELL in a discrete "universe".

So you're 100% wrong on that one...again - you're guessing/hoping that what you say is true...you don't know enough to understand where your thinking is wrong.

All of this strengthens our questioning of the math which predicts infinitely approaching perspective lines.

I don't think it does.   We can chop the space into 1 pico-meter chunks and divide time into 1 nanosecond intervals - and you still can't explain how photons get from the sun to my eye at sunset.

So this is all just typical flim-flam - and I'm not falling for it!

Tell me how the photon moves in a discretized universe - you still can't do it.

[Roger G]

I never got beyond calculus at school, but still use basic trigonometry for navigation but 99% of the folks on this forum probably have no more knowledge of higher maths than I do. The problem is that FEs will see Tom's entertaining and amusing discussions with 3D and the maths will fly way above their heads. That won't though stop them gleefully seeing Tom refuting everything that 3D throws at him as proof that the world is flat, even though Tom is completely unable to come up with any arguments that are not baseless.

With reference to the perspective of parallel railway lines, the fact that they do not actually converge and meet at infinity seems to me to be quite easy to show with virtually no knowledge of maths and to have quite clear and empirical evidence that any FE can find. Just find a continuous straight stretch of track alongside a road, that appears to converge or almost converge in the distance. Measure the exact distance between the tracks at the point you are looking from. If you are unable to read a measure, use a length of wood or other rigid material and make a mark to show the distance between the tracks. Then jump in a car and travel down the road alongside the tracks for lets say 5 miles, although the distance doesn't really matter. Measure the distance between the tracks again, then do the same a couple of times more. As the tracks will be a standard gauge set by the railroad company the measurements will all be the same. Once you are satisfied that the rails are not converging, even though your eyes seem to tell you they are, you have proved that whatever distance you travel to take the measurements, you will always get the same result. The difference between the measurements will be zero, so if you have taken 4 measurements over 20 miles, the 20x0=0 so there is no convergence whatever your eyes tell you. If the tracks travel to infinity, infinity x zero will still be still be zero convergence so the tracks will never meet.

FEs get your head out of the computer and Youtube, get out in the fresh air and do it yourself and prove that Tom is just talking BS even though you want to believe him.

Roger

[Mark_1984]

That's been fun to watch !!  I can safely predict you won't have anybody accept your invitation.  They know when they are outgunned, hence the very few flat earth believers here. 

My three body prediction.  Tom would say occultations are caused by magic parallax and you should prove it otherwise, and then pretend to ignore all your proofs.
ScaryGary will find some big words and string them into a sentence which sounds impressive but is completely meaningless.
J-man will say it was aliens, and god will smite you if you say otherwise.

[3DGeek]

I never got beyond calculus at school, but still use basic trigonometry for navigation but 99% of the folks on this forum probably have no more knowledge of higher maths than I do. The problem is that FEs will see Tom's entertaining and amusing discussions with 3D and the maths will fly way above their heads. That won't though stop them gleefully seeing Tom refuting everything that 3D throws at him as proof that the world is flat, even though Tom is completely unable to come up with any arguments that are not baseless.

Nobody could possibly imagine that Tom refutes everything I say - a solid 60% of the "Disproof" threads I've started, he's never even contributed to.

In most cases, where he has no countervailing narrative - he just skips the thread and hopes that it sinks off the bottom of the forum list without too many people noticing.

Tom's "railroad track" thing is getting increasingly bizarre as he gets increasingly desperate to come up with an explanation.   We started with him (deliberately?) confusing what happens "in reality" and what happens in "a picture of reality"...then he started introducing some very weird vocabulary definitions between "location", "position" and "orientation" to throw more confusion into the situation.   Then, when I came up with a STUNNINGLY clear description of how perspective math applies - he said that diagrams cannot represent reality.   So I did the same thing with the path a photon literally takes - which HE STILL refuses to talk about - despite many times claiming that he would do so.   Then I came up with another disproof of sunsets that doesn't even involve eyes or cameras - and works solely by the heat you feel on your face.   That one was one of the "ignored" ones...because if you can show there are no FE sunsets WITHOUT requiring perspective - then he's really screwed.

In the latest round of desperation, he's started in on this crap about "continuous" versus "discrete" universe and mathematics.   Bouncing around between the two like an over-inflated beachball.   Sadly, the math works out the same no matter which model you choose...as I demonstrated with the Zeno paradox.

Tom is a desperate man...none of his arguments stand for very long - so he has to reach for more and more desperate niches in which to hide the glaring problem which is THE WORLD ISN'T FLAT.

But this is a guy who also claims that you can cure Ebola and AIDS using large doses of vitamin C and that Cancer can be cured with green peppers.   I imagine a good number of FE'ers flinching at those claims.

So we're not talking the smartest tool in the shed here.

[garygreen]

Astronomy is based on observed patterns. Observed patterns of the moon, observed patterns of the stars. Things are only predictable because they come in patterns. It is possible to create an equation to express those patterns, but they are only valuable in that they might produce a right answer.

read the literature i linked more carefully.  here are the equations of motion:



this is pretty much exactly how eclipse tables are calculated.  the nasa page you always link says this itself at the bottom.