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Messages - Tom Bishop

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6941
Flat Earth Theory / Re: What is and isn't proof
« on: November 17, 2017, 07:16:25 PM »
The answer to the above thought experiment is that you are adopting certain rules to perspective that have never really been demonstrated. The Ancient Greeks alleged that perspective lines operated on the same continuous rules as their trigonometry. But it has never been demonstrated what perspective actually does at long distances. There is no evidence that parallel perspective lines will approach each other forever and never touch, as an example.

There is some empirical evidence that receding bodies get more constant in their progress across the sky as they increase their altitudes, and this can be interpreted to mean that, if the universe does not operate on continuous rules (there is evidence suggesting that we live in a discrete universe), at some point they reach their maximum consistency across the sky. Thus, if the stars are all traveling across the sky consistently, they could not create the angled disk that has been proposed.

See the following article in the Wiki:

https://wiki.tfes.org/Constant_Speed_of_the_Sun

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Q. If the sun is disappearing to perspective, shouldn't it slow down as it approaches the horizon?

A. The sun moves constant speed into the horizon at sunset because it is at such a height that already beyond the apex of perspective lines. It has maximized the possible broadness of the lines of perspective in relation to the earth. It is intersecting the earth at a very broad angle.

It's widely observable that overhead receding bodies move at a more constant pace into the horizon the higher they are. For an example imagine that someone is flying a Cessna into the distance at an illegal altitude of 700 feet. He seems to zoom by pretty fast when he is flies over your head, only slowing down when he is off in the far distance.

Now consider what happens when a jet flies over your head at 45,000 feet. At that altitude a jet appears to move very slowly across the sky, despite that the jet is moving much faster than the Cessna. With greater altitude the plane seems to move more consistently across the sky. It does not zoom by overhead, only seeming to slow when in the far distance.

When a body increases its altitude it broadens its perspective lines in relation to the earth and the observer, and thus appears to move slower and at a more constant pace into the horizon. In FET the stars and celestial bodies are at such a great height that they have maximized the perspective lines. They are descending into the horizon at a consistent or near consistent velocity. As consequence they do not slow down in the distance by any significant degree, and hence the stars do not appear to change configuration and build up in the distance, nor does the sun or moon appear to slow as they approach the horizon.



The rate of descent of two bodies at different altitudes is more constant because it take a lot longer for a high altitude body to reach the horizon than it does for a low altitude body. The higher a body is, the broader its perspective lines, the longer and more constantly it will appear to approach the horizon to the observer.

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Read Earth Not a Globe for diagrams of perspective and for further information.

Looked there, the explanation is flawed.  E.g.  it refers to a row of lamp posts diminishing as they get further away.  True, but on a plane they get closer and closer to the horizon, but never actually touch it.  The sun, on the other hand, clearly drops below the horizon. 
If you do some simple trigonometry, you could work out the lowest angle the sun gets to.



The diagram is flawed in one VERY important way.

It shows the "perspective view" of the lamp posts with the posts getting shorter - but still equally spaced from left to right.  That is NOT how things look in perspective.

http://www.virtourist.com/europe/italy/bologna/imatges/13.jpg

Notice that while the columns get shorter - the also get closer together.  That's because perspective works not just in left-right and up-down - but also in the near-far direction.

Failure to understand this crucial point underpins 99% of the ridiculous things that FE'ers say about perspective - and just about every diagram they post contains the same stupid mistake.

Fix that brain-glitch and they lose their beloved "magic perspective" and everything falls apart for them.

The lamp posts are not equally spaced. Why are you so dishonest in your arguments?

6943
Flat Earth Theory / Re: Satellites
« on: November 17, 2017, 05:27:05 AM »
1. It doesn’t matter how much wind there is up there, it’s getting them to the right place in the first place.  Wind on the way up !

And you don't think it's possible to put some mode of transporation on there?

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2. Reddit.com ?  Not exactly a reliable source of evidence

It is a pretty striking example.

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3. Of course NASA was a key player during the space race which was part of the Cold War.  However, why every country (with space technology) participate in this charade ?  The Cold War is over !

Incorrect. The Cold War never ended. Look at the proxy war in Syria between the US and Russia. Vladimir Putin himself says that it never ended.

6944
Flat Earth Theory / Re: Satellites
« on: November 17, 2017, 04:53:50 AM »
Yeah, giant hydrogen balloons really takes the biscuit. As people have already said, the position of satellites is very precise, and balloons get blown by the winds.  Especially really big balloons.

I will suggest looking up how much wind there is at the edge of the atmosphere.

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You’d see the balloons above the satellites, especially big satellites like the ISS.  Hydrogen balloons have a limited life.  The hydrogen weeps through the membrane (think how quickly a helium party balloon goes flat) so they have a limited life span.  Some satellites have been up there for well over 10 years.

https://www.reddit.com/r/mildlyinteresting/comments/6y1qnu/this_1985_balloononastick_that_has_never_lost_its/

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Top secret security clearance on a need to know basis is the sort of phrase a 10 year old comes out with.
You can go and watch satellite launches. You can go and see these huge, expensive rockets being launched yourself.  Why would anybody put on a ridiculously expensive stage show, then go and dangle their satellite off a balloon.

Because they need to fake the concept of space travel in order to achieve military dominance. Did you think NASA was started at the birth of the Cold War to conduct innocent science?

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Read Earth Not a Globe for diagrams of perspective and for further information.

6946
Flat Earth Community / Re: Anyone for a public discussion?
« on: November 16, 2017, 09:58:07 PM »
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.

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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.

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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.

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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.

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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.

6947
Flat Earth Community / Re: Anyone for a public discussion?
« on: November 16, 2017, 09:45:19 PM »
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.

6948
Flat Earth Community / Re: Anyone for a public discussion?
« on: November 16, 2017, 09:25:51 PM »
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.

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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.

6949
Flat Earth Community / Re: Anyone for a public discussion?
« on: November 16, 2017, 08:15:00 PM »
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.

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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.

6950
Flat Earth Community / Re: Anyone for a public discussion?
« on: November 16, 2017, 06:43:22 PM »
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.

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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.

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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.

6951
Flat Earth Community / Re: Anyone for a public discussion?
« on: November 16, 2017, 06:39:00 PM »
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.

6952
Flat Earth Community / Re: Anyone for a public discussion?
« on: November 16, 2017, 06:22:38 PM »
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.

Nearly all of our math is based on the teachings of the Ancient Greeks. Even new forms of maths are based on their fundamental premises. Under the teachings of the Ancient Greeks the number lines are infinitely long and infinitely divisible. There is no discrete concept of a number. These teachings are also applied to the universe; the math which describes how the world and the universe operate also makes such assumptions.

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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.pdf

But 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.

Elucid was wrong about a lot of things. The Greek model of the universe is flimsy.

The continuous universe model, the basic concepts of line and point graphs, which are infinitely indivisible and infinitely long, was disproven by Zeno of Elea. His numerous critiques show that the continuous universe model is a sham and does not translate to the real world. For example, this math makes it impossible to walk through a door, or for a rabbit to overcome a tortoise in a  race.

Look up Zeno's Paradox. Zeno's Paradox deals with how space and time work on the smallest scales.

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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.

I don't see any evidence of anything. Line up how? I don't see any pictures.

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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"

The definition of parallel does not account for perspective. If the definition were true than railroad tracks could never be angled at each other.

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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.

The matter on how photons travel has been addressed several times for you. You keep pointing back to your illustrations of a continuous universe model as if it proves something about how the world works. You are assuming conclusions based on an Ancient Greek fantasy model where things are continuous, rather than an experience of the real world.

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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.

All of your proofs require us to assume several hypothesis' as true.

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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.

It is not that it is not or cannot be true; the premise is unfounded and so that must first be addressed.

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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

We are far more familiar with these topics than you are. We do understand "high school geometry" and have summarily rejected it until certain fundamental tenets have been demonstrated.

6953
Flat Earth Community / Re: Anyone for a public discussion?
« on: November 16, 2017, 05:52:17 PM »
I think you mean parallel lines here. How would one prove to your satisfaction that they approach for infinity but don't touch? I suspect the only way would be to examine them at infinity, which is clearly impossible. To paraphrase, I refuse to talk to you until you prove something impossible to prove. Just childish.

I don't really care if it is impossible to prove for you. It just goes to show that it cannot be demonstrated and so we should not assume it in the premise.

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And for the last time (I wish). Parallel lines APPEAR to approach to our eyes. This has nothing to do with how they exist in the real world.

We have no evidence other than what we experience. You are trying to combat an empirical experience with an ancient hypothesis.

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that a body thousands of miles away will appear a certain number of degrees above the horizon

Viewed from Atlanta, GA on December 30, 2017. The moon will block the view of Aldebaran starting at 18:09:36 with the moon at 28 degrees above the horizon at azimuth 88 degrees.
Ending at 18:52:22 with the moon at 37 degrees above the horizon at azimuth 94 degrees. This is sourced from http://www.lunar-occultations.com/iota/bstar/1230zc692.htm

What were you saying about not predicting things?

So go on with your usual diatribe about astronomy. Do you expect these predictions to be correct or not?

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.

6954
Flat Earth Community / Re: Anyone for a public discussion?
« on: November 16, 2017, 05:43:40 PM »
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.
You have never shown that it does not. This is your claim, you need to show evidence that the rules change at long distances. I've told you this now repeatedly.

Nope. You are the one coming here and saying that perspective operates according to certain rules of trigonometry. Therefore it is YOU who needs to back up your claims.

Show that two parallel perspective lines will never meet. In our experience they do appear to meet. Show that the merging of the lines in perspective is an illusion.

Your position is that illusions are occurring. How is it NOT your responsibility to demonstrate that?

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You are claiming they stop working past them. Where is your evidence for this claim? Where is your proof?

I am not asserting anything more that what is empirical; the meeting of perspective lines. You are asserting something contrary to experience and so it is your responsibility to prove that perspective operates on certain rules.

6955
Flat Earth Community / Re: Anyone for a public discussion?
« on: November 16, 2017, 03:08:48 AM »
I will try once more, and then sign off. If a flat-earth theorist wants to accept our invitation, please send me a private message. Transportation costs are out of the question; our Board of Directors won't allow it.

Here's why lunar (or asteroid) occultations are important to the question of the earth's shape.

In the flat earth model, to account for the ~5 degree shift in the positions of the sun, moon, planets, and stars as one moves ~350 miles north or south, you must argue that those celestial objects are no more than about 4000 miles away, from simple trigonometry. Never mind that radar measurements of the moon contradict that argument; let's go with your conspiracy theory for the moment.

The stars must be somewhat farther away than the moon, or else occultations would not occur at all, but can't be much farther because the shifts (as one moves north or south) observed for stars would be much less than for the moon (in the flat earth model), contrary to observations.

Therefore in the flat-earth model, an occultation of Aldebaran either occurs or doesn't occur depending on whether the moon crosses in front of Aldebaran. So any place where both moon and Aldebaran are visible at the right time should observe the occultation, and there would be no difference in the circumstances of the occultation (i.e. where on the face of the moon the star disappears and subsequently reappears) whether you move south or north as long as the event is above the horizon. 

What is in fact observed is that some locations on earth see a grazing occultation on the northern limb of the moon, some see a grazing occultation on the southern limb, and locations in between see the star disappear at various points around the moon. This is the effect of the moon's parallax - it is much closer to us than the star is. To demonstrate parallax: close one eye, hold your finger at arm's length so that it occults something you see out the window (a tree, chimney, mountain, whatever). Open that eye, close the other one, and the object is no longer occulted. This is one way we measure distances in astronomy.

The moon's parallax with respect to Aldebaran (or any other star it occults) implies that the star must be very much farther away than the moon. Again trigonometry can give you a (very crude) lower limit to the star's distance based on the precision with which you can measure small angles. But this would further imply that the shift in the positions of those stars as you move ~350 miles north or south on a flat earth would be much less than the ~5 degrees observed - a contradiction that can only be resolved by considering the true figure of the earth.

You assume that large distance perspective follows the ancient rules of "simple trigonometry" which assumes a continuous universe model.

That is called an assumption. A hypothesis. Something which has never been demonstrated. The Ancient Greeks never proved their perspective theories.

You want us to make explanations based on a model you have not shown to be accurate.

If you were challenged to show proof of the rules of the same model that two horizontal parallel perspective 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.

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.

6956

Sure, waves can be taller than your head.  How about showing us how waves on an obviously calm sea are taller than the height to which a helicopter can fly?

Great video, shows altitude brings the sun back into view.

Tom said in a thread that waves and trees and things cause the vanishing point at the horizon. When I said therefore sufficient altitude should overcome this and there would never be a sunset seen from a plane at altitude on FE. No more response from Tom on that thread of course.

When you rise in altitude, the horizon rises as well, keeping at your eye level. See this page: https://wiki.tfes.org/Basic_Perspective

6957
Flat Earth Theory / Re: In the bipolar map - what is around the edge?
« on: November 14, 2017, 05:55:45 PM »
Presumably water beyond the sun's light would naturally freeze, but the matter is TBD.

6958
In which case, I should be able to see it 24 hours a day, or at least, it would stay above the horizon but get dimmer. 

Here you go:

Increasing your altitude changes your perspective lines and allows you to see more distant lands. It will take a further amount of land to reach the Vanishing Point.

This is why it would take longer for the sun to set while you are at higher altitudes, and why the sun can be restored by rapidly increasing your altitude immediately after sunset.

Technically the explanation for why the sun sets at higher altitudes is also "waves," and whatnot. The perspective lines meet at the horizon and are perfect, but the surface of the earth is not perfect. Any slight increase  in height near the Vanishing Point will allow something to disappear further behind it, much like a dime can obscure an elephant.

I won't be around any longer. I assure you that you can do some simple searches to find answers to your queries.

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In fact, with this argument what you are describing, when a wave runs anything other than toward the observer, you would see multiple sunsets as waves are exactly that.

Its also not only one wave. The waves "build up" in the distance creating the solid line of the horizon you would see when looking out at sea.

I think I have helped you guys out quite enough. Refer to forum searches, wiki searches, and Earth Not a Globe if interested in Flat Earth Theory further.

6960
Oh dear, poor Tom has run out of options, so is simply refusing to discuss the subject.  I think that's the first time I've seen Tom defeated.

The average height of ocean waves is pretty widely available. While the burden of proof is on me on this claim, I have more interesting things to do than find a source for you.

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