Perspective

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Perspective
« on: August 15, 2016, 08:54:38 AM »
Perspective is a common argument used by Flat Earthers to prove that the Sun goes
behind the horizon because it moves so far away it would meet vanishing point and start
being less and less visible until it is entirely gone.

This thead kills the argument.

First of all, no significant assumtions other than those presented by the flat earth itself
are used, but the one: for simplicity I consider a Sun a flat disc. This simplifies the math by
a lot without causing a significant error to qualitative result.

Lets start from a clarification. A vanishing point is the point where all lines of perspective
meet. Since we are on a flat surface, it is infinitely far away from us. If that wasn't the case,
we could zoom in to see that the lines go beyond the finite case.

Since the vanishing point is infinitely far away, we can use other thing, called the
resolution of human's eye. An average person can see objects having at least 1', unless they
are sources of lights, and it that case objects can be much smaller. But lets stick to 1', we will
need it in a moment.

Let us place our observer at the equator and wait for the equinox. Then, at noon, the Sun is directly overhead,
at altitude H km. In that case, he can see that the Sun has 36' angular diameter.

This setting is our frame of reference. The choise is so that the math is a bit easier, but one can
repeat the math for any other point on the Earth. Qualitative results will be maintaned, however quantitative
won't.

Now let us move the Sun horizontally by A km.  Then, a straight line joining the new position of the Sun
with our observer has the length D=(A^2+H^2)^{1/2) and the angle a between this line and the surface is equal
to a=arctan(H/A).

We want our Sun to ,,vanish'', so it has to be so far its angular diameter falls to 1'. At that distance
it wouldn't be distinguished from the star. At least by a naked eye, which is our base anyway.
In order to achieve that, the Sun must shrink. Since 36'=36*1', the shrinking
scale is exactly 36. Thus D=36H. Since D>>H, D/A is close to 1, and then A is close to D.
Thus A=36H. Substitute your favourite distance.

Furthermore, since H/A=1/36 is small, we have a=arctan(1/36)=1/36 rad. This is equal to
almost 1.6 degrees. Definitiely higher than the horizon is. Also, it is more likely that
we won't see the Sun dissapearing due to perspective because on either natural or human-made
objects.

Questions:
1. What if the atmosphere can magnify the Sun so it always keeps it size?
In that case, the Sun would never be so small. In order to touch the horizon, the angular
distance between the Sun and the horizon must be smaller than 1'. This angle is achieved
when A=~3200A . Also, the magnification is a pretty complicated time dependant
function.
2. What if the atmosphere bends the light and magnify it so the angles and the size perfectly
match observation?
This is impossible. The light goes from near vacuum to densier area, thus the light bends down, towards the surface.
It should bend the light in the opposite direction.
This would cause even more problems - we would see the Sun higher than it actually is.

Myths:
1. Perspective lines converg to a point within our eye's sight of range.
2. Perspective causes objects on the ground to loose their "ground parts", like legs, wheels, or ship hulls.

Comments?

Re: Perspective
« Reply #1 on: August 15, 2016, 08:56:22 AM »
Great post. Time to see them squeal, or wait for jroa to shoe up and derail it.
I wonder how obnoxious I can make my signature?
Please give me ideas.

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Ski

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Re: Perspective
« Reply #2 on: August 16, 2016, 07:58:13 PM »
Perspective does account for the sinking ship phenomena, but is insufficient to account for the setting of the sun (though the effect can frequently be seen in evidence here, too).
You are espousing a sort of art school perspective, but that is not Dr. Rowbotham's position.
"Never think you can turn over any old falsehood without a terrible squirming of the horrid little population that dwells under it." -O.W. Holmes "Truth forever on the scaffold, Wrong forever on the throne.."

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rabinoz

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Re: Perspective
« Reply #3 on: August 16, 2016, 10:53:16 PM »
Perspective does account for the sinking ship phenomena, but is insufficient to account for the setting of the sun (though the effect can frequently be seen in evidence here, too).
You are espousing a sort of art school perspective, but that is not Dr. Rowbotham's position.

Really?

Dr. Rowbotham's position on perspective seems to be quite inconsistent with itself.

In , CHAPTER XIV of "Zetetic Astronomy" by Samuel Birley Rowbotham (18161884), writing under the pseudonym, Parallax we find:
Quote
"The range of the eye, or diameter of the field of vision, is 110; consequently this is the largest angle under which an object can be seen. The range of vision is from 110 to 1.  The smallest angle under which an object can be seen is upon an average, for different sights, the sixtieth part of a degree, or one minute in space; so that when an object is removed from the eye 3000 times its own diameter, it will only just be distinguishable; consequently the greatest distance at which we can behold an object like a shilling of an inch in diameter, is 3000 inches or 250 feet."

The above may be called the law of perspective. It may be given in more formal language, as the following: when any object or any part thereof is so far removed that its greatest diameter subtends at the eye of the observer, an angle of one minute or less of a degree, it is no longer visible.

Actually, what Rowbotham meaning is not simply seeing the presence of an object, but being able to separate it from an adjacent one, such as the hull of a boat from its superstructure. This would become clear if you read more of that section.

I completely agree with this treatment of vanishing point and perspective. Even when he gets to his explanation of ships "disappearing" he makes more very pertinent and correct explanations:
Quote
From the above it follows:
  • That the larger the object the further will it require to go from the observer before it becomes invisible.
  • The further any two bodies, or any two parts of the same body, are asunder, the further must they recede before they appear to converge to the same point.
  • Any distinctive part of a receding body will become invisible before the whole or any larger part of the same body.
The first and second of the above propositions are self-evident. The third may be illustrated by the following diagram, fig. 73.

FIG. 73.
Let A represent a disc of wood or card-board, say one foot in diameter, and painted black, except one inch diameter in the centre. On taking this disc to about a hundred feet away from an observer at A, the white centre will appear considerably diminished--as shown at B--and on removing it still further the central white will become invisible, the disc will appear as at C, entirely black. Again, if a similar disc is coloured black, except a segment of say one inch in depth at the lower edge, on moving it forward the lower segment will gradually disappear, as shown at A, B, and C, in diagram fig. 74. If the

Fig. 74.
disc is allowed to rest on a board D, the effect is still more striking. The disc at C will appear perfectly round--the white segment having disappeared.
You will note in Fig 73 and Fig 74 that the object has not changed shaped shape, only that the smaller part of the object is no longer separately discernable. The whole object has been reduced proportionately.

Up to this point, I find Rowbotham's explanation of perspective far better than most on the topic, but then in my opinion, he starts to distort it, with:
Quote
If a receding train be observed on a long, straight, and horizontal portion of railway, the bottom of the last carriage will seem to gradually get nearer to the rails, until at about the distance of two miles the line of rail and the bottom of the carriage will seem to come together, as shown in fig. 79.

Fig. 79.
Now Rowbotham has truncated the object by merging the wheels with the ground. I would contend that, while the wheels might not be separately discernable, the rest of the loco must not be "squashed" into the ground. The whole object must be reduced in size proportionately!

Perspective simply reduces the apparent size of the whole object in proportion to the distance, when that apparent size of a part of the object gets below the limit of the eye's resolving power, that part is no longer separately dsicernable. In the diagram above we have a completely unjustified distortion of the loco. A more correct diagram would be:
where the wheels don't artificially "burrow" into the ground. Normal real perspective will make those smaller parts "disappear" in good time.

Now, on to ships disappearing and re-appearing.

Sure, a hull of a small boat might disappear due simply because it has gone past the point where the naked eye can resolve the hull from the rest of the boat. For a horizon distance of 5 miles (eye height 16 feet) a good pair of eyes (better than mine!) could resolve objects about 16 feet apart. So the whole boat may appear as a white blob - the sails.

A boat on the horizon (not hidden by the horizon) might be seen, but not resolved into hull and sails and the whole boat would be brought back into view by a telescope!

But, get a large boat behind a more distant horizon and it's a whole different kettle of fish (as they say in the classics).

This ship seems certainly partly hidden to me:

Diamond Princess leaving Harbour
 

Diamond Princess partly over horizon
 

Diamond Princess well over horizon (framed for overlay)
 

Diamond Princess original ship overlayed on prev picture
In my opinion this ship is clearly partly hidden behind the horizon.

And the fact of ships being partly hidden by the horizon has been used for centuries by sailors to estimate the distance to ships and buoys.

This is from a USN Handbook (Yes, I guess they are part of the conspiracy!)
Quote from: Lookout Training Handbook NAVEDTRA 12968-D
RANGE ESTIMATION
Question CIC concerning the radar ranges to visual contacts and compare them
with your estimated range. 
HEIGHT OF EYE
     RANGE TO   HORIZON
FEET
YARDS
MILES
20
10,200
5.1
40
14,400
7.2
60
17,800
8.9
80
20,600
10.3
Figure 5-5: Range Height Table
The only readily available reference point you can use when estimating ranges is the
horizon.  Knowing your height above the waterline will help you estimate ranges because
the distance to the horizon varies with the height of the eye (Figure 5-5).

At a height of 50 feet, for example, the distance to the horizon is about 16,000 yards (8
miles); at a height of 100 feet, the distance is about 23,000 yards (11-1/2 miles).  Practice estimating ranges to other vessels in company whose distances are known or can be easily determined. 
 
::) Do you think those poor sailors got confused when they found that the Navy had lied to them?  ::)

You know something I have NEVER seen a convincing video or photo of any object that has actually disappeared over the horizon "brought back" by telescope or zoom lens. I have seen ships and buildings hidden numerous times, though the actual amount does vary considerably due to refraction. If you are interested you could read Refraction, ROHAN Academic Computing.

<< sorry for the tl;dr >>

« Last Edit: July 07, 2017, 01:29:20 AM by rabinoz »

Re: Perspective
« Reply #4 on: August 17, 2016, 12:10:26 AM »
Perspective does account for the sinking ship phenomena, but is insufficient to account for the setting of the sun (though the effect can frequently be seen in evidence here, too).
How is this hand-waving going to answer any question or explain anything? I've started the thread regarding sinking ship too and explained why it won't work, but no respone from FE-ers.

You are espousing a sort of art school perspective, but that is not Dr. Rowbotham's position.
Why Rowbotham's position is the one I should take? His is clearly wrong, which was well described by rabinoz, especially when he writes about trains and ships.

I've seen lots of videos, read lots of posts about the perspective and they all had the same in common. Hand-waving and placing the Sun in impossible position with respect to the observer to "prove" it can go behind the horizon I've seen a lot of misconceptions from FE-ers, especially from those repeating after Rowbotham's.

Who's on real discussion and not hand-waving?

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Ski

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Re: Perspective
« Reply #5 on: August 17, 2016, 12:16:05 AM »
Read it again, rabinoz: Dr. Rowbotham states most clearly that objects nearer the eyeline recede more quickly than those farther from it. Art school perspective makes no account of this and this is the difficulty it finds itself in.
"Never think you can turn over any old falsehood without a terrible squirming of the horrid little population that dwells under it." -O.W. Holmes "Truth forever on the scaffold, Wrong forever on the throne.."

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rabinoz

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Re: Perspective
« Reply #6 on: August 17, 2016, 05:36:14 AM »
Read it again, rabinoz: Dr. Rowbotham states most clearly that objects nearer the eyeline recede more quickly than those farther from it. Art school perspective makes no account of this and this is the difficulty it finds itself in.

Yes, "Dr. Rowbotham states most clearly that objects nearer the eyeline recede more quickly" but he can claim what he likes. I said that I went so far with his reasoning, then when he starts having things converge at different rates, I disagree.

I did say that I agreed with most of his part on "The Law of Perspective"
Quote
The above may be called the law of perspective. It may be given in more formal language, as the following:. when any object or any part thereof is so far removed that its greatest diameter subtends at the eye of the observer, an angle of one minute or less of a degree, it is no longer visible.
Even in this part I disagree with "it is no longer visible" and claim he should have said that two objects separated by "an angle of one minute or less of a degree" cannot be resolved into separate objects.

There are numerous cases where an object "that (at) its greatest diameter subtends at the eye of the observer, an angle of one minute or less of a degree" is quite visible! The most extreme example is stars, which are mere fractions of seconds of arc, yet are clearly visible. Any well lit white object on a black background is often visible when the apparent size is less than one minute of arc.

What we cannot do is discern as separate objects two objects separated by less than the resolution limit - there is a big difference!

"Art school perspective" is just that "Art school perspective" and any of its "Laws of Perspective" are just guides to be used in drawings.

My whole point is that the apparent size of whole object is must be reduced in proportion to its distance, in exactly the way Rowbotham showed in his Fig 73 and 74:

FIG. 73.
         

Fig. 74.
Parts thereby separated by less than the resolution limit will not be seen as separate objects.

Those diagrams are fine, but then he somehow seems to treat eye level as something special, and shows the parts of the object below eye level as being artificially truncated. He shows:

Fig. 82.
which when seen from one end is supposed to look like:

Fig. 81.
He reduces the sea-wall down to nothing, but only reduces the lighthouse by about around 50%.
All parts of a scene at the same distance should get reduced by the same amount.
The best photo I could get of Poolbeg Lighthouse was

Poolbeg Lighthouse, Dublin Bay
While I don't have a side on view, I believe it shows all parts reducing in size proportionately.

Re: Perspective
« Reply #7 on: August 17, 2016, 06:02:10 AM »
My whole point is that the apparent size of whole object is must be reduced in proportion to its distance, in exactly the way Rowbotham showed in his Fig 73 and 74:

FIG. 73.
         

Fig. 74.
Parts thereby separated by less than the resolution limit will not be seen as separate objects.

Those diagrams are fine, but then he somehow seems to treat eye level as something special, and shows the parts of the object below eye level as being artificially truncated. He shows:

Fig. 82.
which when seen from one end is supposed to look like:

Fig. 81.
He reduces the sea-wall down to nothing, but only reduces the lighthouse by about around 50%.
All parts of a scene at the same distance should get reduced by the same amount.
These images shows the biggest flaw of Rowbotham's perspective that, based on my personal obesrvation, are just repeated without questioning.

The thing with truncated parts is plain error. It seems like it causes convergence to occur at much closer distance (as I stated in OP, one could zoom in to move the convergence point/line further).

Also, Fig. 74. shows a white part that is getting smaller and smaller. Even though the white part seems to be invisible at (C), the shape doesn't get truncated and "sink" partially under the stand (object D). C and D can seem to be merging, but the shape of C must be preserved since C remains its respective position to D.

This should be even more obvious once you consider objects suspended thousands of km above the Earth (see the math from OP).

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neutrino

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Re: Perspective
« Reply #8 on: August 17, 2016, 06:50:46 AM »
Very nice. I'm amazed how much effort you invest in this. Why do you do that? The perspective law is ridiculous. Are you trying to convince those psychopaths? Are you trying to convince yourself? This 'law' is not worthy to even read. Not to mention investigate and discuss it. It's like discussing about Flat Everest. Really. have you seen it with your eyes?
FET is religion. No evidence will convince a FE-er. It would be easier to convince Muslims they are wrong.

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Ski

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Re: Perspective
« Reply #9 on: August 17, 2016, 11:25:37 AM »
Yes, "Dr. Rowbotham states most clearly that objects nearer the eyeline recede more quickly" but he can claim what he likes. I said that I went so far with his reasoning, then when he starts having things converge at different rates, I disagree.

Well, since that is the point of contention, I'd spend more time demonstrating your belief and less time laying out fundamentals on which we already agree...
"Never think you can turn over any old falsehood without a terrible squirming of the horrid little population that dwells under it." -O.W. Holmes "Truth forever on the scaffold, Wrong forever on the throne.."

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Ski

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Re: Perspective
« Reply #10 on: August 17, 2016, 11:29:20 AM »
These images shows the biggest flaw of Rowbotham's perspective that, based on my personal obesrvation, are just repeated without questioning.


Perhaps you could share something of your observation beyond  "you're wrong" so we could have something to discuss, if that were your intention. 
"Never think you can turn over any old falsehood without a terrible squirming of the horrid little population that dwells under it." -O.W. Holmes "Truth forever on the scaffold, Wrong forever on the throne.."

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zork

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Re: Perspective
« Reply #11 on: August 17, 2016, 01:50:08 PM »
1. Perspective lines converg to a point within our eye's sight of range.

  Parallel lines should converge to a point on flat surface. Somehow there is no real life demonstration about that but you can observe that parallel lines reach to the horizon and there is still space between them.
Rowbotham had bad eyesight
-
http://thulescientific.com/Lynch%20Curvature%202008.pdf - Visually discerning the curvature of the Earth
http://thulescientific.com/TurbulentShipWakes_Lynch_AO_2005.pdf - Turbulent ship wakes:further evidence that the Earth is round.

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robintex

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Re: Perspective
« Reply #12 on: August 17, 2016, 02:32:19 PM »
"Rowbotham had bad eyesight"

Ships and railway carriages were much smaller in Dr. (Doctor of Philosophy and Doctor of Medicine) Rowbotham's time. Besides, he suffered from myopia.

He also had cataracts so he only saw a blur instead of the horizon or he just did his observations during those  "pea soup fog" days or nights in foggy Olde London Towne.
« Last Edit: August 17, 2016, 03:01:49 PM by Googleotomy »
Stick close , very close , to your P.C.and never go to sea
And you all may be Rulers of The Flat Earth Society

Look out your window , see what you shall see
And you all may be Rulers of The Flat Earth Society

Chorus:
Yes ! Never, never, never,  ever go to sea !

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rabinoz

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Re: Perspective
« Reply #13 on: August 17, 2016, 07:49:14 PM »
Yes, "Dr. Rowbotham states most clearly that objects nearer the eyeline recede more quickly" but he can claim what he likes. I said that I went so far with his reasoning, then when he starts having things converge at different rates, I disagree.

Well, since that is the point of contention, I'd spend more time demonstrating your belief and less time laying out fundamentals on which we already agree...

I don't know what more I can say without simply repeating myself. I could try to list my salient points as
  • Light in the atmosphere travels in straight lines - apart from very slight refraction where there is a temperature gradient.

  • The apparent size (the angle subtended at the eye or camera) of an object and its parts is simply (relevant dimension/distance from the eye) in radians.

  • The apparent size of all parts of an object (irrespective of the closeness to the eye line) reduce at the same rate.

  • The angular resolution limit of the eye (or any optical device) is the smallest apparent angular separation for which the eye (or other device) can detect that two objects are distinct. This does not mean that the eye cannot detect objects of smaller apparent size.
    This limit for healthy well-focussed eyes in good light is accepted as being about 1 arcminute. This means that the distance limit for two objects to be able to be resolved apart is about 3,000 times the separation of the objects.
    The contention with Rowbotham to this point is that he claims that this limit "the smallest angle under which an object can be seen". I am claiming that it is "The smallest angle for which objects can be separated". There is a big difference.

  • Under favourable circumstances much smaller objects can be detected with the naked eye (or camera). The most obvious examples are stars. Even Betelgeuse, a very bright star and easily visible, has an angular size of only 50 mas (about 0.0008 arc minutes). The estimated distance (not measured) that candle could be seen on a clear night is about 2.7 km (if the flame is 1cm in diameter, that puts the angular size at about 0.013 arcminutes).
    Placing a limit of how small an object we can detect is actually very difficult. On a dark, given 100 photons of light, we would certainly see a flash.
    The reader can look this up as well as I, and it's probably not too relevant here.

As you can see, my difference with Rowbotham is with his claiming that this limit is "the smallest angle under which an object can be seen",
While I am claiming that it is "The smallest angle for which objects can be separated".

Rowbotham's claim that "objects nearer the eyeline recede more quickly" seems tied to this idea that the object disappears at its limit.

It does not disappear, we simply cannot resolve parts of objects closer than that.
For example in Fig.74 from Rowbotham:

Fig. 74.
You will note that the object has not changed shaped shape, only that the smaller part of the object is no longer separately discernable. The whole object has been reduced proportionately.

But then he shows us:

Fig. 79.
Now Rowbotham has truncated the object by merging the wheels with the ground. I would contend that, while the wheels might not be separately discernable, the rest of the loco must not be "squashed" into the ground.

Perspective simply reduces the apparent size of the whole object in proportion to the distance, when that apparent size of a part of the object gets below the limit of the eye's resolving power, that part is no longer separately disccernable. In the diagram above we have a completely unjustified distortion of the loco. A more correct diagram would be:
where the wheels don't artificially "burrow" into the ground.  Real perspective will make those smaller parts "disappear" in good time.

The crux of the whole matter is that the angular size of the whole object always reduces in proportion.

Maybe someone better at putting things on paper can translate this.




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SpJunk

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Re: Perspective
« Reply #14 on: August 17, 2016, 09:28:15 PM »
Perspective does account for the sinking ship phenomena, but is insufficient to account for the setting of the sun (though the effect can frequently be seen in evidence here, too).
You are espousing a sort of art school perspective, but that is not Dr. Rowbotham's position.

Sinking ship phenomena shows inconsistency of usage of perspective there.
Is perspective lagging? Working layer by layer, and only vertically?

"Ship sinks" because lower part of its image gets "converged" vertically to vanishing,
but the rest of the ship (vertically) is "closer and didn't converge yet".

Meanwhile, horizontally nothing converged to vanishing.
And ship is on the surface.

For Sun itself, at Flat Earth, 3000 miles of distance from surface "converge" much more than 30 miles of diameter.

We all saw top half of the Sun still visible in the middle of sunset.
Vertical diameter "converges" layer by layer from bottom, while horizontal diameter remains the same during the whole sunset.
« Last Edit: August 17, 2016, 09:34:18 PM by SpJunk »
"If the facts don't fit the theory, change the facts." - Albert Einstein

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Ski

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Re: Perspective
« Reply #15 on: August 17, 2016, 11:34:43 PM »
The wheels are nearer the eyeline and hence those lines of perspective have converged more rapidly than the part of the train that is above it (farther from the eyeline). This is why they have not decreased in size proportionately.

This is the crux of Dr. Rowbotham's perspective, and as it is somewhat abstract and difficult to convey it is frequently overlooked. It took me some time and multiple readings before the idea registered fully for me, but was quite a "eureka" moment.

I think you're playing a sort of rhetorical game with "separated", "discerned", and "seen". I'm not in disagreement with you there, and I'm not convinced Dr. Rowbotham would be either.
"Never think you can turn over any old falsehood without a terrible squirming of the horrid little population that dwells under it." -O.W. Holmes "Truth forever on the scaffold, Wrong forever on the throne.."

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zork

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Re: Perspective
« Reply #16 on: August 18, 2016, 01:38:15 AM »
The wheels are nearer the eyeline and hence those lines of perspective have converged more rapidly than the part of the train that is above it (farther from the eyeline). This is why they have not decreased in size proportionately.

  Still, why parallel lines will not converge to the point at horizon line? Ship wake is quite good demonstration for that.
Rowbotham had bad eyesight
-
http://thulescientific.com/Lynch%20Curvature%202008.pdf - Visually discerning the curvature of the Earth
http://thulescientific.com/TurbulentShipWakes_Lynch_AO_2005.pdf - Turbulent ship wakes:further evidence that the Earth is round.

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rabinoz

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Re: Perspective
« Reply #17 on: August 18, 2016, 03:23:00 AM »
The wheels are nearer the eyeline and hence those lines of perspective have converged more rapidly than the part of the train that is above it (farther from the eyeline). This is why they have not decreased in size proportionately.

This is the crux of Dr. Rowbotham's perspective, and as it is somewhat abstract and difficult to convey it is frequently overlooked. It took me some time and multiple readings before the idea registered fully for me, but was quite a "eureka" moment.

I think you're playing a sort of rhetorical game with "separated", "discerned", and "seen". I'm not in disagreement with you there, and I'm not convinced Dr. Rowbotham would be either.
There is nothing simply a "rhetorical game with 'separated', 'discerned', and 'seen'."

An group of objects smaller than the "angular resolution" of the eye might be detected,but not separated into its components.
For example the "star" we call Alpha Centauri is actually three stars, a binary pair Alpha Centauri A, Alpha Centauri B and the very small Proxima Centauri.

The binary pair has a major axis of about 0.035 arc minutes, so is well under our resolution limit. The pair of stars is quite easily  visible, but there is no possibility of separating these stars with the naked eye.
Alpha Centauri

α Centauri and β Centauri, with Proxima circled
from Wikipedia, Alpha Centauri.

Someone else can tackle the other bit, though I still maintain that the angular size of the whole object (including its parts) reduces proportionately. The hull or the wheels might end up indiscernible as separate objects, but that does not "pull" the rest of the object down.

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rabinoz

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Re: Perspective
« Reply #18 on: August 18, 2016, 03:41:41 AM »
The wheels are nearer the eyeline and hence those lines of perspective have converged more rapidly than the part of the train that is above it (farther from the eyeline). This is why they have not decreased in size proportionately.

  Still, why parallel lines will not converge to the point at horizon line? Ship wake is quite good demonstration for that.
Do you mean like this?

Ship's Wake
   

Suez Canal
   

Looking East along the "Bight"

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zork

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Re: Perspective
« Reply #19 on: August 18, 2016, 05:36:57 AM »
The wheels are nearer the eyeline and hence those lines of perspective have converged more rapidly than the part of the train that is above it (farther from the eyeline). This is why they have not decreased in size proportionately.

  Still, why parallel lines will not converge to the point at horizon line? Ship wake is quite good demonstration for that.
Do you mean like this?

Ship's Wake
   

Suez Canal
   

Looking East along the "Bight"
  Yes, like that.
Rowbotham had bad eyesight
-
http://thulescientific.com/Lynch%20Curvature%202008.pdf - Visually discerning the curvature of the Earth
http://thulescientific.com/TurbulentShipWakes_Lynch_AO_2005.pdf - Turbulent ship wakes:further evidence that the Earth is round.

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SpJunk

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Re: Perspective
« Reply #20 on: August 18, 2016, 06:57:31 AM »
The wheels are nearer the eyeline and hence those lines of perspective have converged more rapidly than the part of the train that is above it (farther from the eyeline). This is why they have not decreased in size proportionately.
...
And if I move my eye line a bit up (look higher), what happens then?
Climbing on pile of rocks behind you doesn't make you stand closer.
« Last Edit: August 18, 2016, 06:59:37 AM by SpJunk »
"If the facts don't fit the theory, change the facts." - Albert Einstein

"Your lack of simplicity is main reason why not many people would bother to try to understand you." - S.M.

Re: Perspective
« Reply #21 on: August 18, 2016, 10:58:39 AM »
The wheels are nearer the eyeline and hence those lines of perspective have converged more rapidly than the part of the train that is above it (farther from the eyeline).

This is awfully wrong.

The lines are converging to a point. They are lines, hence if you pick an object and mark few points for a reference, then these points will draw few lines when the object moves away. Lines. Also relative proportions of the object remain the same, so must relative positions of points. This implies in particular that despite different rate on which some lengths may reduce, they are decreasing at the same rate. Which then implies that what is higher above the eyeline will "converg" faster at the beginning, and then slower. What is closer, slower than what is higher.

This is why they have not decreased in size proportionately.
The shape of an object moving away from you is preserved. If what you said above was true, then the parts closer to eyeline would squizze gradually into something indistinguishable from its neighboorhoud. We don't see gradual process.

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Ski

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Re: Perspective
« Reply #22 on: August 18, 2016, 11:19:23 AM »
The shape is obviously not preserved and they do converge at different rates.  This is not demonstrated in art school perspective,  which is why we're having this discussion.
"Never think you can turn over any old falsehood without a terrible squirming of the horrid little population that dwells under it." -O.W. Holmes "Truth forever on the scaffold, Wrong forever on the throne.."

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SpJunk

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Re: Perspective
« Reply #23 on: August 18, 2016, 09:53:24 PM »
The shape is obviously not preserved and they do converge at different rates.  This is not demonstrated in art school perspective,  which is why we're having this discussion.

Because "Dr" Samuel Birley Rowbotham said so?

~~~~~

Have you ever been to Arch Cape in Oregon, at the coast of Pacific ocean.
There's nice little mountain about 3.7 miles behind, 3080 ft high (939 meters), named West Onion Peak.
It has relatively steep sides, nice to look at, or use as screen.

During sunset you can clearly see the shadow of the horizon slowly climbing uphill.
Or it is some other shadow?
Since the Sun is still 3000 miles above the Earth (and horizon) during "sunconverge", it must be shadow of something else. :-)

Of what?

If you go to Bar in Montenegro, there's also nice mountain, Rumija, (room-e-yah) even closer to sea.
You can see the same uphill crawling of the shadow of "not-a-horizon-but-something-else" on it.

If Sun simply converges, and physically doesn't get even close to
that horizon where converges, then what casts those shadows?

What would "Dr" say?
But I'd like to know what would YOU say.
« Last Edit: August 18, 2016, 10:25:41 PM by SpJunk »
"If the facts don't fit the theory, change the facts." - Albert Einstein

"Your lack of simplicity is main reason why not many people would bother to try to understand you." - S.M.

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Ski

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Re: Perspective
« Reply #24 on: August 18, 2016, 10:42:10 PM »
Perspective does account for the sinking ship phenomena, but is insufficient to account for the setting of the sun (though the effect can frequently be seen in evidence here, too).
"Never think you can turn over any old falsehood without a terrible squirming of the horrid little population that dwells under it." -O.W. Holmes "Truth forever on the scaffold, Wrong forever on the throne.."

*

SpJunk

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Re: Perspective
« Reply #25 on: August 18, 2016, 10:55:26 PM »
Perspective does account for the sinking ship phenomena, but is insufficient to account for the setting of the sun (though the effect can frequently be seen in evidence here, too).
So, what casts those shadows?
"If the facts don't fit the theory, change the facts." - Albert Einstein

"Your lack of simplicity is main reason why not many people would bother to try to understand you." - S.M.

Re: Perspective
« Reply #26 on: August 29, 2016, 04:32:16 AM »
The shape is obviously not preserved and they do converge at different rates.  This is not demonstrated in art school perspective,  which is why we're having this discussion.
Can you demonstrate the shape changes? I haven't seen a single thing in my life that would change the shape due to perspective.

Perspective does account for the sinking ship phenomena, but is insufficient to account for the setting of the sun (though the effect can frequently be seen in evidence here, too).
How are they able not to hide buildings 200m tall 25km away (125:1 proportion) but now the Sun 5000km above and up to 30000km away (6:1 proportion)?

There is still no explaination from any FE-er on the topic. Just statements without any actual detail.