Here is the SDSU link for Looming
https://aty.sdsu.edu/mirages/mirsims...oom.html#LandS

From the Link:
----------------
Here are some simulations of terrestrial refraction phenomena that do not involve mirages. The four types named in the title all involve refraction anomalies, but without inverted or multiple images — and therefore without mirages.
================

Note that looming is not a mirage type phenomenon. Looming refers to when you have an object beyond the apparent horizon so that the bottom of the object is obstructed according to how far it is from the apparent horizon. Looming makes more of the bottom of the object visible than you would normally expect from the object's distance to the apparent horizon.

There's nothing about the Looming phenomenon that says the formula I used above for calculating distance from observer to apparent horizon does not still hold for curvatures of light between 1/2 Earth's curvature and just less than 1xEarth's curvature. So my calculation for light curvature of 80/81 of Earth's giving 9x distance of geometric horizon is valid. Furthermore, the discussion on the SDSU website shows such refraction is certainly possible, especially over the ocean and near shore.

I think it's pretty clear that Billy's representations of refraction are not trustworthy.


PairTheBoard

You evidently don't understand mathematics. It's the difference in curvatures between Earth's curvature and the curvature of light due to refraction that matters. R' is simply a mathematical device which represents the radius that would be required of a theoretical ball whose curvature matched that difference in curvatures. If the difference in curvatures is small, i.e. the curvature of refracted light is close to Earth's curvature, then the mathematical term R' is large. You are ridiculing a mathematical term in a calculation.


I don't know what your problem is but I don't think it's one that can be fixed on this forum.


PairTheBoard

Is the double horizon the same as the bottom of the marine layer or were those different things?

Your argument is insane. It is precisely obviously manifestly a begging the question fallacy. You are looking at a horizon at distance x where x can approach infinity and then deciding what radius earth has to appear be to create the effect of a geometric sphere edge horizon appearing at this position, then working backwards to make the calculation fit that reduces down to a radius of 3959 miles always, regardless of the observed distance.

The desired conclusion being earth radius 3959 miles and the entire set up working towards this outcome.

The refraction coefficient is entirely arbitrary, based not on the specific atmospheric features you claim it to be based on but by the necessity of a sphere edge at fixed distance and a horizon at variable distance. There is literally no distance the horizon can be at for the sphere model not to be claimed, you ipso facto have no sphere geometry beyond that in the sphere model. PTB just did this right here, he literally chose a refraction coefficient to give earth a radius that would create a 9 mile horizon. It is more than 9 miles. No problem, we will just increase earth radius even more to make it fit the observation. What's that? Perspective means we can't see past a certain point? Forget that, we are assuming a spherical earth here and then making stuff up to justify it! Such as - there is really no horizon! This is in the realm beyond fantasy, beyond ludicrous absurdity. Train wreck.

You have no mechanism for the effect in any case, looming and any other types of refraction apply to objects such as being made to appear higher ABOVE a horizon, not making the horizon itself appear behind and higher up than an object.

Your geometric horizon is that which is necessitated by a sphere edge being mathematically modelled at a fixed distance depending on observer height and earth radius, 3959 miles (varying according to oblate spheroidness but whatever).

Your observed horizon is this same geometric edge that appears to be shifted to various distances because the light from the ground has a bent trajectory according to temperatures and air moisture.

This is why you are now unofficially arguing for flat earth. Your sphere geometry cannot be observed.

So absolutely nothing to do with my argument or the oil rigs video then.

What it actually says is

Not 80/81 then is it.

See begging the question fallacy as explained clearly to BeaucoupFish.

Obfuscation and ad hominem attack reflective of you having lost the argument. Your ball cannot deviate from its 3959 mile radius or your entire religion crumbles. So obviously you will not be claiming earth radius can be bigger than this. Yet if you want to have it that

Then you must have an effective radius that is infinitely large ie a flat plane. It is how you as a glober reconcile your Fundamentalist religious belief in a sphere with observations that clearly show a flat plane.

I haven't made an argument. All I've done is apply the math from the SDSU link to show that a curvature of light from refraction that's 80/81 the curvature of Earth (assuming the round Earth) produces an apparent horizon 9 times further than the geometric horizon.

Making an assumption for the sake of argument is not "begging the question". Billy claims his video is a black swan which can't be explained under the assumption of a round earth. My calculation proves that under the assumption of a round earth the video can be explained. What Billy red-lines as the apparent horizon could be the apparent horizon at such a distance due to refraction with large light curvature such as 80/81 that of Earth's curvature. I'm not claiming that's actually the case. I'm arguing that could be the case. Therefore, Billy's video is not a black swan that disproves a round Earth.

Aaron, BeaucoupFish, and others may have other ideas for what's going on with the video. It may be more complicated. Or it may be much simpler, like a much higher elevation for the observer than is reported.

If flat earthers really wanted to produce more serious evidence based on this video they should go to that location and repeat the identical filming every week for a year with documentation for observer height. If the effect is due to unusually high refraction then it should vary significantly week by week according to atmospheric conditions. But I doubt they will do this. They know they can't really produce serious evidence disproving the round Earth.


PairTheBoard

No. Refraction allows you to actually see further. The apparent horizon due to refraction is actually further away than the geometric horizon.


PairTheBoard

You've reached a truly astounding level of the ridiculous.


PairTheBoard

Nothing you brought up after "you are..." includes a thing I've said. Why tf are you talking to me about refraction coefficients as if I brought it up?! Who are you even arguing against?!

All I showed in my comment was how your modus tollens was unsound and invalid.

Nothing you have said to me since has been a defense of that. Increasing observer height / refraction coefficients / missing perspective - none of these are parts of your modus tollens claim.




Here's another direct question that you didn't answer:

There are varying degrees of absurdity from all of you, that is true. To state it isn't begging the question to make an assumption for the sake of argument is at the more absurd end of what is being said here. You have assumed earth radius 3959 miles and worked the calculation to justify this conclusion while reconciling the horizon being 10+ miles away. Precisely begging the question. To claim this is not a black swan assumes that your potentiality for the image being justified on a 3959 mile radius globe is actually based on a sound argument. It is not.

To be clear, no reference I have seen states the horizon can be manipulated in the way it is claimed to be here in the oil rigs video, ie being sent behind the images. What the references state is that refraction affects IMAGES OF OBJECTS including making them appear ABOVE the horizon, or making them rise from below the horizon. It is to explain how an image can be observed at or above the horizon, it does not apply to the black swan situation which is the position of the horizon itself. This is somehow completely ignored yet it is what is stated plainly in the wiki from me and in your reference:

Somehow this simple statement that has NOTHING to do with the black swan has been bypassed in favour of an entirely different concept which is that of an effective flattening of the entire scene thereby destroying sphere geometry.

To summarise as succinctly as possible:

If the logical statement not q (horizon not at 1.22 miles) therefore not p (not a globe radius 3959 miles) is accepted then the globe is debunked. If it is rejected then there is no observable sphere geometry. Which is quite a statement - there can never be observable proof of a globe earth. The mechanism for this claimed effect is not cited here in these pages and as far as I am aware no such mechanism exists:

https://en.m.wikipedia.org/wiki/Atmospheric_refraction

https://aty.sdsu.edu/glossary.html#looming

What we actually have in the black swan argument is nothing to do with the above. Refraction effects apply to objects around the horizon, not to the horizon itself.

If the apparent horizon is 10 miles away because of high curvature of light due to refraction, why wouldn't you see the oil rigs in front of that apparent horizon? You really have no idea what you're talking about do you?

Do you agree or disagree with this statement. "If the apparent horizon is 10 miles away that means you can see everything up to 10 miles, given visibility."


PairTheBoard

Billy is claiming that refraction never moves the horizon, only objects. So there is no such thing as an "apparent horizon" in his book.

He applied the same formula I used to calculate distance to the apparent horizon in the case the curvature of light due to refraction was 1/2 that of Earth's curvature. He accepted my correction to his botched calculation to conclude in this case the apparent horizon is sqr(2) times further than the geometric horizon, for the height of the observer. He thinks the fact that looming can occur at that refraction coefficient means the formula is invalid for light curvature greater than 1/2 up to just less than full Earth curvature. However, he has no reference for that. In fact, other discussion on the SDSU link indicates the formula does hold for those larger curvatures of light. And such levels of refraction do occur, especially over the ocean and near shore.


PairTheBoard

Ha, what a faux pas. You don't realise the term "apparent" in "apparent horizon" is redundant do you?

By definition, it's apparent.

Another acknowledgement there is no geometric horizon, keep em coming.

Just tell me again, you claim you are not begging the question correct? And then give me the formula you used to calculate the distance to what you are calling the "apparent horizon" please.

The answer to your question is here:

here:

here:

and here:

https://en.m.wikipedia.org/wiki/Atmospheric_refraction
https://aty.sdsu.edu/glossary.html#looming

Nothing here about the horizon being refracted is there? Now give me your citation that says the horizon is refracted.

You say "high curvature of light due to refraction". Curvature? What would it be curving around exactly? That would be a presupposed sphere correct? Do you still claim you are not begging the question?

You use earth radius in the refraction calculation. The radius of a geometric sphere. Which you then piss all over by asserting an "apparent horizon" not a geometric one - you don't have sphere geometry.

I would not put my name to such a badly worded statement. Let me rephrase for you:

"If the horizon is 10 miles away that means you can see everything up to 10 miles, given visibility."

Refraction is used in this context to allow for objects to be seen that would otherwise be behind the curve. That is all. Such as this



The idea the mountain can be brought in front of the horizon line is just beyond absurd. It just appears higher up above the horizon which stays where it is. The calculation simply increases the distance to the presupposed ball earth horizon because otherwise how the heck will the mountain be observed unless the horizon distance is increased. This is the crux of all this obfuscation - there was never a geometric horizon beyond that predicted by a radius 3959 miles as is asserted by flat earthers. Now the globers are in agreement. the horizon is apparent.

And bear in mind this is me jumping into their begging the question fallacy to expose how they cannot use this refraction get out clause. They are really shafted with this. The horizon being sent back beyond the objects as in the black swan is completely unsupported anywhere.

This is irrelevant to what luckbox said. He said Billy is claiming refraction does not move the horizon, only objects. Now find the citation that actually says the horizon is refracted or moved back beyond objects or objects moved in front.

https://aty.sdsu.edu/explain/atmos_refr/horizon.html

Read the link and study the diagram in the section "Refraction, considered simply".


You really don't know what you're talking about do you? The apparent horizon can be further than sqr(2) times distance to geometric horizon for higher rates of light curvature than 1/2 that of Earth's curvature. Looming refers to seeing more of the bottom of tall objects which are behind the apparent horizon. Looming is not relevant to seeing everything in front of the apparent horizon.

You didn't answer my question. Do you agree or disagree with the following? "If the apparent horizon is 10 miles away, that means you can see everything up to 10 miles, given visibility."


PairTheBoard

The point of this quote from the link ...
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"In conditions that produce superior mirages, there are inversion layers in which the ray curvature exceeds that of the Earth. Then, in principle, you can see infinitely far — there really is no horizon. "
===========

is to show that ray curvature greater than 1/2 that of the Earth happens. In fact, ray curvature sometimes exceeds that of the Earth under conditions that produce superior mirages. This also implies that short of exceeding Earth curvature the distance to the apparent horizon can get arbitrarily large, just as application of the formula in my last post calculates.


PairTheBoard

Not exactly a citation but anyway

So we have something resembling a citation to support the idea of the horizon being refracted. Does it make sense though? The position H identified on the diagram is a position on a presupposed sphere. This is therefore an actual position on a sphere but with light from it following a bent trajectory around the presupposed earth curvature "that lets us see a little further" they say. But wait, they call this the "apparent horizon" which they define as

Except they have identified this as an actual location on a presupposed sphere. So it is not apparent at all. It is an actual geometric position on an actual geometric spheroidy thingy. But they have just destroyed the geometry with this increased distance to the horizon which does not use earth radius but assumes an increased earth radius and which is now not geometric at all, but apparent. So no, it does not make sense at all.

Well the "real one" I take issue with being a flat earther but OK, how much bigger?

Wait a minute scallywags I have already done this calc and it gives a horizon distance less than 4 miles from observer height of 6 feet. No help for PTB here friends.

"earths curvature" is based on earth radius. Are you sure you ain't beggin no question?

So you claim refraction can produce the effect of

For which you say looming is not relevant. That's fine. Now we just need that citation that refraction effects can include

Where the distance to the horizon is predicted in the earth curve calculator as being in front of "everything".

Atmospheric refraction effects include

- wiki

Is "Images of distant objects" the same thing or inclusive of "the apparent line that separates earth from sky"? Therefore atmospheric refraction cannot be applied to the horizon.

What about terrestrial refraction:

- wiki

Hmm, sounds rather like looming which is

- https://aty.sdsu.edu/glossary.html#looming

But since looming is "not relevant" we shall ignore.

So, you have a calculation that does not work to produce a distance to the horizon that is anything like the distance observed in reality - that is in any case based on fallacious reasoning - that produces an apparent horizon that is in fact a claimed geometric horizon based on a geometric calculation that on application destroys the very geometry it is based on, that is itself based on an effect that cannot move the horizon anywhere only images of objects up and down relative to the horizon.

I actually did but anyway, no I don't agree with it because it is sloppily worded. I would not put the name of William Shepherd to this offence to the Queen's English. My statement is

"If the horizon is 10 miles away, that means you can see everything up to 10 miles, given visibility."

He said it again

You really can see your own backside.

From geometric to apparent to none at all. The end.

I think the "no horizon at all" (even assuming all the math checks out) is only theoretical and there haven't been any documented instances of people actually being able to see around the earth. But it does seem clear that you'll need to move onto another facet as your "black swan" has been shot down.

Or it would be that horizontal line that clearly cuts across the rectangular-shaped thing in the middle marking the horizon, followed by another cut off image further "up."

Then you don't understand the argument. Maybe because of the obfuscation from the Fundamentalists such is the power of this argument they are scared of. Or maybe you just haven't got your head around it or maybe you also fear the ramifications that you are willfully misunderstanding this.

Firstly to state the horizon is apparent which the globers are now asserting is a de facto acceptance that there is no observable geometric sphere edge. Therefore no geometric calculation can be applied. The globe model is imaginary, it cannot represent real observations. I can stop here, this kills the whole thing.

The refraction argument is really quite simple. An object is observed above the horizon such as



To account for why this is observed above the horizon instead of being behind the curve, the radius of earth is increased to a bigger, effective radius. By necessity this has to increase the "distance to the horizon" which is bigger than a direct line would be to the actual sphere edge, hence they call this the "apparent horizon" because it does not match that necessitated by the geometry. What this clown PTB has done is to then reify this calculation into reality and claim everything now appears in front of this imaginary number. This is not what we see. The Sun, or whatever we are observing, just appears higher.

What makes you the arbiter of this debate and when it should be moved on? What shape is the earth, globe, flat, concave, something else?