Bendy Light Disproof?

This isn't the same ray of light. Obviously two different rays can and do coexist, and by applying your equation to them this is the result produced.

No. You started with assumptions about the path of light (specifically, two points that it passes through and the gradient at one of those points). You did not produce this path from the equation.

Alright I didn't mean slightly but yea, it is closer of course. The second ray is following your equation too, so there must be a flaw with it.

No, only with your understanding of it. Again, you started with an assumption that makes no sense; that the light is horizontal at the second observer. You then applied my equation to your nonsensical starting assumptions and produced nonsensical results. The flaw is in your assumptions, not the equation.

Like I said, the math doesn't even matter 100%, but I'll use it so long as you provide the equation. If I did graph a closer point this would still show up, I just chose that number.

Correct, but the fact that you chose a point so far away from the first observer makes the flaw in your reasoning readily apparent.

You have said yourself that the light would have to bend on its way back up.

Yes.

Also, we both know the equation you have presented may not be the most accurate, but it still portrays the theory.

Yes.

However, it still represents what would happen in reality.

If bendy light is true, yes.

Even if the equation were to change, this problem would still arise, due to the light still acting similarly.

As long as you continue to make baseless initial assumptions, then yes, problems will continue to arise with your conclusions.

What Parsifal is trying to get at is that if the observer of the sun is not at the day/night barrier, then the sun will not be observed to be at the horizon. Both lines on your graph would produce the illusion that the sun is on the horizon at both points, which is not observed in reality.

Parsifal, can you make a graphic of it, with two light rays in directions similar to those that bollybill used to show how they dont intersect?

Quote from: Bollybill on March 22, 2013, 08:05:03 PM

This isn't the same ray of light. Obviously two different rays can and do coexist, and by applying your equation to them this is the result produced.

Let me dumben this down for you. Gravitational acceleration in RET is (roughly) constant. If you drop two items out of your window, they should pretty much share g. If I tell you that, while remaining on Earth, I dropped one item with g=9.81ms^-2 and another item with g=60ms^-2, the problem is not that Newtonian physics suddenly stopped working. The problem is that I arbitrarily decided to fuck with a constant. That's exactly what you're doing here.

The earth's gravitational constant is well known, the value of the Bishop constant has never been stated.

No. You started with assumptions about the path of light (specifically, two points that it passes through and the gradient at one of those points). You did not produce this path from the equation.

Honest question here, how is that not from the equation? I showed my work, as you know, in the OP.

No, only with your understanding of it. Again, you started with an assumption that makes no sense; that the light is horizontal at the second observer. You then applied my equation to your nonsensical starting assumptions and produced nonsensical results. The flaw is in your assumptions, not the equation.

I never assumed the second ray is viewed as horizontal, that would be ridiculous. Although, according to this (the last picture) light would be viewed as horizontal from two separate points many miles away, although the light would have to take a left/right turn in addition to the horizontal bending. Your equation does allow for this to happen though, and that seems like a problem to me.

The earth's gravitational constant is well known, the value of the Bishop constant has never been stated.

Let's talk about an unspecified planet X, then. We know that the gravitational acceleration is still going to be a constant, but we don't know its value. However, we will never try to reason about the constant having two values at once, because that would be silly.

Quote from: Bollybill on March 23, 2013, 10:48:42 AM

The earth's gravitational constant is well known, the value of the Bishop constant has never been stated.

Let's talk about an unspecified planet X, then. We know that the gravitational constant is still going to be a constant, but we don't know its value. However, we will never try to reason about the constant having two values at once, because that would be silly.

Then which value is correct, or is constant a misnomer? Surely the creator of the equation would have given us the value.

Quote from: Bollybill on March 23, 2013, 10:48:42 AM

The earth's gravitational constant is well known, the value of the Bishop constant has never been stated.

Let's talk about an unspecified planet X, then. We know that the gravitational constant is still going to be a constant, but we don't know its value. However, we will never try to reason about the constant having two values at once, because that would be silly.

Don't confuse G with g (I know right).

G (gravitational constant)=6.67398x10^-11m^3kg^-1s^-2. This does not vary and is the constant we speak of when talking about the gravitational constant.

g (local gravitational strength)=(Gm1m2)/r^2. This varies from place to place.

Then which value is correct

Judging by the OP's methodology, it's not very likely that either of your arbitrary guesses is correct.

or is constant a misnomer?

It is not.

Surely the creator of the equation would have given us the value.

"Surely"? I've only just named a situation where it wouldn't be given. The value of the constant has not yet been measured. This is why it hasn't been provided.

Don't confuse G with g[...]

Yes. Hence the "roughly" in

Gravitational acceleration in RET is (roughly) constant.

Also, it was precisely to avoid confusion between G and g that I didn't use "G" nor "g". I referred to gravitational acceleration as "gravitational acceleration".

Quote from: Bollybill on March 23, 2013, 02:18:59 PM

Then which value is correct

Judging by the OP's methodology, it's not very likely that either of your arbitrary guesses is correct.

Quote from: Bollybill on March 23, 2013, 02:18:59 PM

or is constant a misnomer?

It is not.

Quote from: Bollybill on March 23, 2013, 02:18:59 PM

Surely the creator of the equation would have given us the value.

"Surely"? I've only just named a situation where it wouldn't be given. The value of the constant has not yet been measured. This is why it hasn't been provided.

Quote from: Rama Set on March 23, 2013, 02:20:29 PM

Don't confuse G with g[...]

Yes. Hence the "roughly" in

Quote from: PizzaPlanet on March 22, 2013, 08:11:17 PM

Gravitational acceleration in RET is (roughly) constant.

Also, it was precisely to avoid confusion between G and g that I didn't use "G" nor "g". I referred to gravitational acceleration as "gravitational acceleration".

You did not use gravitational acceleration in the Planet X example. I am glad there is no confusion.

You did not use gravitational acceleration in the Planet X example. I am glad there is no confusion.

Egg on my face. I corrected my post now.

Quote from: Rama Set on March 23, 2013, 04:38:43 PM

You did not use gravitational acceleration in the Planet X example. I am glad there is no confusion.

Egg on my face. I corrected my post now.

Fair enough. No egg required. Glad it's cleared up.

Quote from: RealScientist on March 22, 2013, 09:10:37 AM

Axioms exist in Mathematics, not in Science.

Incorrect. From Wiktionary:

"An established principle in some artistic practice or science that is universally received."

So, the third definition in Wiktionary is the best you can do? Can't you even get a real scientist to define what an axiom is for the world of science?

But, even if we accept that there are some scientists who think that axioms are theoretically applicable to science, (and that is a huge if) you will never find a single scientific organization of any importance that postulates a single claim as an axiom. No respectable scientist in any field of science has ever, to my knowledge, claimed that there is a higher grade of scientifically accepted knowledge than the theory.

And now, if we want to say that the Bishop constant is even related to some kind of axiom, we cannot even make that relationship with the definition in Wiktionary. There is no universal reception of the idea of a flat Earth. Even in the community of flat Earthers (all ten of them) there is no universal reception of the idea of bendy light. And even among the three or so members who accept the existence of bendy light there is no universal reception of a single thing about the Bishop Constant, except for its existence. So, if "Universally received" means three people, then it is an axiom of human society that I should be "King of Humanity and All the Lower Species".

Quote

No. You started with assumptions about the path of light (specifically, two points that it passes through and the gradient at one of those points). You did not produce this path from the equation.

Honest question here, how is that not from the equation? I showed my work, as you know, in the OP.

You used the equation to fill in intermediate points in the path. The path is not fully derivated from the equation because you started with assumptions that the equation does not provide.

I never assumed the second ray is viewed as horizontal, that would be ridiculous.

Then why is the second ray assumed to be horizontal at ground level in your working in the OP?

Although, according to this (the last picture) light would be viewed as horizontal from two separate points many miles away

Yes, at sunrise and sunset, which would be on opposite sides of the Sun.

Your equation does allow for this to happen though, and that seems like a problem to me.

It only allows for this to happen if you disregard the fact that the Bishop constant is a constant. Your scenario is impossible precisely because the Bishop constant is a constant.

So, the third definition in Wiktionary is the best you can do? Can't you even get a real scientist to define what an axiom is for the world of science?

But, even if we accept that there are some scientists who think that axioms are theoretically applicable to science, (and that is a huge if) you will never find a single scientific organization of any importance that postulates a single claim as an axiom. No respectable scientist in any field of science has ever, to my knowledge, claimed that there is a higher grade of scientifically accepted knowledge than the theory.

No.

And even among the three or so members who accept the existence of bendy light there is no universal reception of a single thing about the Bishop Constant, except for its existence.

Since it is defined as a constant, accepting its existence is to accept that it is a constant. If it were not constant, then the Bishop constant would not exist, because it would not be constant.

So, if "Universally received" means three people, then it is an axiom of human society that I should be "King of Humanity and All the Lower Species".

"Universally received" within a domain means that it is universally received within that domain. If your domain is "bendy light theory", then the requirement is that it be universally received within the domain of bendy light theory. If your domain is "human society", then the requirement is that it be universally received within all of human society.

This is the debate section of the forum. In order to produce meaningful debate, there is an expectation that you have some basic working knowledge of fundamental concepts, such as definitions of words. I will not be providing any more explanations of simple concepts for your benefit; if you would like clarification on such things, please use a more appropriate forum to request information.

Quote from: Bollybill on March 23, 2013, 10:59:32 AM

Your equation does allow for this to happen though, and that seems like a problem to me.

It only allows for this to happen if you disregard the fact that the Bishop constant is a constant. Your scenario is impossible precisely because the Bishop constant is a constant.

If the Bishop constant is constant - and I also don't understand why the OP doesn't keep it as such - rays emitted from the sun indeed wouldn't cross. That was not clear to me in my previous post.

Quote from: RealScientist on March 23, 2013, 07:17:58 PM

So, if "Universally received" means three people, then it is an axiom of human society that I should be "King of Humanity and All the Lower Species".

"Universally received" within a domain means that it is universally received within that domain. If your domain is "bendy light theory", then the requirement is that it be universally received within the domain of bendy light theory. If your domain is "human society", then the requirement is that it be universally received within all of human society.

This is the debate section of the forum. In order to produce meaningful debate, there is an expectation that you have some basic working knowledge of fundamental concepts, such as definitions of words. I will not be providing any more explanations of simple concepts for your benefit; if you would like clarification on such things, please use a more appropriate forum to request information.

Then, by Parsifal's definition, every claim ever made is an axiom because it is held true among those who hold it true. Nothing else can be said about Parsifal's understanding of axioms. No, you do not get to define the domain for your axiom anyway you like. The domain is all people who show any interest at all in the subject.

But wait a minute. "universally received" in the context of this discussion would, at the very least, include the three FE believers who hold bendy light true and Bollybill, who even calculated the value of the constant, only to find at least two values for it. Therefore among the four of you who are interested in the Bishop Constant there are only 3/4 who still accept it as a constant. "Universally received" does no longer apply to this "axiom".

The word "axiom" refers to a lot more than what Parsifal wants it to refer. So much so that in Science nothing is held as an axiom.

Quote from: Parsifal on March 24, 2013, 03:58:26 AM

Quote from: Bollybill on March 23, 2013, 10:59:32 AM

Your equation does allow for this to happen though, and that seems like a problem to me.

It only allows for this to happen if you disregard the fact that the Bishop constant is a constant. Your scenario is impossible precisely because the Bishop constant is a constant.

If the Bishop constant is constant - and I also don't understand why the OP doesn't keep it as such - rays emitted from the sun indeed wouldn't cross. That was not clear to me in my previous post.

The problem is that you have several constraints on the problem you are trying to solve. The "constant" must be always constant, the observed apparent position of the Sun must match the value that comes from the formula, the height of the Sun above the flat Earth must remain constant, among other things.

You can set any group of constraints except one and find if that one holds. For example, you can set all the other constraints except for the one about the height of the Sun, and check whether the calculated height is always 3000 miles. Or, as Bollybill did, you can set all the constraints except for the one about the Bishop Constant, and check whether the supposed constant varies.

The fact that the supposed "constant" varies does not mean that Bollybill varied it on purpose. It means that in a wrong model at least one assumption always fails.

Quote from: Parsifal on March 24, 2013, 03:58:26 AM

Quote from: Bollybill on March 23, 2013, 10:59:32 AM

Your equation does allow for this to happen though, and that seems like a problem to me.

It only allows for this to happen if you disregard the fact that the Bishop constant is a constant. Your scenario is impossible precisely because the Bishop constant is a constant.

If the Bishop constant is constant - and I also don't understand why the OP doesn't keep it as such - rays emitted from the sun indeed wouldn't cross. That was not clear to me in my previous post.

That's the point, it can't be a constant. I would upload a picture to explain it but for some reason I'm having trouble. Try going to this website and put in these two lines (you will need to zoom out):
(.75)((369902/186000^2)*x^4)^(1/3)
(.75)((369902/186000^2)*(x-1838)^4)^(1/3)
They are the same as in my first picture, but in the second I used the  Bishop Constant from the first equation, like people have suggested. When they are plotted, you will see that not only do the two lines cross, but there is no origin from where the two lines come from (the sun at ~ (9,000, 3,000)). This is only true if the 'constant' does indeed change like in the OP.

You used the equation to fill in intermediate points in the path. The path is not fully derivated from the equation because you started with assumptions that the equation does not provide.

That's my point, this does not happen yet the equation makes it look like it would.

Yes, at sunrise and sunset, which would be on opposite sides of the Sun.

No, I'm talking about the same side.

It only allows for this to happen if you disregard the fact that the Bishop constant is a constant. Your scenario is impossible precisely because the Bishop constant is a constant.

Then what is the value of this constant? Also, what is the constant even measuring?



Edit: Does anyone know the distance from the person just starting to see the light be horizontal (sunset) to the person where it is ending? Oddly phrased lol...

That's the point, it can't be a constant. I would upload a picture to explain it but for some reason I'm having trouble. Try going to this website and put in these two lines (you will need to zoom out):
(.75)((369902/186000^2)*x^4)^(1/3)
(.75)((369902/186000^2)*(x-1838)^4)^(1/3)
They are the same as in my first picture, but in the second I used the  Bishop Constant from the first equation, like people have suggested. When they are plotted, you will see that not only do the two lines cross, but there is no origin from where the two lines come from (the sun at ~ (9,000, 3,000)). This is only true if the constant does indeed change like in the OP.

So what you're saying is that you've created a new ray of light that for some inexplicable reason doesn't come from the Sun, and this disproves bendy light?

I've just disproven RET. Check out the blue ray in this diagram, it doesn't even come from the Sun:



Clearly light can't travel in straight lines, since this doesn't happen.

Quote

You used the equation to fill in intermediate points in the path. The path is not fully derivated from the equation because you started with assumptions that the equation does not provide.

That's my point, this does not happen yet the equation makes it look like it would.

No, your initial assumptions are what produces the nonsensical results. How many times do I need to spell this out?

Quote

Yes, at sunrise and sunset, which would be on opposite sides of the Sun.

No, I'm talking about the same side.

Well, there is actually a continuous circle around the Sun at which it appears to be on the horizon. However, the two points in your graph are not equidistant from the Sun.

Then what is the value of this constant?

Unknown.

Also, what is the constant even measuring?

Its physical interpretation is described on the wiki.

Quote from: Bollybill on March 24, 2013, 07:49:10 AM

That's the point, it can't be a constant. I would upload a picture to explain it but for some reason I'm having trouble. Try going to this website and put in these two lines (you will need to zoom out):
(.75)((369902/186000^2)*x^4)^(1/3)
(.75)((369902/186000^2)*(x-1838)^4)^(1/3)
They are the same as in my first picture, but in the second I used the  Bishop Constant from the first equation, like people have suggested. When they are plotted, you will see that not only do the two lines cross, but there is no origin from where the two lines come from (the sun at ~ (9,000, 3,000)). This is only true if the constant does indeed change like in the OP.

So what you're saying is that you've created a new ray of light that for some inexplicable reason doesn't come from the Sun, and this disproves bendy light?

I've just disproven RET. Check out the blue ray in this diagram, it doesn't even come from the Sun:



Clearly light can't travel in straight lines, since this doesn't happen.

Lol, the ray of light is supposed to come from the same source, it's a ray of sunlight. It doesn't disprove bendy light or the equation, just that the Bishop Constant is not a constant.

Lol, the ray of light is supposed to come from the same source, it's a ray of sunlight. It doesn't disprove bendy light or the equation, just that the Bishop Constant is not a constant.

No, the only thing it proves is that your understanding of bendy light is flawed. You are making the following assumptions which are not directly imposed by bendy light theory or the equation in the wiki (note: I've helpfully filled in the units you forgot to include in your calculations):

• There exists a ray of light which, for a given co-ordinate system in miles:
• passes through the point (0,0); and
  
• has a gradient of 0 at x = 0.
  
• There exists a second ray of light which, for a given co-ordinate system in miles:
• passes through the point (1838,0); and
  
• has a gradient of 0 at x = 1838;
  
• The Bishop constant has a value of 369902 mi s^-2.
  
• The Sun has an altitude of 3000 mi.
  

You then correctly observe that there is no point at which these lines cross where y = 3000. The error you make is to conclude that the Bishop constant is not a constant, rather than considering that one of your other assumptions may be flawed (hint: removing any of your three other assumptions also produces consistent results).

Quote from: Bollybill on March 24, 2013, 07:56:38 AM

Quote

You used the equation to fill in intermediate points in the path. The path is not fully derivated from the equation because you started with assumptions that the equation does not provide.

That's my point, this does not happen yet the equation makes it look like it would.

No, your initial assumptions are what produces the nonsensical results. How many times do I need to spell this out?

If you do not like BollyBill's assumptions, then why don't you give yours? The very assumption that a cubic formula, of which the Bishop Constant is just the constant of the cubic part, is, as far as I know, nonsensical. And you have not given even a single argument to the contrary.

If you want to even claim some kind of sense in the cubic formula with the Bishop constant then you have to show it yourself.

Quote from: Homesick Martian on March 24, 2013, 06:57:41 AM

Quote from: Parsifal on March 24, 2013, 03:58:26 AM

Quote from: Bollybill on March 23, 2013, 10:59:32 AM

Your equation does allow for this to happen though, and that seems like a problem to me.

It only allows for this to happen if you disregard the fact that the Bishop constant is a constant. Your scenario is impossible precisely because the Bishop constant is a constant.

If the Bishop constant is constant - and I also don't understand why the OP doesn't keep it as such - rays emitted from the sun indeed wouldn't cross. That was not clear to me in my previous post.

That's the point, it can't be a constant. I would upload a picture to explain it but for some reason I'm having trouble. Try going to this website and put in these two lines (you will need to zoom out):
(.75)((369902/186000^2)*x^4)^(1/3)
(.75)((369902/186000^2)*(x-1838)^4)^(1/3)
They are the same as in my first picture, but in the second I used the  Bishop Constant from the first equation, like people have suggested. When they are plotted, you will see that not only do the two lines cross, but there is no origin from where the two lines come from (the sun at ~ (9,000, 3,000)). This is only true if the 'constant' does indeed change like in the OP.

Thank you! Now I understand the problem. I should refrain from making statements, when they are only out of intuition, for I know from experience that my intuition often prooves wrong, especially in things like that.  You cleared that up for me.

OK. The rays are bound to cross, because the function has a minimal point. So if we apply that to a life flat earth scenario, there is a point on the light ray where the ray curves upwards again. Right? But where is this point? Is it above ground? Directly on the ground? Or below the ground? For if it is below ground rays will get absorbed before getting the chance to curve upwards, consequently the Bollybill effect wouldn't happen.

Quote from: Bollybill on March 24, 2013, 07:49:10 AM

Quote from: Homesick Martian on March 24, 2013, 06:57:41 AM

Quote from: Parsifal on March 24, 2013, 03:58:26 AM

Quote from: Bollybill on March 23, 2013, 10:59:32 AM

Your equation does allow for this to happen though, and that seems like a problem to me.

It only allows for this to happen if you disregard the fact that the Bishop constant is a constant. Your scenario is impossible precisely because the Bishop constant is a constant.

If the Bishop constant is constant - and I also don't understand why the OP doesn't keep it as such - rays emitted from the sun indeed wouldn't cross. That was not clear to me in my previous post.

That's the point, it can't be a constant. I would upload a picture to explain it but for some reason I'm having trouble. Try going to this website and put in these two lines (you will need to zoom out):
(.75)((369902/186000^2)*x^4)^(1/3)
(.75)((369902/186000^2)*(x-1838)^4)^(1/3)
They are the same as in my first picture, but in the second I used the  Bishop Constant from the first equation, like people have suggested. When they are plotted, you will see that not only do the two lines cross, but there is no origin from where the two lines come from (the sun at ~ (9,000, 3,000)). This is only true if the 'constant' does indeed change like in the OP.

Thank you! Now I understand the problem. I should refrain from making statements, when they are only out of intuition, for I know from experience that my intuition often prooves wrong, especially in things like that.  You cleared that up for me.

OK. The rays are bound to cross, because the function has a minimal point. So if we apply that to a life flat earth scenario, there is a point on the light ray where the ray curves upwards again. Right? But where is this point? Is it above ground? Directly on the ground? Or below the ground? For if it is below ground rays will get absorbed before getting the chance to curve upwards, consequently the Bollybill effect wouldn't happen.

Perhaps in a sufficiently deep chasm?

OK. The rays are bound to cross, because the function has a minimal point. So if we apply that to a life flat earth scenario, there is a point on the light ray where the ray curves upwards again. Right? But where is this point? Is it above ground? Directly on the ground? Or below the ground? For if it is below ground rays will get absorbed before getting the chance to curve upwards, consequently the Bollybill effect wouldn't happen.

If the light curves away above the ground, we'd never see it. If it curves at the ground, we get the Bollybill Effect. If it does not curve above or at the ground, it hits the ground while traveling relatively straight, like rays of sunlight would without the bendy light effect. At least, that's how it looks to me.

Quote from: Homesick Martian on March 24, 2013, 11:38:15 AM

OK. The rays are bound to cross, because the function has a minimal point. So if we apply that to a life flat earth scenario, there is a point on the light ray where the ray curves upwards again. Right? But where is this point? Is it above ground? Directly on the ground? Or below the ground? For if it is below ground rays will get absorbed before getting the chance to curve upwards, consequently the Bollybill effect wouldn't happen.

If the light curves away above the ground, we'd never see it. If it curves at the ground, we get the Bollybill Effect. If it does not curve above or at the ground, it hits the ground while traveling relatively straight, like rays of sunlight would without the bendy light effect. At least, that's how it looks to me.

Did you now repeat what I said or did you correct me?

Quote from: Scintific Method on March 25, 2013, 03:20:17 AM

Quote from: Homesick Martian on March 24, 2013, 11:38:15 AM

OK. The rays are bound to cross, because the function has a minimal point. So if we apply that to a life flat earth scenario, there is a point on the light ray where the ray curves upwards again. Right? But where is this point? Is it above ground? Directly on the ground? Or below the ground? For if it is below ground rays will get absorbed before getting the chance to curve upwards, consequently the Bollybill effect wouldn't happen.

If the light curves away above the ground, we'd never see it. If it curves at the ground, we get the Bollybill Effect. If it does not curve above or at the ground, it hits the ground while traveling relatively straight, like rays of sunlight would without the bendy light effect. At least, that's how it looks to me.

Did you now repeat what I said or did you correct me?

Pretty much said the same thing in a different way. Also, expanded just slightly on what would happen in the three scenarios.

Quote from: Homesick Martian on March 24, 2013, 11:38:15 AM

Quote from: Bollybill on March 24, 2013, 07:49:10 AM

Quote from: Homesick Martian on March 24, 2013, 06:57:41 AM

Quote from: Parsifal on March 24, 2013, 03:58:26 AM

Quote from: Bollybill on March 23, 2013, 10:59:32 AM

Your equation does allow for this to happen though, and that seems like a problem to me.

It only allows for this to happen if you disregard the fact that the Bishop constant is a constant. Your scenario is impossible precisely because the Bishop constant is a constant.

If the Bishop constant is constant - and I also don't understand why the OP doesn't keep it as such - rays emitted from the sun indeed wouldn't cross. That was not clear to me in my previous post.

That's the point, it can't be a constant. I would upload a picture to explain it but for some reason I'm having trouble. Try going to this website and put in these two lines (you will need to zoom out):
(.75)((369902/186000^2)*x^4)^(1/3)
(.75)((369902/186000^2)*(x-1838)^4)^(1/3)
They are the same as in my first picture, but in the second I used the  Bishop Constant from the first equation, like people have suggested. When they are plotted, you will see that not only do the two lines cross, but there is no origin from where the two lines come from (the sun at ~ (9,000, 3,000)). This is only true if the 'constant' does indeed change like in the OP.

Thank you! Now I understand the problem. I should refrain from making statements, when they are only out of intuition, for I know from experience that my intuition often prooves wrong, especially in things like that.  You cleared that up for me.

OK. The rays are bound to cross, because the function has a minimal point. So if we apply that to a life flat earth scenario, there is a point on the light ray where the ray curves upwards again. Right? But where is this point? Is it above ground? Directly on the ground? Or below the ground? For if it is below ground rays will get absorbed before getting the chance to curve upwards, consequently the Bollybill effect wouldn't happen.

Perhaps in a sufficiently deep chasm?

Certainly not! For then the bending rate of the rays at ground level would be too low and we had no sunsets.