[Tom Bishop]

How about answer how celestial navigation can be used to get a fix?

The method used predicts what angle certain stars should appear to an observer at a location at a certain time. 

This is  real world application that was and is(much rarely now) with accurate and reliable results.  This suggest that the math you say fails at those distances does work at them.

If celestial navigation works what changes when predicting what angle the Sun should appear to a person?

I would prefer to keep these threads on topic.

[Tom Bishop]

No, it does not. It predicts that two objects that are not touching will always have a non-zero angular diameter between them. It does not predict anything to be at infinity.

It predicts that the objects will continue to forever approach the horizon, but never touch it.

If the sun seems to touch the horizon then it does.
If an object seems to be hidden behind the horizon then it is.

Am I determining the truth correctly now?

Sure, reality is always a good barometer of truth. The train tracks meet on the horizon due to perspective, so it makes sense that the sun can meet the horizon due to perspective as well. Also, as I mentioned on page 1, it is part of Earth Not a Globe that the sinking effect is explained by hiding behind things on the horizon. So far, so good.

If two train tracks are laid out in front of you at an angle pointing towards each other, then obviously, two lines oriented in that position that will intersect at some point. Only parallel lines can continue into infinity and never intersect.

Yes, we agree on this. Parallel lines never intersect. Brilliant deduction Sherlock.

The type of math you are using says that the train tracks should approach each other but NEVER meet.

But from what we see and experience the tracks are angled toward each other in a way that they MUST meet.

So what's right? Are our experiences correct, or is a theoretical calculation which takes place outside of the universe and is missing a dimension correct?

[TotesNotReptilian]

If two train tracks are laid out in front of you at an angle pointing towards each other, then obviously, two lines oriented in that position that will intersect at some point. Only parallel lines can continue into infinity and never intersect.

Yes, we agree on this. Parallel lines never intersect. Brilliant deduction Sherlock.

The type of math you are using says that the train tracks should approach each other but NEVER meet.

But from what we see and experience the tracks are angled toward each other in a way that they MUST meet.

So what's right? Are our experiences correct, or is a theoretical calculation which takes place outside of the universe and is missing a dimension correct?

We have been through this already. Stop arguing in a circle.

Yes, parallel lines are angled towards each other from our perspective.
No, they will never actually meet each other.
Yes, it appears that they meet each other because the angle between them becomes too small for our eyes to distinguish. Using a telescope can extend the range that they appear to not touch at, obviously.
Yes, we can calculate exactly what this angle is using trigonometry, as shown previously on this thread.
Yes, the "out of this universe" diagram can correctly portray this angle, as shown previously on this thread.
No, the math doesn't predict an infinity. It predicts that they will never touch, because they can never reach infinity.
Yes, this math can be demonstrated to work at small, testable scales.
No, you have no evidence that it magically stops working at larger scales, other than blind faith in your model.

Ok, now that I have brought us back full circle, can you stop dodging the question, and just answer how you think this stuff can be calculated, if the math is indeed wrong?

"take the distance between the tracks and the angle of their progression" -- Um... how do I take a distance between an object and an angle?
"determine where they would intersect in the distance" -- How? Is there a special Bishop equation that I can use?
"Calculate based on what we and experience" -- Ok. Great. How do I perform this calculation?

[Tom Bishop]

If two train tracks are laid out in front of you at an angle pointing towards each other, then obviously, two lines oriented in that position that will intersect at some point. Only parallel lines can continue into infinity and never intersect.

Yes, we agree on this. Parallel lines never intersect. Brilliant deduction Sherlock.

The type of math you are using says that the train tracks should approach each other but NEVER meet.

But from what we see and experience the tracks are angled toward each other in a way that they MUST meet.

So what's right? Are our experiences correct, or is a theoretical calculation which takes place outside of the universe and is missing a dimension correct?

We have been through this already. Stop arguing in a circle.

Yes, parallel lines are angled towards each other from our perspective.
No, they will never actually meet each other.
Yes, it appears that they meet each other because the angle between them becomes too small for our eyes to distinguish. Using a telescope can extend the range that they appear to not touch at, obviously.
Yes, we can calculate exactly what this angle is using trigonometry, as shown previously on this thread.
Yes, the "out of this universe" diagram can correctly portray this angle, as shown previously on this thread.
No, the math doesn't predict an infinity. It predicts that they will never touch, because they can never reach infinity.
Yes, this math can be demonstrated to work at small, testable scales.
No, you have no evidence that it magically stops working at larger scales, other than blind faith in your model.

Ok, now that I have brought us back full circle, can you stop dodging the question, and just answer how you think this stuff can be calculated, if the math is indeed wrong?

"take the distance between the tracks and the angle of their progression" -- Um... how do I take a distance between an object and an angle?
"determine where they would intersect in the distance" -- How? Is there a special Bishop equation that I can use?
"Calculate based on what we and experience" -- Ok. Great. How do I perform this calculation?

No, two lines angled towards each other WILL meet. The angle is not "just too small that you can't see it and it actually continues forever". That is not possible. We have two lines angled towards each other. Think about it. What you are describing is impossible. The only way for the lines to continue forever without meeting is if they appeared as PARALLEL lines.

[TotesNotReptilian]

No, two lines angled towards each other WILL meet. The angle is not "just too small that you can't see it and it actually continues forever". That is not possible. We have two lines angled towards each other. Think about it. What you are describing is impossible. The only way for the lines to continue forever without meeting is if they appeared as PARALLEL lines.

Ok, let's say an object is travelling along one of these lines. For simplicity's sake, let's say that these lines make a right angle with each other.

A ---------- B
|
|
|
C

Let's say Bob is travelling from B to A. There are 10 dashes between A and B. Let's say Bob is travelling at a rate of 10/t² dashes per second. t is the time in seconds and starts at 1. How long before Bob intersects the line AC?

Obligatory stop dodging the question:

"take the distance between the tracks and the angle of their progression" -- Um... how do I take a distance between an object and an angle?
"determine where they would intersect in the distance" -- How? Is there a special Bishop equation that I can use?
"Calculate based on what we and experience" -- Ok. Great. How do I perform this calculation?

[garygreen]

yo tom: do you think this photo is of a woman who is taller than the leaning tower of pisa?  why or why not?

[Woody]

How about answer how celestial navigation can be used to get a fix?

The method used predicts what angle certain stars should appear to an observer at a location at a certain time. 

This is  real world application that was and is(much rarely now) with accurate and reliable results.  This suggest that the math you say fails at those distances does work at them.

If celestial navigation works what changes when predicting what angle the Sun should appear to a person?

I would prefer to keep these threads on topic.

How is it off topic?

I am asking about predicting the angle stars appear to the observer.  This thread is talking about predicting the angle of the nearest star to us, the Sun.

Your claim the math does not work or is unreliable.  Celestial navigation being used to get a fix using math suggest you are wrong about distance causing the math to fail.

Your last post on the subject of celestial navigation was only partially correct. You can get a line of position without using math.  To get a fix math is involved.  I really suggest you look into how to navigate and finding your position using the stars.  It will give you an insight on the distances of where math still works. Since long before GPS, LORAN and computers people figured out using the math you claim is wrong to determine their position anywhere on Earth as long as they could see the stars and horizon. (When someone figured out they could use an artificial horizon they only needed to see the stars)
 

[Tom Bishop]

How is it off topic?

I am asking about predicting the angle stars appear to the observer.  This thread is talking about predicting the angle of the nearest star to us, the Sun.

Your claim the math does not work or is unreliable.  Celestial navigation being used to get a fix using math suggest you are wrong about distance causing the math to fail.

Your last post on the subject of celestial navigation was only partially correct. You can get a line of position without using math.  To get a fix math is involved.  I really suggest you look into how to navigate and finding your position using the stars.  It will give you an insight on the distances of where math still works. Since long before GPS, LORAN and computers people figured out using the math you claim is wrong to determine their position anywhere on Earth as long as they could see the stars and horizon. (When someone figured out they could use an artificial horizon they only needed to see the stars)

You're going to have to show us an example of what you mean.

yo tom: do you think this photo is of a woman who is taller than the leaning tower of pisa?  why or why not?

According to our perspective the woman is taller.

No, two lines angled towards each other WILL meet. The angle is not "just too small that you can't see it and it actually continues forever". That is not possible. We have two lines angled towards each other. Think about it. What you are describing is impossible. The only way for the lines to continue forever without meeting is if they appeared as PARALLEL lines.

Ok, let's say an object is travelling along one of these lines. For simplicity's sake, let's say that these lines make a right angle with each other.

A ---------- B
|
|
|
C

Let's say Bob is travelling from B to A. There are 10 dashes between A and B. Let's say Bob is travelling at a rate of 10/t² dashes per second. t is the time in seconds and starts at 1. How long before Bob intersects the line AC?

Obligatory stop dodging the question:

"take the distance between the tracks and the angle of their progression" -- Um... how do I take a distance between an object and an angle?
"determine where they would intersect in the distance" -- How? Is there a special Bishop equation that I can use?
"Calculate based on what we and experience" -- Ok. Great. How do I perform this calculation?

I don't know what you are getting at, and I don't have an equation for you. I was explaining the method of calculation. You would calculate based on what we see and experience -- angled lines clearly approaching each other to a point in the distance, not on what is theorized. Two lines angled towards each other will clearly meet at some point. They do not go on and on for infinity.

[TotesNotReptilian]

No, two lines angled towards each other WILL meet. The angle is not "just too small that you can't see it and it actually continues forever". That is not possible. We have two lines angled towards each other. Think about it. What you are describing is impossible. The only way for the lines to continue forever without meeting is if they appeared as PARALLEL lines.

Ok, let's say an object is travelling along one of these lines. For simplicity's sake, let's say that these lines make a right angle with each other.

A ---------- B
|
|
|
C

Let's say Bob is travelling from B to A. There are 10 dashes between A and B. Let's say Bob is travelling at a rate of 10/t² dashes per second. t is the time in seconds and starts at 1. How long before Bob intersects the line AC?

Obligatory stop dodging the question:

"take the distance between the tracks and the angle of their progression" -- Um... how do I take a distance between an object and an angle?
"determine where they would intersect in the distance" -- How? Is there a special Bishop equation that I can use?
"Calculate based on what we and experience" -- Ok. Great. How do I perform this calculation?

I don't know what you are getting at, and I don't have an equation for you. I was explaining the method of calculation. You would calculate based on what we see and experience -- angled lines clearly approaching each other to a point in the distance, not on what is theorized. Two lines angled towards each other will clearly meet at some point. They do not go on and on for infinity.

Ugh, should've stuck with middle school math rather than high school math. Whatever. The answer is never. Bob will never reach A at that rate, even though he is following a line going towards A.

The key here is that there is a difference between the lines meeting and objects following the lines meeting. Obviously, the lines themselves meet on the projection. In fact, the lines cross each other and then spread apart. Are you implying that at some point, two objects following parallel paths will not only meet, but cross each other and then appear to separate? Because that is the logical conclusion of your reasoning.

[garygreen]

yo tom: do you think this photo is of a woman who is taller than the leaning tower of pisa?  why or why not?

According to our perspective the woman is taller.

this is oddly evasive.  do you agree that the woman in this photo is, physically, probably not taller than the tower of pisa?

[Tom Bishop]

yo tom: do you think this photo is of a woman who is taller than the leaning tower of pisa?  why or why not?

According to our perspective the woman is taller.

this is oddly evasive.  do you agree that the woman in this photo is, physically, probably not taller than the tower of pisa?

If you change the perspective you might get a different result. But from this perspective she is taller.

[Tom Bishop]

Ugh, should've stuck with middle school math rather than high school math. Whatever. The answer is never. Bob will never reach A at that rate, even though he is following a line going towards A.

The key here is that there is a difference between the lines meeting and objects following the lines meeting. Obviously, the lines themselves meet on the projection. In fact, the lines cross each other and then spread apart. Are you implying that at some point, two objects following parallel paths will not only meet, but cross each other and then appear to separate? Because that is the logical conclusion of your reasoning.

Yes, the lines meet on the projection. Therefore they meet in visual reality. The railroad tracks appear to meet in the distance, and if you were to shine a laser pointer at that point where they meet, a second observer would see that the dot would spread out to cover the entire railroad and a good chunk of the land around it, not merely one track at a time. The point where the tracks merge is very real for all visual purposes.

As per your claim that the perspective lines meet and then separate in opposite directions, I don't believe anything has been observe to that effect and therefore your interpretation must be wrong.

[garygreen]

yo tom: do you think this photo is of a woman who is taller than the leaning tower of pisa?  why or why not?

According to our perspective the woman is taller.

this is oddly evasive.  do you agree that the woman in this photo is, physically, probably not taller than the tower of pisa?

If you change the perspective you might get a different result. But from this perspective she is taller.

cool.  do you agree that the woman in this photo is, physically, probably not taller than the tower of pisa?

[Tom Bishop]

yo tom: do you think this photo is of a woman who is taller than the leaning tower of pisa?  why or why not?

According to our perspective the woman is taller.

this is oddly evasive.  do you agree that the woman in this photo is, physically, probably not taller than the tower of pisa?

If you change the perspective you might get a different result. But from this perspective she is taller.

cool.  do you agree that the woman in this photo is, physically, probably not taller than the tower of pisa?

Maybe not. But we would need to change the perspective to see that.

[garygreen]

yo tom: do you think this photo is of a woman who is taller than the leaning tower of pisa?  why or why not?

According to our perspective the woman is taller.

this is oddly evasive.  do you agree that the woman in this photo is, physically, probably not taller than the tower of pisa?

If you change the perspective you might get a different result. But from this perspective she is taller.

cool.  do you agree that the woman in this photo is, physically, probably not taller than the tower of pisa?

Maybe not. But we would need to change the perspective to see that.

lol maybe not?  so you think maybe this woman is taller than the tower of pisa?

[TotesNotReptilian]

<irrelevant crap about lasers removed>

As per your claim that the perspective lines meet and then separate in opposite directions, I don't believe anything has been observe to that effect and therefore your interpretation must be wrong.

Another brilliant deduction! That was my point. I was using your logic to come to that conclusion. Remember saying this?

Yes, the lines meet on the projection. Therefore they meet in visual reality.

Yes, the lines cross on the projection. Therefore they cross in visual reality.

Both use the same logic. Both are just as wrong.

I don't have an equation for you. I was explaining the method of calculation. You would calculate based on what we see and experience -- angled lines clearly approaching each other to a point in the distance, not on what is theorized.

You think I should "calculate based on what I see", but not on what is theorized, but you don't have an equation for me? Perhaps you can do an example for me, to show me how it is done? I have a strong suspicion that you have no earthly idea what you are talking about.

[Tom Bishop]

yo tom: do you think this photo is of a woman who is taller than the leaning tower of pisa?  why or why not?

According to our perspective the woman is taller.

this is oddly evasive.  do you agree that the woman in this photo is, physically, probably not taller than the tower of pisa?

If you change the perspective you might get a different result. But from this perspective she is taller.

cool.  do you agree that the woman in this photo is, physically, probably not taller than the tower of pisa?

Maybe not. But we would need to change the perspective to see that.

lol maybe not?  so you think maybe this woman is taller than the tower of pisa?

You seem to have some difficulty here. I obviously agreed with you.

[Tom Bishop]

Another brilliant deduction! That was my point. I was using your logic to come to that conclusion. Remember saying this?

My logic is that we must take our queues for how things are from reality. We don't see the effect you claim exists, therefore it does not exist.

Yes, the lines cross on the projection. Therefore they cross in visual reality.

Both use the same logic. Both are just as wrong.

I don't see any perspective lines crossing over each other in reality. I just see that they meet and end where they meet. Not sure where you got your cross-over ideas from.

You think I should "calculate based on what I see", but not on what is theorized, but you don't have an equation for me? Perhaps you can do an example for me, to show me how it is done? I have a strong suspicion that you have no earthly idea what you are talking about.

Why should I do any equations? Do you really need an equation to know that two lines which are angled towards each other will eventually meet?

[TotesNotReptilian]

I don't see any perspective lines crossing over each other in reality. I just see that they meet and end where they meet. Not sure where you got your cross-over ideas from.

Your argument was that they are angled towards each other, therefore they must touch. By that logic, they are angled towards each other, therefore they must cross. It's bad logic.

Your other argument was that "they appear to touch, therefore they touch, therefore the math is wrong". However, the math predicts that as they move away from you, they will appear to get closer together. Close enough that there is no way to visually distinguish whether they are touching or not. The math predicts that they can become so close that they will appear to touch. So why on earth are you using "they appear to touch" as an argument that the math is wrong? More bad logic.

You think I should "calculate based on what I see", but not on what is theorized, but you don't have an equation for me? Perhaps you can do an example for me, to show me how it is done? I have a strong suspicion that you have no earthly idea what you are talking about.

Why should I do any equations? Do you really need an equation to know that two lines which are angled towards each other will eventually meet?

What? No, that's not what I was asking at all. Good grief, do I have to spell out everything 12 times?

If the math is wrong, as you claim, what is the correct way to determine the angle between the sun and the horizon? Or any 2 objects for that matter? In other words, if I told you the location of several objects relative to you, how would you calculate the apparent angle between them?

[Tom Bishop]

Your argument was that they are angled towards each other, therefore they must touch. By that logic, they are angled towards each other, therefore they must cross. It's bad logic.

Two lines angled towards each other must touch, that is logically sound, and the lines are seen to touch, which places the concept in reality as well.

Your cross-over idea does not have a component in reality, and is a mere theoretical concept like the bad mathematics which you have presented in the OP.

Your other argument was that "they appear to touch, therefore they touch, therefore the math is wrong". However, the math predicts that as they move away from you, they will appear to get closer together. Close enough that there is no way to visually distinguish whether they are touching or not. The math predicts that they can become so close that they will appear to touch. So why on earth are you using "they appear to touch" as an argument that the math is wrong? More bad logic.

If they appear to touch, they touch, okay? The human eye can see a single photon in a dark room. That is very good resolution. If the tracks are appearing to merge at a point then it means that black photons are arriving side by side without any gap. There is no "almost" touching. The gap is gone.

What? No, that's not what I was asking at all. Good grief, do I have to spell out everything 12 times?

If the math is wrong, as you claim, what is the correct way to determine the angle between the sun and the horizon? Or any 2 objects for that matter? In other words, if I told you the location of several objects relative to you, how would you calculate the apparent angle between them?

The correct way to determine the angle of the sun is to make our determinations based on reality, not theoretical mathematics which lack a dimension. Take a protractor. When the sun is overhead at noontime the sun is at 90 degrees and at sunset the sun is at 0 degrees. There are your angles for the sun. It's quite simple.