[TotesNotReptilian]

Again, a mathematical proof doesn't have anything to do with reality.

You just asked for a proof. Now that it has been given to you, you are making a blanket declaration that mathematical proofs have nothing to do with reality?? What??? If you don't think it has to do with reality, then go test it in reality, like I have stated numerous times. Your entire argument seems to be based on incredulity that angles can be measured from our point of view, which is ridiculous. Stop whining about the ancient Greek mathematicians and go test it.

I do not wish to continue this discussion.

Cognitive dissonance starting to get uncomfortable?

[Tom Bishop]

Again, a mathematical proof doesn't have anything to do with reality.

You just asked for a proof. Now that it has been given to you, you are making a blanket declaration that mathematical proofs have nothing to do with reality?? What??? If you don't think it has to do with reality, then go test it in reality, like I have stated numerous times. Your entire argument seems to be based on incredulity that angles can be measured from our point of view, which is ridiculous.

Come on, didn't you pass middle school algebra? Look up the definition of a mathematical proof:

https://en.wikipedia.org/wiki/Mathematical_proof

In mathematics, a proof is a deductive argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms, along with accepted rules of inference.

Stop whining about the ancient Greek mathematicians and go test it.

Test what, that there aren't any hidden infinite distances as predicted by the ancients? That sounds more like a positive claim that you have to prove to support your claim.

[TotesNotReptilian]

Again, a mathematical proof doesn't have anything to do with reality.

You just asked for a proof. Now that it has been given to you, you are making a blanket declaration that mathematical proofs have nothing to do with reality?? What??? If you don't think it has to do with reality, then go test it in reality, like I have stated numerous times. Your entire argument seems to be based on incredulity that angles can be measured from our point of view, which is ridiculous. Stop whining about the ancient Greek mathematicians and go test it.

I do not wish to continue this discussion.

Cognitive dissonance starting to get uncomfortable?

Come on, didn't you pass middle school algebra? Look up the definition of a mathematical proof:

https://en.wikipedia.org/wiki/Mathematical_proof

In mathematics, a proof is a deductive argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms, along with accepted rules of inference.

Yes, I know what a mathematical proof is. Yes, I am aware that if you start with bad assumptions then the conclusion may not agree with reality, just like any other kind of proof. Obviously.

Let's be specific. This is what I am arguing is true:



Given objects at locations A, B, and C, with distances between the objects given by a and b. The angle α can be measured by a person at location A. This angle will be equal to arctan(a/b).

There are several ways of measuring this angle, all of which should agree:
1. Using a theodolite.
2. Stretching a string between the objects and using a protractor.
3. Pointing two sticks at the objects and measuring the angle between them with a protractor.
4. Measuring the distance between the objects in a picture, and calculating the angle based on the FOV of the camera. (Approximation based on the distortion of the camera.)

Forget the mathematical proof if you want. This is common sense to most people, but if it isn't common sense to you, then go test it. It is easily testable in reality.

[Tom Bishop]

Test what, that there aren't any hidden infinite distances as predicted by the ancients? That sounds more like a positive claim that you have to prove to support your claim.

[TotesNotReptilian]

Test what, that there aren't any hidden infinite distances as predicted by the ancients? That sounds more like a positive claim that you have to prove to support your claim.

Ok, I am just going sidestep the whole "hidden infinite distances" thing, because you are just trying to use Zeno's Paradox to pretend that nothing can be measured.

Here is what you test:

1. Set up two objects so that they make a right triangle with each other and you. (In the above diagram, the objects go at locations B and C. Place yourself at location A.)
2. Measure the distances between the objects. (a and b in the above diagram)
3. Measure the angle between the objects using one or more of the prescribed methods.
4. Calculate the angle between the objects using arctan(a/b). Does the measurement agree with the calculation?
5. Change the position of the objects. Repeat steps 1-4 until you are convinced that this process works.

Did the process ever not work? Did Zeno's Paradox ever hinder the process? Did "hidden infinite distances" ever hinder the process? If the process always works, then why are you assuming that it won't work for the sun?

[Tom Bishop]

You must test long distance perspective, not something else entirely.

[TotesNotReptilian]

You must test long distance perspective, not something else entirely.

Ah, and here we get to the crux of your argument. So your argument is this:

"Yes, this process works for any relatively short, easily testable distance. No, there is no reason to believe it stops working at long distances. However, if the process does work at long distances, then my model would be proved false. Therefore, I am going to assume it stops working at long distances, despite the lack of evidence."

Is this correct? Am I missing something?

[Tom Bishop]

You must test long distance perspective, not something else entirely.

Ah, and here we get to the crux of your argument. So your argument is this:

"Yes, this process works for any relatively short, easily testable distance. No, there is no reason to believe it stops working at long distances. However, if the process does work at long distances, then my model would be proved false. Therefore, I am going to assume it stops working at long distances, despite the lack of evidence."

Is this correct? Am I missing something?

Of course things work differently at different scales. We have an entire different branch of physics for the very small and the very large. Any model is nothing more than an approximation for reality within a limited range.

[TotesNotReptilian]

You must test long distance perspective, not something else entirely.

Ah, and here we get to the crux of your argument. So your argument is this:

"Yes, this process works for any relatively short, easily testable distance. No, there is no reason to believe it stops working at long distances. However, if the process does work at long distances, then my model would be proved false. Therefore, I am going to assume it stops working at long distances, despite the lack of evidence."

Is this correct? Am I missing something?

Of course things work differently at different scales. We have an entire different branch of physics for the very small and the very large. Any model is nothing more than an approximation for reality within a limited range.

True enough, but it is important to know exactly how and when a model stops being useful. We know exactly how inaccurate Newtonian physics is at any given scale. We know why it is inaccurate at that scale. On the other hand, you have no notion of why geometry stops working. You have no notion of at what scale geometry stops working. All you know is that it must stop working or else your model is wrong. You are just using this as an excuse to ignore evidence that contradicts your model.

[Rama Set]

Apparently you and several people are completely uneducated as to what a mathematical proof actually is. I do not wish to continue this discussion.

You think Trig doesn't work in the real world?  Wow. Good thing you are leaving the conversation. The fields of surveying and engineering would be fraught with failures at every turn if this were the case. Bye Tom!

It's really sad that you try and make this argument but will hold up Rowbotham's examples from ENaG as valid. Do you not see how you internal contradictions make you untrustworthy?

[TotesNotReptilian]

Apparently you and several people are completely uneducated as to what a mathematical proof actually is. I do not wish to continue this discussion.

You think Trig doesn't work in the real world?  Wow. Good thing you are leaving the conversation. The fields of surveying and engineering would be fraught with failures at every turn if this were the case. Bye Tom!

It's really sad that you try and make this argument but will hold up Rowbotham's examples from ENaG as valid. Do you not see how you internal contradictions make you untrustworthy?

It's amazing the kind of arguments that someone can justify in his mind when his belief system is on the line. People sometimes ask why anyone would come to this forum if they don't believe the earth is flat. For me, this right here is it. Some people like watching olympic gymnastics. I like watching mental gymnastics.

[Tom Bishop]

True enough, but it is important to know exactly how and when a model stops being useful. We know exactly how inaccurate Newtonian physics is at any given scale. We know why it is inaccurate at that scale. On the other hand, you have no notion of why geometry stops working. You have no notion of at what scale geometry stops working. All you know is that it must stop working or else your model is wrong. You are just using this as an excuse to ignore evidence that contradicts your model.

In your example, you did not demonstrate the mathematical infinities of perspective. How is it supposed to prove the subject-matter true?

Will one trigonometric equation prove the rest of trigonometry true? I think not.

[Woody]

I have seen this conversation with Tom play out before.

It always ended with Tom claiming something along the lines at some unspecified distance math stops working.  Except when it supports his belief.  I believe he accepts the calculations used to determine the Sun' altitude be various FE's.

I think we can define this distance as how ever far the horizon is from the observer when ships disappear from the bottom up.  So about 2-12 miles in most cases.

[Tom Bishop]

I have seen this conversation with Tom play out before.

It always ended with Tom claiming something along the lines at some unspecified distance math stops working.

The math actually claims that something infinite happens at long distances. This has not been demonstrated to be true. You are expecting us to place our faith in the intellectual prowess of a group of people who believed that flies spontaneously generate from rotting meat.

[Woody]

I have seen this conversation with Tom play out before.

It always ended with Tom claiming something along the lines at some unspecified distance math stops working.

The math actually claims that something infinite happens at long distances. This has not been demonstrated to be true. You are expecting us to place our faith in the intellectual prowess of a group of people who believed that flies spontaneously generate from rotting meat.

Then you have to answer what distance math fails.  I certainly can accurately predict the angles things will appear to be to an observer at different distances and locations.  It is easy to verify this with a simple experiment.  So at what distance does math fail and why?  1 mile? 100? 1,000? 10,000?

The math certainly seems to work for celestial navigation.  The entire method involves predicting what angle stars will appear to the observer.  How come?  Math is certainly needed to get a fix and the stars are further away than the Sun in the FE models I am aware of. They are certainly much further away in the RE model.

[TotesNotReptilian]

The math actually claims that something infinite happens at long distances.

What?? You are going to have to be more specific. Stop being vague. Are you still trying to drag Zeno's Paradox into this somehow?

True enough, but it is important to know exactly how and when a model stops being useful. We know exactly how inaccurate Newtonian physics is at any given scale. We know why it is inaccurate at that scale. On the other hand, you have no notion of why geometry stops working. You have no notion of at what scale geometry stops working. All you know is that it must stop working or else your model is wrong. You are just using this as an excuse to ignore evidence that contradicts your model.

In your example, you did not demonstrate the mathematical infinities of perspective. How is it supposed to prove the subject-matter true?

Will one trigonometric equation prove the rest of trigonometry true? I think not.

Your logical progression is bewildering. I see no logical connection between these statements. Please stop dodging the question. I would like to re-emphasize Woody's question:

At what distance does the math fail? Why does it fail? In what way, specifically, does it fail? What is the correct way to calculate the angle?

[TotesNotReptilian]

I have seen this conversation with Tom play out before.

It always ended with Tom claiming something along the lines at some unspecified distance math stops working.  Except when it supports his belief.

Oh, I know. But it is fascinating and hilarious every time.

[Tom Bishop]

What?? You are going to have to be more specific. Stop being vague. Are you still trying to drag Zeno's Paradox into this somehow?

Please follow the thread. The math claims that it is impossible for an overhead body to reach the place where the perspective lines intersect. It predicts that the horizon would be an infinite distance away on a plane. This has not been demonstrated.

Please stop dodging the question. I would like to re-emphasize Woody's question:

At what distance does the math fail? Why does it fail? In what way, specifically, does it fail? What is the correct way to calculate the angle?

The correct way to determine the truth is by taking our que from the real world. If train tracks seem to intersect then they do, according to our present perception. If two train tracks are laid out in front of you are at angles 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.

To calculate where they intersect take the distance between the tracks and the angle of their progression and determine where they would meet in the distance. Calculate based on what we experience, not on some theoretical dimension outside of the universe.

[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?

[TotesNotReptilian]

What?? You are going to have to be more specific. Stop being vague. Are you still trying to drag Zeno's Paradox into this somehow?

Please follow the thread. The math claims that it is impossible for an overhead body to reach the place where the perspective lines intersect. It predicts that the horizon would be an infinite distance away on a plane. This has not been demonstrated.

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.

Please stop dodging the question. I would like to re-emphasize Woody's question:

At what distance does the math fail? Why does it fail? In what way, specifically, does it fail? What is the correct way to calculate the angle?

The correct way to determine the truth is by taking our que from the real world. If train tracks seem to intersect then they do.

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?

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.

To calculate where they intersect take the distance between the tracks and the angle of their progression and determine where they would intersect in the distance. Calculate based on what we and experience, not on some theoretical side view dimension outside of the universe.

"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?