The Flat Earth Society
Flat Earth Discussion Boards => Flat Earth Community => Topic started by: retiredAstrophysicist on November 10, 2017, 08:15:15 PM
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Hi folks - As my moniker suggests, I'm a retired astrophysicist, well-traveled and with many observations "with my own eyes" over my career. Together with several other retired astrophysicists and other scientists, we present programs for the public at the Planetarium belonging to the Los Alamos Nature Center, in Los Alamos, New Mexico (home to the Los Alamos National Laboratory). Of course we all regard the Flat Earth Model as a joke. Nevertheless, it has been brought to our attention that a growing number of people adhere to this fallacy, and we would therefore like to hold a discussion on the topic.
We think the most appropriate time for such a discussion will be Sunday 1 April 2018. Since none of us could present the arguments for a Flat Earth Model with a straight face, we were wondering if any member of the society would be willing to join us to present your case. Because Los Alamos is a highly scientifically literate community, you might expect to field questions of a fairly complex nature, for example regarding Foucault's Pendulum, occultations of stars by the moon (also eclipse prediction, of course), and trans-oceanic tsunami propagation. The latter case is similar to the long-distance flight problem that I've seen discussed in these pages, but doesn't involve recruiting airline companies and pilots into a fictitious conspiracy.
Our Planetarium is run by a nonprofit organization, and we can therefore not afford to pay transportation costs, but we would be glad to offer a meal beforehand and a beer afterwards from our local brewery. Treat this in good fun; we do not intend to hurl insults or indulge in name-calling. Our mission is public education, pure and simple.
Thanks for your attention.
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If I go over there you will just get schooled more badly than you do here. At least here you have the chance to google up some ancient hypothesis and insist that it is fact.
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Hi folks - As my moniker suggests, I'm a retired astrophysicist, well-traveled and with many observations "with my own eyes" over my career. Together with several other retired astrophysicists and other scientists, we present programs for the public at the Planetarium belonging to the Los Alamos Nature Center, in Los Alamos, New Mexico (home to the Los Alamos National Laboratory). Of course we all regard the Flat Earth Model as a joke. Nevertheless, it has been brought to our attention that a growing number of people adhere to this fallacy, and we would therefore like to hold a discussion on the topic.
We think the most appropriate time for such a discussion will be Sunday 1 April 2018. Since none of us could present the arguments for a Flat Earth Model with a straight face, we were wondering if any member of the society would be willing to join us to present your case. Because Los Alamos is a highly scientifically literate community, you might expect to field questions of a fairly complex nature, for example regarding Foucault's Pendulum, occultations of stars by the moon (also eclipse prediction, of course), and trans-oceanic tsunami propagation. The latter case is similar to the long-distance flight problem that I've seen discussed in these pages, but doesn't involve recruiting airline companies and pilots into a fictitious conspiracy.
Our Planetarium is run by a nonprofit organization, and we can therefore not afford to pay transportation costs, but we would be glad to offer a meal beforehand and a beer afterwards from our local brewery. Treat this in good fun; we do not intend to hurl insults or indulge in name-calling. Our mission is public education, pure and simple.
Thanks for your attention.
This is a rather interesting proposal. Can you provide some sources or references to verify your role and a confirmation this will take place. Holding it on April 1 seems a bit suspicious.
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If I go over there you will just get schooled more badly than you do here. At least here you have the chance to google up some ancient hypothesis and insist that it is fact.
Does that mean you are accepting his invitation?
Sounds like an interesting event.
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This is a rather interesting proposal. Can you provide some sources or references to verify your role and a confirmation this will take place. Holding it on April 1 seems a bit suspicious.
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The idea of holding such a discussion was suggested to me by a colleague at the Planetarium. I was reluctant to do this; holding a public discussion on bad science is a disservice to good science. When the idea of holding it on April Fools Day was mooted, I assented, and volunteered to make inquiries. Because the Flat Earth Model and essentially all of modern science are mutually exclusive, one of us will turn out to be a Fool. Nevertheless, we will reward ourselves with good beer afterwards.
As to a confirmation that this will take place, I cannot yet offer one. We plan our programs at the Planetarium quarter-by-quarter, and will meet to discuss the April - June quarter some time in January. As I said, I don't think we can do a good job with the discussion unless we have someone prepared to defend the Flat Earth Model against some rather difficult questions. If one of you sincerely wants to do this, we should probably have an offline discussion to make sure you have studied the issues carefully. Astronomy, we feel, is your weakest point. The "waffle" about stars in your Cosmos page on the Wiki simply won't cut it. If we don't find someone to skillfully defend the Flat Earth Model, the event won't take place. It's as simple as that.
You can find the website for our planetarium at peecnature.org/events/planetarium. I am one of the presenters mentioned on that page. I won't tell you my name at this moment, but will give you some hints. PhD University of Cambridge 1976 astrophysics. Postdocs at the University of Leiden and Kitt Peak National Observatory. Staff scientist at the National Radio Astronomy Observatory. The bulk of my career was at Los Alamos National Laboratory, and subsequently at the University of Oslo.
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Holding it on April 1 seems a bit suspicious.
I agree Junker. It's almost as if they don't take the idea of flat earth seriously.
Plus who has time on a Sunday for this type of debate, why not Sat 31st, I mean they mention Beers afterwards, ON a SUNDAY! With people having to work next day, no no no, let's make it Saturday dudes, I'll fly over and we'll make a night of it science style!
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So, Bob. I'm going to call you Bob. You sound like a Bob.
Bob, you suffer from the same strain of arrogance as many academics, especially those with a bit of British education in them. You think we're wrong - fine. You're bloody damn sure we're wrong - fine. You're convinced that, having peer-reviewed the evidence available, we're completely wrong about everything ever - and that's also fine. But what you clearly don't understand is the damage you're doing to your own cause.
First of all: Bob, if you want to invite someone to debate you, no matter how insane you may perceive them as, it is not a good idea to write multiple paragraphs about how all you intend to do is take the Mickey. Combining this with a half-hearted sentence about how you mean no harm is extremely unconvincing. Now, if you're doing this to deliberately sabotage your "efforts" in setting up the event - fair enough. I understand that you don't want to be doing this, but perhaps it'd be better to show some integrity and just tell your colleagues that you're unwilling?
Secondly: you say that because you're a non-profit, you ask that we cover our own travel costs - for an event which, as you clearly stated, you only expect to benefit you (as a source of cheap laughs). We're also a non-profit. In fact, we have precisely no sources of income. So, Bob, I'd like to propose a counter-offer: you pay for my travel costs (after all, it's your event, and you do charge for admission to most events by the looks of it), and I'll bring you a couple beers from our local brewery.
Thirdly: you repeatedly said that you would want to vet potential "candidates" on their scientific literacy. You have made no attempt at making a similar offer back, and judging by what you've described so far, your understanding of the Flat Earth Theory is rather poor. Once again, you make it clear that you're interested in a very one-sided joke, and not a discussion.
These attitudes, as I've said many times before, greatly contribute to our growth. So, by all means, please continue to act like this in public. It draws great amounts of attention to us and really helps us develop a movement that now spans the plane. However, as far as your "event" goes, I'd like to recommend following common sense and being sincere with your colleagues. You don't have what it takes to respectfully recruit someone who disagrees with you. If they want to get serious about this, they need to find someone more qualified than yourself. Perhaps someone with his head not stuck so firmly in the stars, and one who can actually put aside differences for a moment.
Alternatively, you can go the "welp, I've tried, these lunatics couldn't be convinced by my perfectly rational offer" route, and skip straight to that local brewery of yours.
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If I go over there you will just get schooled more badly than you do here. At least here you have the chance to google up some ancient hypothesis and insist that it is fact.
Wow! I'd like to see that debate. Heck, even I (as a non-astronomer) can dance rings around your arguments...I'd love to see a professional do it.
You're currently resorting to blanket "Show me the data" arguments because you can't deny 90% of the disproofs I've posted...and when we DO show you the data (eg PVoutput.org, airline flight data, the mathematics behind how the ephemeris is calculated) you have to resort to very vague and ineffectual complaints about it to avoid facing the undoubted truth.
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Thirdly: you repeatedly said that you would want to vet potential "candidates" on their scientific literacy. You have made no attempt at making a similar offer back, and judging by what you've described so far, your understanding of the Flat Earth Theory is rather poor. Once again, you make it clear that you're interested in a very one-sided joke, and not a discussion.
Thanks for this, Pete. I agree with you, that the vetting that takes place prior to the discussion should be two-sided. I have indeed been looking for more of a "Theory" on the Flat-Earth side, and haven't found your wiki of much help, unfortunately.
Perhaps you could start me off by showing me how the occultations of the bright star Aldebaran (Alpha Tau) during 2017 (9 Jan, observed from Asia; 5 Feb, from north Africa and southern Europe; 5 Mar, from USA, Mexico, and Central America; 1 Apr, observed from Japan and Korea; 28 Apr, Europe; 19 Jul, southwest Asia; etc.) are explained to have occurred and been visible only from the locations indicated. Because Aldebaran has a magnitude of 1.35, these occultations are visible even with good binoculars. Such observations, done with modest telescopes, have helped us to pin down the sizes of this and other stars that are regularly occulted by the moon. Once you've explained the 2017 occultations, you might go farther and predict those that will occur in 2018. Then we can make a head-to-head comparison of your predictions and ours. (Don't cheat, and don't waffle; be precise and take all the time you need, but let me know that you're working on it.)
If you doubt that these occultations occur and are observed, you can simply type "occultation Aldebaran" into Google Scholar and get some 2000 results spanning hundreds of years. A recent one, from the Devasthal Observatory in India, is abstracted at http://www.sciencedirect.com/science/article/pii/S1384107617302610 with the full article to come out next February. You can find lots more, of course.
Thanks for your help.
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Look at you getting all optimistic with your occultation talk.
I can't even get them to tell me if they think latitude is a thing.
Oh but hey, if you're aware of actual observations of things like sunrise/sunset times we could use that. The closest we've found is there's about a million solar panel installations around the world hooked up to the internet but if you've got some gray haired astronomer in a tower somewhere observing when the sun actually appears, and writing it down in an old-timey notebook I'm sure that would finally convince them to believe timeanddate.com.
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Perhaps you could start me off by showing me how the occultations of the bright star Aldebaran (Alpha Tau) during 2017 (9 Jan, observed from Asia; 5 Feb, from north Africa and southern Europe; 5 Mar, from USA, Mexico, and Central America; 1 Apr, observed from Japan and Korea; 28 Apr, Europe; 19 Jul, southwest Asia; etc.) are explained to have occurred and been visible only from the locations indicated.
Surely you have a better question than this. Because the stars and the moon are relatively near the same altitude in the Flat Earth model, it is possible for an occultation of a star by the moon to line up for only a narrow location beneath the moon, and not for all observers.
Because Aldebaran has a magnitude of 1.35, these occultations are visible even with good binoculars. Such observations, done with modest telescopes, have helped us to pin down the sizes of this and other stars that are regularly occulted by the moon. Once you've explained the 2017 occultations, you might go farther and predict those that will occur in 2018. Then we can make a head-to-head comparison of your predictions and ours. (Don't cheat, and don't waffle; be precise and take all the time you need, but let me know that you're working on it.)
Pete can simply explain that because the occultations have occurred before, at such and such time, in a pattern over the years, that it will happen again on the same pattern. You know, using the same technique that astronomers use to predict its occurrence.
If I were Pete I would next challenge you to show that astronomers have predicted the occultation of this star geometrically, which would involve solving the general three body problem (earth-moon-star in this case), a rather embarrassing geometrical problem which has been unsolved in classical physics for the last 500 years. Except for in some some very specific (and ridiculous imo) setups, a general three body problem has never been solved.
See: Three Body Problem on Wikipedia (https://en.wikipedia.org/wiki/Three-body_problem)
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Tom, why should hard-working people of intelligence be embarrassed by a difficult problem? You can’t even be assed to recreate your observation across the bay with any sort of rigor, if anyone should feel embarrassed, and I don’t think anyone should, it’s you.
Edit: I also agree with what Pete said.
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Perhaps you could start me off by showing me how the occultations of the bright star Aldebaran (Alpha Tau) during 2017 (9 Jan, observed from Asia; 5 Feb, from north Africa and southern Europe; 5 Mar, from USA, Mexico, and Central America; 1 Apr, observed from Japan and Korea; 28 Apr, Europe; 19 Jul, southwest Asia; etc.) are explained to have occurred and been visible only from the locations indicated.
Surely you have a better question than this. Because the stars and the moon are relatively near the same altitude in the Flat Earth model, it is possible for an occultation of a star by the moon to line up for only a narrow location beneath the moon, and not for all observers.
Because Aldebaran has a magnitude of 1.35, these occultations are visible even with good binoculars. Such observations, done with modest telescopes, have helped us to pin down the sizes of this and other stars that are regularly occulted by the moon. Once you've explained the 2017 occultations, you might go farther and predict those that will occur in 2018. Then we can make a head-to-head comparison of your predictions and ours. (Don't cheat, and don't waffle; be precise and take all the time you need, but let me know that you're working on it.)
Pete can simply explain that because the occultations have occurred before, at such and such time, in a pattern over the years, that it will happen again on the same pattern. You know, using the same technique that astronomers use to predict its occurrence.
If I were Pete I would next challenge you to show that astronomers have predicted the occultation of this star geometrically, which would involve solving the general three body problem (earth-moon-star in this case), a rather embarrassing geometrical problem which has been unsolved in classical physics for the last 500 years. Except for in some some very specific (and ridiculous imo) setups, a general three body problem has never been solved.
See: Three Body Problem on Wikipedia (https://en.wikipedia.org/wiki/Three-body_problem)
Is that your new lighthouse on Plymouth beach?? lol - the three body problem doesn't point to a flat Earth, nor does orbital patterns of celestial objects.
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Tom, why should hard-working people of intelligence be embarrassed by a difficult problem?
The location of three moving bodies cannot be predicted. It is quite a stain on classical physics, and is absolutely embarrassing to physicists.
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Tom, why should hard-working people of intelligence be embarrassed by a difficult problem?
The location of three moving bodies cannot be predicted. It is quite a stain on classical physics, and is absolutely embarrassing to physicists.
It is strange to answer a question by reiterating what prompted the question in the first place. What exactly should embarrass them about solving a currently unsolvable mathematical problem?
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a general three body problem has never been solved.
See: Three Body Problem on Wikipedia (https://en.wikipedia.org/wiki/Three-body_problem)
it's only accurate to say that no analytic solution has been found. it's still more accurate to say that no useful analytic solutions have been found.
numerical solutions are most definitely available and are used regularly.
http://ccar.colorado.edu/asen5050/projects/projects_2013/Brown_Harrison/Code/Brown_H.pdf
https://arxiv.org/pdf/1508.02312.pdf
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Tom, why should hard-working people of intelligence be embarrassed by a difficult problem?
The location of three moving bodies cannot be predicted. It is quite a stain on classical physics, and is absolutely embarrassing to physicists.
Why do you continue to attempt to derail threads? If you feel the n-body issue should be discussed, create a thread. This thread is about a public discussion of FET.
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Tom, why should hard-working people of intelligence be embarrassed by a difficult problem?
The location of three moving bodies cannot be predicted. It is quite a stain on classical physics, and is absolutely embarrassing to physicists.
It is strange to answer a question by reiterating what prompted the question in the first place. What exactly should embarrass them about solving a currently unsolvable mathematical problem?
They should be embarrassed because it is seemingly a simple problem on its face, but they don't have the tools to do it.
a general three body problem has never been solved.
See: Three Body Problem on Wikipedia (https://en.wikipedia.org/wiki/Three-body_problem)
it's only accurate to say that no analytic solution has been found. it's still more accurate to say that no useful analytic solutions have been found.
numerical solutions are most definitely available and are used regularly.
http://ccar.colorado.edu/asen5050/projects/projects_2013/Brown_Harrison/Code/Brown_H.pdf
https://arxiv.org/pdf/1508.02312.pdf
Read through the first PDF. They are running a simulation of three bodies, tracing the patterns of its movement, and then making a prediction on the pattern they saw. This is not a real solution to the Three Body Problem.
Pete and the OP in this thread can both predict the occultation of the star based on patterns which have been seen before. This is not a geometric (or analytical, if you prefer) solution to the Three Body Problem and does not actually predict using the physics of the model.
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They should be embarrassed because it is seemingly a simple problem on its face, but they don't have the tools to do it.
why do you believe that this is a simple problem?
Read through the first PDF. They are running a simulation of three bodies, tracing the patterns of its movement, and then making a prediction on the pattern they saw. This is not a real solution to the Three Body Problem.
can you point me to the passage you're referring to? i'm not seeing anything about pattern recognition.
numerical integration is not a process of finding patterns. it's literally just using a computer to solve equations of motion derived from newton's laws. it's not pattern reognition; it's geometry + calculus + computers.
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can you point me to the passage you're referring to? i'm not seeing anything about pattern recognition.
The whole paper is about creating a simple 3D model of rotating bodies and then concluding that because a simulation can be made of moving bodies, that the n-body problem has been solved.
Read page 5 of 8. It describes the creation of a computer simulation of 3 bodies. They run the simulation for several rotations and then provide an image which illustrates the path of how the the bodies moved. A sample earth-moon-sun system was run for several "years" and the path of those bodies where they repeated their paths is shown in that diagram. They conclude that because they were able to create a computer simulation that the 3-body problem has been solved. The page is concluded with "Therefore, it is possible to use the n-Body equations and a selection of the system’s physical properties to create a model of the Sun, Earth, Luna system."
At no point do they actually come up with a solution to the three body problem. They think that they can create a 3D model of moving bodies, run it a few times, see the pattern, and therefore they can predict future occurrences from the pattern and the three body problem has been solved.
This is like saying that you solved the 3 body problem because you went online to one of those comet gravity simulators and tossed some balls around to rotate around each other, traced out where they were moving, and that you therefore solved the 3 body problem. It is not a solution. You found a pattern in your gravity simulator. It is not useful for solving problems.
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The whole paper is about creating a simple 3D model of rotating bodies and then concluding that because a simulation can be made of moving bodies, that the n-body problem has been solved.
At no point do they actually come up with a solution to the three body problem. They think that they can create a 3D model of moving bodies, run it a few times, see the pattern and therefore they can predict future occurrences from the pattern and the three body problem has been solved.
This is like saying that you solved the 3 body problem because you went online to one of those comet gravity simulators and tossed some balls around to rotate around each other, traced out where they were moving and that you therefore solved the 3 body problem.
It is not the same at all. In your example, you are finding a pattern where there is none, whereas, in the 3 body problem, they have run the simulations so many times that they can see the same pattern repeat itself so many times that they can formulate a guess that it is accurate to a close enough margin that it doesn't really matter
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This is like saying that you solved the 3 body problem because you went online to one of those comet gravity simulators and tossed some balls around to rotate around each other, traced out where they were moving, and that you therefore solved the 3 body problem. It is not a solution. You found a pattern in your gravity simulator. It is not useful for solving problems.
3 body problem, eclipses, etc.
Isn't this where Junker or someone usually criticizes posts for being off topic and derailing threads?
Tom, are you accepting or declining his invitation?
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Hmm, interesting storm of responses.
I'll reply here to Tom Bishop's assertion that modern astronomy predicts occultations by using patterns derived from previous observations. This goes to the heart of how science works.
Indeed, science always starts from observed patterns; then people produce models to understand those patterns, and eventually laws to systematize them. The relevant example here is Kepler's Laws of Planetary Motion, which then led to Newton's Theory of Universal Gravitation. Modern astronomy uses gravitational theory (Newtonian or Einsteinian, depending on the accuracy needed) to calculate the motion of the moon in its orbit about the earth and the planets in their orbits about the sun. Patterns tell us that occultations of Aldebaran by the moon occur regularly, but theory predicts that a particular occultation can be observed at a particular site at a time specified to within a tenth of a second. Observations feed back into the theory, giving us ever better predictive capability.
This is what I ask from a flat-earth theorist. Not patterns, but precise predictions.
That modern astronomy no longer relies on mere patterns to predict occultations is shown by the fact that we can predict occultations of stars by newly discovered asteroids. The popular astronomy magazine Sky and Telescope regularly publishes such predictions to encourage backyard astronomers to look for them.
And since the theme of the three-body problem has crept into this discussion, I should remark that ephemeris calculations of newly discovered asteroids (or of any other solar system object) are routinely done by numerical integration of the equations of motion of that body in the gravitational field produced by the sun, all the planets, and the several largest asteroids. This is not an impossible problem; it is solved thousands of times daily.
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At no point do they actually come up with a solution to the three body problem. They think that they can create a 3D model of moving bodies, run it a few times, see the pattern, and therefore they can predict future occurrences from the pattern and the three body problem has been solved.
you're severely misunderstanding two things: 1) what the paper is saying, and 2) what an analytic solution means.
first, the paper is not describing patter recognition. the parts you're describing are meant to demonstrate that the code does what it's supposed to do by asking it to find numerical solutions to problems for which there are known analytic solutions. the author starts by demonstrating that it correctly solves two-body problems. then he shows that it correctly solves a special case of the three-body problem. and so on.
second, you're conflating "does not have an analytic solution" with "cannot be solved." that's not what it means, though. here's an example:
suppose you make a graph of an object's position over time and you get a graph like this. there's a function that will tell you the value of the graph at any arbitrary point along the horizontal axis. this "motion" has an anlytical solution. it can be described by functions we know.
(https://i.imgur.com/6cTAE2i.png)
now suppose you see this graph. there is no function that will tell you the value of the graph at any arbitrary point along the horizontal axis. it's just a bunch of random chaotic movement. it's hardly a failure of physics that mathematics does not have analytic functions to describe a graph like this.
(https://www.johndcook.com/ec55.png)
the only reason two-body problems can be solved analytically is that it's circular/elliptical motion, and we have lots of functions for that. if two-body motion were like the second graph, then we wouldn't have analytic solutions for them, either. it's not a coincidence that the special cases for which there are analytic solutions to the three-body problem all involve circular motion.
ironically, these simulations are exactly about using geometry and physics to solve a problem that has no purely mathematical solution.
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Indeed, science always starts from observed patterns; then people produce models to understand those patterns, and eventually laws to systematize them. The relevant example here is Kepler's Laws of Planetary Motion, which then led to Newton's Theory of Universal Gravitation. Modern astronomy uses gravitational theory (Newtonian or Einsteinian, depending on the accuracy needed) to calculate the motion of the moon in its orbit about the earth and the planets in their orbits about the sun.
Except that NASA still uses the Saros Cycle for its Lunar Eclipse and Solar Eclipse predictions, which is an ancient pattern-based method for finding the time of the eclipse. They are not using a geometric model.
Go to NASA's Eclipse Website (https://eclipse.gsfc.nasa.gov/eclipse.html) -> Resources -> Eclipses and the Saros (https://eclipse.gsfc.nasa.gov/SEsaros/SEsaros.html)
That is the only method given on that entire website. They do not describe "motion laws" and "gravitational theory". They describe a method used by an ancient society of people who believed that the earth was flat.
It is mentioned on the NASA site that the Solar Ecliple may also be predicted with Besselian Elements (https://eclipse.gsfc.nasa.gov/SEcat5/beselm.html), but we can see from this description of the method on stackexchange (https://astronomy.stackexchange.com/questions/231/what-is-the-formula-to-predict-lunar-and-solar-eclipses-accurately) (at the bottom) that it is just another pattern-based method.
That modern astronomy no longer relies on mere patterns to predict occultations is shown by the fact that we can predict occultations of stars by newly discovered asteroids. The popular astronomy magazine Sky and Telescope regularly publishes such predictions to encourage backyard astronomers to look for them.
Why are you lying to us?
Go here to find how Sky and Telescope makes such predictions of the occultations of stars by asteroids: http://www.skyandtelescope.com/observing/planetary-occultation-highlights-for-2002/
Do you see any equations on that page? Do you see any assumptions of the distances to stars or asteroids?
They are making a map of the path stars travel over the surface of the earth (they don't move much, unlike the moon) and determining where the path of the astroid will intersect. This is absoutely a method that relies on patterns. They are determining what the pattern of the stars over the earth are, and determining whether the asteroids will intersect that path. This is pattern based. There are no geometric equations or any real Round Earth Theory assumptions.
This is what I ask from a flat-earth theorist. Not patterns, but precise predictions.
I don't see why we need to give any predictions more than the pattern based method which already exist. Sky and Telescope tells us that this can all be predicted without needing to know much about the Round Earth model.
And since the theme of the three-body problem has crept into this discussion, I should remark that ephemeris calculations of newly discovered asteroids (or of any other solar system object) are routinely done by numerical integration of the equations of motion of that body in the gravitational field produced by the sun, all the planets, and the several largest asteroids. This is not an impossible problem; it is solved thousands of times daily.
You will have to show that any such geometric models are accurate.
NASA certainly isn't using a three body problem to give us its eclipse predictions. Sky and Telescope is not using complex gravitational equations for their asteroid occultations predictions.
Are we to believe in this assertion without evidence?
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First, NASA does use a special solve of the three body problem for eclipses. If you haven't managed to piece that together after last time I'm not bothering to go over it again.
Second, as I pointed out last time, not insignificant evidence has been found pointing to the astronomers of the time period of the Saros Cycles creation, believed in a round Earth. I presented this last time you brought this up as well, so I don't expect it to sick this time either. I'll dig things up when I'm not on mobile, but a heliocentric globe model was found.
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you're severely misunderstanding two things: 1) what the paper is saying, and 2) what an analytic solution means.
first, the paper is not describing patter recognition. the parts you're describing are meant to demonstrate that the code does what it's supposed to do by asking it to find numerical solutions to problems for which there are known analytic solutions. the author starts by demonstrating that it correctly solves two-body problems. then he shows that it correctly solves a special case of the three-body problem. and so on.
second, you're conflating "does not have an analytic solution" with "cannot be solved." that's not what it means, though. here's an example:
suppose you make a graph of an object's position over time and you get a graph like this. there's a function that will tell you the value of the graph at any arbitrary point along the horizontal axis. this "motion" has an anlytical solution. it can be described by functions we know.
(https://i.imgur.com/6cTAE2i.png)
now suppose you see this graph. there is no function that will tell you the value of the graph at any arbitrary point along the horizontal axis. it's just a bunch of random chaotic movement. it's hardly a failure of physics that mathematics does not have analytic functions to describe a graph like this.
(https://www.johndcook.com/ec55.png)
the only reason two-body problems can be solved analytically is that it's circular/elliptical motion, and we have lots of functions for that. if two-body motion were like the second graph, then we wouldn't have analytic solutions for them, either. it's not a coincidence that the special cases for which there are analytic solutions to the three-body problem all involve circular motion.
ironically, these simulations are exactly about using geometry and physics to solve a problem that has no purely mathematical solution.
Gary, what are you talking about?
In the article you linked the authors basically created a scenerio where three bodies moved around each other and decided that they solved the three body problem. When you make a graph with a function you are computing a pattern.
Solving the three body problem is actually much more complicated than that; it's providing a solution that will allow us to solve the problems in space and physics, where we do not know the exact "function" that brings the scenerio to its conclusion. You admitted yourself that the solution of the page was not very useful.
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First, NASA does use a special solve of the three body problem for eclipses. If you haven't managed to piece that together after last time I'm not bothering to go over it again.
A simple link will suffice. I have been all over that website and have found no such thing.
Second, as I pointed out last time, not insignificant evidence has been found pointing to the astronomers of the time period of the Saros Cycles creation, believed in a round Earth. I presented this last time you brought this up as well, so I don't expect it to sick this time either. I'll dig things up when I'm not on mobile, but a heliocentric globe model was found.
Here was your post:
What I stated is all laid out right here (https://en.wikipedia.org/wiki/Babylonian_astronomy#Neo-Babylonian_astronomy) and I'm not speaking about Babylonia as a whole, but the astronomers and astrologers of the time. Even in Greece the idea of a round Earth was (at least early on) largely a view among the higher educated populace. At least based on what I've read while looking into this.
Under your Babylonian Astronomy section you linked us to as your evidence there is no mention of Round Earth anywhere. Do a search for "round" on that page. We do see the word Heliocentric, however (and that Wiki section says it was just one guy who supported Heliocentricism, FYI). You asserted that because they believed that the planetary model was Heliocentric, that this must also be a Round Earth model.
You are incorrect on all points. The word "round" or "sphere" does not appear on the Babylonian Astronomy page on the page you linked us to in reference to the earth's shape, and Heliocentric merely means sun at the center.
Under our current Flat Earth model, in fact, the planetary model is also Heliocentric. The sun is the center of our solar system. The Babylonians were smart enough to figure that out that the earth is flat and that the planetary model is Heliocentric. They were truly ahead of their time.
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Tom, the Saros cycle as it was used 1,000s of years ago is not sufficient to predict eclipses worldwide. You also have to perform a transformatiom of the coordinates based on, what kind of earth shape? Anyone? Anyone? Yes, a round earth.
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Is Babylon the center of the world and weren't there mythological objects on the babylonian map.
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Is Babylon the center of the world and weren't there mythological objects on the babylonian map.
Irrelevant. The Saros cycle was and is a very good way to predict eclipses.
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Why are you lying to us?
Go here to find how Sky and Telescope makes such predictions of the occultations of stars by asteroids: http://www.skyandtelescope.com/observing/planetary-occultation-highlights-for-2002/
Do you see any equations on that page? Do you see any assumptions of the distances to stars or asteroids?
They are making a map of the path stars travel over the surface of the earth (they don't move much, unlike the moon) and determining where the path of the asteroid will intersect. This is absolutely a method that relies on patterns. They are determining what the pattern of the stars over the earth are, and determining whether the asteroids will intersect that path. This is pattern based. There are no geometric equations or any real Round Earth Theory assumptions.
For the ease of argument, let's say this is all pattern-based. In what way does that disprove a round Earth? You use this pattern thing as a strawman to attack astronomy as a whole, but you really haven't thought it through. Here is your problem - even if everything in the sky is based on a repeating pattern, the ability to accurately tell you when and where something is going to occur requires a map that is highly accurate. Can FET make similar predictions over a large area? Can FET make any predictions at all?
Sky and Telescope magazine is for a lay audience. They are not going to include equations... smh
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First, NASA does use a special solve of the three body problem for eclipses. If you haven't managed to piece that together after last time I'm not bothering to go over it again.
A simple link will suffice. I have been all over that website and have found no such thing.
https://eclipse.gsfc.nasa.gov/SEpubs/5MCSE.html
Not sure how you've missed these considering they're the references on the bottom of the eclipse website. Please direct your attention to the 'Predictions' section of the page.
Second, as I pointed out last time, not insignificant evidence has been found pointing to the astronomers of the time period of the Saros Cycles creation, believed in a round Earth. I presented this last time you brought this up as well, so I don't expect it to sick this time either. I'll dig things up when I'm not on mobile, but a heliocentric globe model was found.
Here was your post:
What I stated is all laid out right here (https://en.wikipedia.org/wiki/Babylonian_astronomy#Neo-Babylonian_astronomy) and I'm not speaking about Babylonia as a whole, but the astronomers and astrologers of the time. Even in Greece the idea of a round Earth was (at least early on) largely a view among the higher educated populace. At least based on what I've read while looking into this.
Under your Babylonian Astronomy section you linked us to as your evidence there is no mention of Round Earth anywhere. Do a search for "round" on that page. We do see the word Heliocentric, however (and that Wiki section says it was just one guy who supported Heliocentricism, FYI). You asserted that because they believed that the planetary model was Heliocentric, that this must also be a Round Earth model.
You are incorrect on all points. The word "round" or "sphere" does not appear on the Babylonian Astronomy page on the page you linked us to in reference to the earth's shape, and Heliocentric merely means sun at the center.
Under our current Flat Earth model, in fact, the planetary model is also Heliocentric. The sun is the center of our solar system. The Babylonians were smart enough to figure that out that the earth is flat and that the planetary model is Heliocentric. They were truly ahead of their time.
Yes you would need to actually follow the link to https://en.wikipedia.org/wiki/Seleucus_of_Seleucia where it's explained what his model was. Considering he has the Earth rotating about it's own axis, I have my doubts it was a flat Earth in use. As for the other scholars mentioned, neither system discussed makes reference to globe/flat (I personally feel if it was flat it would be noted though) so we have 25% of noted figures of that period holding to a round Earth.
I would argue on yours being 'Heliocentric' as it's more a bastardization of Geocentric and Heliocentric and not quite either, but that's neither here nor there.
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Is Babylon the center of the world and weren't there mythological objects on the babylonian map.
Irrelevant. The Saros cycle was and is a very good way to predict eclipses.
Does it not contradict then being ahead of their time? Your response is more of a deflection from that; I see that a lot on here.
I don't really intend to post much on here, I was just curious.
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This is like saying that you solved the 3 body problem because you went online to one of those comet gravity simulators and tossed some balls around to rotate around each other, traced out where they were moving, and that you therefore solved the 3 body problem. It is not a solution. You found a pattern in your gravity simulator. It is not useful for solving problems.
3 body problem, eclipses, etc.
Isn't this where Junker or someone usually criticizes posts for being off topic and derailing threads?
Tom, are you accepting or declining his invitation?
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imagine you bring a pebble inside and drop it from some height. you make a plot of its position over time (its lateral motion, let's say) and you get a straight line. neat! there is a mathematical function that describes straight lines. you have an analytic solution for the object's position with respect to time or displacement or something.
now imagine you bring a leaf inside and drop it from some height. you plot its position over time, but now the plot is all messy, like graph #2 from my previous post. damn. there is no analytic solution that describes this motion.
where did the failure of physics happen? you didn't do any physics. you just plotted the position of an object over time. one of them happened to be describable by well-known analytic functions. the other did not. nothing failed at anything. it's just that lots of stuff can't be described analytically.
now imagine that i have a phd in fluid dynamics or something, and i simulate your leaf-dropping in a computer. i tell it how to update the position of the leaf over time using equations of motion from physics. if my code makes correct predictions, then it's asinine to say "your solution isn't analytical therefore it's wrong and/or meaningless." the opposite is true. i've used the laws of physics to get a numerical solution to an analytically unsolvable problem. that's a success, not a failure.
In the article you linked the authors basically created a scenerio where three bodies moved around each other and decided that they solved the three body problem. When you make a graph with a function you are computing a pattern.
Solving the three body problem is actually much more complicated than that; it's providing a solution that will allow us to solve the problems in space and physics, where we do not know the exact "function" that brings the scenerio to its conclusion. You admitted yourself that the solution of the page was not very useful.
you are completely misunderstanding both what this paper is saying, and what an analytic solution represents. and what a function is, if i'm being completely honest.
also i did not say that the solution from that paper is not very useful. i said that there do exist analytic solutions to 3bp, but they are not useful. numerical solutions are useful and make accurate predictions. numerical solutions are computationally expensive (you're iterating lots of tiny time-steps, for example), but they're not less useful/accurate/valuable than analytic solutions.
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imagine you bring a pebble inside and drop it from some height. you make a plot of its position over time (its lateral motion, let's say) and you get a straight line. neat! there is a mathematical function that describes straight lines. you have an analytic solution for the object's position with respect to time or displacement or something.
now imagine you bring a leaf inside and drop it from some height. you plot its position over time, but now the plot is all messy, like graph #2 from my previous post. damn. there is no analytic solution that describes this motion.
where did the failure of physics happen? you didn't do any physics. you just plotted the position of an object over time. one of them happened to be describable by well-known analytic functions. the other did not. nothing failed at anything. it's just that lots of stuff can't be described analytically.
now imagine that i have a phd in fluid dynamics or something, and i simulate your leaf-dropping in a computer. i tell it how to update the position of the leaf over time using equations of motion from physics. if my code makes correct predictions, then it's asinine to say "your solution isn't analytical therefore it's wrong and/or meaningless." the opposite is true. i've used the laws of physics to get a numerical solution to an analytically unsolvable problem. that's a success, not a failure.
In the article you linked the authors basically created a scenerio where three bodies moved around each other and decided that they solved the three body problem. When you make a graph with a function you are computing a pattern.
Solving the three body problem is actually much more complicated than that; it's providing a solution that will allow us to solve the problems in space and physics, where we do not know the exact "function" that brings the scenerio to its conclusion. You admitted yourself that the solution of the page was not very useful.
you are completely misunderstanding both what this paper is saying, and what an analytic solution represents. and what a function is, if i'm being completely honest.
also i did not say that the solution from that paper is not very useful. i said that there do exist analytic solutions to 3bp, but they are not useful. numerical solutions are useful and make accurate predictions. numerical solutions are computationally expensive (you're iterating lots of tiny time-steps, for example), but they're not less useful/accurate/valuable than analytic solutions.
I submit he is not misunderstanding anything. He knows that science and logic defeat his arguments so he can't acknowledge anything that blows holes in his theories. Fear is all it is.
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Argh - not the "three body problem" nonsense again!
The three body problem cannot be solved ANALYTICALLY - using a handy equation. There is no equation that you can give the positions and speeds of three objects and ask "Where will they be after N seconds."
HOWEVER:
In most practical situations, one or more of the bodies are so small compared to the others that you can neglect their influence on the larger body. So for objects like spacecraft in orbit around the Earth or the Sun or something - we have excellent math that isn't 100% accurate - but which has errors too tiny to ever matter.
Even in situations where you can't do that because all three masses are comparable in size - you can still do a stepwise approximation - and with suitably chosen time-steps, the answer can be constrained to be within reasonable bounds. This lets you do the math more than sufficiently well to come up with a good-enough answer.
So PLEASE stop saying that NASA can't solve the problem. Any idiot with a clue how to look up equations and the knowledge to program a computer can solve the three body problem to within whatever degree of precision you demand.
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Tom, are you accepting or declining his invitation?
If you really believe this FE stuff, you should welcome the opportunity.
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I will try once more, and then sign off. If a flat-earth theorist wants to accept our invitation, please send me a private message. Transportation costs are out of the question; our Board of Directors won't allow it.
Here's why lunar (or asteroid) occultations are important to the question of the earth's shape.
In the flat earth model, to account for the ~5 degree shift in the positions of the sun, moon, planets, and stars as one moves ~350 miles north or south, you must argue that those celestial objects are no more than about 4000 miles away, from simple trigonometry. Never mind that radar measurements of the moon contradict that argument; let's go with your conspiracy theory for the moment.
The stars must be somewhat farther away than the moon, or else occultations would not occur at all, but can't be much farther because the shifts (as one moves north or south) observed for stars would be much less than for the moon (in the flat earth model), contrary to observations.
Therefore in the flat-earth model, an occultation of Aldebaran either occurs or doesn't occur depending on whether the moon crosses in front of Aldebaran. So any place where both moon and Aldebaran are visible at the right time should observe the occultation, and there would be no difference in the circumstances of the occultation (i.e. where on the face of the moon the star disappears and subsequently reappears) whether you move south or north as long as the event is above the horizon.
What is in fact observed is that some locations on earth see a grazing occultation on the northern limb of the moon, some see a grazing occultation on the southern limb, and locations in between see the star disappear at various points around the moon. This is the effect of the moon's parallax - it is much closer to us than the star is. To demonstrate parallax: close one eye, hold your finger at arm's length so that it occults something you see out the window (a tree, chimney, mountain, whatever). Open that eye, close the other one, and the object is no longer occulted. This is one way we measure distances in astronomy.
The moon's parallax with respect to Aldebaran (or any other star it occults) implies that the star must be very much farther away than the moon. Again trigonometry can give you a (very crude) lower limit to the star's distance based on the precision with which you can measure small angles. But this would further imply that the shift in the positions of those stars as you move ~350 miles north or south on a flat earth would be much less than the ~5 degrees observed - a contradiction that can only be resolved by considering the true figure of the earth.
This coming December 31st offers a nice occultation of Aldebaran by the moon. Try it for yourselves: get an army of flat-earthers to observe the occultation from various (widely-spaced) locations, and bring them together to discuss the results. Sketches or photographs, please. Then let me know by private message whether you wish to engage in a public face-to-face discussion next April Fools' Day.
Farewell, folks, and thanks for the amusing interchange.
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I will try once more, and then sign off. If a flat-earth theorist wants to accept our invitation, please send me a private message.
Thanks for the effort, I didn't expect any of the FE faithful would accept.
This coming December 31st offers a nice occultation of Aldebaran by the moon. Try it for yourselves: get an army of flat-earthers to observe the occultation from various (widely-spaced) locations, and bring them together to discuss the results. Sketches or photographs, please. Then let me know by private message whether you wish to engage in a public face-to-face discussion next April Fools' Day.
Thanks for the heads up on that event, it would be an interesting experiment. Although I think that to prevent any claims of faking evidence, it would be useful to have FE & RE believers observe and photograph it together to maintain a kind of chain of evidence. I would be glad to participate from Northern Atlanta, GA. Although the best instrument I have to observe with is a basic DSLR with zoom.
I found a couple of articles on this and some reference to it happening on Dec 30, 2017. Can you clarify? I suspect it is happening on Dec 31 in UTC, but before midnight local time in the US, so Dec 30 there.
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I will try once more, and then sign off. If a flat-earth theorist wants to accept our invitation, please send me a private message. Transportation costs are out of the question; our Board of Directors won't allow it.
I'd be willing to contribute towards transportation costs, just for fun.
Here's why lunar (or asteroid) occultations are important to the question of the earth's shape.
In the flat earth model, to account for the ~5 degree shift in the positions of the sun, moon, planets, and stars as one moves ~350 miles north or south, you must argue that those celestial objects are no more than about 4000 miles away, from simple trigonometry. Never mind that radar measurements of the moon contradict that argument; let's go with your conspiracy theory for the moment.
The stars must be somewhat farther away than the moon, or else occultations would not occur at all, but can't be much farther because the shifts (as one moves north or south) observed for stars would be much less than for the moon (in the flat earth model), contrary to observations.
Therefore in the flat-earth model, an occultation of Aldebaran either occurs or doesn't occur depending on whether the moon crosses in front of Aldebaran. So any place where both moon and Aldebaran are visible at the right time should observe the occultation, and there would be no difference in the circumstances of the occultation (i.e. where on the face of the moon the star disappears and subsequently reappears) whether you move south or north as long as the event is above the horizon.
What is in fact observed is that some locations on earth see a grazing occultation on the northern limb of the moon, some see a grazing occultation on the southern limb, and locations in between see the star disappear at various points around the moon. This is the effect of the moon's parallax - it is much closer to us than the star is. To demonstrate parallax: close one eye, hold your finger at arm's length so that it occults something you see out the window (a tree, chimney, mountain, whatever). Open that eye, close the other one, and the object is no longer occulted. This is one way we measure distances in astronomy.
The moon's parallax with respect to Aldebaran (or any other star it occults) implies that the star must be very much farther away than the moon. Again trigonometry can give you a (very crude) lower limit to the star's distance based on the precision with which you can measure small angles. But this would further imply that the shift in the positions of those stars as you move ~350 miles north or south on a flat earth would be much less than the ~5 degrees observed - a contradiction that can only be resolved by considering the true figure of the earth.
This coming December 31st offers a nice occultation of Aldebaran by the moon. Try it for yourselves: get an army of flat-earthers to observe the occultation from various (widely-spaced) locations, and bring them together to discuss the results. Sketches or photographs, please. Then let me know by private message whether you wish to engage in a public face-to-face discussion next April Fools' Day.
Farewell, folks, and thanks for the amusing interchange.
This is great, but the assumption that you can measure distances on Earth is what will trip up argument here.
On the bright side, it sounds like latitude might be a thing after all, so baby steps.
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I will try once more, and then sign off. If a flat-earth theorist wants to accept our invitation, please send me a private message. Transportation costs are out of the question; our Board of Directors won't allow it.
Here's why lunar (or asteroid) occultations are important to the question of the earth's shape.
In the flat earth model, to account for the ~5 degree shift in the positions of the sun, moon, planets, and stars as one moves ~350 miles north or south, you must argue that those celestial objects are no more than about 4000 miles away, from simple trigonometry. Never mind that radar measurements of the moon contradict that argument; let's go with your conspiracy theory for the moment.
The stars must be somewhat farther away than the moon, or else occultations would not occur at all, but can't be much farther because the shifts (as one moves north or south) observed for stars would be much less than for the moon (in the flat earth model), contrary to observations.
Therefore in the flat-earth model, an occultation of Aldebaran either occurs or doesn't occur depending on whether the moon crosses in front of Aldebaran. So any place where both moon and Aldebaran are visible at the right time should observe the occultation, and there would be no difference in the circumstances of the occultation (i.e. where on the face of the moon the star disappears and subsequently reappears) whether you move south or north as long as the event is above the horizon.
What is in fact observed is that some locations on earth see a grazing occultation on the northern limb of the moon, some see a grazing occultation on the southern limb, and locations in between see the star disappear at various points around the moon. This is the effect of the moon's parallax - it is much closer to us than the star is. To demonstrate parallax: close one eye, hold your finger at arm's length so that it occults something you see out the window (a tree, chimney, mountain, whatever). Open that eye, close the other one, and the object is no longer occulted. This is one way we measure distances in astronomy.
The moon's parallax with respect to Aldebaran (or any other star it occults) implies that the star must be very much farther away than the moon. Again trigonometry can give you a (very crude) lower limit to the star's distance based on the precision with which you can measure small angles. But this would further imply that the shift in the positions of those stars as you move ~350 miles north or south on a flat earth would be much less than the ~5 degrees observed - a contradiction that can only be resolved by considering the true figure of the earth.
This coming December 31st offers a nice occultation of Aldebaran by the moon. Try it for yourselves: get an army of flat-earthers to observe the occultation from various (widely-spaced) locations, and bring them together to discuss the results. Sketches or photographs, please. Then let me know by private message whether you wish to engage in a public face-to-face discussion next April Fools' Day.
Farewell, folks, and thanks for the amusing interchange.
That's an interesting observation.
Certainly the different elevations of a star (or moon or sun) from different locations means that EITHER that body is around 4000 miles away OR the Earth is a sphere with a radius of 4000 miles and the object in question is a very long way away.
The precision with which that number can be measured is critical.
Eratosthenes measured it for the sun - and came up with a number OVER 4,000 miles - which means that the FE'ers are mistaken with their 3,000 mile number.
With modern equipment, we have a better measurement than Eatosthenes - so the number for the sun elevation must be VERY close to the RET mean radius of the Earth (3,959 miles). The distance from sun/moon/planets/stars to the Flat Earth must be VERY close to that number. The only difference could be the error in the measurement of the size of the Earth...which is less than the 31 mile claimed diameter of sun.
So if the stars are far enough away to being hit by the sun or moon - then they are already too far away to account for the measurements we have.
IMHO, the Flat Earthers should be predicting that Aldeberan will hit the moon and disappear from the skies forever!
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IMHO, the Flat Earthers should be predicting that Aldeberan will hit the moon and disappear from the skies forever!
Has FE ever predicted anything? I doubt they will start with this.
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I will try once more, and then sign off. If a flat-earth theorist wants to accept our invitation, please send me a private message. Transportation costs are out of the question; our Board of Directors won't allow it.
Here's why lunar (or asteroid) occultations are important to the question of the earth's shape.
In the flat earth model, to account for the ~5 degree shift in the positions of the sun, moon, planets, and stars as one moves ~350 miles north or south, you must argue that those celestial objects are no more than about 4000 miles away, from simple trigonometry. Never mind that radar measurements of the moon contradict that argument; let's go with your conspiracy theory for the moment.
The stars must be somewhat farther away than the moon, or else occultations would not occur at all, but can't be much farther because the shifts (as one moves north or south) observed for stars would be much less than for the moon (in the flat earth model), contrary to observations.
Therefore in the flat-earth model, an occultation of Aldebaran either occurs or doesn't occur depending on whether the moon crosses in front of Aldebaran. So any place where both moon and Aldebaran are visible at the right time should observe the occultation, and there would be no difference in the circumstances of the occultation (i.e. where on the face of the moon the star disappears and subsequently reappears) whether you move south or north as long as the event is above the horizon.
What is in fact observed is that some locations on earth see a grazing occultation on the northern limb of the moon, some see a grazing occultation on the southern limb, and locations in between see the star disappear at various points around the moon. This is the effect of the moon's parallax - it is much closer to us than the star is. To demonstrate parallax: close one eye, hold your finger at arm's length so that it occults something you see out the window (a tree, chimney, mountain, whatever). Open that eye, close the other one, and the object is no longer occulted. This is one way we measure distances in astronomy.
The moon's parallax with respect to Aldebaran (or any other star it occults) implies that the star must be very much farther away than the moon. Again trigonometry can give you a (very crude) lower limit to the star's distance based on the precision with which you can measure small angles. But this would further imply that the shift in the positions of those stars as you move ~350 miles north or south on a flat earth would be much less than the ~5 degrees observed - a contradiction that can only be resolved by considering the true figure of the earth.
You assume that large distance perspective follows the ancient rules of "simple trigonometry" which assumes a continuous universe model.
That is called an assumption. A hypothesis. Something which has never been demonstrated. The Ancient Greeks never proved their perspective theories.
You want us to make explanations based on a model you have not shown to be accurate.
If you were challenged to show proof of the rules of the same model that two horizontal parallel perspective lines will approach each other for infinity but never touch, or that a body thousands of miles away will appear a certain number of degrees above the horizon, or that perspective behaves the same at all scales, you will be embarrassingly unable to do so.
Unless you can substantiate the underlying assumptions of your challenge I see no reason why anyone should attempt an answer or take your questions seriously.
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If you were challenged to show proof of the rules of the same model that two horizontal lines will approach each other for infinity but never touch, or that a body thousands of miles away will appear a certain number of degrees above the horizon, or that perspective behaves the same at all scales, you will be embarrassingly unable to do so.
You have never shown that it does not. This is your claim, you need to show evidence that the rules change at long distances. I've told you this now repeatedly. Trig - when using numbers to account for the limits of the eye - accurately represents perspective. I showed you this with the railroad tracks. You claim those rules break down at some unknown distance for some reason. Prove it. This is your claim. The numbers work for all testable distances. You are claiming they stop working past them. Where is your evidence for this claim? Where is your proof?
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You assume that large distance perspective follows the ancient rules of "simple trigonometry" which assumes a continuous universe model.
That is called an assumption. A hypothesis. Something which has never been demonstrated. The Ancient Greeks never proved their perspective theories.
You want us to make explanations based on a model you have not shown to be accurate.
If you were challenged to show proof of the rules of the same model that two horizontal lines will approach each other for infinity but never touch, or that a body thousands of miles away will appear a certain number of degrees above the horizon, you will be unable to do so.
We therefore win by default as the challenger has based his premise on an unproven tenet. The conversation cannot continue, and no further consideration can be made to that challenge, unless those basic tenets are substantiated.
There, I saved myself a weekend.
Just when I think the nonsense here can't become any more absurd.
Tom, while I think your grasp of science is completely flawed, usually I think you show some effort to at least portray some level of thinking, even if it is completely wrong. Your posts on this thread really come off as desperate to avoid facing his logic and knowledge in public. I expected this, but I expected it by inaction.
two horizontal lines will approach each other for infinity but never touch
I think you mean parallel lines here. How would one prove to your satisfaction that they approach for infinity but don't touch? I suspect the only way would be to examine them at infinity, which is clearly impossible. To paraphrase, I refuse to talk to you until you prove something impossible to prove. Just childish.
And for the last time (I wish). Parallel lines APPEAR to approach to our eyes. This has nothing to do with how they exist in the real world.
that a body thousands of miles away will appear a certain number of degrees above the horizon
Viewed from Atlanta, GA on December 30, 2017. The moon will block the view of Aldebaran starting at 18:09:36 with the moon at 28 degrees above the horizon at azimuth 88 degrees.
Ending at 18:52:22 with the moon at 37 degrees above the horizon at azimuth 94 degrees. This is sourced from http://www.lunar-occultations.com/iota/bstar/1230zc692.htm (http://www.lunar-occultations.com/iota/bstar/1230zc692.htm)
What were you saying about not predicting things?
So go on with your usual diatribe about astronomy. Do you expect these predictions to be correct or not?
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You assume that large distance perspective follows the ancient rules of "simple trigonometry" which assumes a continuous universe model.
I have to break this news to you, trigonometry works. I challenge you to corroborate your statement that trigonometry is in anyway based on an assumption of a "continuous universe model".
Maybe you could start by defining "continuous universe model".
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You assume that large distance perspective follows the ancient rules of "simple trigonometry" which assumes a continuous universe model.
That is called an assumption. A hypothesis. Something which has never been demonstrated. The Ancient Greeks never proved their perspective theories.
You want us to make explanations based on a model you have not shown to be accurate.
If you were challenged to show proof of the rules of the same model that two horizontal lines will approach each other for infinity but never touch, or that a body thousands of miles away will appear a certain number of degrees above the horizon, or that perspective behaves the same at all scales, you will be embarrassingly unable to do so.
Unless you can substantiate the underlying assumptions of your challenge I see no reason why anyone should attempt an answer or take your questions seriously.
Tom, you are embarrassingly unable to prove anything about FET. You ASSUME parallel lines touch at some point due to perspective. You need this to be true so you can have a vanishing point (which is an art term) to explain the horizon and setting sun, etc. The problem is, there is no proof this ever happens.
I'm assuming when you refer to a non-continuous universe, you are referring to Max Planck's work? (Planck length basically quantizes the universe. There is a length below which spacetime ceases to exist) You probably also know that this has no bearing on our everyday existence. You should probably also know that this is unobservable, so you couldn't possibly believe it anyways. That pesky empiricism thing.
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You assume that large distance perspective follows the ancient rules of "simple trigonometry" which assumes a continuous universe model.
Yes, I do. But you characterize "simple trigonometry" as "ancient" and (by implication) old and outdated. But the proofs of what they said are still valid. Every logical step they take is still true. These are truths about mathematics - no some concept that can become outdated.
But I'm intrigued by your complaint that we're assuming a "continuous universe model".
This is not a clear-cut term. If you google it - you get arguments about the continuous universe as an alternative to Big Bang theory...and that the continuous universe model is outdated. So if THAT is what you're talking about, then (a) No, I'm not assuming that - the Big Bang seems a well-proven thing...and (b) I don't see how trigonometry and perspective and all of that relates in any way to whether you assume one or the other.
So I can only assume you assign some other meaning to the phrase. Deeper searching yields the possibility that you are talking about "discrete versus continuous" physics. But this is stuff about whether quantum theory is an artifact of a continuous underlying structure or one that is truly quantized...and again, I see nothing in either belief that changes my answers on trigonometry and perspective.
So in order for conversation to proceed - you'll need to explain what you mean by "continuous universe model" and in what ways discarding it helps your case.
That is called an assumption. A hypothesis. Something which has never been demonstrated. The Ancient Greeks never proved their perspective theories.
Euclid's "Optics" is the first serious mathematical treatment of perspective - and it most certainly does contain proofs. You can find a modern translation of it here: http://philomatica.org/wp-content/uploads/2013/01/Optics-of-Euclid.pdf
But everything in it can be proven - and I have done so in at least two thread here - which you do not seem to have been able to follow. You just said something like "But that's just a diagram" and went back to talking about it in ways that double-dip on perspective by (in effect) applying it twice...which is simply an error.
You want us to make explanations based on a model you have not shown to be accurate.
There are many ways to show that it's accurate. One is to take the mathematics that I derive from nothing more than:
* a pinhole camera.
* straight light rays.
* the law of similar triangles.
This yields the equations:
x' = x k / z
y' = y k / z
(where x' and y' are the post-perspective coordinates, x,y,z are the real world coordinates and k is a constant related to the size of the camera versus the size of the image).
Using a computer (as I do, literally every day) to produce pictures of the world produces images that line up perfectly with real world photography. This is PROOF that the math is correct.
If you were challenged to show proof of the rules of the same model that two horizontal lines will approach each other for infinity but never touch, or that a body thousands of miles away will appear a certain number of degrees above the horizon, or that perspective behaves the same at all scales, you will be embarrassingly unable to do so.
I never said that "two horizontal lines will approach each other for infinity but never touch" - perhaps you mean "two parallel lines will never touch" (in the real world) or that with perspective "two parallel lines will touch at infinity". Those things can be proven from the definition of the word "parallel" and the equations above that I derived from pinhole camera/straight lines/similar triangles.
That "perspective behaves the same at all scales" is inevitable if light travels in straight lines and the law of similar triangles is true. You seem to agree that light travels in straight lines (although you "embarrassingly" are unable to write that thread you TWICE promised us in which you'd explain how photons get from the sun to the eye at sunset)...if you don't agree that the law of similar triangles is true - then I'd be happy to regurgitate the proof for you in small words that you'd understand.
Far *FAR* from being "embarrassingly unable" to prove those things - I HAVE proven them...many times and in many ways - you simply choose to simply dismiss or ignore all of my proofs.
Never once have you taken my careful step by step arguments and said..."HERE! Step 4 - that's not true because..." and explained precisely where my reasoning breaks down.
The reason you cannot is because my geometric arguments are 100% correct and either you can't follow them because you're poorly educated and don't understand high school geometry - or you willfully ignore them because you know they prove conclusively that there cannot be sunsets in a flat earth.
That a body some distance away will appear a certain number of degrees above the horizon is also proven in at least a couple of diagrams I posted and some posts which you basically ignored or dismissed as "just diagrams".
Unless you can substantiate the underlying assumptions of your challenge I see no reason why anyone should attempt an answer or take your questions seriously.
Ah - so after twice saying that you WOULD explain how those photons travel from sun to eye at sunset - you're now saying that you're not going to answer me.
The underlying assumptions of my arguments are CLEARLY stated...light travels in straight lines...pinhole cameras really do take good photos...the law of similar triangles is true.
The steps from that to "Here are the laws of perspective and they don't allow sunsets in FET" are laid out in at least two previous threads that you responded to and failed to follow up with your explanation.
OK - well that tells us a lot about your level of intellect and the weakness of your arguments. Would you prefer to be labelled ignorant or a liar?
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If you were challenged to show proof of the rules of the same model that two horizontal parallel perspective lines will approach each other for infinity but never touch, you will be embarrassingly unable to do so.
Tom this is just nonsense! The dictionary definition of parallel:
https://www.google.com/search?q=define+parallel&oq=define+parallel&aqs=chrome..69i57.3967j0j7&sourceid=chrome&ie=UTF-8&safe=active&ssui=on (https://www.google.com/search?q=define+parallel&oq=define+parallel&aqs=chrome..69i57.3967j0j7&sourceid=chrome&ie=UTF-8&safe=active&ssui=on)adjective
1.
(of lines, planes, or surfaces) side by side and having the same distance continuously between them.
The very MEANING of the word parallel is that the line have the same space between them therefore THEY CAN NEVER TOUCH! You do not require proof of this, the proof is in the very words you are using!
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If you were challenged to show proof of the rules of the same model that two horizontal lines will approach each other for infinity but never touch, or that a body thousands of miles away will appear a certain number of degrees above the horizon, or that perspective behaves the same at all scales, you will be embarrassingly unable to do so.
You have never shown that it does not. This is your claim, you need to show evidence that the rules change at long distances. I've told you this now repeatedly.
Nope. You are the one coming here and saying that perspective operates according to certain rules of trigonometry. Therefore it is YOU who needs to back up your claims.
Show that two parallel perspective lines will never meet. In our experience they do appear to meet. Show that the merging of the lines in perspective is an illusion.
Your position is that illusions are occurring. How is it NOT your responsibility to demonstrate that?
You are claiming they stop working past them. Where is your evidence for this claim? Where is your proof?
I am not asserting anything more that what is empirical; the meeting of perspective lines. You are asserting something contrary to experience and so it is your responsibility to prove that perspective operates on certain rules.
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I think you mean parallel lines here. How would one prove to your satisfaction that they approach for infinity but don't touch? I suspect the only way would be to examine them at infinity, which is clearly impossible. To paraphrase, I refuse to talk to you until you prove something impossible to prove. Just childish.
I don't really care if it is impossible to prove for you. It just goes to show that it cannot be demonstrated and so we should not assume it in the premise.
And for the last time (I wish). Parallel lines APPEAR to approach to our eyes. This has nothing to do with how they exist in the real world.
We have no evidence other than what we experience. You are trying to combat an empirical experience with an ancient hypothesis.
that a body thousands of miles away will appear a certain number of degrees above the horizon
Viewed from Atlanta, GA on December 30, 2017. The moon will block the view of Aldebaran starting at 18:09:36 with the moon at 28 degrees above the horizon at azimuth 88 degrees.
Ending at 18:52:22 with the moon at 37 degrees above the horizon at azimuth 94 degrees. This is sourced from http://www.lunar-occultations.com/iota/bstar/1230zc692.htm (http://www.lunar-occultations.com/iota/bstar/1230zc692.htm)
What were you saying about not predicting things?
So go on with your usual diatribe about astronomy. Do you expect these predictions to be correct or not?
Astronomy is based on observed patterns. Observed patterns of the moon, observed patterns of the stars. Things are only predictable because they come in patterns. It is possible to create an equation to express those patterns, but they are only valuable in that they might produce a right answer.
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If you were challenged to show proof of the rules of the same model that two horizontal lines will approach each other for infinity but never touch, or that a body thousands of miles away will appear a certain number of degrees above the horizon, or that perspective behaves the same at all scales, you will be embarrassingly unable to do so.
You have never shown that it does not. This is your claim, you need to show evidence that the rules change at long distances. I've told you this now repeatedly.
Nope. You are the one coming here and saying that perspective operates according to certain rules of trigonometry. Therefore it is YOU who needs to back up your claims.
Show that two parallel perspective lines will never meet. In our experience they do appear to meet. Show that the merging of the lines in perspective is an illusion.
You are claiming they stop working past them. Where is your evidence for this claim? Where is your proof?
I am not asserting anything more that what is empirical; the meeting of perspective lines. You are asserting something contrary to experience and so it is your responsibility to prove that perspective operates on certain rules.
Perspective is not relevant to any discussion about the shape of the earth. 'Perspective lines' are not real lines, but what we appear to see. Look it up.
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You assume that large distance perspective follows the ancient rules of "simple trigonometry" which assumes a continuous universe model.
Yes, I do. But you characterize "simple trigonometry" as "ancient" and (by implication) old and outdated. But the proofs of what they said are still valid. Every logical step they take is still true. These are truths about mathematics - no some concept that can become outdated.
But I'm intrigued by your complaint that we're assuming a "continuous universe model".
This is not a clear-cut term. If you google it - you get arguments about the continuous universe as an alternative to Big Bang theory...and that the continuous universe model is outdated. So if THAT is what you're talking about, then (a) No, I'm not assuming that - the Big Bang seems a well-proven thing...and (b) I don't see how trigonometry and perspective and all of that relates in any way to whether you assume one or the other.
So I can only assume you assign some other meaning to the phrase. Deeper searching yields the possibility that you are talking about "discrete versus continuous" physics. But this is stuff about whether quantum theory is an artifact of a continuous underlying structure or one that is truly quantized...and again, I see nothing in either belief that changes my answers on trigonometry and perspective.
So in order for conversation to proceed - you'll need to explain what you mean by "continuous universe model" and in what ways discarding it helps your case.
Nearly all of our math is based on the teachings of the Ancient Greeks. Even new forms of maths are based on their fundamental premises. Under the teachings of the Ancient Greeks the number lines are infinitely long and infinitely divisible. There is no discrete concept of a number. These teachings are also applied to the universe; the math which describes how the world and the universe operate also makes such assumptions.
Euclid's "Optics" is the first serious mathematical treatment of perspective - and it most certainly does contain proofs. You can find a modern translation of it here: http://philomatica.org/wp-content/uploads/2013/01/Optics-of-Euclid.pdf
But everything in it can be proven - and I have done so in at least two thread here - which you do not seem to have been able to follow. You just said something like "But that's just a diagram" and went back to talking about it in ways that double-dip on perspective by (in effect) applying it twice...which is simply an error.
Elucid was wrong about a lot of things. The Greek model of the universe is flimsy.
The continuous universe model, the basic concepts of line and point graphs, which are infinitely indivisible and infinitely long, was disproven by Zeno of Elea. His numerous critiques show that the continuous universe model is a sham and does not translate to the real world. For example, this math makes it impossible to walk through a door, or for a rabbit to overcome a tortoise in a race.
Look up Zeno's Paradox (http://barang.sg/index.php?view=achilles). Zeno's Paradox deals with how space and time work on the smallest scales.
You want us to make explanations based on a model you have not shown to be accurate.
There are many ways to show that it's accurate. One is to take the mathematics that I derive from nothing more than:
* a pinhole camera.
* straight light rays.
* the law of similar triangles.
This yields the equations:
x' = x k / z
y' = y k / z
(where x' and y' are the post-perspective coordinates, x,y,z are the real world coordinates and k is a constant related to the size of the camera versus the size of the image).
Using a computer (as I do, literally every day) to produce pictures of the world produces images that line up perfectly with real world photography. This is PROOF that the math is correct.
I don't see any evidence of anything. Line up how? I don't see any pictures.
I never said that "two horizontal lines will approach each other for infinity but never touch" - perhaps you mean "two parallel lines will never touch" (in the real world) or that with perspective "two parallel lines will touch at infinity". Those things can be proven from the definition of the word "parallel"
The definition of parallel does not account for perspective. If the definition were true than railroad tracks could never be angled at each other.
That "perspective behaves the same at all scales" is inevitable if light travels in straight lines and the law of similar triangles is true. You seem to agree that light travels in straight lines (although you "embarrassingly" are unable to write that thread you TWICE promised us in which you'd explain how photons get from the sun to the eye at sunset)...if you don't agree that the law of similar triangles is true - then I'd be happy to regurgitate the proof for you in small words that you'd understand.
The matter on how photons travel has been addressed several times for you. You keep pointing back to your illustrations of a continuous universe model as if it proves something about how the world works. You are assuming conclusions based on an Ancient Greek fantasy model where things are continuous, rather than an experience of the real world.
Far *FAR* from being "embarrassingly unable" to prove those things - I HAVE proven them...many times and in many ways - you simply choose to simply dismiss or ignore all of my proofs.
All of your proofs require us to assume several hypothesis' as true.
Never once have you taken my careful step by step arguments and said..."HERE! Step 4 - that's not true because..." and explained precisely where my reasoning breaks down.
It is not that it is not or cannot be true; the premise is unfounded and so that must first be addressed.
The reason you cannot is because my geometric arguments are 100% correct and either you can't follow them because you're poorly educated and don't understand high school geometry
We are far more familiar with these topics than you are. We do understand "high school geometry" and have summarily rejected it until certain fundamental tenets have been demonstrated.
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Show that two parallel perspective lines will never meet. In our experience they do appear to meet. Show that the merging of the lines in perspective is an illusion.
Your position is that illusions are occurring. How is it NOT your responsibility to demonstrate that?
I have never seen 2 parallel lines converge. If you think they do, I suggest you go back to grade school and relearn what parallel means.
You've asked this illusion thing in the past. It is either real or an illusion, correct? We know, without any doubt that train tracks never converge. It is, therefore, an illusion. Perspective doesn't change reality, it only changes your perception of it.
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Tom - please explain your non-continuous universe and how it relates to FET. Much like perspective, no one knows exactly what you are talking about.
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If you were challenged to show proof of the rules of the same model that two horizontal lines will approach each other for infinity but never touch, or that a body thousands of miles away will appear a certain number of degrees above the horizon, or that perspective behaves the same at all scales, you will be embarrassingly unable to do so.
You have never shown that it does not. This is your claim, you need to show evidence that the rules change at long distances. I've told you this now repeatedly.
Nope. You are the one coming here and saying that perspective operates according to certain rules of trigonometry. Therefore it is YOU who needs to back up your claims.
Show that two parallel perspective lines will never meet. In our experience they do appear to meet. Show that the merging of the lines in perspective is an illusion.
I have never ever said that. You are the one who keeps conflating parallel lines and perspective lines. They are NOT the same thing. Parallel lines will never meet. Fact. Parallel lines will appear to meet in the eye due to the limits of perspective. Fact. I showed you exactly how the math works in another thread.
You are claiming they stop working past them. Where is your evidence for this claim? Where is your proof?
I am not asserting anything more that what is empirical; the meeting of perspective lines. You are asserting something contrary to experience and so it is your responsibility to prove that perspective operates on certain rules.
I've said repeatedly that perspective lines meet, and exactly how the math shows they meet in our eyes. You are claiming that 20 degrees is small enough to not see because of perspective at long distances with no proof or evidence to back up that claim.
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Tom - please explain your non-continuous universe and how it relates to FET. Much like perspective, no one knows exactly what you are talking about.
The ancients tried to apply their math and ideas about number lines, how they are infinitely long and infinitely discrete, in addition to other continuous mathematical concepts, to the real world. This is why, according to their math, the perspective lines never meet.
We challenge that assertion and would like to see more evidence than a mathematical hypothesis about how perspective would behave before concluding what should or should not happen with long perspective lines.
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The definition of parallel does not account for perspective. If the definition were true than railroad tracks could never be angled at each other
You realize that railroad tracks aren't ACTUALLY angled at each other, right? The tracks only APPEAR to be angled at each other.
"Parallel" describes things as they actually are in the world. "Perspective" describes how things appear to the observer.
You cannot mix the two. Perspective lines appear to meet at infinity, you (and Rowbotham) are the one insisting that perspective lines meet before infinity, without evidence.
Show that two parallel perspective lines will never meet. In our experience they do appear to meet. Show that the merging of the lines in perspective is an illusion.
What experience do you have of travelling to infinity to see if the lines have met yet or not? I have not taken any hallucinogenics, but if it would help please recommend some.
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I have never ever said that. You are the one who keeps conflating parallel lines and perspective lines. They are NOT the same thing. Parallel lines will never meet. Fact.
According to "definitions," any "parallel" lines should never get closer to each other, either. But in a railroad perspective scene, they do.
Parallel lines will appear to meet in the eye due to the limits of perspective. Fact.
Meet in the eye? Do you have any evidence that this phenomenon is an effect of the eye? There are cameras without lenses which see perspective.
I showed you exactly how the math works in another thread.
The math you post is ancient greek continuous universe math we can throw right out the window until the fundamentals have been demonstrated otherwise.
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Tom - please explain your non-continuous universe and how it relates to FET. Much like perspective, no one knows exactly what you are talking about.
The ancients tried to apply their math and ideas about number lines, how they are infinitely long and infinitely discrete, in addition to other continuous mathematical concepts, to the real world. This is why, according to their math, the perspective lines never meet.
We challenge that assertion and would like to see more evidence than a mathematical hypothesis about how perspective would behave before concluding what should or should not happen with long perspective lines.
While the Greeks played a large role in math, they are hardly alone. Many other cultures contributed greatly to our understanding. Given how incredibly successful mathematics are for so many varied applications, your burden of proof is absurdly high.
I mentioned Max Planck and his work on a discrete universe that isn't infinitely divisible. The scales at which this has any effect are FAR too small to be noticed in the real world. The gaps between atoms in a table are far larger (by a massive amount), but that isn't relevant to what we see in the world. Number lines are infinitely long. You can N+1 for eternity and never run out of numbers. Seems a very weird bone of contention.
So, how exactly does any of this relate to perspective??
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I have never ever said that. You are the one who keeps conflating parallel lines and perspective lines. They are NOT the same thing. Parallel lines will never meet. Fact.
According to "definitions," any "parallel" lines should never get closer to each other, either. But in a railroad perspective scene, they do.
Parallel lines will appear to meet in the eye due to the limits of perspective. Fact.
Meet in the eye? Do you have any evidence that this phenomenon is an effect of the eye? There are cameras without lenses which see perspective.
I showed you exactly how the math works in another thread.
The math you post is ancient greek continuous universe math we can throw right out the window until the fundamentals have been demonstrated otherwise.
What do you by scene. We know we, yes we, have parallell tracks, it is just like they look to get closer simply because they are further away.
No need to reply as you know I am correct.
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I have never ever said that. You are the one who keeps conflating parallel lines and perspective lines. They are NOT the same thing. Parallel lines will never meet. Fact.
According to "definitions," any "parallel" lines should never get closer to each other, either. But in a railroad perspective scene, they do.
Parallel lines will appear to meet in the eye due to the limits of perspective. Fact.
Meet in the eye? Do you have any evidence that this phenomenon is an effect of the eye? There are cameras without lenses which see perspective.
I showed you exactly how the math works in another thread.
The math you post is ancient greek continuous universe math we can throw right out the window until the fundamentals have been demonstrated otherwise.
There you go using perspective in the wrong context again. The perspective effect is due to light traveling in straight lines, and a few other things as explained by 3D above. *Where* they appear to meet is a function of the eye, or whatever happens to be 'focusing' the light rays.
Once again. Parallel lines =/= perspective lines. Perspective lines are a construct of art, not math. Math CAN however still tell us how things will look, once again explained by 3D above in greater detail. If math couldn't you would never have a computer generated image that looked 'true to life' such as can be seen in any modern video game.
'Continuous universe' is another nonsense term at the moment, as neither standard definition has anything to do on the scales we are talking about. The fundamentals of trig have been demonstrated to work for buildings and more for a few thousand years by now, so your claim is without merit.
Once again. We claim math works, and we can show it reflects reality at any measurable distance. There is no inherent reason to think it stops working past those distances. You claim it does. What is your proof?
"We can see railroad tracks meeting"? Yeah, and the math shows us where/how/why and can be used to accurately model this in a computer. So this isn't proof. Try again.
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While the Greeks played a large role in math, they are hardly alone. Many other cultures contributed greatly to our understanding. Given how incredibly successful mathematics are for so many varied applications, your burden of proof is absurdly high.
What do you mean incredibly successful? That math can't even explain how a rabbit could overcome a tortoise in a race (http://barang.sg/index.php?view=achilles).
I mentioned Max Planck and his work on a discrete universe that isn't infinitely divisible.
Yes, that is a good example. Zeno was right in that the universe is non-continuous. The ancients got it wrong.
That's one of the big problems with finding a Grand Unified Theory. Quantum Mechanics says that the universe is discrete, and that there are discrete units of space and time, while General Relativity says that the universe is continuous in space and time. The concepts are not compatible.
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While the Greeks played a large role in math, they are hardly alone. Many other cultures contributed greatly to our understanding. Given how incredibly successful mathematics are for so many varied applications, your burden of proof is absurdly high.
What do you mean incredibly successful? That math can't even explain how a rabbit could overcome a tortoise in a race (http://barang.sg/index.php?view=achilles).
I mentioned Max Planck and his work on a discrete universe that isn't infinitely divisible.
Yes, that is a good example. Zeno was right in that the universe is non-continuous. The ancients got it wrong.
That's one of the big problems with finding a Grand Unified Theory. Quantum Mechanics says that the universe is discrete, and that there are discrete units of space and time, while General Relativity says that the universe is continuous in space and time. The concepts are not really that compatible and there are issues in translation.
Which is not relevant when discussing distances of several thousand miles.
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What do you mean incredibly successful? That math can't even explain how a rabbit could overcome a tortoise in a race (http://barang.sg/index.php?view=achilles).
Oh good grief. Even Zeno didn't believe Zeno's paradox.
You seriously think math can't sum an infinite series? Good grief - you really didn't pay attention in high school math class did you? This is literally child's play.
OK - so firstly you got the story wrong it wasn't a "hare" or a "rabbit" - it was Achilles.
Achilles gives the tortoise a head start of (say) 100 feet. Achilles runs at 10 feet per second and the tortoise runs one foot per second. So Zeno says - that in the time it takes Achilles to run 100 feet (10 seconds), the tortoise has covered 10 feet. Achilles hasn't reached the tortoise, he runs 10 feet in one second and by then the tortoise has covered another foot...Achilles runs another foot in 1/10th of a second and by then the tortoise has covered a 1/10th of a foot...and so on.
Since at each step of the process - the amount of time we're considering halves - if we want to know how much time it takes for Achilles to catch up with the tortoise we have to sum an infinite series of time steps:
10 + 1 + 0.1 + 0.01 + ...
Well - I think I can do that sum in my head - its 11.11111111....recurring. No matter how many 1's you add after the decimal point, after 11.2 seconds - Achilles has definitely passed the tortoise.
If you want to know the distance at which he passes the lumbering beast:
100' + 10' + 1' + 0.1' + 0.01' + ...
Same deal - it happens at 111.1111... feet. So the tortoise is definitely overtaken before he can cross the 112' mark.
This is child's play math Tom. Do you SERIOUSLY think we can't solve it in this modern world? It's ridiculously easy.
There are some infinite series that are harder to sum (pi, for example) - and some which "blow up in your face" and sum to infinity or something like that - and even some that have no definite answer (eg: 1-1+1-1+1-1....).
But Zeno's paradox isn't a paradox at all, it's simple math problem.
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What do you mean incredibly successful? That math can't even explain how a rabbit could overcome a tortoise in a race (http://barang.sg/index.php?view=achilles).
Does anyone else find it ironic that Tom trots out Zeno's paradox as an unsolvable problem for the math, by linking to a site that shows how we can solve the problem with math? Although irony might not be quite the right word I feel it's close enough.
Thanks for laying it out here for everyone though 3D. I found the whole thing actually quite fascinating when I came across it in an earlier thread. I love math but have never delved into the slightly more peculiar corners of it.
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The ancients tried to apply their math and ideas about number lines, how they are infinitely long and infinitely discrete, in addition to other continuous mathematical concepts, to the real world. This is why, according to their math, the perspective lines never meet.
We challenge that assertion and would like to see more evidence than a mathematical hypothesis about how perspective would behave before concluding what should or should not happen with long perspective lines.
Be careful: Parallel lines don't meet in the real world. That's the definition of the word "parallel".
We know the math for perspective - I mentioned it before: x' = x k / z and y' = y k / z (and incidentally z' = z k / z...not that we necessarily care)...we can choose a camera where the constant 'k' is 1.0 to make life easier.
x' and y' are the locations of the point (x,y,z) in your two-dimensional image. z'=k ...so the image is located on the back of the camera.
I'm using x-is-right, y-is-up and z is distance away from the camera...which is conventional in 3D graphics.
So if we take two parallel lines - like railroad tracks - that are two units apart. They are one unit below the camera and start one unit in front of the camera and end up at infinity: In the real world (x,y,z) the left rail runs from (-1,-1,1) to (-1,-1,infinity) and the right rail runs from (1,-1,1) to (1,-1,infinity).
So in our image, the lefthand rail goes from x' = -1/1 = -1 units to x' = -1/infinity = 0 units. The righthand rail goes from x'= +1/1 = 1 units to x'= 1/infinity = 0 units. y' is -1/1 to -1/infinity for both rails.
So the coordinates of the ends of the two rails in our image is: (-1,-1) to (0,0) and (+1,-1) to (0,0). Hence both rails meet IN THE IMAGE at (0,0)...which is where you'd expect them to meet in a flat earth world with an infinite horizon. In the round earth, the rails curve over the horizon and disappear before they can meet...however, they might get VERY close and require high magnification to actually see the gap between them as the go over the horizon.
So - that proves what math and actual perspective says.
All you have left to complain about is my equations (x'= x k / z, etc)
Those I proved for you in another post - and are self evident from the principles of a pinhole camera, straight light rays and similar triangles. If you'd like me to re-post that proof, I'd be happy to do so.
You see the things that are claimed are childishly easy to prove. Your claims that we CAN'T prove them are founded entirely on your own lack of knowledge.
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What do you mean incredibly successful? That math can't even explain how a rabbit could overcome a tortoise in a race (http://barang.sg/index.php?view=achilles).
Oh good grief. Even Zeno didn't believe Zeno's paradox.
You seriously think math can't sum an infinite series? Good grief - you really didn't pay attention in high school math class did you? This is literally child's play.
OK - so firstly you got the story wrong it wasn't a "hare" or a "rabbit" - it was Achilles.
Achilles gives the tortoise a head start of (say) 100 feet. Achilles runs at 10 feet per second and the tortoise runs one foot per second. So Zeno says - that in the time it takes Achilles to run 100 feet (10 seconds), the tortoise has covered 10 feet. Achilles hasn't reached the tortoise, he runs 10 feet in one second and by then the tortoise has covered another foot...Achilles runs another foot in 1/10th of a second and by then the tortoise has covered a 1/10th of a foot...and so on.
Since at each step of the process - the amount of time we're considering halves - if we want to know how much time it takes for Achilles to catch up with the tortoise we have to sum an infinite series of time steps:
10 + 1 + 0.1 + 0.01 + ...
Well - I think I can do that sum in my head - its 11.11111111....recurring. No matter how many 1's you add after the decimal point, after 11.2 seconds - Achilles has definitely passed the tortoise.
You can't ever get to 11.2 seconds because the Greeks believed that time is continuous and infinitely divisible too. It's not just space. Achilles and the tortoise would continue to exchange positions, getting into smaller and smaller fractions of space and time, without being able to get to a final discrete unit of time and space to progress further.
But Zeno's paradox isn't a paradox at all, it's simple math problem.
You did not solve Zeno's Paradox. The only way to solve it is to decide that space and time are discrete; which pretty much admits that the Ancient Greeks were wrong and the universe is not continuous.
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Tom finding my points too difficult for them to answer?
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The ancients tried to apply their math and ideas about number lines, how they are infinitely long and infinitely discrete, in addition to other continuous mathematical concepts, to the real world. This is why, according to their math, the perspective lines never meet.
We challenge that assertion and would like to see more evidence than a mathematical hypothesis about how perspective would behave before concluding what should or should not happen with long perspective lines.
Be careful: Parallel lines don't meet in the real world. That's the definition of the word "parallel".
We know the math for perspective - I mentioned it before: x' = x k / z and y' = y k / z (and incidentally z' = z k / z...not that we necessarily care)...we can choose a camera where the constant 'k' is 1.0 to make life easier.
x' and y' are the locations of the point (x,y,z) in your two-dimensional image. z'=k ...so the image is located on the back of the camera.
I'm using x-is-right, y-is-up and z is distance away from the camera...which is conventional in 3D graphics.
So if we take two parallel lines - like railroad tracks - that are two units apart. They are one unit below the camera and start one unit in front of the camera and end up at infinity: In the real world (x,y,z) the left rail runs from (-1,-1,1) to (-1,-1,infinity) and the right rail runs from (1,-1,1) to (1,-1,infinity).
So in our image, the lefthand rail goes from x' = -1/1 = -1 units to x' = -1/infinity = 0 units. The righthand rail goes from x'= +1/1 = 1 units to x'= 1/infinity = 0 units. y' is -1/1 to -1/infinity for both rails.
So the coordinates of the ends of the two rails in our image is: (-1,-1) to (0,0) and (+1,-1) to (0,0). Hence both rails meet IN THE IMAGE at (0,0)...which is where you'd expect them to meet in a flat earth world with an infinite horizon. In the round earth, the rails curve over the horizon and disappear before they can meet...however, they might get VERY close and require high magnification to actually see the gap between them as the go over the horizon.
So - that proves what math and actual perspective says.
All you have left to complain about is my equations (x'= x k / z, etc)
Those I proved for you in another post - and are self evident from the principles of a pinhole camera, straight light rays and similar triangles. If you'd like me to re-post that proof, I'd be happy to do so.
You see the things that are claimed are childishly easy to prove. Your claims that we CAN'T prove them are founded entirely on your own lack of knowledge.
I just see a thought experiment here.
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You can't ever get to 11.2 seconds because the Greeks believed that time is continuous and infinitely divisible too. It's not just space. Achilles and the tortoise would continue to exchange positions, getting into smaller and smaller fractions of space and time, without being able to get to a final discrete unit of time and space to progress further.
So does time somehow cease at 11.111... seconds? As far as I'm aware it does not. My math is unassailable.
What you're talking about is a deeper proposition that an infinite number of TASKS must be completed before Achilles can overtake the tortoise - but the concept of "completing a task" isn't any kind of real world requirement here. So long as the muscles in Achilles' legs are functioning - he'll overtake the tortoise.
Sure the greeks liked to argue about this stuff - but it doesn't mean that mathematics cannot solve it...as indeed, they so clearly do. If you ran that race, I guarantee that Achilles would overtake the tortoise a moment before 11.11112 seconds.
What worries most people is that the number has an infinite number of digits - but that's just an issue of the units you happen to choose. If I measure time in units of 1/9th of a second - then Achilles reaches the tortoise in exactly 100 time units.
You did not solve Zeno's Paradox. The only way to solve it is to decide that space and time are discrete; which pretty much admits that the Ancient Greeks were wrong and the universe is not continuous.
You didn't ask me to solve a philosophical debate about whether an infinite number of "tasks" can be performed (clearly they can because people win races).
You said "That math can't even explain how a rabbit could overcome a tortoise in a race."...which it most certainly can - and without hardly breaking a sweat.
A true zetetic would have no truck with philosophers...I see that people can win races...I see that we can sum infinite series...QED.
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So does time somehow cease at 11.111... seconds? As far as I'm aware it does not. My math is unassailable.
You can only progress time further if you assume that time is discrete.
Sure the greeks liked to argue about this stuff - but it doesn't mean that mathematics cannot solve it...as indeed, they so clearly do. If you ran that race, I guarantee that Achilles would overtake the tortoise a moment before 11.11112 seconds.
In a real race Achilles would overtake the tortoise, but that says nothing about whether the continuous universe math of the Ancient Greeks is correct.
What worries most people is that the number has an infinite number of digits - but that's just an issue of the units you happen to choose. If I measure time in units of 1/9th of a second - then Achilles reaches the tortoise in exactly 100 time units.
If you measure time in 1/9th of a second you have decided that the universe is discrete and that we do not live in a continuous universe like the Ancient Greeks said we did, and which almost all math is founded upon.
You didn't ask me to solve a philosophical debate about whether an infinite number of "tasks" can be performed (clearly they can because people win races).
Yes I did. This whole discussion is about whether the universe is continuous or not.
You said "That math can't even explain how a rabbit could overcome a tortoise in a race."...which it most certainly can - and without hardly breaking a sweat.
A true zetetic would have no truck with philosophers...I see that people can win races...I see that we can sum infinite series...QED.
A true experiment showing people winning races would be empirical evidence that space and time are discrete; and would act as a disprove against a continuous universe, therefore showing that continuous math is fallacious and not translatable to the real world.
All of this strengthens our questioning of the math which predicts infinitely approaching perspective lines.
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I just see a thought experiment here.
No you see the answer to your typically ill-informed question:
The ancients tried to apply their math and ideas about number lines, how they are infinitely long and infinitely discrete, in addition to other continuous mathematical concepts, to the real world. This is why, according to their math, the perspective lines never meet.
I pointed out that "according to their math" - the perspective lines most certainly DO meet.
I answered the thing that you said was impossible.
We challenge that assertion and would like to see more evidence than a mathematical hypothesis about how perspective would behave before concluding what should or should not happen with long perspective lines.
So now you ask for more than "a mathematical hypothesis". Well mathematics doesn't deal with "hypotheses" - there are axioms and there are theorems. I lay out my axioms and then I prove a theorem. If the axioms are correct and if there are no errors in the steps leading to the theorem - then the theorem is true.
The problem for you is that you HAVE NO MATH for your magic perspective (which is indeed a "hypothesis" - you can't explain why it happens or even prove that it does).
So you know that you can't allow math to enter into the debate because the moment it does - it proves you wrong...and I do mean "proves". A mathematical proof is unassailable. You can only deny the axioms - which in this case means denying that light travels in straight lines - or denying that similar triangles have sides with identical ratios...which in turn requires denying Euclid's theorems - which in turn denies basic geometrical precepts such as the definition of a line.
That is a bear trap from which there is no escape.
Instead you childishly demand to see parallel lines of infinite length - when YOUR concept will fall apart for parallel lines of FINITE length - so I merely have to stand on a long straight railroad track and pull out a pair of binoculars.
So rather than try to produce empirical evidence to disprove the impossible - let's just disprove what you believe to be possible. That's vastly simpler and directly
demolishes your crazy thinking rather than leading to more infinite regress.
So...I repeat: TELL US HOW PHOTONS TRAVEL FROM THE SUN TO YOUR EYE AT SUNSET.
You know you can't...if you could - you'd have done it already - as you twice rashly promised you would - right before you (presumably) realised that you can't.
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You can only progress time further if you assume that time is discrete.
Not at all - I don't have to use whole numbers - we have decimals! I can express time (and the race) either way - the result is the same.
I work in computer graphics - we have "discrete time" - everything happens in steps of 1/60th of a second (one video frame). We can simulate races just as easily in discrete steps.
You wind up with Achilles being some short distance behind the tortoise - and you advance the distance of each one by it's speed multiplied by the time step - and in the next time step Achilles is ahead of the tortoise.
The discontinuous "jumps" are equally spaced - and not exponentially smaller chunks of time - so there still is no paradox.
To propose that Achilles can't beat the tortoise REQUIRES that you discretize time into smaller and smaller steps...which if "real" would mean it would indeed take an infinite number of steps. But the real world (even if discrete) can't work that way because there are multiple events (different races, if you like) where the time steps would have to be different in order for those races to exhibit the same paradox. The universe can't be jumping around in different length time steps because then you couldn't have interactions between events.
So - you want a discretized time...fine - no problem. You want discretized space too...well that implies discretized energy - and therefore mass. But that's not a problem.
You can formulate any of the things we've been discussing in either continuous or discrete forms...the answer comes out the same.
In a real race Achilles would overtake the tortoise, but that says nothing about whether the continuous universe math of the Ancient Greeks is correct.
Indeed.
If you measure time in 1/9th of a second you have decided that the universe is discrete and that we do not live in a continuous universe like the Ancient Greeks said we did, and which almost all math is founded upon.
I didn't say "integer numbers of 1/9th seconds" - you can still have fractions of 1/9th. It's no different than measuring distances in centimeters instead of inches to get nice round numbers.
You didn't ask me to solve a philosophical debate about whether an infinite number of "tasks" can be performed (clearly they can because people win races).
Yes I did. This whole discussion is about whether the universe is continuous or not.
Well, you may have intended that - but it's not what you said. You said that math can't do this or that or the other...and I show that it most certainly can. I happened to use a continuous model - but the results come out exactly the same either way.
You said "That math can't even explain how a rabbit could overcome a tortoise in a race."...which it most certainly can - and without hardly breaking a sweat.
A true zetetic would have no truck with philosophers...I see that people can win races...I see that we can sum infinite series...QED.
A true experiment showing people winning races would be empirical evidence that space and time are discrete; and would act as a disprove against a continuous universe, therefore showing that continuous math is fallacious and not translatable to the real world.
Woooaaah...that's one step beyond what you're arguing.
I showed that math can demonstrate how people can win races using repeated addition of a series of steps...summing an infinite series. That was a "discrete" solution to Zeno's paradox. The "continuous" solution would be to write an equation for the position of the tortoise against time - and another one for Achilles - to solve those two simultaneous equations - and get the time (or distance) at which Achilles overtakes the tortoise from that.
The answer comes out EXACTLY the same - and math works in both approaches.
Your idea that math can't solve problems in a discrete universe is CLEARLY bullshit because math works great for making video games where the computer has only 64 bits in a word and can only display images once every 1/60th of a second. That's all math - and it works SUPERBLY WELL in a discrete "universe".
So you're 100% wrong on that one...again - you're guessing/hoping that what you say is true...you don't know enough to understand where your thinking is wrong.
All of this strengthens our questioning of the math which predicts infinitely approaching perspective lines.
I don't think it does. We can chop the space into 1 pico-meter chunks and divide time into 1 nanosecond intervals - and you still can't explain how photons get from the sun to my eye at sunset.
So this is all just typical flim-flam - and I'm not falling for it!
Tell me how the photon moves in a discretized universe - you still can't do it.
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I never got beyond calculus at school, but still use basic trigonometry for navigation but 99% of the folks on this forum probably have no more knowledge of higher maths than I do. The problem is that FEs will see Tom's entertaining and amusing discussions with 3D and the maths will fly way above their heads. That won't though stop them gleefully seeing Tom refuting everything that 3D throws at him as proof that the world is flat, even though Tom is completely unable to come up with any arguments that are not baseless.
With reference to the perspective of parallel railway lines, the fact that they do not actually converge and meet at infinity seems to me to be quite easy to show with virtually no knowledge of maths and to have quite clear and empirical evidence that any FE can find. Just find a continuous straight stretch of track alongside a road, that appears to converge or almost converge in the distance. Measure the exact distance between the tracks at the point you are looking from. If you are unable to read a measure, use a length of wood or other rigid material and make a mark to show the distance between the tracks. Then jump in a car and travel down the road alongside the tracks for lets say 5 miles, although the distance doesn't really matter. Measure the distance between the tracks again, then do the same a couple of times more. As the tracks will be a standard gauge set by the railroad company the measurements will all be the same. Once you are satisfied that the rails are not converging, even though your eyes seem to tell you they are, you have proved that whatever distance you travel to take the measurements, you will always get the same result. The difference between the measurements will be zero, so if you have taken 4 measurements over 20 miles, the 20x0=0 so there is no convergence whatever your eyes tell you. If the tracks travel to infinity, infinity x zero will still be still be zero convergence so the tracks will never meet.
FEs get your head out of the computer and Youtube, get out in the fresh air and do it yourself and prove that Tom is just talking BS even though you want to believe him.
Roger
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That's been fun to watch !! I can safely predict you won't have anybody accept your invitation. They know when they are outgunned, hence the very few flat earth believers here.
My three body prediction. Tom would say occultations are caused by magic parallax and you should prove it otherwise, and then pretend to ignore all your proofs.
ScaryGary will find some big words and string them into a sentence which sounds impressive but is completely meaningless.
J-man will say it was aliens, and god will smite you if you say otherwise.
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I never got beyond calculus at school, but still use basic trigonometry for navigation but 99% of the folks on this forum probably have no more knowledge of higher maths than I do. The problem is that FEs will see Tom's entertaining and amusing discussions with 3D and the maths will fly way above their heads. That won't though stop them gleefully seeing Tom refuting everything that 3D throws at him as proof that the world is flat, even though Tom is completely unable to come up with any arguments that are not baseless.
Nobody could possibly imagine that Tom refutes everything I say - a solid 60% of the "Disproof" threads I've started, he's never even contributed to.
In most cases, where he has no countervailing narrative - he just skips the thread and hopes that it sinks off the bottom of the forum list without too many people noticing.
Tom's "railroad track" thing is getting increasingly bizarre as he gets increasingly desperate to come up with an explanation. We started with him (deliberately?) confusing what happens "in reality" and what happens in "a picture of reality"...then he started introducing some very weird vocabulary definitions between "location", "position" and "orientation" to throw more confusion into the situation. Then, when I came up with a STUNNINGLY clear description of how perspective math applies - he said that diagrams cannot represent reality. So I did the same thing with the path a photon literally takes - which HE STILL refuses to talk about - despite many times claiming that he would do so. Then I came up with another disproof of sunsets that doesn't even involve eyes or cameras - and works solely by the heat you feel on your face. That one was one of the "ignored" ones...because if you can show there are no FE sunsets WITHOUT requiring perspective - then he's really screwed.
In the latest round of desperation, he's started in on this crap about "continuous" versus "discrete" universe and mathematics. Bouncing around between the two like an over-inflated beachball. Sadly, the math works out the same no matter which model you choose...as I demonstrated with the Zeno paradox.
Tom is a desperate man...none of his arguments stand for very long - so he has to reach for more and more desperate niches in which to hide the glaring problem which is THE WORLD ISN'T FLAT.
But this is a guy who also claims that you can cure Ebola and AIDS using large doses of vitamin C and that Cancer can be cured with green peppers. I imagine a good number of FE'ers flinching at those claims.
So we're not talking the smartest tool in the shed here.
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Astronomy is based on observed patterns. Observed patterns of the moon, observed patterns of the stars. Things are only predictable because they come in patterns. It is possible to create an equation to express those patterns, but they are only valuable in that they might produce a right answer.
read the literature i linked more carefully. here are the equations of motion:
(https://i.imgur.com/V6i8mOr.png?1)
this is pretty much exactly how eclipse tables are calculated. the nasa page you always link says this itself at the bottom.
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Astronomy is based on observed patterns. Observed patterns of the moon, observed patterns of the stars. Things are only predictable because they come in patterns. It is possible to create an equation to express those patterns, but they are only valuable in that they might produce a right answer.
read the literature i linked more carefully. here are the equations of motion:
(https://i.imgur.com/V6i8mOr.png?1)
this is pretty much exactly how eclipse tables are calculated. the nasa page you always link says this itself at the bottom.
The problem is a good deal more subtle than that. We know what the equations are - but we cannot solve them for more than two bodies. So we can say (for two bodies) - here are there masses, here is where they are in space - here is an equation into which you can plug any future time and the equation will tell you the location of the two bodies. THAT can be solved.
However, for three or more bodies - no such equation is possible (it can actually be proven to be impossible). Hence you cannot write an equation to tell you PRECISELY when the next eclipse will happen because the sun, moon and earth constitute a three body system.
BUT this doesn't mean that we use "patterns" to figure it out. We simply don't use a single equation - we can do one of two things:
1) We can calculate the Earth/Moon orbits precisely as a "two-body problem" - then we can calculate how "EarthMoon" orbits the Sun as a two-body problem. The solution isn't exact - but it's good enough to predict eclipses to within a fraction of a second over a century. If we continually correct the data after the time of each eclipse is measured - then the results will be essentially perfect.
2) We can use "numerical integration". So we calculate the two-body solution above over a time-step of (say) 1 second. Over such a tiny time interval, the error will be about the diameter of an atom. Definitely too small to matter. Then we take the new positions and do it again over 1 second...we repeat this (using a computer) over a hundred billion seconds - and we arrive at a series of eclipse predictions over the next 3,100 years. Then, we change the time step from 1 second to (say) a half second - and repeat the calculations. The result is a new series of predictions. If the difference between the first set of predictions and the second is "close enough" then we can be happy to say that this approach isn't introducing large errors.
In practice, it's worse than this because Jupiter and Saturn add significantly to the motion - but by breaking the problem down into separate 2-body steps, and integrating over tiny time intervals - we can produce answers as accurately as you'd like. With modern computers, we can narrow down the answers to the point where we're talking distances the size of an atom and times down to nanoseconds.
So just because there is no single equation - we can still predict eclipses without using the idea of seeing "patterns"...which in itself isn't ever going to produce a perfect result because the effects of the gravity of the very slow moving outer planets means that the pattern of eclipses isn't ever "perfect" and has never precisely repeated over all of human history.
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The problem is a good deal more subtle than that.
i can't really tell who you're arguing with.
but yes, that's how numerical integration works.
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The problem is a good deal more subtle than that.
i can't really tell who you're arguing with.
but yes, that's how numerical integration works.
The deal is that the FE'ers claim that "because mathematicians can't solve the three-body problem" the use recurring patterns in the dates of eclipses to predict them in the future...or that there is no way people could have gone to the moon because the three-body problem is insoluable, etc, etc.
They like this because an absence of math makes it harder for people to show the paths of sun and moon and it throws hefty amounts doubt about mathematics into the eyes of the gullible.
However, this ISN'T how sunsets are actually predicted in the modern world. The math works perfectly well - it just has to be integrated numerically rather than by symbolic means...and Sir Isaac Newton figured that out (the approach is actually called "Newton's method").
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While the Greeks played a large role in math, they are hardly alone. Many other cultures contributed greatly to our understanding. Given how incredibly successful mathematics are for so many varied applications, your burden of proof is absurdly high.
What do you mean incredibly successful? That math can't even explain how a rabbit could overcome a tortoise in a race (http://barang.sg/index.php?view=achilles).
I mentioned Max Planck and his work on a discrete universe that isn't infinitely divisible.
Yes, that is a good example. Zeno was right in that the universe is non-continuous. The ancients got it wrong.
That's one of the big problems with finding a Grand Unified Theory. Quantum Mechanics says that the universe is discrete, and that there are discrete units of space and time, while General Relativity says that the universe is continuous in space and time. The concepts are not compatible.
are you serious?
I am the hare. You are the tortoise.
I travel at 10km/hr you travel at 1 km/hr.
you have a 5 km headstart.
In one hour I have travelled 10km from zero. You have travelled 1km from 5.
Clearly I am ahead by 4km. My 5 year old son could work this out, and he has not begun grade 1 of school.
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While the Greeks played a large role in math, they are hardly alone. Many other cultures contributed greatly to our understanding. Given how incredibly successful mathematics are for so many varied applications, your burden of proof is absurdly high.
What do you mean incredibly successful? That math can't even explain how a rabbit could overcome a tortoise in a race (http://barang.sg/index.php?view=achilles).
I mentioned Max Planck and his work on a discrete universe that isn't infinitely divisible.
Yes, that is a good example. Zeno was right in that the universe is non-continuous. The ancients got it wrong.
That's one of the big problems with finding a Grand Unified Theory. Quantum Mechanics says that the universe is discrete, and that there are discrete units of space and time, while General Relativity says that the universe is continuous in space and time. The concepts are not compatible.
are you serious?
I am the hare. You are the tortoise.
I travel at 10km/hr you travel at 1 km/hr.
you have a 5 km headstart.
In one hour I have travelled 10km from zero. You have travelled 1km from 5.
Clearly I am ahead by 4km. My 5 year old son could work this out, and he has not begun grade 1 of school.
Read the link that was provided.
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Well I did; what you are attempting is mathematical gymnastics. I could apply simple arithmetic to how a hare may overcome a tortoise in a race. You on the otherhand attempt to deflect or deny any contention that does not fit to your small world view. Greek maths work when you want, and are unproven phallacies when undesiref outcomes are derived. Surely a true scholar would be tiresome of such nonsense by now. But then, google is everyones friend.
You really are a tool of the highest order.
#edit. Ok, sorry junker and tom bishop. I will refrain from personal attack in future.
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Well I did; what you are attempting is mathematical gymnastics. I could apply simple arithmetic to how a hare may overcome a tortoise in a race. You on the otherhand attempt to deflect or deny any contention that does not fit to your small world view. Greek maths work when you want, and are unproven phallacies when undesiref outcomes are derived. Surely a true scholar would be tiresome of such nonsense by now. But then, google is everyones friend.
You really are a tool of the highest order.
Refrain from personal attacks in the upper fora. Warned.
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Well I did; what you are attempting is mathematical gymnastics. I could apply simple arithmetic to how a hare may overcome a tortoise in a race. You on the otherhand attempt to deflect or deny any contention that does not fit to your small world view. Greek maths work when you want, and are unproven phallacies when undesiref outcomes are derived. Surely a true scholar would be tiresome of such nonsense by now. But then, google is everyones friend.
You really are a tool of the highest order.
#edit. Ok, sorry junker and tom bishop. I will refrain from personal attack in future.
The site I provided (http://barang.sg/index.php?view=achilles) addresses that and goes over how such generalizations are just skirting the real issue of whether time and space are continuous like a number line or not.
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Well I did; what you are attempting is mathematical gymnastics. I could apply simple arithmetic to how a hare may overcome a tortoise in a race. You on the otherhand attempt to deflect or deny any contention that does not fit to your small world view. Greek maths work when you want, and are unproven phallacies when undesiref outcomes are derived. Surely a true scholar would be tiresome of such nonsense by now. But then, google is everyones friend.
You really are a tool of the highest order.
#edit. Ok, sorry junker and tom bishop. I will refrain from personal attack in future.
The site I provided (http://barang.sg/index.php?view=achilles) addresses that and goes over how such generalizations are just skirting the real issue of whether time and space are continuous like a number line or not.
Tom, this has been discussed before. The universe, at the very smallest distances, is thought to be discreet. That has no bearing on our daily lives. You can't take Planck's work and try to extrapolate it to macro levels.(which is what you want to do to save your failed sunset/perspective hypothesis)
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Well I did; what you are attempting is mathematical gymnastics. I could apply simple arithmetic to how a hare may overcome a tortoise in a race. You on the otherhand attempt to deflect or deny any contention that does not fit to your small world view. Greek maths work when you want, and are unproven phallacies when undesiref outcomes are derived. Surely a true scholar would be tiresome of such nonsense by now. But then, google is everyones friend.
You really are a tool of the highest order.
#edit. Ok, sorry junker and tom bishop. I will refrain from personal attack in future.
The site I provided (http://barang.sg/index.php?view=achilles) addresses that and goes over how such generalizations are just skirting the real issue of whether time and space are continuous like a number line or not.
Tom, this has been discussed before. The universe, at the very smallest distances, is thought to be discreet.
That is correct, and the point of Zeno's Paradox. The Ancient Greeks are wrong about the universe being continuous. Math which is based on continuous number lines is NOT applicable to the real world. So don't tell us that according to that continuous math the sun will never set.
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Well I did; what you are attempting is mathematical gymnastics. I could apply simple arithmetic to how a hare may overcome a tortoise in a race. You on the otherhand attempt to deflect or deny any contention that does not fit to your small world view. Greek maths work when you want, and are unproven phallacies when undesiref outcomes are derived. Surely a true scholar would be tiresome of such nonsense by now. But then, google is everyones friend.
You really are a tool of the highest order.
#edit. Ok, sorry junker and tom bishop. I will refrain from personal attack in future.
The site I provided (http://barang.sg/index.php?view=achilles) addresses that and goes over how such generalizations are just skirting the real issue of whether time and space are continuous like a number line or not.
Tom, this has been discussed before. The universe, at the very smallest distances, is thought to be discreet.
That is correct, and the point of Zeno's Paradox. The Ancient Greeks are wrong about the universe being continuous. Math which is based on continuous number lines is NOT applicable to the real world. So don't tell us that according to that continuous math the sun will never set.
You are 100% wrong. You do not understand what it is. It was calculated as the smallest measurement of the universe that could be made. The energy required to measure anything smaller would create a black hole and spacetime would cease to exist in the that location. You are applying way too much significance to the discrete portion of this. It's sort of like saying you can't use a ruler because it is made up of atoms. In fact, Planck's length has no physical implications and is still theoretical.
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You are 100% wrong. You do not understand what it is. It was calculated as the smallest measurement of the universe that could be made. The energy required to measure anything smaller would create a black hole and spacetime would cease to exist in the that location. You are applying way too much significance to the discrete portion of this. It's sort of like saying you can't use a ruler because it is made up of atoms. In fact, Planck's length has no physical implications and is still theoretical.
If you read through the Zeno's Paradox link (http://barang.sg/index.php?view=achilles) you will find that there are other ways to know that the universe does not operate on a continuous ruleset. The discovery of the Planck is not even necessary. If we try to calculate movement of things in the universe on the basis of a continuous number line it does not work. Zeno's Paradox disproves the assumption that space and time are continuous, and shows that there must be a discrete unit for anything to work.
The application of continuous concepts to the universe is, therefore, in error. We cannot say that we can calculate what will happen over long or small distances if there is no real demonstration that the universe operates on those continuous rule sets.
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You are 100% wrong. You do not understand what it is. It was calculated as the smallest measurement of the universe that could be made. The energy required to measure anything smaller would create a black hole and spacetime would cease to exist in the that location. You are applying way too much significance to the discrete portion of this. It's sort of like saying you can't use a ruler because it is made up of atoms. In fact, Planck's length has no physical implications and is still theoretical.
If you read through the Zeno's Paradox link (http://barang.sg/index.php?view=achilles) you will find that there are other ways to know that the universe does not operate on a continuous ruleset. The discovery of the Planck is not even necessary. If we try to calculate movement of things in the universe on the basis of a continuous number line it does not work. Zeno's Paradox disproves the assumption that space and time are continuous, and shows that there must be a discrete unit for anything to work.
The application of continuous concepts to the universe is, therefore, in error. We cannot say that we can calculate what will happen over long or small distances if there is no real demonstration that the universe operates on those continuous rule sets.
SMDH - Tom, do you ever find yourself stuck drawing ever closer to your something, but never able to reach it? Ever unable to reach your destination because the geometry of the world just isn't what you think? If not, you can thank your lucky stars that paradoxes aren't always factually accurate and prove nothing. And please give me an example of us not being able to calculate the movement of something in space. If I remember calc correctly, we could do that all day long.
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SMDH - Tom, do you ever find yourself stuck drawing ever closer to your something, but never able to reach it? Ever unable to reach your destination because the geometry of the world just isn't what you think?
I don't have that problem because the universe is discrete, and does not adhere to the continuous mathematical construct the Ancient Greeks asserted.
If not, you can thank your lucky stars that paradoxes aren't always factually accurate and prove nothing. And please give me an example of us not being able to calculate the movement of something in space. If I remember calc correctly, we could do that all day long.
See the link on Zeno's Paradox for an example of a situation where we are not able to calculate movement in a universe where space and time are conceptualized like continuous number lines.
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SMDH - Tom, do you ever find yourself stuck drawing ever closer to your something, but never able to reach it? Ever unable to reach your destination because the geometry of the world just isn't what you think?
I don't have that problem because the universe is discrete, and does not adhere to the continuous mathematical construct the Ancient Greeks asserted.
If not, you can thank your lucky stars that paradoxes aren't always factually accurate and prove nothing. And please give me an example of us not being able to calculate the movement of something in space. If I remember calc correctly, we could do that all day long.
See the link on Zeno's Paradox for an example of a situation where we are not able to calculate movement in a universe where space and time are conceptualized like continuous number lines.
Zeno’s paradox can be solved with Calculus. What is your proof the universe is discreet?
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Zeno's Paradox can only be solved by assuming that the universe is discrete or by generalizing the issue and ignoring the main issue of whether space can be described with continuous number lines. This is all described in the link I provided.
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Math which is based on continuous number lines is NOT applicable to the real world...If we try to calculate movement of things in the universe on the basis of a continuous number line it does not work. Zeno's Paradox disproves the assumption that space and time are continuous, and shows that there must be a discrete unit for anything to work.
this is empirically untrue. calculus works fine (gives you the measurably-correct answers) even for quantities we know for sure are discrete. for example, we know for sure that electric charge comes in discrete units. you can still treat the charge distribution of, say, a charged conducting sphere, as a continuous quantity, and calculate the correct values for quantities like the electric field/potential/whatever else. good luck getting there with pi=4.
calculating quantities "based on continuous number lines" actually works very well.
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If you were challenged to show proof of the rules of the same model that two horizontal parallel perspective lines will approach each other for infinity but never touch, or that a body thousands of miles away will appear a certain number of degrees above the horizon, or that perspective behaves the same at all scales, you will be embarrassingly unable to do so.
Aren't you 'embarrassingly unable' to produce a map of a flat earth?