[3DGeek]

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:



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.

[garygreen]

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.

[3DGeek]

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").

[DSC]

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.

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.

[Tom Bishop]

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.

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.

[DSC]

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.

[juner]

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.

[Tom Bishop]

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 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.

[StinkyOne]

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 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)

[Tom Bishop]

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 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.

[StinkyOne]

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 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.

[Tom Bishop]

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 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.

[StinkyOne]

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 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.

[Tom Bishop]

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.

[Rama Set]

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?

[Tom Bishop]

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.

[garygreen]

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.

[AATW]

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?