[Tom Bishop]

Branding math for orbital calculations as an embarrassing failure that doesn't "work" seems rather disingenuous given we've sent orbiters, landed probes and/or rovers on a large number of objects in the solar system, and have established continuous monitoring of solar activity by installing satellites at lagrange points.

And now you are bringing in NASA to explain that they are sending space ships to explore a system that can't mathematically exist under the Newtonian laws used to get there. Right. 

[Iceman]

Yes, I suppose I am. Among other space agencies (and I realise you have previously suggested they're all in on things together, given their collaboration)

Given the terabytes and terabyte of data they've made publicly available over the last few decades, including live streams from the ISS, pictures from mars, pictures of earth, which can be correlated with observed atmospheric conditions from the ground, people bouncing signals of the moon.

I weigh that against "space bubbles", the #marsrat, green screen ISS acrobats and other recent anti-NASA explanations I've seen and I make up my own mind

[SteelyBob]

You haven't shown that the issue with three bodies is anything like those other situations. I don't see a valid comparison.

Your inability to see doesn't change the facts. The full 3D N-S equations are unsolvable analytically without resorting to some degree of simplification (eg https://inis.iaea.org/collection/NCLCollectionStore/_Public/32/049/32049286.pdf), which is why numerical methods dominate in practical fluid dynamics problems. Saying 'real bodies aren't going to use approximations' is just plain silly - air molecules flowing past a wing don't use approximations either, but we are equally unable to analytically solve their motion. If you don't doubt aerodynamics, why doubt orbital mechanics? What's the difference?

It's very telling that none of the papers you have cherry-pick quoted actually casts any doubt at all on the actual underlying theory of gravitational attraction, or indeed the orbital motion of planets and the shape of the earth. Martin Gutzwiller, in the quote below, is quite obviously talking about the beautiful challenge of apparently simple equations that contain enormous amounts of complexity and nuance when you start to unpick them, and how simplifications made to solve one detail of planetary motion don't necessarily translate to other areas - eg lunar motion versus asteroid. He would have roared with laughter to see you using a quote of his to suggest that the planet we live on is flat.

https://wiki.tfes.org/Three_Body_Problem

Martin Gutzwiller

The end section of a paper titled Moon-Earth-Sun: The oldest three-body problem (Archive) by physicist Martin C. Gutzwiller (bio) concludes that Newton's laws are not a sufficient explanation:

  “ The three-body problem teaches us a sobering lesson about our ability to comprehend the outside world in terms of a few basic mathematical relations. Many physicists, maybe early in their careers, had hopes of coordinating their field of interest, if not all of physics, into some overall rational scheme. The more complicated situations could then be reduced to some simpler models in which all phenomena would find their explanation. This ideal goal of the scientific enterprise has been promoted by many distinguished scientists [see Weinberg’s (1992) Dream of a Final Theory, with a chapter ‘‘Two Cheers for Reductionism’’]....Many physicists may be tempted to see in Newton’s equations of motion and his universal gravitation a sufficient explanation for the three-body problem, with the details to be worked out by the technicians. But even a close look at the differential equations (29) and (30) does not prepare us for the idiosyncracies of the lunar motion, nor does it help us to understand the orbits of asteroids in the combined gravitational field of the Sun and Jupiter. ”

The actual three body problem doesn't work to explain the orbits of asteroids under the combined gravitational field of the Sun and Jupiter.

Yet you continue to post that we can just approximate it, while also admitting that the real bodies in the solar system aren't going to use approximations. Absurd.

[WTF_Seriously]

The three body problem has no comparison with Parsifal's equation. The difference in effort and resources is substantial. The greatest mathematicians in history have been unable to get the RE astronomy system to work. It is quite an embarrassing failure.

From another thread. https://forum.tfes.org/index.php?topic=17884.msg234879#msg234879

In the next section, it will be shown that two additional integrals can be obtained when N = 2 from the considerations of relative motion of the two bodies. Hence, a two-body problem is analytically solvable. However, with N > 2, the number of unknown motion variables exceeds the total number of integrals; thus, no analytical solution exists for the N-body problem when N > 2. Due to this reason, we cannot mathematically prove certain observed facts (such as the stability of the solar system) concerning N-body motion. The best we can do is to approximate the solution to the N-body problem either by a set of two-body solutions or by numerical solutions.

You do understand what "no analytical soultions exists" means, correct?  It means the math doesn't fit the problem.  It doesn't mean what your trying to analyze doesn't exist.  Your continued use of the n-body problem as some giant 'gotcha' is hysterical.  It means zero to the shape of the earth, but you go ahead.

[Tom Bishop]

You do understand what "no analytical soultions exists" means, correct?

I certainly understand the difference between an analytical and numerical solution. It is apparent that you may not, however.

https://wiki.tfes.org/Numerical_Solutions#General_Quotes

From a question posted on researchgate.net (Archive):

  “ Q. What kind of problem solutions do you rate higher: analytical or numerical? More problems can be solved numerically, using computers. But some of the same problems can be solved analytically. What would your preference be? ”

Mohammad Firoz Khan, Ph.D. (bio) responds:

  “ A researcher would like to solve it analytically so that it is clear what are premises, assumptions and mathematical rules behind the problem. As such problem is clearly understood. Numerical solution using computers give solution, not the understanding of the problem. It is quite blind. However, in emergency one may resort to this option. ”

[WTF_Seriously]

a, b, c, d are real numbers

3a+     5c       =9
 a+2b+    12d =2
     7b+2c+3d=19

Tom:  It can't be solved.  a,b,c,and d don't exist.

[Tom Bishop]

The planets and asteroids aren't going to use fudges of the laws or approximations with two bodies at a time to move around in free space. If it can't be done based on a full simulation of gravity with the underlying laws then it can't be done.

[WTF_Seriously]

If it can't be done based on a full simulation of gravity with the underlying laws then it can't be done.

That would be correct.  You seem to remain confused by the fact that it's mathematically impossible to create the full simulation of gravity because, well, math.  You're welcome to keep presenting the n-body problem as if it means something, though.

[WTF_Seriously]

Do these Eddy currents exist?  We certainly don't have the ability to mathematically model them.

[SteelyBob]

The planets and asteroids aren't going to use fudges of the laws or approximations with two bodies at a time to move around in free space. If it can't be done based on a full simulation of gravity with the underlying laws then it can't be done.

How's about:

The air molecules aren't going to use fudges of the laws or approximations to flow around a wing. If it can't be done based on a full simulation of airflow with the underlying laws then it can't be done.

Or perhaps:

The sub-atomic particles aren't going to use fudges of the laws or approximations to form atoms and molecules. If it can't be done based on a full simulation with the underlying laws then it can't be done.

Interesting that you chose to use the phrase 'full simulation'. Do you therefore assert that anything that doesn't use an analytical set of derived equations to simulate any system isn't really a 'full simulation'? So a 6DOF flight simulator, for example, isn't a full simulation because it uses approximations for the mechanics of the aircraft body and its associated aerodynamic coefficients?

[Tom Bishop]

The sub-atomic particles aren't going to use fudges of the laws or approximations to form atoms and molecules. If it can't be done based on a full simulation with the underlying laws then it can't be done.

That's right. Particle physics also has trouble simulating things with multi-body problems. You are arguing that because they can't simulate it that its theories must be nonetheless true. That does not follow at all. Since they can't simulate it or get it to work based on the underlying laws it means that the theories lean towards being false.

Classical particle physics is increasingly rebutted in many ways by other theories, such as theories in quantum mechanics, and it should not be surprising that classical particle physics is incorrect.

[SteelyBob]

The sub-atomic particles aren't going to use fudges of the laws or approximations to form atoms and molecules. If it can't be done based on a full simulation with the underlying laws then it can't be done.

That's right. Particle physics also has trouble simulating things with multi-body problems. You are arguing that because they can't simulate it that its the theories must be nonetheless true. That does not follow at all. Since they can't simulate it or get it to work based on the underlying laws it means that the theories lean towards being false.

Classical particle physics is increasingly rebutted in many ways by other theories, such as theories in quantum mechanics, and it should not be surprising that classical particle physics is incorrect.

So do you accept computational fluid dynamics as valid, or are you rejecting that too?

[existoid]

Of course, the eagle-eyed among beings who cannot to cease to be will have already noticed that his proof is impossible - but I am still curious to see him either reach that conclusion himself or deny it.

Got it - I am content now that I understand. 

[fisherman]

The sub-atomic particles aren't going to use fudges of the laws or approximations to form atoms and molecules. If it can't be done based on a full simulation with the underlying laws then it can't be done.

That's right. Particle physics also has trouble simulating things with multi-body problems. You are arguing that because they can't simulate it that its theories must be nonetheless true. That does not follow at all. Since they can't simulate it or get it to work based on the underlying laws it means that the theories lean towards being false.

Does that same logic apply to your inability to account for the "Bishop's Constant".  (I have a hard time even typing that with a straight face)  You can't get it to work...so it must be false. 

Or how about all of UA?  You can't explain it based on the current underlying laws of physics...so it must be false.

[Tom Bishop]

The sub-atomic particles aren't going to use fudges of the laws or approximations to form atoms and molecules. If it can't be done based on a full simulation with the underlying laws then it can't be done.

That's right. Particle physics also has trouble simulating things with multi-body problems. You are arguing that because they can't simulate it that its theories must be nonetheless true. That does not follow at all. Since they can't simulate it or get it to work based on the underlying laws it means that the theories lean towards being false.

Does that same logic apply to your inability to account for the "Bishop's Constant".  (I have a hard time even typing that with a straight face)  You can't get it to work...so it must be false. 

Or how about all of UA?  You can't explain it based on the current underlying laws of physics...so it must be false.

Regarding FE there are no underlying laws for its systems to falsify. If we did publish underlying laws, and you put it into a simulation that expressed those underlying laws, then you can go ahead and say that they are falsified.

Since RE has published underlying laws for its systems that don't work in a simulation, we can say that they are falsified. Pretty simple. Your problem is that Newton published laws that he himself discovered don't work with more than two bodies, and you just kept it around as cannon for your model.

[AATW]

Regarding FE there are no underlying laws for its systems to falsify.

So you’re backing a model of reality which you have discovered no underlying laws for.
And have no working map. This is the horse you’re backing?

The closest you seem to have is an equation for EA which contains a constant you have no value for and which has no ability to predict anything. Compelling.

As for RE laws “not working”, you’ll have to tell that to GPS, the ISS and the rover sitting on Mars right now. Your only counter argument is to shout “FAKE!!” even though you use GPS and can see the ISS from earth if you care to look.

A model doesn’t have to be perfect to be useful. There are mathematical reasons why these models cannot make perfect predictions - it’s the same reason weather forecasts are imperfect. But they’re clearly good enough to be of use. And the practical applications of them prove that we live on a globe.

[WTF_Seriously]

You are arguing that because they can't simulate it that its theories must be nonetheless true.

Nope.  You're the only one saying that.  What YOU are actually saying is that because they can't simulate it, it must be false.  That's what you're saying.  No one has ever stated 'can't be simulated = true'.  What has been shown to you is that despite a perfect simulation being possible things are still true.  Big difference between those two that you'll continue to deflect from as it's the only way for you to make an argument here.

We can't model eddies yet they exist.
We can't precisely model air over a wing yet our underlying theoretical approximations allow planes to fly.
We can't precisely model the weather yet the weatherman told me a week ago it would sunny today and behold, it is.
We can't precisely model ocean currents yet they flow.

The inability of human math to model something has no bearing on it's existence.  You know this.

[Tom Bishop]

Regarding FE there are no underlying laws for its systems to falsify.

So you’re backing a model of reality which you have discovered no underlying laws for.

I would rather have no laws than adopting your lame tactic of holding up false ones and trying to justify its massive failures.

You are arguing that because they can't simulate it that its theories must be nonetheless true.

Nope.  You're the only one saying that.  What YOU are actually saying is that because they can't simulate it, it must be false.  That's what you're saying.  No one has ever stated 'can't be simulated = true'.  What has been shown to you is that despite a perfect simulation being possible things are still true.  Big difference between those two that you'll continue to deflect from as it's the only way for you to make an argument here.

We can't model eddies yet they exist.
We can't precisely model air over a wing yet our underlying theoretical approximations allow planes to fly.
We can't precisely model the weather yet the weatherman told me a week ago it would sunny today and behold, it is.
We can't precisely model ocean currents yet they flow.

The inability of human math to model something has no bearing on it's existence.  You know this.

Since you can't do much I would suggest that you spend less time posting and more time fixing your tarnished model.

[SteelyBob]

Your problem is that Newton published laws that he himself discovered don't work with more than two bodies, and you just kept it around as cannon for your model.

But by ‘don’t work’, you mean ‘can’t be solved analytically’ don’t you Tom?

Again, I ask you - are you suggesting that the science of aerodynamics is flawed, because its equations also can’t be solved analytically, and CFD has to rely on numerical methods?
[/quote]

[WTF_Seriously]

Regarding FE there are no underlying laws for its systems to falsify.

So you’re backing a model of reality which you have discovered no underlying laws for.

I would rather have no laws than adopting your lame tactic of holding up false ones and trying to justifying its massive failures.

You are arguing that because they can't simulate it that its theories must be nonetheless true.

Nope.  You're the only one saying that.  What YOU are actually saying is that because they can't simulate it, it must be false.  That's what you're saying.  No one has ever stated 'can't be simulated = true'.  What has been shown to you is that despite a perfect simulation being possible things are still true.  Big difference between those two that you'll continue to deflect from as it's the only way for you to make an argument here.

We can't model eddies yet they exist.
We can't precisely model air over a wing yet our underlying theoretical approximations allow planes to fly.
We can't precisely model the weather yet the weatherman told me a week ago it would sunny today and behold, it is.
We can't precisely model ocean currents yet they flow.

The inability of human math to model something has no bearing on it's existence.  You know this.

Since you can't do much I would suggest that you spend less time posting and more time fixing your tarnished model.

Why?  The model works just fine.  In fact, I'm hopping on a flight in couple weeks for a little vacay.  Sure hope those numerical approximations of airflow hold up.