Offline SteelyBob

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Re: Is there anything that RET cannot explain?
« Reply #40 on: March 23, 2021, 11:00:03 PM »
Numerical solutions tend to be workarounds which are not based on the underlying laws.

https://wiki.tfes.org/Numerical_Solutions

Quote
From a question posted on researchgate.net:

  “ 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. 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. ”

Jason Brownlee, Ph.D., tells us on machinelearningmastery.com:

  “ An analytical solution involves framing the problem in a well-understood form and calculating the exact solution. A numerical solution means making guesses at the solution and testing whether the problem is solved well enough to stop. ”

http://www.math.pitt.edu/~sussmanm/2071Spring09/lab02/index.html

  “ With rare exceptions, a numerical solution is always wrong; the important question is, how wrong is it? ”

First of all let's remove Jason Brownlee from the discussion - he is clearly talking about something very different when he refers to 'numerical solutions'. He's isn't wrong in what he's saying, but the problems he is solving are completely different - he is describing using machine learning to search complex problem/solution spaces, hence discussions of techniques like gradient ascent etc, which is indeed a trial-based technique. In numerical methods such as FE in structures, or CFD in aerodynamics, we aren't making guesses and refining by trial and error, we are taking a set of equations that cannot be solved algebraically and applying expertise and judgment to simplify the problem enough to be able to compute an answer that is useful. The methods used to tackle the n-body problem are similar - there's no guesswork involved.

To your opening line:

Quote
Numerical solutions tend to be workarounds which are not based on the underlying laws.

You are always demanding evidence. Well, let's see some then. That's a massive statement, and you haven't provided a shred of evidence to support it. Of course, any scientist will always prefer an analytical solution if one is possible, but that doesn't mean that numerical solutions are invalid or indicative of a fallacious theory, as you seem to be trying to suggest. Your last post sums it up quite well - yes, any numerical solution will have a degree of error in it. The skill is in deciding how significant that error is. Given that most aircraft are designed using CFD, we are clearly able to refine results to a usable degree of precision, and the need for CFD does not render the navier stokes equations invalid, nor the underlying theories of aerodynamics.

Evidence then, please, for numerical methods tending to be 'workarounds' and 'not based on the underlying laws'.

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Offline Tom Bishop

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Re: Is there anything that RET cannot explain?
« Reply #41 on: March 23, 2021, 11:26:49 PM »
Quote from: SteelyBob
First of all let's remove Jason Brownlee from the discussion - he is clearly talking about something very different when he refers to 'numerical solutions'.

I don't see that you are as qualified to correct or contradict him. He clearly expresses that the analytical solutions are the problems in well-understood form like the other references.

You are always demanding evidence. Well, let's see some then. That's a massive statement, and you haven't provided a shred of evidence to support it.

Actually, I have. It is you who has not provided evidence for their statements. In that same link it shows that they are combining multiple two-body problems as a workaround for the problem of computing multiple bodies:

https://wiki.tfes.org/Numerical_Solutions

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https://academic.oup.com/mnras/article/440/1/719/1747624

 “ We developed a Keplerian-based Hamiltonian splitting for solving the gravitational N-body problem. This splitting allows us to approximate the solution of a general N-body problem by a composition of multiple, independently evolved two-body problems. While the Hamiltonian splitting is exact, we show that the composition of independent two-body problems results in a non-symplectic non-time-symmetric first-order map. A time-symmetric second-order map is then constructed by composing this basic first-order map with its self-adjoint. The resulting method is precise for each individual two-body solution and produces quick and accurate results for near-Keplerian N-body systems, like planetary systems or a cluster of stars that orbit a supermassive black hole. ”

https://hanspeterschaub.info/Papers/UnderGradStudents/ConicReport.pdf

  “ The patched-conic approximation has thus been developed as a more accurate solution to interplanetary transfer description. It involves partitioning the overall transfer into distinct conic solutions. For instance, as a spacecraft travels from Earth to Mars, its orbit is approximated as a hyperbolic departure, an elliptic transfer, and a hyperbolic arrival. The patched-conic approximation breaks the entire orbit down into several two-body problems. In other words, only one celestial body’s influence is considered to be acting upon the spacecraft at all times. ”

https://academic.oup.com/mnras/article/452/2/1934/1069988

  “ In this paper, we present a new symplectic integrator for collisional gravitational N-body dynamics. The integrator is inspired by the non-symplectic and non-reversible integrator in Gonçalves Ferrari et al. (2014), SAKURA, and makes use of Kepler solvers. Like SAKURA we decompose the N-body problem into two-body problems. In contrast to SAKURA, our two-body problems are not independent. The integrator is reversible and symplectic and conserves nine integrals of motion of the N-body problem to machine precision. ”
« Last Edit: March 24, 2021, 12:03:09 AM by Tom Bishop »

Offline SteelyBob

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Re: Is there anything that RET cannot explain?
« Reply #42 on: March 24, 2021, 12:05:06 AM »


I don't see that you are as qualified to contradict or correct him. He clearly expresses that the analytical solutions are the problems in well-understood form like the other references.


My qualifications and his are completely irrelevant. That's your second appeal to authority in this thread alone - it's a bone mistake in any debate, and all the more embarrassing because you aren't even doing it right, given that I'm not contradicting or correcting either of the people whose authority you are appealing to.

I'm not disagreeing with Jason - I'm saying he's working in a different field, and the meaning he is assigning to 'numerical solution' is somewhat different to that which we are discussing. I don't think have time, nor would the mods wish for me to explain the difference between machine learning and solving partial differential equations. If you don't appreciate the difference, it's probably best not to make assertions about those subjects.


You are always demanding evidence. Well, let's see some then. That's a massive statement, and you haven't provided a shred of evidence to support it.

Actually, I have. It is you who has not provided evidence for their statements. In that same link it shows that they are combining multiple two-body problems as a workaround for the problem of computing multiple bodies:

I asked for evidence to show that numerical solutions ‘tend to be workarounds not based on the underlying laws.

Your Dunning-Kruger statement there has two important parts. 'Tend' implies 'more often than not', so we need not just one example, but some evidence to support your contention that it is the norm. Furthermore, the one example you've given there clearly is based on the underlying laws. It's not just some stuff they guessed, as you keep implying.


[edited to fix a quote error]
« Last Edit: March 24, 2021, 07:22:04 AM by SteelyBob »

Re: Is there anything that RET cannot explain?
« Reply #43 on: March 24, 2021, 09:41:25 AM »
In that same link it shows that they are combining multiple two-body problems as a workaround for the problem of computing multiple bodies

Right. And? You previously said that:

Numerical solutions tend to be workarounds which are not based on the underlying laws.

And now you're providing links and evidence that the numerical solution here DOES use the underlying laws, it just splits the problem into a series of problems which can be solved.
And given that there's a rover sitting on Mars right now and we have close up pictures of all the planets from probes which were sent there, I'd say that approach works rather well.

Meanwhile, the closest the FE come to having anything which could be called a theory or law is EA which has an equation with no derivation and an unknown constant and can't be used to make any predictions at all. ???
"On a very clear and chilly day it is possible to see Lighthouse Beach from Lovers Point and vice versa...Upon looking into the telescope I can see children running in and out of the water, splashing and playing. I can see people sun bathing at the shore
- An excerpt from the account of the Bishop Experiment. My emphasis

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Offline Tumeni

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Re: Is there anything that RET cannot explain?
« Reply #44 on: March 24, 2021, 10:08:54 AM »
Is acceptance of a three-body problem in the first place an acceptance of the presence of the three bodies concerned  ...  and therefore an acceptance of RE?
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Offline Action80

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Re: Is there anything that RET cannot explain?
« Reply #45 on: March 24, 2021, 10:43:25 AM »
Next time I believe you could spare us the long winded sentences and simply state the following:

"There is no numerical solution to the n-body problem."

Well, no I couldn't, because that's almost the precise opposite of what I said. There are almost no algebraic solutions to the n-body problem, aside from certain very specific unique cases, and almost every other solution is a numeric one of some kind.

Moreover, it is important to understand that the example Tom is using to highlight his point is in itself a numeric solution - he has completely failed to understand that, or is deliberately misrepresenting it.

at the 2.52 minute mark which represents our solar system according to modern physics I notice that none of the marbles turned into moons and orbited other planets.

at the 4:40 mark he tries to demonstrate the three body system but it sure looks to me like both marbles are just orbiting the "sun" in that example. One marble does not do more than bump into the other once or twice. They never form what to me looks like a three body system which exists in our solar system with the sun, the earth, and the moon.

That's a ridiculous interpretation of an experiment that is clearly intended as an illustrative teaching aid, and not an accurate simulation of things.
LOL! that's the issue.

A numerical solution that you claim to exist can be modeled, right out in the open.

But it cannot in this case, because gravity is entirely fictional.

Offline SteelyBob

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Re: Is there anything that RET cannot explain?
« Reply #46 on: March 24, 2021, 12:34:02 PM »
LOL! that's the issue.

A numerical solution that you claim to exist can be modeled, right out in the open.

But it cannot in this case, because gravity is entirely fictional.

Eh? I’m sorry, but that just makes no sense at all. Are you suggesting that numerical solutions to the n-body problem don’t exist? There’s loads of them out there - even Tom has linked to some in his wiki (not that he realised they were numerical methods, but that’s another story...)

Offline Action80

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Re: Is there anything that RET cannot explain?
« Reply #47 on: March 24, 2021, 12:43:39 PM »
LOL! that's the issue.

A numerical solution that you claim to exist can be modeled, right out in the open.

But it cannot in this case, because gravity is entirely fictional.

Eh? I’m sorry, but that just makes no sense at all. Are you suggesting that numerical solutions to the n-body problem don’t exist? There’s loads of them out there - even Tom has linked to some in his wiki (not that he realised they were numerical methods, but that’s another story...)
Numerical solutions can be modeled.

I have no clue why this is difficult for you to understand.

Trouble is, mythical gravity cannot.

Offline SteelyBob

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Re: Is there anything that RET cannot explain?
« Reply #48 on: March 24, 2021, 01:26:39 PM »

Numerical solutions can be modeled.


Mmmmm..sort of. A numerical solution is, generally speaking, a model of something. It's not something you would model.

I have no clue why this is difficult for you to understand.

To be honest, you don't seem to be reading or comprehending what's being said - your comments seem to be slightly inconsistent non-sequiturs.

Trouble is, mythical gravity cannot.

That doesn't really follow. Even if you take the view that gravity doesn't exist, to suggest that it can't be modelled is ridiculous. The formula for working out gravitational attraction is very simple indeed - it's just a function of the mass of the two objects in question and the distance between them. Whether you agree that gravity exists or not, that's the formula, and models of gravity's effects are all based on it.

The fact that you can't create a formula to express the positions and velocities over time for more than 2 bodies (in most situations) has nothing to do with gravity being real or not, it's just maths. We can't calculate the positions of electrons around an atom for the same reason, nor can we calculate the airflow around a car or aircraft. But aircraft fly - the inability to build plug-in formulae to describe the airflow does not make the principles of aerodynamics invalid.

The numerical solutions models that have been made replicate planetary orbits very well indeed. As with all models, they have limitations, but we can accurately work out the position of the planets over timeframes spanning centuries. That's excellent, and strongly suggests that the underlying theory is valid. That predictive power is enormously important - FET has none whatsoever, which should really make FET proponents wonder if something is amiss with the model.

Offline Action80

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Re: Is there anything that RET cannot explain?
« Reply #49 on: March 24, 2021, 03:36:01 PM »

Numerical solutions can be modeled.


Mmmmm..sort of. A numerical solution is, generally speaking, a model of something. It's not something you would model.

I have no clue why this is difficult for you to understand.

To be honest, you don't seem to be reading or comprehending what's being said - your comments seem to be slightly inconsistent non-sequiturs.

Trouble is, mythical gravity cannot.

That doesn't really follow. Even if you take the view that gravity doesn't exist, to suggest that it can't be modelled is ridiculous. The formula for working out gravitational attraction is very simple indeed - it's just a function of the mass of the two objects in question and the distance between them. Whether you agree that gravity exists or not, that's the formula, and models of gravity's effects are all based on it.

The fact that you can't create a formula to express the positions and velocities over time for more than 2 bodies (in most situations) has nothing to do with gravity being real or not, it's just maths. We can't calculate the positions of electrons around an atom for the same reason, nor can we calculate the airflow around a car or aircraft. But aircraft fly - the inability to build plug-in formulae to describe the airflow does not make the principles of aerodynamics invalid.

The numerical solutions models that have been made replicate planetary orbits very well indeed. As with all models, they have limitations, but we can accurately work out the position of the planets over timeframes spanning centuries. That's excellent, and strongly suggests that the underlying theory is valid. That predictive power is enormously important - FET has none whatsoever, which should really make FET proponents wonder if something is amiss with the model.
2 bodies.

That is all.

Watching something for several years will give you a good idea of what is going to happen. Insurance companies make a killing off of this principle. Past practice is the best indicator of future performance.

You do not need gravity to make this true which is a good thing since it doesn't exist.

Offline SteelyBob

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Re: Is there anything that RET cannot explain?
« Reply #50 on: March 24, 2021, 04:35:15 PM »

2 bodies.

That is all.


There seems to be a belief creeping into the thread that all numerical solutions of the n-body problem are based on, or are somehow limited to 2-body calculations. That is simply not the case at all. Hamiltonian splitting is one such option, but there are countless others using a wide variety of methods. There are even guides out there on building your own n-body simulator, if you're interested. Here's one: https://medium.com/swlh/create-your-own-n-body-simulation-with-python-f417234885e9 - note that the code involves building a set of matrices with the gravitational force of each n-body acting on each of the other bodies. The simulation works in a step-wise manner - the smaller the step, the longer it takes to process, but the more accurate it is. Whilst you can't necessarily know how accurate the end result is, you can check the energy states of the system - the more constant, the better the simulation.

Here's another study: https://lup.lub.lu.se/luur/download?func=downloadFile&recordOId=4780668&fileOId=4780676 - note they back test the models against 2 and 3 body problems with known solutions, demonstrating the accuracy of the different methods.

This stuff isn't new. The planet Neptune was actually discovered because people noticed that the known planets weren't conforming to the models at the time, meaning that something else must be in the system causing the error. So they looked at the right piece of sky at the right time and...voila...a new planet. That's pretty awesome, considering it was mid-19th century. 

Watching something for several years will give you a good idea of what is going to happen. Insurance companies make a killing off of this principle. Past practice is the best indicator of future performance.

You do not need gravity to make this true which is a good thing since it doesn't exist.

You can run these models yourself and verify the accuracy if you wish (although you need major computing power to get decent results). If you are suggesting that all the cutting edge solar-system and indeed galaxy/ universal modals are actually just fudges based on observations then, once again, we have a FET proponent making an appeal to a massive conspiracy where just one dissenting voice could achieve global superstar status if they blew the cover off...but nobody ever does. Could it not just be that, actually, the models are pretty good and the solar system is actually the way we think it is, with a round earth in orbit around the sun and gravity operating as theorised and measured?

Your skepticism is a positive trait, but unless you have an alternative predictive model that outperforms what we already have and aligns with our observed world...why believe in it?

Your arguments that the mathematical difficulty of solving n-body is indicative of gravity not existing is just ludicrous - the same problems exist in countless of other scientific problems. Do you doubt aerodynamics for the same reason?

Re: Is there anything that RET cannot explain?
« Reply #51 on: March 24, 2021, 09:22:29 PM »
I think action80 has described the problem very well, despite any slight inconsistencies of verbiage you may see.

The concept itself is intractable, which is to say directly paradoxical, which is to say non-real.  The fact that what we observe cannot be modeled with the concept is unsurprising, and shows that newton was wrong (about a great many things, unsurprisingly).

We know where a light in the sky will be because of its past "performance" as action80 rightly points out.  It's how we "predict" eclipses too, from charts.

Another way to describe / aspect of the paradox is in the answerS to the question, "what happens to you at the center of the earth"?

Newton didn't know, and we don't either.  The concept suggests that the immense weight of everything crushes you, AND that you get rend asunder by the gravitational forces pulling you outward in all directions, AND that you feel nothing because all gravitational forces cancel themselves out.

Gravitation is a philosophically unsound and unscientific posit, which newton understood and admitted. He asked that his name not be associated with it as a result.
« Last Edit: March 25, 2021, 07:53:36 AM by jack44556677 »

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Offline Tumeni

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Re: Is there anything that RET cannot explain?
« Reply #52 on: March 24, 2021, 09:38:39 PM »
We know where a light in the sky will be because of its past "performance" as action80 rightly points out.  It's how we "predict" eclipses too, from charts

You may well be able to predict the occurrence from past history, but the actual behaviour (duration, path, etc) which will be seen by observers on the day is determined with respect to a globe Earth.

Look at the predicted behaviour of the Great American Eclipse of a few years back. Charts were shown months in advance of what to expect. When and were it would first be seen making landfall on the USA, where it would leave. Where observers would need to be to see totality. How long totality would last. How much less would be seen as one moved off the central path. How the speed of the eclipse shadow varied according to which part of the globe it was projected upon, and how this affected the timing of the eclipse shadow's progress.

All shown in advance, and NOBODY reported any deviation from this.

Impossible to predict all of this, to this degree of accuracy, simply by extrapolation of dates from previous eclipses.
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Offline Tom Bishop

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Re: Is there anything that RET cannot explain?
« Reply #53 on: March 24, 2021, 09:42:11 PM »
Impossible to predict all of this, to this degree of accuracy, simply by extrapolation of dates from previous eclipses.

If the eclipses repeat themselves, why not?

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Offline Tumeni

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Re: Is there anything that RET cannot explain?
« Reply #54 on: March 24, 2021, 09:43:46 PM »
Impossible to predict all of this, to this degree of accuracy, simply by extrapolation of dates from previous eclipses.

If the eclipses repeat themselves, why not?

because the various factors that I outlined do not repeat.

EDIT for image(s)





See in the second one, how the time segments expand and contract? Because the eclipse is passing over a curved surface.

How the %age visible lines, above and below, vary in separation? Because of the curved surface.

etc etc
« Last Edit: March 24, 2021, 09:56:16 PM by Tumeni »
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Offline Tumeni

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Re: Is there anything that RET cannot explain?
« Reply #55 on: March 24, 2021, 10:38:23 PM »
We know where a light in the sky will be because of its past "performance" as action80 rightly points out.  It's how we "predict" eclipses too, from charts

Impossible to predict all of this, to this degree of accuracy, simply by extrapolation of dates from previous eclipses.

If the eclipses repeat themselves, why not?

Well ... you stated in another thread, that Astronomy is a pseudoscience, and broadly that observations (of "lights in the sky") should be discounted, etc. ...
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Offline Tom Bishop

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Re: Is there anything that RET cannot explain?
« Reply #56 on: March 24, 2021, 11:44:13 PM »
Impossible to predict all of this, to this degree of accuracy, simply by extrapolation of dates from previous eclipses.

If the eclipses repeat themselves, why not?

because the various factors that I outlined do not repeat.

Actually, they do:

https://eclipse.gsfc.nasa.gov/SEsaros/SEsaros.html

"The periodicity and recurrence of eclipses is governed by the Saros cycle, a period of approximately 6,585.3 days (18 years 11 days 8 hours). It was known to the Chaldeans as a period when lunar eclipses seem to repeat themselves, but the cycle is applicable to solar eclipses as well."

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Offline Tumeni

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Re: Is there anything that RET cannot explain?
« Reply #57 on: March 25, 2021, 05:17:29 AM »
Impossible to predict all of this, to this degree of accuracy, simply by extrapolation of dates from previous eclipses.

If the eclipses repeat themselves, why not?

because the various factors that I outlined do not repeat.

Actually, they do:

https://eclipse.gsfc.nasa.gov/SEsaros/SEsaros.html

"The periodicity and recurrence of eclipses is governed by the Saros cycle, a period of approximately 6,585.3 days (18 years 11 days 8 hours). It was known to the Chaldeans as a period when lunar eclipses seem to repeat themselves, but the cycle is applicable to solar eclipses as well."

I cited a number of different factors which vary with each, you refer to ONLY the period between each recurrence.
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Offline Tom Bishop

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Re: Is there anything that RET cannot explain?
« Reply #58 on: March 25, 2021, 05:32:09 AM »
I cited a number of different factors which vary with each, you refer to ONLY the period between each recurrence.

If it repeats then the attributes are the same.

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Offline Tumeni

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Re: Is there anything that RET cannot explain?
« Reply #59 on: March 25, 2021, 05:39:45 AM »
I cited a number of different factors which vary with each, you refer to ONLY the period between each recurrence.

If it repeats then the attributes are the same.

No, they are not. Please refer again to the images above.

Attributes which vary;

Observable duration
Place in which eclipse can be observed (or not)
Width of central path in which eclipse can be seen
Fall-off of visibility each side of central path

etc
etc

EDIT for image from the webpage you quoted;



All different. With different attributes.
« Last Edit: March 25, 2021, 05:45:35 AM by Tumeni »
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