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Scientists find an effective solution for the three-body problem

phys.technion.ac.il

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Re: Scientists find an effective solution for the three-body problem

#201

Post by robocat »

deltasixeight wrote: post #186
konschubert wrote: post #175

Earlier quoted context omitted.

No. We know there is a deterministic solution, even if we can't calculate it.

Prove it. I guarantee you 100% you don't know how and you can't ever prove it. You are completely and utterly wrong and you don't know what you're talking about. That is a fact. In fact I'm willing to put money on it. $1000 over venmo to you, a random stranger. You down? Give me a formal and correct proof that if a solution exists and that it is deterministic and I swear I'll venmo $1000 to whatever address you wish.…

Unfortunately your aggressiveness and rudeness make your comment of lower quality than the one you are answering - read https://news.ycombinator.com/newsguidelines.html to see what site rules you are breaking as well. Betting doesn't make your argument truer, it only points to your own irrationality.

Disclaimer: I am no mathematician nor physicist.

However the intuition is that any set of equations must be deterministic, unless they refer to a non-deterministic function like random(x).

Should you wish to argue that the three body problem can generate true randomness, I think it is your responsibility to refer to links that support your argument. I would expect an argument to refer to mathematical concepts and have nothing to do with the three body problem in particular. I suspect it verges on tautological that if you can define equations then it is deterministic.

Re: Scientists find an effective solution for the three-body problem

#202

Post by spekcular »

deltasixeight wrote: post #196
spekcular wrote: post #190

Earlier quoted context omitted.

You think Newtonian physics is non-deterministic? I haven't checked but I think existence and uniqueness for the classical three body problem likely follows from standard theorems on ODEs. If you can articulate why this is not the case, please do. edit: Yes, see section 2.1 of this term paper: https://sites.math.washington.edu/~morrow/336_13/papers/pete... . In fact, more is known: the solution exists and is analytic…

I didn't say that. For the three body problem we don't know the closed form solution under Newtonian physics. So if we don't know it, then a closed solution may not even exist. If we don't know whether a closed form solution exists then how can we even know if it's deterministic. You can prove determinism by finding me a solution that's closed and deterministic. My answer is the same as stated: we don't know, and tha…

"If we don't know whether a closed form solution exists then how can we even know if it's deterministic.

You can prove determinism by finding me a solution that's closed and deterministic."

Why would it be necessary to have a closed form solution to know that the solution is deterministic? By the first reference in my previous comment, two identical initial conditions lead to identical time evolutions. That is literally the definition of determinism.

Re: Scientists find an effective solution for the three-body problem

#203

Post by WalterBright »

smolder wrote: post #177
WalterBright wrote: post #158

Earlier quoted context omitted.

> It can be extremely comforting to surround yourself with explanations that nothing is actually within your control or that others’ success or happiness is the result of randomness. On the other hand, accepting responsibility for results is empowering, because it means one can be successful. I don't see anything happy about deciding one is a hapless victim of others.

The comfort in shifting your locus of control outward comes from relieving the shame of failure, not from being an overall positive experience. In fact, it's common for people to both take credit for their successes while blaming their failures on external factors to relieve the shame.

Blaming failure on others or external factors doesn't lead to success. It leads to bitterness and resentment.

Re: Scientists find an effective solution for the three-body problem

#204

Post by deltasixeight »

robocat wrote: post #201
deltasixeight wrote: post #186

Earlier quoted context omitted.

Prove it. I guarantee you 100% you don't know how and you can't ever prove it. You are completely and utterly wrong and you don't know what you're talking about. That is a fact. In fact I'm willing to put money on it. $1000 over venmo to you, a random stranger. You down? Give me a formal and correct proof that if a solution exists and that it is deterministic and I swear I'll venmo $1000 to whatever address you wish.…

Unfortunately your aggressiveness and rudeness make your comment of lower quality than the one you are answering - read https://news.ycombinator.com/newsguidelines.html to see what site rules you are breaking as well. Betting doesn't make your argument truer, it only points to your own irrationality. Disclaimer: I am no mathematician nor physicist. However the intuition is that any set of equations must be determinis…

>Unfortunately your aggressiveness and rudeness make your comment of lower quality than the one you are answering - read https://news.ycombinator.com/newsguidelines.html to see what site rules you are breaking as well. Betting doesn't make your argument truer, it only points to your own irrationality.

Did you not notice the person who replied to me literally just commented a single sentence and left it at that? It's called an unsubstantiated comment and it is also addressed int the rules you link here: https://news.ycombinator.com/newsguidelines.html

I simply made a bet. There's no aggression here. I like to back up my claims with more seriousness rather then single line comments. Also claiming my post is rude and aggressive when it isn't is in itself rude. I just make claims and I offer to back up my claim with money. Why? I would offer a proof but no proof is known because my answer is: We don't know.

>Should you wish to argue that the three body problem can generate true randomness, I think it is your responsibility to refer to links that support your argument

Except this is not my wish and I never stated such. My statement is that we don't know if it's deterministic. My offer is that I put money on the fact we don't have any definitive proof we do know.

>However the intuition is that any set of equations must be deterministic,

Intuition is just hand waving. There is nothing definitive here I'm sorry. My offer stands to the first person that can give me a proof, $1000. That includes you even though I found the first paragraph of your post dishonest and rude. You called me irrational, that's practically an insult and a flagrant violation of the rules. I did no such violation.

What's going on here is not that I'm violating the rules. But that you're biased. You disagree with me so your bias senses aggression and violations of rules on my side even though I did no such thing. In fact your bias blinds you to your own violation. You called me irrational. Might as well call me stupid. Same personal insult just disguised with smarter wording.

Re: Scientists find an effective solution for the three-body problem

#205

Post by WalterBright »

PaulDavisThe1st wrote: post #180
WalterBright wrote: post #173

Earlier quoted context omitted.

Leaving off crucial parts of the statement makes it a hatchet job. Just like if someone says "more or less" and the journalist leaves out the "or less".

You believe that the first clause somehow balances the second? When this (partial) quote is used, it's generally in a context where the first clause is arguably irrelevant. I don't think it's like your "more or less" analogy. There are not many corporations that fail to benefit when the country does well, so the first clause is broadly agreed upon. The second clause, however, is controversial, and has implications th…

> You believe that the first clause somehow balances the second?

It doesn't matter if I believe it or not. It's a hatchet job to selectively misquote people to pursue the journalist's agenda.

Re: Scientists find an effective solution for the three-body problem

#206

Post by deltasixeight »

spekcular wrote: post #202
deltasixeight wrote: post #196

Earlier quoted context omitted.

I didn't say that. For the three body problem we don't know the closed form solution under Newtonian physics. So if we don't know it, then a closed solution may not even exist. If we don't know whether a closed form solution exists then how can we even know if it's deterministic. You can prove determinism by finding me a solution that's closed and deterministic. My answer is the same as stated: we don't know, and tha…

"If we don't know whether a closed form solution exists then how can we even know if it's deterministic. You can prove determinism by finding me a solution that's closed and deterministic." Why would it be necessary to have a closed form solution to know that the solution is deterministic? By the first reference in my previous comment, two identical initial conditions lead to identical time evolutions. That is litera…

No look at my wording more carefully. You are misinterpreting it. I said we don't know if a "closed form solution" is deterministic because we don't even know if there is a "closed form solution."

I also said that you CAN prove determinism to me by finding a closed form solution that is deterministic. I never said you needed to nor did I say that was the only way.

Your examples are for special cases. Can you prove it to me that for N-bodies and all possible initial conditions that all solutions are deterministic?

Re: Scientists find an effective solution for the three-body problem

#207

Post by kergonath »

deltasixeight wrote: post #196
spekcular wrote: post #190

Earlier quoted context omitted.

You think Newtonian physics is non-deterministic? I haven't checked but I think existence and uniqueness for the classical three body problem likely follows from standard theorems on ODEs. If you can articulate why this is not the case, please do. edit: Yes, see section 2.1 of this term paper: https://sites.math.washington.edu/~morrow/336_13/papers/pete... . In fact, more is known: the solution exists and is analytic…

I didn't say that. For the three body problem we don't know the closed form solution under Newtonian physics. So if we don't know it, then a closed solution may not even exist. If we don't know whether a closed form solution exists then how can we even know if it's deterministic. You can prove determinism by finding me a solution that's closed and deterministic. My answer is the same as stated: we don't know, and tha…

> So if we don't know it, then a closed solution may not even exist. If we don't know whether a closed form solution exists then how can we even know if it's deterministic.

We can prove that something has some properties even if we don’t know everything about it. Newton’s second law in a many-body system is (in the case of Newtonian gravity) basically a system of independent second-order ODEs. We know a thing or two about these beasts.

Anyway, let me try something (without LaTeX, so I apologise in advance for the notation).

Let’s think about a many-body system (following Newtonian mechanics, and interacting via Newtonian gravity) from the point of view of its positions-velocities phase space. The solution is not deterministic if there are points (i.e., sets of positions and velocities for all the particles) that are part of at least two trajectories.

Let’s assume we are looking at such a point. The forces F and all their derivatives dF/dr are the same along all trajectories, because they depend only on the positions (which are identical). The velocities and the positions are the same because it is the same point in the phase space.

The third derivatives of the positions w.r.t time are also identical (d^3r/dt^3 = 1/m dF/dt, and dF/dt = dF/dr dr/dt, and the dr/dt are identical).

You can go on to the n-th derivative, n being arbitrary large (d^4 r/dt^4 is a function of only dF/dr, dr/dt, d^2 r/dt^2 and d^2 F/dr^2, all of which are identical along both trajectories, etc).

So, it means that both trajectories have the same position in the phase space, and all their derivatives are identical, i.e., both trajectories are identical. So it is deterministic (there is no point in the phase space that belongs to more than one trajectory).

It is somewhat related to Liouville’s theorem.

Re: Scientists find an effective solution for the three-body problem

#208

Post by deltasixeight »

kergonath wrote: post #194
deltasixeight wrote: post #170

>So theoretically speaking, they are deterministic, but practically they are unpredictable. The three body problem is REFERING to the ideal case where only a perfect model is considered. Within this model we don't even know the math to calculate it. So, in short, we lack a "deterministic theory" about this problem at all. What's going on here is an assumption. We assume that an idealistic scenario will always produce…

We can have these problems simply with classical mechanics’ equations of motion (Newton, Lagrange, Hamilton, whatever). These equations are deterministic, there is no doubt about this. We just don’t have an analytical form. We know that exactly the same initial conditions will lead to the exact same trajectory. What we also know is that the tiniest error will make the trajectories diverge exponentially. It is still d…

After some research I've come to the conclusion that my statement is in fact definitively wrong.

What I said was this: We do not know if classical mechanics is deterministic.

I am wrong. The correct statement is: We do know that classical mechanics is not deterministic.

So essentially I'm wrong but so is everyone else so I'm paying nobody.

Source: https://sites.pitt.edu/~jdnorton/Goodies/Dome/

Essentially this is proof by contradiction. Classical mechanics is not deterministic.

My answer was, however, better than everyone else's given that my answer was in itself not absolute and encompassed this possibility and the opposing possibility as well.

Re: Scientists find an effective solution for the three-body problem

#209

Post by deltasixeight »

kergonath wrote: post #207
deltasixeight wrote: post #196

Earlier quoted context omitted.

I didn't say that. For the three body problem we don't know the closed form solution under Newtonian physics. So if we don't know it, then a closed solution may not even exist. If we don't know whether a closed form solution exists then how can we even know if it's deterministic. You can prove determinism by finding me a solution that's closed and deterministic. My answer is the same as stated: we don't know, and tha…

> So if we don't know it, then a closed solution may not even exist. If we don't know whether a closed form solution exists then how can we even know if it's deterministic. We can prove that something has some properties even if we don’t know everything about it. Newton’s second law in a many-body system is (in the case of Newtonian gravity) basically a system of independent second-order ODEs. We know a thing or two…

https://news.ycombinator.com/item?id=28184786

Re: Scientists find an effective solution for the three-body problem

#210

Post by deltasixeight »

spekcular wrote: post #202
deltasixeight wrote: post #196

Earlier quoted context omitted.

I didn't say that. For the three body problem we don't know the closed form solution under Newtonian physics. So if we don't know it, then a closed solution may not even exist. If we don't know whether a closed form solution exists then how can we even know if it's deterministic. You can prove determinism by finding me a solution that's closed and deterministic. My answer is the same as stated: we don't know, and tha…

"If we don't know whether a closed form solution exists then how can we even know if it's deterministic. You can prove determinism by finding me a solution that's closed and deterministic." Why would it be necessary to have a closed form solution to know that the solution is deterministic? By the first reference in my previous comment, two identical initial conditions lead to identical time evolutions. That is litera…

https://news.ycombinator.com/item?id=28184786
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