6 ms·

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

deltasixeight 5y ago
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. Can you do the same? No, you can't. If not then I'm right. We don't KNOW whether it's deterministic because our BEST model is probabilistic. We really should raise the stakes and seriousness of HN comments to prevent random uneducated people who really don't know anything from posting random comments. Like come on... HN is better than reddit but some random set of "rules" against unsubstantiated comments doesn't stop people like this guy from posting unsubstantiated comments.
- spekcular 5y ago
  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/peter.pdf https://sites.math.washington.edu/~morrow/336_13/papers/pete.... In fact, more is known: the solution exists and is analytic. From Wikipedia: "However, in 1912 the Finnish mathematician Karl Fritiof Sundman proved that there exists an analytic solution to the three-body problem in the form of a power series in terms of powers of t1/3. This series converges for all real t, except for initial conditions corresponding to zero angular momentum. In practice, the latter restriction is insignificant since initial conditions with zero angular momentum are rare, having Lebesgue measure zero. "
  - deltasixeight 5y ago
    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 that the claim that we do know, is completely wrong. >In fact, more is known: the solution exists and is analytic These are special cases, under special conditions. A general solution is not actually known. We don't know. We are only assuming that it's deterministic. Also the solution you provided is analytic not closed.
    - spekcular 5y ago
      "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.
      - deltasixeight 5y ago
        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?
      - deltasixeight 5y ago
        https://news.ycombinator.com/item?id=28184786 https://news.ycombinator.com/item?id=28184786
        5y ago
- robocat 5y ago
  Unfortunately your aggressiveness and rudeness make your comment of lower quality than the one you are answering - read https://news.ycombinator.com/newsguidelines.html 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.
  - deltasixeight 5y ago
    >Unfortunately your aggressiveness and rudeness make your comment of lower quality than the one you are answering - read https://news.ycombinator.com/newsguidelines.html 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 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.
- dang 5y ago
  Please don't take HN threads into flamewars like this. It's not what the site is for. https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
  - deltasixeight 5y ago
    If you read the thread. There's no flame war going on at all. It is just discussion. Seriously.
    - dang 5y ago
      "You are completely and utterly wrong and you don't know what you're talking about" is not "just discussion", it's obvious flamewar. Posting like that to HN will get you banned, because it violates what the site is supposed to be for, namely curious conversation. If you don't want to be banned on HN, please follow the rules and don't post like this again. https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
      - deltasixeight 5y ago
        Well he posted an unsubstantiated comment. I Had a long post and he dismissed it with one line. So there's a little aggression in my response, but I told the truth, did not insult him or do anything of the sort. There is obviously Zero flame war going on as it's a single post and the rest of the thread extends into a long and "namely curious" discussion which you essentially just hidden from view. This is selective enforcement and you can totally ban me if you want but if you do I would say you're being unfair, dismissive and a bad moderator. Yeah ban me for that minor thing, but please explain to me how you just completely ignored the person who I responded to. Additionally a person responding to the post you flagged decided to call me irrational out of nowhere. I flagged, but again ignored. How is this fair at all?
        dang 5y ago
        When someone describes their comments as having "a little aggression", usually they vastly and egregiously broke the site guidelines. Objects in the mirror are closer than they appear—we all have a tendency to overestimate what the other person is doing and underestimate what we've contributed ourselves. You posted a huge number of comments in this largely off topic subthread, provoking others repeatedly with swipes and flamebait (by the time we get to https://news.ycombinator.com/item?id=28193336 https://news.ycombinator.com/item?id=28193336 that's practically all that's left). This is the way that threads degenerate, and I replied to you because you did by far the most to push it in that direction. It may be true that other users broke the site guidelines also, and if so they shouldn't. But that doesn't mean what they did was equally bad. I'd have to see specific links to know; it's impossible for us to read all the threads thoroughly (https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sort=byDate&type=comment&query=likeliest%20by:dang https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sor...), and so it's impossible for moderation to be completely consistent. This is the same reason why cops don't give tickets to all speeders: there are far too many of them. Of course it always feels unfair when you're the one pulled over. https://hn.algolia.com/?dateRange=all&page=0&prefix=true&query=cops%20speed%20by%3Adang&sort=byDate&type=comment https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que... https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sort=byDate&type=comment&query=%22always%20feels%22%20mods%20by:dang https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sor...
deltasixeight 5y ago
https://sites.pitt.edu/~jdnorton/Goodies/Dome/ https://sites.pitt.edu/~jdnorton/Goodies/Dome/ we don't.

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. Can you do the same? No, you can't. If not then I'm right. We don't KNOW whether it's deterministic because our BEST model is probabilistic. We really should raise the stakes and seriousness of HN comments to prevent random uneducated people who really don't know anything from posting random comments. Like come on... HN is better than reddit but some random set of "rules" against unsubstantiated comments doesn't stop people like this guy from posting unsubstantiated comments.

spekcular 5y ago
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/peter.pdf https://sites.math.washington.edu/~morrow/336_13/papers/pete.... In fact, more is known: the solution exists and is analytic. From Wikipedia: "However, in 1912 the Finnish mathematician Karl Fritiof Sundman proved that there exists an analytic solution to the three-body problem in the form of a power series in terms of powers of t1/3. This series converges for all real t, except for initial conditions corresponding to zero angular momentum. In practice, the latter restriction is insignificant since initial conditions with zero angular momentum are rare, having Lebesgue measure zero. "
- deltasixeight 5y ago
  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 that the claim that we do know, is completely wrong. >In fact, more is known: the solution exists and is analytic These are special cases, under special conditions. A general solution is not actually known. We don't know. We are only assuming that it's deterministic. Also the solution you provided is analytic not closed.
  - spekcular 5y ago
    "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.
    - deltasixeight 5y ago
      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?
    - deltasixeight 5y ago
      https://news.ycombinator.com/item?id=28184786 https://news.ycombinator.com/item?id=28184786
      - 5y ago
robocat 5y ago
Unfortunately your aggressiveness and rudeness make your comment of lower quality than the one you are answering - read https://news.ycombinator.com/newsguidelines.html 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.
- deltasixeight 5y ago
  >Unfortunately your aggressiveness and rudeness make your comment of lower quality than the one you are answering - read https://news.ycombinator.com/newsguidelines.html 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 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.
dang 5y ago
Please don't take HN threads into flamewars like this. It's not what the site is for. https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
- deltasixeight 5y ago
  If you read the thread. There's no flame war going on at all. It is just discussion. Seriously.
  - dang 5y ago
    "You are completely and utterly wrong and you don't know what you're talking about" is not "just discussion", it's obvious flamewar. Posting like that to HN will get you banned, because it violates what the site is supposed to be for, namely curious conversation. If you don't want to be banned on HN, please follow the rules and don't post like this again. https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
    - deltasixeight 5y ago
      Well he posted an unsubstantiated comment. I Had a long post and he dismissed it with one line. So there's a little aggression in my response, but I told the truth, did not insult him or do anything of the sort. There is obviously Zero flame war going on as it's a single post and the rest of the thread extends into a long and "namely curious" discussion which you essentially just hidden from view. This is selective enforcement and you can totally ban me if you want but if you do I would say you're being unfair, dismissive and a bad moderator. Yeah ban me for that minor thing, but please explain to me how you just completely ignored the person who I responded to. Additionally a person responding to the post you flagged decided to call me irrational out of nowhere. I flagged, but again ignored. How is this fair at all?
      - dang 5y ago
        When someone describes their comments as having "a little aggression", usually they vastly and egregiously broke the site guidelines. Objects in the mirror are closer than they appear—we all have a tendency to overestimate what the other person is doing and underestimate what we've contributed ourselves. You posted a huge number of comments in this largely off topic subthread, provoking others repeatedly with swipes and flamebait (by the time we get to https://news.ycombinator.com/item?id=28193336 https://news.ycombinator.com/item?id=28193336 that's practically all that's left). This is the way that threads degenerate, and I replied to you because you did by far the most to push it in that direction. It may be true that other users broke the site guidelines also, and if so they shouldn't. But that doesn't mean what they did was equally bad. I'd have to see specific links to know; it's impossible for us to read all the threads thoroughly (https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sort=byDate&type=comment&query=likeliest%20by:dang https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sor...), and so it's impossible for moderation to be completely consistent. This is the same reason why cops don't give tickets to all speeders: there are far too many of them. Of course it always feels unfair when you're the one pulled over. https://hn.algolia.com/?dateRange=all&page=0&prefix=true&query=cops%20speed%20by%3Adang&sort=byDate&type=comment https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que... https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sort=byDate&type=comment&query=%22always%20feels%22%20mods%20by:dang https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sor...

deltasixeight 5y ago

https://sites.pitt.edu/~jdnorton/Goodies/Dome/ https://sites.pitt.edu/~jdnorton/Goodies/Dome/ we don't.