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johncarlosbaez's profile
John Carlos Baez
John Carlos Baez
John Carlos Baez
@johncarlosbaez

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John Carlos Baez

@johncarlosbaez

I do math, physics, network theory at U. C. Riverside and the Centre for Quantum Technologies in Singapore.

Riverside, CA
math.ucr.edu/home/baez/
Joined September 2016

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    John Carlos Baez‏ @johncarlosbaez Jan 11
    • Report Tweet

    John Carlos Baez Retweeted Simon Tardivel

    A beautiful solution of the gravitational 4-body problem. But keep watching, because it's not stable!https://twitter.com/simon_tardivel/status/1215728659010670594 …

    John Carlos Baez added,

    0:16
    Simon Tardivel @simon_tardivel
    Par exemple, prenons une jolie configuration à... 4 corps désormais ! Regardez les premiers tours, c'est joli hein... Ouais continuez à regarder... #SpoilerAlert CA VA MAL FINIR ! pic.twitter.com/rxQeBkJ2kr
    Show this thread
    9:45 AM - 11 Jan 2020
    • 1,023 Retweets
    • 4,217 Likes
    • nina miguel snufkin stan account Garibaldi Cristian James Mainwaring Alexey Alekhin Anshul Choudhary Evelyn Almgren
    50 replies 1,023 retweets 4,217 likes
      1. John Carlos Baez‏ @johncarlosbaez Jan 11
        • Report Tweet

        John Carlos Baez Retweeted Simon Tardivel

        This solution of the 3-body problem is stable, apparently:https://twitter.com/simon_tardivel/status/1215726342421041152 …

        John Carlos Baez added,

        0:45
        Simon Tardivel @simon_tardivel
        La 2eme particularité... C'est que c'est stable ! Si on n'est pas exactement sur les bonnes conditions initiales des particules, et bah on va quand même voir le même comportement. Et ça, c'est vraiment étrange, voyez plutôt. Vous comprenez ce qu'il se passe ? pic.twitter.com/j8xBpMkkus
        Show this thread
        9 replies 104 retweets 500 likes
        Show this thread
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      1. New conversation
      2. Venu Madhav Govindu‏ @venugovindu Jan 11
        • Report Tweet
        Replying to @johncarlosbaez

        Assuming its not a numerical issue, I am not sure I understand why symmetry should fall apart.

        4 replies 0 retweets 27 likes
      3. John Carlos Baez‏ @johncarlosbaez Jan 11
        • Report Tweet
        Replying to @venugovindu

        If it's not perfectly symmetrical at the start, it can become extremely asymmetric later. Or maybe it's symmetrical at the start but the numerical errors are asymmetric for some reason. In the real world, outside influences can introduce the asymmetry.

        4 replies 2 retweets 92 likes
      4. 4 more replies
      1. New conversation
      2. Josh Foster‏ @JoshuaDFoster1 Jan 11
        • Report Tweet
        Replying to @johncarlosbaez @InertialObservr

        I don't understand why it's unstable. I'm the farthest thing from a physicist, so I'm sure I'm missing something obviously, but it seems to me like it should be stable. Is something influencing their movement besides each other?

        3 replies 0 retweets 3 likes
      3. John Carlos Baez‏ @johncarlosbaez Jan 11
        • Report Tweet
        Replying to @JoshuaDFoster1 @InertialObservr

        Lots of systems are unstable, and then they can *look* like they're doing something simple, but in reality they're not quite, and the deviation from simple behavior gradually builds up over time and suddenly spirals out of control. Just solve the equations...

        3 replies 0 retweets 33 likes
      4. 15 more replies
      1. New conversation
      2. Vitalii Akimov‏ @vitalii_akimov Jan 11
        • Report Tweet
        Replying to @johncarlosbaez

        does this have some nice 4d interpretation like you wrote about 2 body problem?

        1 reply 0 retweets 1 like
      3. John Carlos Baez‏ @johncarlosbaez Jan 11
        • Report Tweet
        Replying to @vitalii_akimov

        I doubt it! The gravitational 2-body problem is very special in having a secret 4-dimensional rotation symmetry.https://johncarlosbaez.wordpress.com/2015/03/17/planets_in_the_4th_dimension/ …

        0 replies 3 retweets 30 likes
      4. End of conversation
      1. New conversation
      2. Daniele Pinna‏ @PestoPoppa Jan 11
        • Report Tweet
        Replying to @johncarlosbaez

        How can we say this isn't the result of a numerical rounding error in the integration script breaking the symmetry? Did someone try reproducing this result?

        1 reply 0 retweets 16 likes
      3. John Carlos Baez‏ @johncarlosbaez Jan 11
        • Report Tweet
        Replying to @PestoPoppa

        It's either the result of a numerical rounding error, or a deliberately introduced imperfection in the initial conditions. It doesn't really matter much: either way, a slight deviation from symmetry is getting amplified.

        1 reply 1 retweet 47 likes
      4. 1 more reply
      1. New conversation
      2. Pedro Larroy  🇺🇳 ∞‏ @plarroy Jan 12
        • Report Tweet
        Replying to @johncarlosbaez

        Is the author using floating point for this simulation?

        1 reply 0 retweets 4 likes
      3. John Carlos Baez‏ @johncarlosbaez Jan 12
        • Report Tweet
        Replying to @plarroy

        I don't know. Are you, @simon_tardivel ? Either numerical errors or deliberate errors introduced into the initial conditions are being amplified by the instability of this trajectory.

        2 replies 0 retweets 3 likes
      4. 7 more replies

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