Problème des Trois Corps

June 9, 2012

Thanks for the infographic on celestial mechanics: very interesting.  Definitely saved me the effort of looking up my ephemeris tables, my planetary size table, and my history of science/technology papers.  Though I must say, when I worked at Syracuse Research Corporation one summer, I enjoyed getting TLE from NORAD and generating animations with the Satellite Tool Kit.  Interestingly, both now have new three-letter names: SRC and STK

The alignment of three bodies like Venus, Earth, and Sun on Tuesday is somewhat related to a classical problem of mechanics: the three-body problem, where the goal is to predict what will happen under gravitational forces given initial conditions.  One of the nice results that comes out of the three-body problem is the existence of so-called Lagrangian points, which are stationary points of the dynamics.  Do you happen to know if there are any frame-theoretic interpretations of the Lagrangian points?

Mechanics and mechanical engineering are old subjects, but you can still come up with new things.  I was just reading an article in the special issue of IEEE Spectrum on money, and came across an intriguing technology for transferring money from one person’s cell phone to another person’s.  Let me quote from the article:

Silicon Valley start-up Bump Technologies recently announced Bump Pay, which cleverly uses accelerometers and geolocation to let users exchange money between phones.  To transfer money to a friend who also has the Bump Pay app, you just enter the amount, then bump the two phones together.  Bump Pay’s system uses geolocation to limit the search to nearby phones.  Next, it compares the timing of accelerometer events to match up two phones that recorded an impact at the same time.  Finally, it executes the transaction via PayPal.  Compared to NFC, it’s an extremely convoluted solution for proximity sensing.

Although I would probably enjoy fist bumping transactions, I hope that near field communication (NFC) also grows a little more, especially since I have been working with Pulkit Grover and Anant Sahai on securing inductively-coupled communication.

The problem studied in the work with Pulkit and Anant is the wire-tap channel, with three bodies: transmitter, legitimate receiver, and eavesdropper, but also makes use of the underlying physics of inductively-coupled channels.  Indeed, a lot of classic multiterminal information theory problems are “three-body” problems and many of them are not completely solved.

In comments to a previous post, Gireeja had brought up the new robust optimization approach to multiterminal information theory which sacrifices exact characterization for computability.  The deterministic approach to information theory has a similar philosophical basis and somewhat harkens back to the days of Nyquist and Hartley.  Likewise with network equivalence approaches.  Thus, information theorists seem to be following, in some sense, the approach taken by physicists to hard problems: approximation.  What would be nice, however, are information-theoretic analogues (e.g. about single-letterization) to the fact it is impossible to solve the n-body problem in general only using the method of first integrals.

Now that would get a fist bump from me!  I’d add a little Bump Pay to the Ashvins Fist Bump Prize, but perhaps that isn’t particularly useful.



  1. […] Ashvins The Ultimate Machinists « Problème des Trois Corps Lifting the Weight of History June 23, […]

  2. […] are things going Señor Vishnu Vardhan?  Sorry, I don’t know anything about Lagrangian points in orbits being related to frames in linear […]

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