Math behind Bump(ing)?

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+5 Q:

Math behind Bump(ing)?

I was randomly looking at the FAQ for bu.mp (http://bu.mp/faq), and this part caught my eye:

Q: No way. What if somebody else bumps at the same time?

Way. We use various techniques to limit the pool of potential matches, including location information and characteristics of the bump event. If you are bumping in a particularly dense area (ex, at a conference), and we cannot resolve a unique match after a single bump, we'll just ask you to bump again. Our CTO has a PhD in Quantum Mechanics and can show the math behind that, but we suggest downloading Bump and trying it yourself!

Is there really any reason why there might be some non-trivial math behind bumping, or is the "Our CTO has a PhD in Quantum Mechanics and can show the math behind that" probably just a bit tongue-in-cheek? [I'm having a hard time imagining why something more complicated than looking at the location+time would be necessary, but maybe I'm just underestimating the problem or the kinds of data an iPhone could collect from a bump (e.g., some kind of tremor waveform?).]

+1 A:

The joke comes from:

One of the most shocking facts of quantum mechanics, first derived by Werner Heisemberg, is that operators does not always commute. There are a lot of different formulations and interpretations of this fact aka "uncertainty principle".

One of the most usual incarnations of the principle, and the historically first stated is

$alt text$

Which can be interpreted as:

"If you measure the linear momentum (mass * velocity) of something up to a great precision, you will not be able to do the same with its position"

This effect and interpretation has been object of tests, perhaps the most famous were those by Einstein (gedanken experiments) some refuted by Niels Bohr.

To be able to observe the effect, the involved mass of course should be very SMALL, so it is "visible" only for subatomic particles, never ever for something so big as an iPhone.

Similar inequalities hold for other conjugate operators, such as time and Energy.

Things are much more complicated when general relativity is taken on account (think for example in the concept of "time" .. which time?) and I think that is the idea behind the phrase "Our CTO has a PhD in Quantum Mechanics and can show the math behind".

To clarify: IF the iPhone should manifest quantum mechanics behavior, then Bump could not do the pairing (position and velocity or time and acceleration) of the phones trying to "bump"

belisarius 2010-06-04 20:46:46

huh, what does this answer explain?

ldog 2010-06-04 21:02:41

Its a joke of the trade, probably meaningless if you have not taken a course on quantum mech

belisarius 2010-06-04 21:05:57

Haha, nice. Yeah, I was pretty sure no QM is involved ;), but now that I think about it, I can believe some harder algorithms would be needed. For example, I think finding the phone you bumped in spacetime is essentially a nearest-neighbors problem, so if you have a ton of bump-enabled iPhones, you might need to use something like a locality-sensitive hashing algorithm. Or maybe if they turn this one day into a "bumper cars" game (so that bumpers are traveling), if there's a delay between the bumping and the location that gets sent, maybe some kind of Kalman Filtering would be useful...

2010-06-04 23:00:47

Indeed is a joke. The main problem there are the space partition granularity, and they solve it just asking you to bump again. BUT if the iPhone were VERY small (subatomic) the pairing could be proven VERY difficult.

belisarius 2010-06-05 04:55:06

(Supposing we have a quantum-mechanical iPhone.) But we don't need to know the position and momentum simultaneously, so the uncertainty principle doesn't really come into play, right? For example, I'm thinking: 1) Start in a "momentum-only" measurement state at first, so that we can get a precise measurement on the momentum (but not position). 2) Once we notice a change in momentum (i.e., a bump has occurred), we enter a "position-only" phase, so that we can get a precise fix on position (but not momentum). Then find the nearest iPhone that also had a bump. Wouldn't this work?

2010-06-05 16:54:20

@user357972 I guess what you need to measure for each phone is the kinetic energy change and the time of the event ... simultaneously

belisarius 2010-06-05 17:22:22

+1 A:

I sincerely doubt there's any overly complex math involved. It just matches "bumps" that occur within a very short span of time in a particular area.

If there is more than one match within that particular timespan AND within that area it probably asks you to bump again.

Il-Bhima 2010-06-04 20:55:56

ansaurus

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Math behind Bump(ing)?

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