[mattbee]

I can't find this post from a physicist, but they had their bicycle stolen and the police had given up searching the CCTV log because it was taking them too long, despite the fact that it was pointed at the bicycle.

He told them that even if the CCTV log went back to the earth's formation, they would only need to take about 57 stills to pinpoint the second the bike was stolen (apparently they were not persuaded).

[joshjje]

Am I missing something? How is that?

[bar94]

2^57 seconds is about 4.5 × 10^9 years, which is the age of the universe. They would only need that many stills because it would be possible to do a binary search on the footage, as each frame either has the bike in it or does not.

[Quekid5]

Maybe I'm just being dense, but I don't see how that would work. The bike's presence is not a monotonic property -- so you never know which half of the search space you need to descend into.

(In fact, you don't even know if a bike was ever there without already having identified a frame with the bike in it. After all, the physicist could be lying.)

[Jtsummers]

Probably exaggeration for effect, don't take it too literally. But if the bike had been there from the beginning of time, finding the second where it disappeared requires no more than 57 frames to be checked. So if searching billions of years of history only requires checking 57 frames, why is it so hard to check a day or a week or a few hours worth of data? (Of course, if this was before digital video records it could actually be tedious, but hardly impossible, to check even a few days worth of data since that may force a linear scan at least partially.)

Given that they knew when the bike was there (presumably the physicist knew when they locked it up or near enough) they could have found that point and looked forward, and it would have taken far fewer than 57 frames to identify where it disappeared if you're only interested in getting down to the second.

So if they knew the bike was present at 1pm, and it was gone by 3pm (hypothetical since not enough information is given) then they can do a binary search on that 2 hour window, that's only 7200 seconds worth of frames. Start at 2pm, is it present? Flip to 2:30, else 1:30. Repeat. Even a week is only 604k seconds, which would require no more than 20 frames to be checked.

[Quekid5]

The bike could have disappeared, then re-appeared and disappeared again, tho. So you might be finding the "wrong" thief.

(Btw, I realize it's just an anecdote, I'm just being extremely nitpicky.)

[joshjje]

Ah I believe the confusion was thinking that 57 snapshots over said billion years would be enough to deduce the second. But instead they mean if you used binary search (or similar) across ALL of the images you could find it within 57 or so.