This is typical birthday paradox stuff right? The chance that these two photographers would ever snap the same thing at the same time is small, but the chance that any two photographers, anywhere, would do so is, I bet, pretty big (even if you factor in millisecond precision). With photographers being photographers and the internet being the internet, there's also a pretty decent change that they'd find out about it and write a blog post like this, no? :-)
> but the chance that any two photographers, anywhere, would do so is, I bet, pretty big
Not necessarily, but the the chance of any crazy coincidence happening and reaching HN homepage is quite big. Next time it might be two people with same name writing the exact same tweet independently. Or perhaps one guy winning the World Series of Poker two times in a row with the same winning hand.
When there's a million "kinds" of crazy coincidences, the chance of any one of them happening is much higher than chance of a specific one happening. This is kind of a selection bias, we only hear about the coincidences that happened.
I think that's an important insight because it also plays a large part in many conspiracy theories. Basically if you look hard enough for any kind of statistical oddity you'll always end up finding something somewhere. If you only cherry-pick these data points and ignore the billions of "true negative" correlations it's easy to reach the craziest of conclusions. It's the same idea behind "anecdotes vs. data".
But the coincidence that makes it to the top of HN is when the poker guy wins his third WS using the exact same hand. (At this point he played the hand entirely out of superstition at a negative EV but got insanely lucky. He will eventually lose all his winnings playing that hand again and again for the rest of his life. But they’ll name the hand after him, so maybe it will all have been worth it.)
I'm curious about your WSOP mention - did you single this one out because it (remarkably) did happen before? Or were you speculating it could happen again in the future?
Interesting! For reference, it did happen once before. In 1976 and 1977, Doyle Brunson won the WSOP with the same hand - 10-2 (a terrible hand), and it's now named after him.
The odds of the same person winning the WSOP now at all are significantly smaller as the fields have grown so much, never mind the compounding of winning it with the same hand twice :)
(To clarify, it was not the exact same hand - different suits in each case. But still pretty remarkable!)
Oh, I was only vaguely aware that he won twice in a row, so I included an additional condition cause I wanted something that didn't happen. But I guess that subconsciously I had the fact that it was the same hand in memory.
The birthday paradox arises because the probability that two candidates do not match is small compared to the number of candidates. In this case, the candidates are photos and a match in fact requires a match on multiple variables (e.g. angle, timing) that are effectively continuous. A match between 2 arbitrary photos must then have zero-ish probability and a non-match must have one-ish. So it still seems inestimably improbable that something like this would happen.
I'm not so sure. While there are multiple variables, chances are the number of landmarks in a given area that a professional photographer will consider likely to stand out as worthwhile in a storm is not all that great. While I'm not a professional photographer, I can think of maybe 3-4 places near me, for example.
And storms do not happen that often, even in places that have them "frequently", and they delimit the time, and even further by e.g. limitations such as whether the wind is too strong or the rain too heavy.
The number of locations they're likely to consider good spots to take the photo from for a given landmark may not be that great either. Both in terms of where you can actually see the landmark from, and in terms of other factors (e.g. in this case the article writer points out that both photographers had found places where they could protect themselves against some of the effects of the weather)
So that narrows locations and timeframe significantly.
Professional photographers are likely to take their time - the article writer mentions 40+ minutes of shots, and using bursts, further increasing the chance for an overlap within already relatively narrow time frames.
Additionally, external events that are the same for both (the waves) will give impulses to both with respect to when to shoot (though of course they might value different things, I'd argue people are more likely to shoot when something dramatic happens - e.g. if you have a dull day and suddenly something happens, you don't expect the pictures of that day to be evenly spaced afterwards).
I'm not saying we should expect it to happen all the time, but I also think it's easy to overestimate the number of possibilities because we've not tried to enumerate which ranges of values are actually likely.
There are probably well over 10 trillion photos taken. Less by professionals, but they are more likely to take the same photo.
Anyway, that low probability applies to every other photo. So, the first photo is compared to every other photo and by the end your talking ~50,000,000,000,000,000,000 comparisons. The odds would have to be mind boggling tiny for this not to happen all the time.
You're missing the other dimension to this: it's not that two photographers took pictures at the exact same time, I'm sure that happens frequently. It's that they took the exact same picture. There were definitely not 10 trillion photos take of this lighthouse in new england.
They don't have to be photos of this lighthouse. Two photos of Old faithful showing the same spray and cloud patterns could be mistaken for copy's of each other.
Another way of thinking about it, what are the odds that out of the ~1,000 photos taken of the same moment they are of the same subject? Now repeat that question 10 million times and the odds don't seem as low.
It's made more remarkable IMO that they were two _professional_ photographers though, and that it's not just two snaps that happen to have the same timestamp, they both chose that moment to feature from the burst they probably took around that moment, the hundreds of other moments in proximity, and the thousands (I suppose? I'm no photographer) they each took throughout the day.
It's made more likely that they (when there's first an overlap in their shooting) would select the same picture by virtue of getting roughly the same shots and their shots being likely to have many of the same qualities. Chances are they'll value many of the same qualities and so would at least exclude shots of many of the same moments for the same reasons.
That they're professional photographers might reduce the odds by virtue of there being fewer of them, but might increase the odds by virtue of them being more likely to be the kind of people to know of specific spots to go out of their way to take pictures from during a storm, and more likely to value the same qualities i their shots, as well as more likely to publicize their photos enough for one of them to find the other persons photo.
That fact makes it possible, but as he pointed out, they were taking photos at different rates of burst mode, and even then they happened to snap at the same millisecond. Usually each picture in burst mode of moving water is completely different. I think in that gas it makes sense that they would choose the same subject and the same photo since it was probably the biggest splash from that wave. As if they were choosing from the same set of photos, even though all their other photos had different moments.
I question the exact same millisecond part. There’s zero proof of that (and actually counter proof examining the photos). Same second, sure. Same millisecond, I think someone is reaching a bit much to make a story.
As I said in another comment, I'm pretty sure "same millisecond" is being used by the photographer in the sense of "same instant" or "same moment in time" not literally same millisecond based on a super-accurate time source. That information does not exist in the photo's EXIF data which is one-second resolution and typically derives from a manual time/date setting in the camera's menu.
I am not taking issue with the author of the post as I agree, that is likely the intent. But folks here seem to be parroting it as fact rather than taking the liberty you and I seemed to do.
I don't think the birthday paradox applies here. The birthday paradox requires a discrete set of pigeon holes, days of year, etc. If that set is infinite, then the countability [1] problem collapses.
While technically the world is discrete in space and time (planck length), for all intents and purposes it is infinite in practice.
[1] yes, there is countably infinite, but that doesn't work with the pigeon hole problem.
Reality may or may not be discrete, but what is a discrete value is the output from a digital camera, so in case of photographs your argument does not hold.
In other words, two photographs off by a planck length will generate the same set of pixels.
Sort of, but instead of 365 distinct birthdays you have many thousands of non-overlapping time buckets (the two different burst mode frame rate), and it also doesn't "wrap around" the way birthdays do.
Correct, but there are about eight orders of magnitude more milliseconds than days, and you need another two or so orders of magnitude because not everyone is a photographer who publishes their photos. Then again, the internet is a medium that reaches many more people, which is not true of the average birthday. So one would still expect this to happen only maybe every few years.
Well, but I am not sure that you would indeed require it to be the same millisecond. I mean I don't know how long the exposure was, but I guess its longer than a millisecond (just took a look at some of my own photos and they were at 4-5ms exposure in very bright sunlight, the blog image exposure is probably more like 10ms). The heading says that the pictures were taken in the same millisecond, but as far as I understand the post, they concluded it from the image, so I wonder what the precision is you can derive from a photo?
They said they compared EXIF metadata, so they should know when each of the shots were taken. I'm not a photographer and don't know what level of detail is recorded there, though.
The time precision that you can derive from the spray of the waves is a lot more precise that anything you will get out of the exif data - the wave will only have that exact captured spray pattern for a small fraction of a second, but the time synchronization on the two photographers cameras is almost certainly out by a larger amount of time than the wave looked that way.
Working with images from multiple photographers cameras who haven't gone out of their way to sync the time beforehand, I've usually had to assume about a 10s time skew. They do not have precise clocks and are not sybchronized often.
The time in the EXIF metadata is just based on the time/date stamp that's been set in the camera. I don't know about the newer Canon but I'm pretty sure the older model would just be something someone manually set.
Re-reading the article, I think saying the pics were shot at the "same millisecond" was just a colloquial expression to mean the look of the waves makes it look as if they were shot at the exact same time. They shared metadata but that seems to have been to share the other shooting parameters. I believe (and this would seem to confirm [1]) that EXIF timestamp data is only precise down to 1 second. added: and only as accurate as the photographer who set the date and time.
Both cameras (5DM4 and 60D) can be set via GPS using a Canon accessory, but I highly doubt that is the case (very few own that from what I have seen). Even then, the camera doesn't preserve millisecond data in the EXIF data.
