Comment by tunesmith | Hacker News Reader

Comment by tunesmith | Hacker News Reader

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One other example of the flaw (I think) that came out in pop culture was a few years ago during the Serial podcast about Adnan Syed.

Near the end when the hosts were wrestling about whether they should think he was guilty, the interviewer's friend (the producer? Dana?) came on and shared why she thought he was guilty, and it was this convoluted argument about if Syed was innocent, he'd have to be the unluckiest guy in the world, so therefore he was probably guilty.

Her point was that it was just too strong a coincidence that it was his ex-girlfriend that got killed, on that particular day during some period of time when he didn't have an alibi, etc etc.

That seemed to me like it could be a bad Bayesian argument - like it would have been a good argument had Serial selected a random citizen to interview, but they selected someone they already knew was connected to the story. Murders happen and by definition the circumstances are always highly unlikely because murders are so rare, and innocent people closely connected to the circumstances of the crime are very, very unlucky by definition. You can't point to that unluckiness as evidence that they're probably guilty.

Add to that, highly unlikely events occur all the time, but most of the time they're not anywhere near a murder. Once you start digging around for unlikely things, you'll find them.

Heck, even if you dig into a random person associated with a murder, you'll find some unlikely things, but if you dig into a person who has already been accused of the crime (rightly or wrongly), of course there will be loads of suspicious circumstances. That's why they were accused in the first place.

> highly unlikely events occur all the time

They do?

Yeah, sure, it's a matter of how you define the event.

Let's say some day you find an acquaintance on the street. Not extraordinary. But that specific acquaintance that you hadn't seen in 10 years. On that specific day, on that specific street, at that specific time. If you had wondered the day before how likely it would be that that specific set of circumstances would come togethet, you would have rightly concluded it was exceedingly unlikely.

This is another way of looking at the first example in the article. The question was not how likely it was that that specific woman had their two children die of natural causes, but how likely it was that someone in the country or the world would have such a thing happen in a large interval of time.

"The chances of this exact event are 1 in a trillion, therefore with a high degree of confidence, it isn't happening and I am in fact hallucinating. You're not real, Bob from highschool!"

And imagine how often you almost run into acquaintances on the street, and don't notice. It must happen more often than when you do notice. If you made a concerted effort to look for near-coincidences, you would suddenly find yourself noticing lots more unlikely things that were happening all along.

Once you start digging into someone's life you'll learn all sorts of things that might seem really unlikely... but you'd find unlikely things in someone's life picked at random, you just never dug into them, because they're not accused of murder.

Yes. Your chance of being hit by lightning in a given year is quite low. The average number of people struck by lightning in the US annually in the last decade is 270, according to https://www.weather.gov/safety/lightning-odds (and while that's an estimate, the 27 average deaths/year over that period is not).

So a specific person being killed by lightning within a given year is pretty unlikely (less than one in 10 million chance), and on average it happens once every two weeks in the US. Lots of people, see.

Same thing with other situations where there are lots of observations...

The likelihood of me being hit by lightning is very low. Therefore, it is an highly unlikely event. And it doesn't happen very often.

The chance of someone being hit by lightning is not very low. Therefore, it is not a highly unlikely event. And it does happen relatively frequently.

Unlikely events don't happen very often. That's just a definition. If event X happens frequently, then it isn't an unlikely event.

Any given unlikely event does not happen very often.

But if you have a whole bunch of possible unlikely events, then one of them (a different one each time, usually) can happen fairly often.

Back to the lightning example, any given person being hit by lightning is an unlikely event. But as you not "someone being hit by lightning" is not, because we are now observing these unlikely events across so many people.

All of which is to say, observing that an unlikely event happened doesn't provide much information on its own, if you have observed a lot of things happening in general...

Beautifully put - I nominate this as the official summary of the subthread. It's the reason why we need to pad time estimates for projects and leave early to catch trains, even when we can't think of any likely reason for delay - the sum of all unlikely reasons can cross the threshold into "likely".

So it's quite correct to say "unlikely events happen all the time".

The odds of you dying from any particular unlikely death (like lightning) is super low. The odds of you dying of any of them (bear mauling, tied to a railway track, spontaneous combustion, etc) is significantly higher. That's the sort of thing I mean.

Individual coincidences are rare. But if you start really looking for them, you will absolutely find some coincidence. The one that happens will have been unlikely and impossible to predict ahead of time, and yet you were more or less absolutely certain some coincidence would occur, because there are so many possible configurations of coincidence that one is bound to happen.

That's nothing, multiple people were struck by lightning several times. https://listverse.com/2018/06/02/10-people-who-have-been-str...

This is fundamental to Chaos theory (how small initial states can lead to rich systems that contain both expected and unexpected outcomes), which isn't a theory as much as an area of mathematical modeling of the most complex systems. Me waving off a butterfly is just as likely to influence a hurricane as the unmolested butterfly flapping.

Any given reader's brain existing to comprehend this comment is highly unlikely, yet it occurs and continues within layers of chaotic systems, that exist turbulently, in perceived reality.

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