How odd is a cluster of plane crashes?

http://www.bbc.com/news/magazine-28481060

by yitchelle • 11 years ago

33 36 11 years ago

simonh2• 11 years ago

One of the first computer programs I ever wrote just put random dots on a screen and I remember looking at how 'lumpy' the results were. Intuitively most people assume that random distributions will be even distributions, but in fact they are usually full of clusters. Some mathematicians can reliably distinguish 'random' sequences created by people from truly random ones because people produce distributions that are too smoothed out. 'I won't put a dot here because it's too close to that other dot', but a truly random distribution doesn't care where previous dots were and won't avoid the conjunction.

dmichulke• 11 years ago

I don't disagree at all and I remember seeing studies or articles writing about that phenomenon.

Just wanted to add that a few years ago (when you wrote your first computer program) a randomly selected random number generator was more likely to be less random than a randomly selected random number generator today.

yitchelle• 11 years ago

The method described in the article on how the statistician approached the problem is very similar to the approach used in the birthday problem[1].

[1] https://en.wikipedia.org/wiki/Birthday_problem

DanBC• 11 years ago

Early random number generation was terrible. You wouldn't get clumps / no clumps, you'd get fuzzy straight lines.

simonh2• 11 years ago

Approximately 35 years ago :)

lordnacho• 11 years ago

The iPod shuffle algo was an example of this. It just didn't feel "random" enough for people to have a truly random generator.

ececconi• 11 years ago

I would think about this all the time when I got a shuffle in high school. After listening to it for a while, I could really predict the next track that would come on even in shuffle mode.

wodenokoto• 11 years ago

Isn't that also why it is shuffle and not random? When shuffling, you don't risk getting the same song twice in a row.

benihana• 11 years ago

Great point. Here's a visualization of what you're talking about:

http://bl.ocks.org/mbostock/fe3f75700e70416e37cd

Uniform random is pretty terrible. There is both severe under- and oversampling: many samples are densely-packed, even overlapping, leading to large empty areas. (Uniform random sampling also represents the lower bound of quality for the best-candidate algorithm, as when the number of candidates per sample is set to one.)

Taken from: http://bost.ocks.org/mike/algorithms/

martin-adams3• 11 years ago

I do wonder if that is down to sample size. For example, I wrote a program to simulate the roll of a dice. There is a one in 6 chance of getting any one number. But roll it 6 million times, you'll be very close to have each number 1 million times.

So I would anticipate the clumping to even out as the sample size increases. Or maybe the evening out is a large collection of clumps. Anyone know if this is the correct way to think about it?

mungoman2• 11 years ago

Well depends of what you mean by very close. It's the relative numbers that approaches the true distribution, not the absolute numbers.

Do the experiment you decribe and look at the numbers.

Osmium2• 11 years ago

So I would anticipate the clumping to even out as the sample size increases.

Clumping won't even out. A useful way of thinking about it is in terms of the distance between samples (e.g. a radial distribution function). If you don't have clumping, that distribution of distances is decidedly non-random and has peaks. Additionally, there's no specific length-scale for the clumping to happen on, it's essentially fractal in nature.

(Happy to be corrected if I'm wrong on this.)

mfenniak• 11 years ago

So I would anticipate the clumping to even out as the sample size increases.

Are you saying we need to crash more planes? That seems a little harsh just to get crashes coming at a consistent rate. ;-)

vmarsy• 11 years ago

What you're describing for the dice is called the law of large numbers : https://en.m.wikipedia.org/wiki/Law_of_large_numbers

It would probably true for that too but as another comment says, we don't want to have an increased sample size here!

leni5362• 11 years ago

An other great example is how random is a terrible algorithm for dithering.

https://en.wikipedia.org/wiki/Dither#Algorithms

detrino2• 11 years ago

Perhaps just an artifact of a weak PRNG or not truly uniform distribution?

Sharlin• 11 years ago

No. A truly uniform random distribution indeed has "clumps".

smoyer2• 11 years ago

Pleases mark as 2014 ... I also believe this is a repeat but can't seem to find the original.

smoyer2• 11 years ago

Here's the previous discussion: https://news.ycombinator.com/item?id=8085254

I had tried the Algolia search box from my tablet and got no results. Using Google (constrained to HN) brought up today's discussion and the one from last year.

site:news.ycombinator.com plane crash cluster

phantom784• 11 years ago

"If there is a crash on 1 August, the chance that the next crash occurs one day later on 2 August is 1/365. But the chance the next crash is on 3 August is (364/365) x (1/365), because the next crash occurs on 3 August only if there is no crash on 2 August."

Is this not the gambler's fallacy? Shouldn't the odds be unaffected by a previous crash?

darkxanthos2• 11 years ago

In this case I would agree with you. I don't understand the reasoning for the last sentence at all.

LeUsername• 11 years ago

The focus is on being the next immediate crash. If you are asking whether there is a crash on 3 August, it is the unaffected odds of 1/365. But if you are asking whether the (first) next crash after 1 August is on 3 August, both the following must happen: a) there is no crash on 2 August b) there is a crash on 3 August

The gambler fallacy would be "I have seen 9 days without crash, on the 10th day there is higher odds of crash". But you are not asking this, you are asking: "What is the chance that in the next 10 days, exactly first 9 days would be no-crash and on the 10th day there is a crash".

EDIT: Also, another view:

If you have seen 9 blacks in a row, there is an even chance 1/2 (roulette without zero) that the next will be black or red. Because in all sequences of length 10 starting with 9 blacks (this is given, you observed this), there is equal number of those with 9 consecutive blacks and a red and of those with 9 consecutive blacks and a black. This is gambler fallacy, believing that after repeated colour, you have higher chance of the other colour.

Here, you are asking: how many of all sequences of length 10 have exactly 9 blacks and 1 red. And there are all kinds of sequences with 1 red in first 9 places, 2 reds, 3 reds, etc., so the odds of observing the 9 blacks in a row in the first place before asking about the 10th spin is lower, but it does not change the odds of the 10th spin itself.

kcorbitt• 11 years ago

You're right that the probability that there is a crash on 3 August is unaffected by a potential crash on the 2 of August, but the chance that the crash on the 3 of August is the next crash (after the 1st of August) is affected.

philh• 11 years ago

Also, pedantically, a plane that crashes on the 2nd August isn't going to crash again on the 3rd.

We can reduce the rate of crashes by taking planes out of the sky, and one way to do that is to crash them.

leni5362• 11 years ago

In probability you have take attention to the very details. The statements "the next crash occurs on 3 August" and "there is a crash on 3 August" are not the same. Only the latter is independent from a crash on 2 August.

How odd is a cluster of plane crashes?

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