
How odd is a cluster of plane crashes? - yitchelle
http://www.bbc.com/news/magazine-28481060
======
simonh
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.

~~~
martin-adams
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?

~~~
Osmium
> 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.)

~~~
eru
I think in order to pass any judgement on the correctness, you'd have to make
your remarks more precise.

Are you talking about a random distribution of points on a line / square, or
about rolling dice?

~~~
Osmium
> Are you talking about a random distribution of points on a line / square, or
> about rolling dice?

Right, exactly. I made my comment in reply to the grandparent problem talking
about dots on a screen. For a discrete distribution like a dice roll in the
parent post it'd be a different matter. (I was going to edit my comment to
clarify, but the edit window had expired.) Which serves to illustrate why it's
important to be precise when talking about what distribution you're sampling.

Also, trying to run this experiment in practice is also problem even for dots
on a screen, because eventually the finite display size of your dots will
become an issue, as will floating point arithmetic (since you only really have
a finite number of floats in a given range).

~~~
eru
Thanks for clarifying.

> Also, trying to run this experiment in practice is also problem even for
> dots on a screen, because eventually the finite display size of your dots
> will become an issue, as will floating point arithmetic (since you only
> really have a finite number of floats in a given range).

Yes, but that's not a problem for the theoretical analysis of fractal
dimension.

Uniformly placed dots do have a characteristic density and a relatively simple
distribution of nearest neighbour distances. Even the clumpiness doesn't lead
to scale invariant lumps.

The lumps get absolutely bigger on bigger scales, but relatively smaller and
smoother.

It would be useful to do the analysis properly, though.

------
phantom784
"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?

~~~
kcorbitt
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
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.

~~~
redcalx
Unless there are reserve planes that come immediately on-line to fill the gap
(or the remaining planes do more fly time).

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

~~~
smoyer
Here's the previous discussion:
[https://news.ycombinator.com/item?id=8085254](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

