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How odd is a cluster of plane crashes?

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Re: How odd is a cluster of plane crashes?

#31

Post by martin-adams »

mfenniak wrote: post #22
martin-adams wrote: post #8

Earlier quoted context omitted.

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 wa…

> 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. ;-)

I'd prefer to simulate this with dots on a screen rather than with planes ;-)

Re: How odd is a cluster of plane crashes?

#32

Post by wodenokoto »

lordnacho wrote: post #6
simonh wrote: post #2

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…

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

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.

Re: How odd is a cluster of plane crashes?

#33

Post by simonh »

dmichulke wrote: post #3
simonh wrote: post #2

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…

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.

Approximately 35 years ago :)

Re: How odd is a cluster of plane crashes?

#34

Post by darkxanthos »

LeUsername wrote: post #26
darkxanthos wrote: post #10

Earlier quoted context omitted.

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

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 odd…

Super helpful! Thanks!

Re: How odd is a cluster of plane crashes?

#35

Post by eru »

Osmium wrote: post #16
martin-adams wrote: post #8

Earlier quoted context omitted.

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 wa…

> 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 fracta…

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?

Re: How odd is a cluster of plane crashes?

#36

Post by eru »

wodenokoto wrote: post #32
lordnacho wrote: post #6

Earlier quoted context omitted.

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

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.

People are seldom precise when they talk about randomness.

For example, you could mean: picking tracks with `putting back'. You could shuffle tracks like you shuffle a deck of cards, ie picking without putting back. It's still random, but with a different distribution.

Even picking the first track with 90% probability, and the rest with some other smaller probability is random. It's just not a uniform distribution.

Re: How odd is a cluster of plane crashes?

#37

Post by Osmium »

eru wrote: post #35
Osmium wrote: post #16

Earlier quoted context omitted.

> 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 fracta…

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?

> 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).

Re: How odd is a cluster of plane crashes?

#38

Post by eru »

Osmium wrote: post #37
eru wrote: post #35

Earlier quoted context omitted.

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?

> 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…

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.

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