[justonepost]

Thanks. Why can't all math teachers talk like that? I mean... I know you're clever and all, but if you were really clever you'd explain it in a way that's easy to understand.

Still, kudos to the OP. That was a great attempt to be precise.

[modeless]

That simple explanation is exactly wrong though! You don't expect to wait 2x the average. You expect to wait 1x the average, but you also expect that when you start waiting the previous block happened 1x the average time ago, and 1+1=2.

[etoir]

But you are waiting 2x the average, because the average waiting time should be half of the period.

Consider buses which arrive every ten minutes, exactly. You arrive at the bus stop at a random time. How long should you expect to wait? Not 10 min but 5 min, on average. You are equally likely to arrive at any point during the 10 minutes wait.

Now change the buses to a Poisson process with mean rate 1 bus every 10 minutes. Now you arrive during an interval of average length 20 min, but wait on average 10 min.

[lordnacho]

This is the best explanation of the phenomenon. Simple and actually explains why it's 2x and not 3x or 4x.

[thaumasiotes]

Is it actually true though? Compare these two comments buried downthread:

https://news.ycombinator.com/item?id=16470358

> The hitchhiker's paradox is correct, taking a point and looking backward or forward will correctly give an average event 10 minutes away, but combining the events to give an average of 20 minutes is false.

https://news.ycombinator.com/item?id=16471544

> I thought this sounded funny, and I did a little simulation to see if it was correct. Given his assumptions (poisson with lambda 10), you do not get that answer. I got right around 10, which is what I would expect.

[modeless]

Yes, it is true. I'm not sure what the first commenter is trying to say exactly. The second commenter's code was wrong, and correcting it gives the expected 20 minute average period.

[axitanull]

Understanding is one thing, explaining in layman or easy to undertand terms is another, and sometimes it takes a lot of effort.

[anonytrary]

https://www.youtube.com/watch?v=FjHJ7FmV0M4

You guys would love Richard Feynman.

[TangoTrotFox]

Another resource there: http://www.feynmanlectures.caltech.edu/

That collection is a series of lectures from Feynman, and his characteristic clarity, on physics across the breadth of all major topics. It's quite amazing to realize how little you, in general, truly understand even really basic concepts like the conservation laws until you read the writings of a person who did genuinely understand what he was talking about and could share that insight in such a uniquely effective way.

[wickawic]

Explaining is usually more difficult than understanding, as well.

[southpawflo]

I've had multiple teachers tell me that if you can't explain something you don't completely understand it yet. grok what I'm saying? :)

[nostalgiac]

I've heard this a few times but thoroughly disagree.

Being able to explain/teach something to others is a very different skill to understanding it and isn't compulsory.

[mnw21cam]

An expert is someone who can take something you already understand, and make it sound confusing.