Covering All Birthdays | Hacker News Reader

Covering All Birthdays

liorsinai.github.io

Nice, this problem is isomorphic to the probability/graph theory problem “hunters and rabbits” from Matousek’s discrete math textbook, except with the slight modification that instead of “n hunters with perfect accuracy each randomly and simultaneously shoot one rabbit among a set of m rabbits”, it’s “n birthday havers each simultaneously have a birthday among m=365 days”

There is a closed form solution to this problem’s expectation for arbitrary n and m, which I’ve linked below:

https://math.stackexchange.com/questions/610250/a-question-o...

The cover of Bayesian Data Analysis 3 shows that empirically, birthdays are not uniformly distributed. The fall has 10-20% more births than other months, and holidays are significantly underrepresented.

https://lh3.googleusercontent.com/proxy/OZtu7ACWp4X283a4e5Pg...

Was going to mention this myself. The nuance of this problem is fascinating! Always check your assumptions on the underlying distributions.

Do hospitals try to move baby’s born near midnight on a holiday to the previous or next day?

I think so. Parents can also make it happen at their convenience by asking doctors. We have technology to induce birth or control its timing over a few days

If you're going to write conditional probabilities with big parentheses don't forget to make the \vert big as well. You can use \middle if you want to automatically match \left and \right.

Also conditional probabilities aren't really the right tool when all you want is to set a parameter, but it works I guess.

Aren't there 366 birthdays, not 365?

Are leap-day births unpersons?

No but they rarely have birthdays

If we're going off of rarity, December 25 has 6,574 average yearly births and September 9 has almost double at 12,301 average yearly births.

Taking a look at Feb 29th, it has 10467 average yearly births (for years that have a Feb 29th).

So what is the level of rarity that makes a day not worth calculating?

https://github.com/fivethirtyeight/data/blob/master/births/U...

> it has 10467 average yearly births (for years that have a Feb 29th)

do you see it?

To spell it out: leap years happen less than every four years, so the average birth rate over four years is actually closer to 2,616 - quite outside the range of 6,574 - 12,301.

“I will leave out extra material from the original including […] accounting for leap years”

I wonder if most celebrate March 1 or February 28 most of the time? March 1 is more accurate time-wise but February 28 keeps within the same month.

Most do March 1. That comports withs the legal recognition of age.

But some will do Feb out of consistency of month.

Some cultures (not the US apparently) consider wishing an early birthday bad luck so I'd expect them never to celebrate on Feb 28. I know this is a thing in Central Europe, not sure how common it is. It was a big culture clash in a company I know when they moved HQ from Germany to the US because the Germans would get offended by Americans wishing them happy birthday when their birthdays were on the weekend or a bank holiday.

The Islamic calendar has 354 or 355 days. https://en.wikipedia.org/wiki/Islamic_calendar

File under "Falsehoods programmers believe about time."

There are approximately 365¼ days in a standard solar year.

I'm curious why the author thought it necessary to default to simulate a numerical distribution.

Perhaps maths is not taught or appreciated in CS much now.

Sometimes simulation is your only option, so this is a good skill to have in that case. This is meant to show both approaches.

Applied mathematics and computational science are both just simulation a lot of the time

Often analytic solutions aren’t required for sufficient insight into most problems, despite their parsimoniousness/prettiness

just wait til you find out how LLMs work

Because my maths is far weaker than my coding skills, I would have chosen simulation to give me a rough figure, rather than no answer; so the OPs simulation fascinated me when compared to the mathematical answer.

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