Covering All Birthdays

Covering All Birthdays(liorsinai.github.io)

42 points by the_origami_fox 1 year ago | 22 comments

fardo 1 year ago |

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...

mxwsn 1 year ago |

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...

madrox 1 year ago | |

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

bobbylarrybobby 1 year ago | |

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

mxwsn 1 year ago | | |

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

contravariant 1 year ago |

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.

Andrex 1 year ago |

Aren't there 366 birthdays, not 365?

Are leap-day births unpersons?

illusive4080 1 year ago | |

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.

paulddraper 1 year ago | | |

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

But some will do Feb out of consistency of month.

brudgers 1 year ago | |

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

File under "Falsehoods programmers believe about time."

ronsor 1 year ago | | |

There are approximately 365¼ days in a standard solar year.

wrs 1 year ago | |

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

paulddraper 1 year ago | |

No but they rarely have birthdays

upon_drumhead 1 year ago | | |

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...

throwaway211 1 year ago |

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.

qingcharles 1 year ago | |

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.

tantalor 1 year ago | |

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

lmpdev 1 year ago | |

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

hipadev23 1 year ago | |

just wait til you find out how LLMs work