Tuesday, February 24, 2015

Hi. I'm Hiram. I Used to OWN Tuesdays. So Today I'm Baffled By Birthdays.

My snowshits have been tremendously unhelpful this semester, and I'm at a point now where every single thing drives me insane.

Apropos of nearly nothing I mentioned that John Steinbeck's birthday was this Friday, the 27th.

A young man in the back says, "Hey, that's my birthday," his eyes sparkling.

"Cool," I said, and I started to write something about the day's discussion on the board.

"Me, too," another voice came, a young woman.

I turned around. "You both have Steinbeck's birthday? Wow. There's, like, 12 of us, and you have the same birthday."

The young woman, said, "Well, mine's not Friday. It's Wednesday."

"That's the 25th," I said.

"And mine is next Monday," the young man said.

"Wait. What? Next Monday is March 1st, or 2nd, actually. And you," I said, pointing at the woman, "Wednesday is February 25th."

Cheerily, the young woman said, "Oh, I know, but I celebrate all week."

"Me, too," the young man in the back said.

They were both happy.

"But you both know, right, that those days are not the same. That the 27th is not the 25th. And it is certainly not a day in March?"

Their smiles faded. I knew I should stop. But I'm Hiram. I baffle easily. I stun. I get winded. I get sweaty.

"You both know that whether or not you celebrate all week, that your only actual birthday is one day, right? I mean, the day you were born. No other day?"

It was silent. I like silence sometimes. Like just before I have a stroke.


30 comments:

  1. Hey, that's my birthday too! Except mine is in late September. But it's close enough to the autumnal equinox that I also celebrate it in the vague vicinity of the vernal equinox, and that makes it the same as John Steinbeck's!

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  2. They expect us to spend the whole first week fo class talking about the syllabus so why shouldn't we deote a week to each of their birthdays?

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  3. I am with you, brother Hiram. My class this semester likewise tests me and I hate how my tolerance for any bullshit is just gone. I try to remember they are kids, but sometimes their sheer stupidity overwhelms me and I get to trance like state that I'm sure they'll notice. But they don't. I can sit for 30 seconds staring at the clock at the back of the room and they just all sit there as well. I may just test them. Stare into the abyss for 50 minutes and see if anyone goes for a doctor or a nice gluten free cookie.

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  4. That was very pedagogical; now they'll all remember Steinbeck's birthday (for a week, at least.)

    I would probably have jumped on the chance to mention the "birthday problem" (in a group of 23 people, there's at least a 50% chance that two share a birthday), just to put them to sleep. Or even better, to ask them to compute the probability for "same birth week", for their class size. That would surely have people getting up and leaving.

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    1. I have heard this before and have not one bit of understanding of how it can be true. There are still 365 days in a year, right? Oh, my PhD is in the humanities.

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    2. Yeah- the chance that any single person in the class will have YOUR birthday is only about 30 in 365, or about 7%, if there's 30 people in the room.

      But it's more tricky than that. Probabilities are hard to compute correctly. In this case, it's easiest to compute the chance that NO ONE matches a birthday.
      Take person p1. They have a birthday. The chance that no one matches it in the group of 30 is about 335/360, or about 93%.
      Take person p2. Now, everyone in the room (minus p1) has to also not match THIS person's birthday, a probability of about 334/360, or about 93% again. So, total probability in getting this far without a hit is 0.93 x 0.93 = 86%.

      Keep going. By the time you get to 30, it's added up to a pretty small probability that EVERYONE in the room will miss EVERYONE else's birthday. You're saying that all 30 birthdays are unique, which would be very unlikely.

      ---Nathaniel

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    3. Yeah- the chance that any single person in the class will have YOUR birthday is only about 30 in 365, or about 7%, if there's 30 people in the room.

      But it's more tricky than that. Probabilities are hard to compute correctly. In this case, it's easiest to compute the chance that NO ONE matches a birthday.
      Take person p1. They have a birthday. The chance that no one matches it in the group of 30 is about 335/360, or about 93%.
      Take person p2. Now, everyone in the room (minus p1) has to also not match THIS person's birthday, a probability of about 334/360, or about 93% again. So, total probability in getting this far without a hit is 0.93 x 0.93 = 86%.

      Keep going. By the time you get to 30, it's added up to a pretty small probability that EVERYONE in the room will miss EVERYONE else's birthday. You're saying that all 30 birthdays are unique, which would be very unlikely.

      ---Nathaniel

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    4. I was with you up until the first percentage sign and then the decimal point!

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    5. Nathaniel, that was true in days of yore when there was a uniform distribution of birthdays. Now, doctors don't like to work weekends, so there are fewer births on Saturdays and Sundays, and since the flakes tend to be from the same year, you will find certain days not being as often as others. Then there's the born-9-months-after-the-Super-Bowl/first-day-of-summer-vacation/Christmas, etc. births.

      I have my students practice basket sorting algorithms by sorting themselves by birthday. We usually have "twins", even had "triplets" one year.

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    6. Say, Hiram, would you like to play cards? As a science geek I'm not good with human interaction so poker is out, but let's play blackjack, it's fun!

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    7. All I have is anecdata: I attended a very small private school for K-8; for most of that time there were 21 students in my class (though the particular people shifted over time a bit); and for most of that time there was another student who shared my (exact) birthday. I'm pretty sure we were the only pair of unrelated "twins" in the classroom (there was also a pair of actual, sibling twins -- identical twins, in fact -- in the class, but that's easier to explain -- siblings of close age usually attend the same elementary school, small school, only one class per grade after grade 3).

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  5. Three things:

    1. My favorite part of this whole post is the first line. "Snowshits." I love it.

    2. The only birthday I care about is Hitler. Why? It's the cheapest way to get a sustained laugh from my students. Seriously, anytime you mention that 4/20 is Hitler's birthday, they go nuts.

    3. I have a very good British ex-pat friend now living in the US who celebrates "Birthday Fortnight." Because he is wealthy, and because he is British, we always give him a pass on this elaborate celebration. It's 14 days surrounding his birthday, each day something special like ice skating or whirly ball or going to see some baseball. The best part is that he pays for about 80% of what we do (he covers entry, we cover food and drinks).

    But despite all the fun I'm having, and the "I know what I'm doing" British accent, part of me is always like "Dude: you're 45. What are you doing? How are you doing this? Am I alive right now? Is this a real thing?"

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    1. My turn to be ignorant: why is 4/20 funny? (And why do Americans insist on doing dates the wrong way around, doing medium significance / least significant / most significant MM/DD/YY instead of the much more natural DD/MM/YY??)

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    2. Ben, Whirly Ball is Jai Alai played in bumper cars with basketball hoops. It is glorious.

      Sigma, legend has it that 420 is the police code for "possession of marijuana" in California. As you can imagine, anything priced 420, dated 420, or timed at 420 leads to ridiculous giggles.

      As for the order of dates, I can't help you, as I did my first few years of primary school in London and had to relearn all my spelling and dates after moving to the States at the age of 8. It was difficult. practise / defense etc still give me issues.

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    3. AM, I was born and raised in the States, yet for whatever reason, when I type it's all about "neighbour" and "colour". However, I've never had issues with "centre" or "defence."

      I've also found that I'm saying "zed" lately instead of "zee."

      Granted, it's the middle of hockey season and my Mom's side of the family is Canadian, but whatever.

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    4. As an astronomer, by pure logic I can prove that both the American standard (mm/dd/yyyy) and the English/Imperial/International standard (dd/mm/yyyy) for writing dates are incorrect. The correct way to write a calendar date is shown on the front cover of any issue of The Astrophysical Journal. This format is: yyyy mm dd.

      As you can see, this goes from large units at left to smaller units at right, the way that times—and indeed, most quantities of all kinds—are written. Today’s date should therefore be written:

      2015 February 25

      and notice that it is preferable to spell out the name of the month.

      (If you want to list a C.E., list it before 2015, of course.)

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    5. Why do the American and the International standards differ? I count it as legitimate language change, which was studied by the brothers Grimm. They were philologists (who would now be called linguists), working at the University of Heidelberg. Their famous book Grimm's Fairy Tales was a by-product of their research on language. Among other things, they discovered Grimm's law of consonantal shift: that consonant sounds tend to soften over time. My Dad was A.B.D. in their department, but long after the brothers Grimm were in it.

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    6. I'm fine with most-to-least significant ordering, a-la SQL format YYYY-MM-DD.

      That's the way I like by endians: big!

      Anyone who gets that joke has spent way too much time on technical stuff.

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    7. I resemble that last remark. I found it curious that Zilog had both big and little endian processors. I never took part in any of the debates, as I was comfortable programming for either scheme.

      I was about to call you to task for saying "the much more natural DD/MM/YY". To me, there's nothing "natural" about either DD/MM/YY or MM/DD/YY, when YYYY-MM-DD is superior for so many reasons, not the least of which is that it sorts properly whether represented internally as text or number.

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  6. I'll have another go at the "birthday problem" and maybe if I can understand it, others can too. As Nathaniel said, it's easier to pose the question, what are the chances of everybody in the room NOT sharing a birthday. Let's also assume that birthdays occur with equal probability on any day of the year, and it's leap year; I'll explain why later.

    Adam sits alone in a room. In walks Beth. For Beth to have a different birthday, she could have any of the 366 days except Adam's. The chances of that are thus 365/366. Now in walks Cain. Cain can't have either Beth or Adam's birthday, so the chances of that are 364/366. Enter Delilah. Delilah has 363/366 chances of having a birthday different from all others previously in the room.

    The chances of Beth, Cain, and Delilah all joining Adam in the room, but with none of them having a birthday in common, are 365/366 x 364/366 x 363/366. Elias walks in. He has 362/366 chances that his birthday is different from the other four, and the chances that all five have different birthdays are 365/366 x 364/366 x 363/366 x 362/366. The pattern becomes even more clear: as each new person enters the room, the chances that none of them shares a birthday are equal to the chances of that new person having a birthday different from all others, multiplied by the chances of all those others having different birthdays in the first place.

    Now we have two possibilities: either nobody shares a birthday, or at least one person shares a birthday with another. The probabilities add up to 1, hence the probability of at least one birthday in common is 1 - 365/366 x 364/366 x . . . x (366-N+1)/366 among N random people. This crosses the 50% probability line at 23 people; at 41 people, it's about 90% that there will be a match, and 99.9% with 70.

    As Stella has alluded to, anything that decreases the randomness will increase the odds of a match. So, going to 365 days increases it, but not by much. Last winter, ice storms knocked out power in my extended neighborhood for 5 days straight: no internet, no TV. In a few years, the local kindergartens will have a higher than typical number of students with birthdays clustered within a few days of each other, and an attendant uptick in shared birthdays.

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    1. Naw, the spread function in delivery dates is too wide - unless there's literally a million births this year in the affected area, it's unlikely you'd be able to spot it even with a complete statistical analysis.

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    2. Naw, the spread function in delivery dates is too wide - unless there's literally a million births this year in the affected area, it's unlikely you'd be able to spot it even with a complete statistical analysis.

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    3. Well, it was a really bad storm.

      I am glad you called me on that. I suspect you are correct and am tempted to run the Monte Carlo simulations to confirm it. If indeed there was spike in births in the 40 +- 2 weeks after the storm, likely it could not be distinguished from typical random noise, certainly not in an individual kindergarten classroom several years hence.

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  7. My lovely spouse is in children's lit and literacy, and she has been volunteering as a reader for pre-school aged children in libraries and Head Start programs for years now. One of the major lessons she has learned is that you never, never read a book or do a little song about birthdays with the children, because they cannot control their urge to be the center of attention, and birthdays just set them off. Sample dialog: "Well, today, children, is an interesting day, and I've brought along some books we can read together about it! It's April 20 -- Hitler's birthday! Isn't that neat? Now let's just read this book about it ... "
    Kid 1: "It's my birthday today!"
    Kid 2: "It's my birthday too!"
    Kid 3: "My mommy's birthday was last week! We had pink cake!"
    Kid 4: "I had pink cake at my birthday tomorrow!"
    Kid 5: "I have a birthday too! I think it's in Octember!"
    Kid 6: "My birthday is coming soon! I'm going to get a super-ninja pony set!"
    Kid 7: "Super-ninja ponies are for girls! For my birthday, I'm getting a megatroid hamster hammer!"
    u.s.w.
    You can see that any lesson is now trashed. She has to take at least five minutes to re-establish some semblance of order, and they are just too cranked up to hear anything.

    [She didn't actually try to use Hitler's birthday, okay?]

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    1. Children's sermons on birthdays (not just the obvious -- Jesus' birthday -- but also the "birthday of the church" -- Pentecost) cause very similar problems.

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    3. "[She didn't actually try to use Hitler's birthday, okay?]"

      Well, that leaves something for the bucket list.

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