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A Little Night Music

I've been in Boston this week at a scientific conference. I've spent nearly all of my time at the conference, but was able to get away a couple of times to see friends.

One night off I went out for pizza with Ekrem and Leanne (and their adorable kids). We went to Stone Hearth Pizza, whose head chef is the brother of Bob, one of my labmates in Minneapolis. (He wasn't at the restaurant the night we went, sadly.) Ekrem and Leanne are moving to their new house in a week, and I helped them out by consuming the remainder of a bottle of scotch that they keep at their house for me. I felt very proud of myself for accomplishing this noble task.

Last night I went to see Andrea perform in Stephen Sondheim's A Little Night Music, one of my favorite musicals. Beforehand, I had dinner with fraternity friends Jan, Jeannie, David, Emily, and Ian. Dinner conversation was wonderful in that MIT-nerdy way that I greatly miss sometimes.

At the end of the meal, for example, my fortune cookie told me my "lucky numbers" were 3, 6, 12, 24, 36, and 42. All multiples of three, I noted with curiosity. In the company of "normal" people, I would very likely have supressed this felicitous fact. With my MIT compatriots, however, I felt I could share without fear of reprisal. "All of my lucky numbers are multiples of three," I exclaimed. In this group, that was encouragement to try to top me. "I have four prime numbers" was thrown out by someone. I responded "I have the most prime numbers I can have given my initial constraint." Jan scoffed, "In other words, one prime?" I replied, "Yes indeed! Three itself is one of my multiples of three." (I leave it as an exercise to the reader whether is it rarer to have all multiples of three or to have four primes out of six.)

Here's the gang sitting and waiting for the musical to begin:

And here's Jan and the 80-year-old Andrea:
She was quite lovely in her role, belting out the low contralto notes in her solo and keeping the audience laughing with her comic lines. A good time was had by all!

Comments

  1. J-W Maessen8:19 PM

    Totally excellent to see you last night!

    Note that there are 25 primes less than 100, so your odds of getting all multiples of 3 are rather better than your odds of getting all primes. If you allow more digits in your lucky numbers, odds get worse as prime density is (if I remember rightly) roughly proportional to n / log n near n.

    Boy, stage makeup really makes people look like ghouls without stage lighting, doesn't it?

    ReplyDelete
  2. kirisutogomen8:04 AM

    Do you mean at least four primes out of six, or exactly four primes out of six?

    http://en.wikipedia.org/wiki/Prime_Number_Theorem

    ReplyDelete
  3. J. Michael Andresen12:07 PM

    I think "at least four primes out of six" is more appropriate.

    And although the Prime Number Theorem is of use if lucky numbers could be five or six digits, but in general, lucky numbers are of little use unless you can use them to play the lottery. That limits then to between 1 and 60. That allows us to calculate the approximate number of primes in this range as 17.

    By my calculation, then, the probability of picking at least four primes is 5%. The probability of picking all multiples of 3 is 0.08%.

    ReplyDelete

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