## Dunder Math-lin

This week, Steve Carell uttered what may well be his last "That's what she said" as Michael Scott, boss extraordinaire on the US version of The Office. Though the show will go on, Michael Scott has (spoiler alert) left Pennsylvania for Colorado and the love of his life. In preparation for this departure, the show has spent the last several episodes easing the audience through the transition.

From a mathematical standpoint, though, there are a couple of inconsistencies. Michael makes no secret of the fact that he has worked for the company for 19 years.  His employees take this loyalty to heart, and in Michael Scott's penultimate episode, "Michael's Last Dundies," they surprise their boss with a song parody of the Rent song "Seasons of Love," which pays homage to such a long period of service. The song begins with a soulful rendition of the following lyrics, courtesy of Andy Bernard (Ed Helms):

9,986,000 minutes,

We actually sat down, and did the math

9,986,000 minutes,

That's how may minutes that you've worked here.

Here's a question: how does this number compare to Scott's claim of 19 years?  Let's make a few estimates.

For a crude estimate, we can simply take the length of a year to be 365 days, and count the number of minutes in 19 years given this assumption.  This isn't hard; the answer is simply 19 (number of years) × 365 (number of days in a year) × 24 (number of hours in a day) x 60 (number of minutes in an hour) = 9,986,400.  This is exceptionally close to the value cited in the song - in fact, due to a syllable constraint needed to maintain faithfulness to the original song, it seems likely that this is how the number crunchers in the office actually came up with the value they sang.

Andy has the voice of an angel.

But how accurate is this number?  This depends on a few factors.  First, if Michael Scott really did begin 19 years ago, this estimate neglects a few leap years.  A better estimate would come from taking 365.25 days in a year, which in turn would give an estimate of 9,993,240 minutes (or 9,993,000 minutes, if one is interested in a number befitting of a Rent song parody).  What's more, it's unlikely that Michael worked exactly 19 years - the true length of his stay is probably somewhere between 19 and 20 years, or between 9,993,240 and 10,519,200 minutes.

Depending on your interpretation of the lyrics, though, any of the numbers given above may be much too large.  When Michael's employees tell him "That's how many minutes that you've worked here," do they mean "that's how many minutes since you've started working here," or "that's how many minutes you've spent working since you started working here?"  If the former, then these estimates seem more or less reasonable.  But if it's the latter, we really should only be counting the minutes Scott spent at the office.  If we say that he spent 40 hours a week, roughly, in the office over the past 19 years, then with 365.25/7 weeks per year, this comes out to only 19 x 365.25/7 x 40 x 60, or roughly 2,379,343 minutes, a far cry from our earlier estimates.  To take things even further, based on the evidence provided by the show, the amount of work Michael actually does while in the office seems fairly minimal - if we're talking strictly about the amount of time he's spent working in those 19 years, I wouldn't be surprised to find a much lower value.  Either way, there seem to be some accounting issues at work here that have been ignored.

Perhaps if accounting spent less time playing solitaire, these issues would have been ironed out.

Also, at the risk of sounding like comic book guy, just two years ago an episode of The Office focused on celebrations for Michael's 15th anniversary with Dunder Mifflin; the subsequent cancellation of the festivities by new manager Stringer Bell Charles Miner drove Michael to quit and start a rival paper company.  One could argue that the time Michael spent not employed by Dunder Mifflin should not count towards his 19 years, but more importantly, 15 + 2 is only 17, not 19.  Before you try to argue that perhaps the show's timeline is simply moving faster than the normal rate of one year per year (as TV shows are occasionally wont to do), one needs only to consider the timeline of Jim and Pam's baby to see that this is not possible.  So in fact, all of the above discussion is fairly moot - indeed, we can't even be sure how long Michael has worked at Dunder Mifflin.

All is not lost, though.  While we can't accurately apply mathematics to this Office-inspired question, others out there have had more success with different questions.  For example, here is a computer science paper on automated recognition of phrases that can reasonably be followed up by the phrase "that's what she said."  What a neat problem!  It looks so hard, but they somehow manage to tame it.

Oh, Michael Scott.  You will be missed.

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