Just for fun: A ten-day week?

This post is by James

The title says it all.  What if the week had ten days?

This all started when I was talking with Jason (my brother and co-blogger) the other day and somehow we started talking about the metric system (centimeters, kilometers, grams, etc.)  The strangest thing about the metric system is that it changed how we measure everything—except time.  Unlike everything else metric, in the metric system, we have 60 seconds in a minutes, 60 minutes in an hour, and 24 hours in a single day (give or take a very little bit.)  This is all very strange. Everything else in the metric system is related by powers of 10.  1 kilometer is 1000 meters and 1 milligram is 0.001 grams.  Why did we stick with these strange numbers for time (24 and 60)?

We didn’t come up with an answer (we aren’t historians of, well, anything, so we didn’t really try), but we did remember that during the French Revolution, they tried to create decimal time.  They had ten hours in a day, one hundred minutes in an hour, and 100 seconds in a minute.  (I’m guessing they finally gave up on that because it made an hour far, far too long.)

I dare say that most of us could live pretty well with a different way of measuring what hour it is.  Most of us only really care about “It’s-far-too-early-in-the-morning,” “time-to-wake-up,” “lunch-time,” better-not-nap-time,” and “evening.”  The really interesting bit is when they tried to fiddle with the length of the week.  Yes, they tried to implement a 10 day week!  I don’t know what effect the ten-day week really had in France in 1800, but it would certainly have some odd effects today.  What would we call the extra days?  Would we still have “hump day”?  Would TGI Friday’s have to change their name?

Most important of all, if we tried to switch to such a system today, you would run into an interesting problem [1], namely that people would really object to getting fewer days of the week off if we just kept the weekend two days long.  Getting two days off out of ten is clearly more work than getting two day off out of seven.  It seemed to us that if a government didn’t want to have instant riots when they made the switch, they would have to offer some kind of compensation to workers.  The obvious choices would be to give the workers more than two days off during the week; it doesn’t much matter when.  Then the workers would have three days off out of ten, instead of just two.  Surely this is fair?  How can we tell?

And this is where we finally get to the math.  How do we compare the two systems?  Which gives you more time off, 3 days out of 10, or 2 days out of 7?  Can we do this kind of comparison in general?

And here is where I fiendishly leave you hanging.  Can you figure it out by yourself?  Do you know?  Which would you pick if time off was the only thing that mattered?  Let me know!


[1] There are other reasons why people would object to this than the ones we list here.  People doubtless objected in 1800 France for the same reasons as well.  We are doing this only as a what-if; we don’t actually want the week length to change.  Because some of the reasons are sensitive, we insist on not going beyond the simple “what if” as given.  Remember that it’s all in fun.

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