How many whats in a which?

In actual use, the decimal system is not always the best.

Our tutor is busily engaged in dragging several students through the process of converting units from one system to another.  The most difficult problems seem to appear in Chemistry, though the perennial need to go from miles per hour to meters per second in Physics shows up often also.  The reason for there being 5280 feet in one mile is unknown to students and an annoyance to many; it would be worse if electronic calculators weren’t as available.  All students learn the metric system in class, which seems much simpler (eventually): everything is an even multiple of ten.  It fits well into our base-ten mathematics and is particularly easy to manipulate with calculators.

And yet. . .

Our writer, who is fond of history, notes that along with the pound sterling a unit of money often used in Medieval England was the mark.  A pound was made up of twenty shillings of twelve pence each (until 1971); a mark was 13 shillings 4 pence.  This rather odd amount is actually two-thirds of a pound, exactly.  (No doubt there were good Medieval reasons to want exactly two-thirds of a pound.)  Nowadays one cannot pay out exactly two-thirds of a dollar, or decimalized pound, in pocket change.  You’re left with the odd third of a cent or (new) penny.  In the Old Days, you could use your tin snips and clip off the offending bit of copper (the way a Spanish real was divided into eight dollars: “pieces of eight”).  That’s frowned upon now, if for no other reason than fractional coins won’t work in vending machines.

There seems to be less problem with calculators, since there is a long string of figures after the decimal point and 0.66667 is very close to two-thirds, after all.  But not quite.  And being exact is important in one kind of mathematics.

We are used to another kind of counting: base-60, sexagesimal.  There are 60 minutes in an hour, 60 seconds in a minute.  60 can be exactly divided by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30, quite useful especially when one is working out a problem before the invention of log tables.  (Alas, trigonometry students nowadays seem to be introduced to the degrees, minutes, seconds system primarily to show how much harder it is to use; which can be true for electronic computers.)  The pre-decimal pound was almost as flexible.

So should we all move to base-60?  No real chance of that, unless maybe humans evolve to have twelve fingers (we dimly recall a science-fiction story about something like that).  Instead, our writer, who is a trouble-maker, has another suggestion.  Conspicous for its absence from the factors of 60 is the number 7.  He suggests a unit of money, or whatever, made up of seven groups of sixty.  Then it would be easy, for instance,  to distribute something evenly among the days of the week, something not possible under either the decimal or sexagesimal systems.

We distracted him by asking what he would call it.  We’ll try avoid mentioning it in the future.