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Date: Sun, 24 Jun 2001 13:58:14 -0500 (EST)
From: Alfred M Kriman <akriman@darwin.helios.nd.edu>
Message-Id: <200106241858.f5OIwE223953@darwin.helios.nd.edu>
To: classics@u.washington.edu
Subject: Re: t.i.d.

I wrote
> Medical prescriptions use a number of conventional Latin abbreviations,
> such as t.i.d. for ter in die, understood as thrice daily.  Given the
> Roman use of inclusive numbering, wouldn't t.i.d. in fact really have
> to mean what we would describe as twice daily?

Patrick Rourke replied
> Nope.  Inclusive counting would begin at the first dose, which would be 1,
> and end with third dose, which would be 3.  

What we do with t.i.d. is take _four_ doses in each twenty-four hour
period.  It just happens that the fourth dose comes at the very end
of that period and we agree, counting exclusively, to count that
fourth only as the first dose of the next day.  One might object that
this is the only sensible way to do things, otherwise the counting
isn't linear.  That is, putative Roman t.i.d. (once every twelve
hours, by my reckoning) is equivalent to putative Roman five every
two days.  This is apparently not the kind of objection that bothered
the Romans, because one week's interval was eight days and two week's
was fifteen (once they used weeks).  I think this is our greatest
intuitive problem with their scheme -- that two weeks don't seem to
contain twice the number of days as one week.  I think the answer is
that natural language conventions may happen not to be convenient for
mathematical discussion.  A general way to state the objection is to
say that inclusive counting double-counts the event or item that
comes at the end of one interval and at the beginning of the next, if
the intervals are counted separately.  The equivalent reply is: what
of it, so long as it's a consistent, unambiguous convention?

Stronger objections exist; I'd like to see them stated and analyzed.

AMK
.