11 September 2007

Fencepost errors, intervals, redeeming coupons, and drinking

A friend of mine asked today: if a coupon says it expires on a certain date, is that the last date that it's usable, or the first date that it's not usable? (He was referring in particular to the customized coupons that print out on receipts at CVS if you participate in their "loyalty program".)

My answer: the last day it's usable. This is basically by analogy with more "traditional" coupons, which are likely to expire on, say, "September 30". It seems reasonable that one could use the coupon on every day in September, and on no day in October; it would not seem reasonable to be able to use the coupon on every day in September but one. Coupons printed out by this program expire on seemingly random dates, but it seems that the same principle should apply there.

Similarly, if I said "the homework is due on Thursday" to my students, and then one of them handed it in on Thursday at noon, I would not say that what I really meant is "Thursday is the first day on which I will not accept the homework", and that therefore the homework is late. (In practice I usually say what time the homework is due in order to avoid this question.)

I'm not sure what the law actually has to say about this, though. I do know that laws in various places endorse different interpretations with regard to the "sell by" date on milk: in some jurisdictions the "sell by" date is the last date on which the milk can be sold, and in others it is the first day on which it cannot.

I'm inclined to say that one is always allowed to do the thing on the date which is stated, so it should be permitted to redeem a coupon, sell a carton of milk, etc. on the date listed on it. Similarly, if there's something that I'm allowed to do if I am "at least N years old" I should be able to do it on my Nth birthday, and the law agrees with me. (There's an exception of sorts for drinking, actually; in some states one cannot drink at midnight on one's 21st birthday, but must wait until the bars have closed and re-opened again. A friend of mine turned 21 in Massachusetts and was disappointed to learn this. Apparently the reason for these laws is that some people were trying to take 21 shots between midnight and last call, often 1am or 2am, and they were dying. Dying was seen by the lawmakers to be a Bad Thing.) There's a symmetry here, in that both of these are "permissive" interpretations.

But the scenario in which one is always forbidden to do a thing on the date stated on the appropriate piece of paper (so no redeeming a coupon on its expiration date, no drinking on your 21st birthday) also is symmetrical, in a way -- one might call it a "strict" interpretation. One could also have "early" and "late" interpretations -- the "early" interpretation would be that you can't redeem the coupon but you can drink, and the "late" interpretation the reverse.

These four cases are roughly analogous to the four sets of inequalites a ≤ x ≤ b, a < x < b, a ≤ x < b, and a < x ≤ b, although making the analogy precise takes more time than I want to spend on this.


Anonymous said...

The English language (and most others I assume) allows you to denote several different things here.

You said:

"I'm inclined to say that one is always allowed to do the thing on the date which is stated, so it should be permitted to redeem a coupon, sell a carton of milk, etc. on the date listed on it."

This is so only if "do the thing" is what the the quoted language speaks of; but sometimes the quoted language speaks of the opposite, and then it takes the boundary case with it.

For example, if my coupon says "good (i.e. redeemable) until" September 30, then the allowed activity is "redeeming". I expect to be able to redeem it on September 30. But if the coupon says it expires on September 30, then I conclude that it remains unexpired on Sept. 29, is expired on Oct. 1, and becomes expired on Sept. 30. Expiration and becoming unredeemable are one and the same event. In order for the coupon to become unredeemable on September 30, as opposed to October 1, then on September 30 I may not redeem it. Expiration and redemption are two mutually exclusive events. Which one you mean to be excluded on a particular day is selected by which language you use to describe the event that happens on the 30th.

But no matter how you slice this logic for mathematicians, some people from common walks of life will get it the other way, and that's what judges interpreting fine print have to deal with. For example, my credit card says "good thru 11/30". To me, that pretty clearly means I may use it on Nov. 30, but not on Dec 1. Therefore, according to my construction of the word, it becomes expired and unusable (i.e., expires) on Dec 1. But I get in trouble if I try to specify an "expiration date" of 12/yy on credit card forms; I must specify 11/yy, which is patently incorrect. But there's no arguing with a credit database, just as there's no arguing with people who insisted 2000 was (or wasn't, take your pick) the first year of the new millenium.

Anonymous said...

what i can't understand is
how people go around talking
about "12 AM" or "12 PM".

a-and ... how come there's
no year 0? (obviously neither
AD or BC ...[BCE and CE for th' PC])

Aaron Denney said...

Djikstra talks about the various ways of specifying an interval by the end points: http://www.cs.utexas.edu/users/EWD/ewd08xx/EWD831.PDF

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