November 7, 2020 https://bit.ly/3mDabcY
Grading online, I spot a notification from our learning management system displayed on a student's assignment entry:
Oct 19 at 8:30am LATE
I glance over to the heading of the assignment and see this text:
Exercise #7 Due:
Oct 19 at 8:30am
Well, that's vexatious, but seen before and easily accommodated by not counting the work late. Because, surely, it's not late! The online instructor help describes this quirk as a feature, not a bug: "... For example, if you set a due date of September 19 at 4:15pm, any student submission made at or after September 19 at 4:15:01 is marked late." So the full minute of interest is not granted. Is this fair? On a high-stakes assignment, a student would have a legitimate objection: Isn't the deadline at the end of the minute, not the start of the minute?
Griping aside, what would we have this system do instead? We intend for the assignment not to be late before 8:31. The programmer, given that specification, could program the expiration at 8:30:59, but that still leaves the gap between that point (8:30:59:00) and the deadline, a gap packed with milliseconds (or other subdivisions such as "jiffies," I see in Wikipedia1). A test of the system time for
LATE = (hh:mm > next(8:30)) is far-fetched because there is no function
next() that computes 8:31 to be the time that comes after 8:30. The instructor doesn't want to say "late at 8:31" anyway, but rather "due at 8:30." The instructor does not want to cross over into the next time unit in order to establish a deadline.
What exactly does the instructor want? "You know what I mean: I want the papers in my possession at 8:30, well, right after 8:30." What the instructor wants is a phenomenon of the physical world—a tidy pile of submissions stacked up the day before, with perhaps one or two students racing to the professor's office in the morning, paper in hand, as the hands of the clock approach 8:30. As the professor sees the submission thrust toward her, she can look at her watch and declare whether the deadline is met, annotating the paper appropriately. She can then shut the door for the grading session, starting right then at 8:30, whatever version of 8:30 she defines. Shifting this scenario to the digital world is not as straightforward as she had expected.
In Communications, George Neville-Neil has pointed out time is a pesky problem for computing, in the establishment of synchronization and syntonization, in the design of clock hardware, in the querying of system time, and in just about every other respect.2 We set aside these interesting issues, as well as those that reach beyond the technical into the social, such as bizarre stock market trends due to lightning-fast high-frequency trading. The philosophical questions include whether time supervenes on events, whether the present is privileged, what sort of formalism is suitable for temporal reasoning, and many other interesting issues,3 but this is not about those either. This is the problem of designating a particular point on a line in a way that cuts the values into "before" and "here." The time just "before" is a block (of the length of whatever unit is in use), a discrete construct, whereas the time "here" is an interstice of length zero.
Consider a significant and well-known time of day: midnight. Suppose I tell my students an assignment is due on a certain date. They know the date ends at midnight, and reasonably infer any clock time bound to that date is acceptable for submission. What is the very last instant that meets the standard? When exactly is the midnight at the end of the day called, say, November 9th? Is it at 1200 hours past noon, or is that time actually November 10th? Apparently, nobody knows. We can fix the accuracy at the level of seconds, avoiding Zeno's paradox and making that very last instant our familiar discrete subdivision of a minute. But which second? Is it 23:59:59 or is it 24:00:00? Oh, dear; it's the point between. If we make our assignments due at noon, do we call it 11:59:59 or 12:00:00? And, if the latter, do we call it "A.M." or "P.M."? Oh, dear—an interstice again, and because A.M. means ante meridiem and P.M. means post meridiem, neither works for the actual meridies.
Let's turn to the authority of a nation well-versed in timetables, Britain's National Physical Lab: "To avoid confusion, it is always better to use the 24-hour clock, so that 12:00 is 12 noon. Therefore 24:00 Sunday or 00:00 Monday are both midnight meaning Sunday to Monday."4 This authority at least validates the ambiguity. So there is no such thing as midnight on a certain day; there is only the transition between one day and the next. Although midnight is a high-profile time of day, this is a problem manifest only in a digital context. The scheduling of an event such as a train departure or a pagan ceremony is performed on a human scale; someone declares it. The simple change from one date to the next is not necessarily declared, but exposed only by the human need for noting some occurrence before or after the placement of midnight.
That gives us a clue about the root of the problem. It is not the artificial construction of our system of time, but the digital turn. The deadline of the past allowed people to take care of it in whatever way seemed appropriate, unhampered by any mandate to locate the exact end of a block of time. Even sharp deadlines were enforced by simple human fiat, and still are, in most daily business. Some force other than time itself does the reckoning, and on a continuum that embraces loose placement along the milliseconds. It is the physical manifestation of the deadline that counts, not the deadline itself. The Stock Exchange opens on a bell, and the New Year arrives when observers in Times Square see that the ball has fallen.
This is not novel, but the same problem as designating a point on the continuum using a real number with a finite decimal expansion, a problem that used to be housed in the applications of mathematics. Now that time is discrete, we are trying to force a discrete representation into a continuous phenomenon. This occurs is many other realms as well, of course—distance, volume, anything measurable.5 We can avoid using 12 A.M. and 12 P.M., but what about those pesky due dates? When I give a deadline, my students trust that I am passing a designation of a block, with the deadline at the end, but that's not a well-defined type. I will avoid using the end of a day, also known as midnight, as a deadline on a digitally timed platform, and I will try telling my students to submit "before 8:30."
1. Wikipedia contributors, "Unit of time." Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Unit_of_time, Accessed 7 Nov. 2020,
4. National Physical Laboratory, Questions and Answers: Is midnight 12am or 12pm? https://www.npl.co.uk/resources/q-a/is-midnight-12am-or-12pm
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