An ineffable moment

[2008-12-31+07:00 / 2009-01-01Z]

If we add it all up, the XML Schema Working Group has spent a lot of time, since the beginning of the group, worrying about leap seconds.

XSD 1.0 attempts to accommodate them in its descriptions of the date/time types, but leaves some aspects of behavior unspecified. Accordingly, implementations of XSD 1.0 vary wildly in how carefully they handle leap seconds; not every implementation comes with built-in knowledge of when leap seconds have occurred in the past, and not every implementation enforces the rules which specify that, when they occur in the future, leap seconds will occur only at midnight, UTC, at the end of a month. You can read some things on the Web that seem to imply leap seconds can only occur at the end of June or December, or possibly also March and September, but that’s not what the relevant spec says. The quarter days are to be preferred, but in principle a leap second could occur at the end of any month. You can also read things on the Web that suggest many people are uncertain whether the responsible authorities could in principle insert (or delete) two leap seconds at a time, or even more. I was unsure myself, until some time after I read the relevant specification it finally dawned on me that the answer is no.

[“The relevant spec?” asked Enrique. “Which is that?” “Well, if you want to be precise, it’s Recommendation ITU-R TF.460-6: Standard-frequency and time-signal emissions, published by the International Telecommunications Union (Geneva: ITU, February 2002). I don’t remember how I managed to acquire a copy.” “And how can you be sure there can never be adjacent leap seconds, if it doesn’t say that flat out?” “What it says is that leap seconds are to be added at the end of some month, UTC, in order to keep UTC within 0.8 seconds of the appropriate solar time measure (maybe UT1 or UT2, but it’s been a while and I forget the details). If after adding two leap seconds, UTC is within 0.8 seconds of solar time, then before they were added it must have been more than 0.8 seconds off. But it’s not allowed to be more than 0.8 seconds off — that’s the point of adding or deleting leap seconds.” “What if there was a large change between January and June?” insisted Enrique. “Then the spec implies that a leap second should be added between January and June. The spec does not limit the insertion of leap seconds to December 31 and June 30, it just says to prefer those dates. I think the implication is pretty clear that if you need to add a leap second at the end of May, you are supposed to do so.”

[“Yeah, but what if the world slowed down by two seconds in the course of a single month? Isn’t that logically possible?” “Logically possible, yeah, I guess so. But astronomically implausible. If the rotation of the earth starts to vary that much, it’s likely to be because a large asteroid just hit us, or something. Under those circumstances, schema-validity is likely to be the least of our worries” “Well, my point exactly,” said Enrique. “If the world is falling apart, that’s the last time you want your systems to start failing because the schema validator doesn’t like your time stamps. There will be more important things to be worrying about!”]

In developing XSD 1.1, we spent a lot of time trying to nail things down better, but ultimately reached the conclusion that there just was no good way to allow all real leap seconds and only real leap seconds, to handle validation of dateTime values for the future, and to maintain the principle that a document’s schema-validity against a given schema is the same today and in the future; it should not change from day to day depending on decisions made by the managers of Universal Coordinated Time. In the end, we said that XSD 1.1 processors just don’t handle leap seconds at all: the moments in the global time-line which are occupied by leap seconds do not correspond to values in the xsd:dateTime value space.

It’s an important principle of schema design (and of the use of other formalisms as well, I think) that in the general case, what the formal notation can express may be only an approximation to the reality you are modeling. Some things may exist without being able to be spoken. Mostly we mean by that that specific rules that apply in a given context may not be expressible in a given formal notation, since the expressive power of the formalism may be hobbled in order to preserve its tractability. It’s nice, I think, that the principle is also instantiated by the dateTime type: there are some moments of UTC time that cannot be captured as values in the dateTime value space.

All this is on my mind, of course, because one of those moments is scheduled to occur today. At midnight UTC. Any moment, now, in fact.


[“Shouldn’t it be midnight local time?” hissed Enrique. “No, you’re thinking of shifting to and from Daylight Savings Time. Leap seconds are inserted at the same moment all around the globe. Hush, now, don’t spoil it. Just wait and watch.”]

And there it went. Midnight UTC has passed, and the sequence of seconds shown by the applet at for Mountain Time went:

  • 16:59:56
  • 16:59:57
  • 16:59:58
  • 16:59:59
  • 16:59:60 [That’s it! That’s it!! “Hey, come look at this!” I wanted to call to my wife.]
  • 17:00:00 [“No, wait, never mind. It’s over already.”
  • 17:00:01

All of these past weeks, as events in W3C and in the economy and in the world have gone from bad to worse, I’ve been waiting impatiently to shake the dust of this year from my feet, and yearning for 2009 and a new leaf. The new year will surely be hard in many ways, I tell myself, but it cannot be as bad as the year just ending. As far as I can tell, I am not alone; 2009 has a heavy freight of hope and expectations to carry. A heavier freight than it’s fair to ask any year to bear.

So I like the idea that between the old year, so widely and deservingly anathematized, and the new one which carries so much fragile hope, time paused, just for a second, to gather its forces before picking up its burden and marching forward again.

Happy New Year, o my readers. Happy New Year.

4 thoughts on “An ineffable moment

  1. Just to clarify a bit:

    It’s not true that we have leap seconds because the Earth’s rotation is slowing down. We have leap seconds because the length of the atomic second was based on the year 1900, and that happened to be an unusually short year, more typical of the 1860s than the turn of the century. Current years are somewhat longer than 60*60*24*365.2422 seconds long on average, and so we’d need leap seconds even if the Earth’s rotation were perfectly constant from now on.

    The fact that the Earth’s rotation is slowing explains why we will eventually need more and more leap seconds in future (quadratically more, in fact, though we are on the flat part of the parabola so far). The fact that the Earth’s rotation slows irregularly explains why leap seconds cannot be predicted in advance.

  2. Just to clarify further… this is not correct. The atomic second traces back to 1/86400 of a day in about the year 1820. And even if the current definition of the second would be defined to be a smidgen longer, we would still have had leap seconds, though fewer of them. For more details see: THE PHYSICAL BASIS OF THE LEAP SECOND, Dennis D. McCarthy et al 2008 The Astronomical Journal 136 1906-1908,

  3. To clarify my clarification: I should have said that we have leap seconds because the Earth has slowed down. If the Earth had never slowed down, we would not have any leap seconds. But we would continue to need them from now on even if the Earth never slowed down any more.

  4. I expect the XSD options were either to allow dateTime to be able to express nonexistent moments in time, or not to be able to express existing moments. I, for one, would have preferred the former – that XSD time can express an extra second for every end-of-the-month day. Can you please shed some light on why the other approach was preferable to the WG?

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