2266: Leap Smearing

Explain xkcd: It's 'cause you're dumb.
Jump to: navigation, search
Leap Smearing
Some people suspect that it started as a "No, I didn't forget Valentine's Day" excuse that got out of hand.
Title text: Some people suspect that it started as a "No, I didn't forget Valentine's Day" excuse that got out of hand.


Clocks usually measure time by regularly-sized intervals, but the natural world is not always so accommodating. Since the solar year is not an integer number of days long, we add leap days every four years (except for years divisible by 100 but not 400) to prevent our calendars from drifting with respect to the seasons. We also add leap seconds to the clock every now and then, to prevent noon on our clocks from drifting away from solar noon. Unfortunately, Earth's day is not as regular as Earth's year, so leap seconds cannot be predicted with a formula but are added as needed, most recently in 2016. Officially, the leap second is added at midnight UTC (so a clock will tick 23:59:59...23:59:60...00:00:00), but this is an extremely inconvenient edge case, to the point that there are many proposals to do away with leap seconds entirely (as of this comic strip's publication, the matter will be discussed in the World Radiocommunication Conference in 2023).

Rather than inserting an extra tick into timestamps and dealing with the resulting hiccups (e.g. programs hard-coded to expect that every minute will contain exactly sixty seconds), Google's services 'smear' the leap second over the course of a 24-hour period, officially called Leap Smear by Google. The smear is centered on the leap second (at midnight) so from noon the day before to noon the day after each second is 11.6 μs longer (1s/(24*60*60) = 11.574 μs). This difference is too small for most of Google's services to be bothered with, and by centering on midnight, the difference in time will never be more than half a second at midnight; just before midnight it will be half a second behind, after midnight it'll be half a second ahead. This comic's joke arises from the idea of extending this practice to smearing leap days over the month of February. This comic strip was published February 10th, 2020, almost three weeks before the leap day on February 29th, 2020.

In the comic, Cueball is visiting one of Google's facilities, presumably during office hours on the 10th day of February, when the comic was released. But when he looks at their clocks he sees they are all around 3:00 AM (which is in the middle of the night). He thus asks Ponytail and Hairy why their clocks are wrong. Ponytail tells him it is because of leap day smearing.

Ponytail explains that adding an extra day creates too many glitches. So they just run their clocks 3.4% slower during February. She thus states that it works approximately like leap smearing for seconds, so that the extra day's 24 hours are spread evenly over the course of February, keeping it at the regular 28 days, but still running over 24*29 = 696 hours, even though their clocks only go through 672 hours = 24*28.

Thus the 24 hours less to count are spread out over the 696 real hours, which means their clocks run 24/696 = 3.445 % slower (matching the 3.4% Ponytail mentions). Every smeared day will thus be about 0.86 hours, or 51 minutes and 40 seconds, longer (24/28) than a standard day. So when day-smearing clocks read 3:02 AM on February 10th (the comic was released on February 10th), about 9.1264 smeared days will have passed. This translates to about 9.4523 standard days (9.1264*29/28), which is approximately 10:51 AM on February 10th, well within normal working hours.

The joke of course is that contrary to leap second smearing this would be very inconvenient for those following it, due to the fact that clocks would be noticeably out of sync with Earth's rotation (and perhaps more importantly, with everyone else's clocks) for most of the month. (Although it does mean they would sync up better with some of their partners abroad; see 1335: Now and 448: Good Morning.) A different kind of time-smearing was looked at in the far earlier comic 320: 28-Hour Day, which was actually designed with a form of convenience in mind, and it would be interesting to see what the results could be of creatively combining both systems.

The title text humorously suggests that some people (at Google) suspect that the real reason for the leap day smearing was actually a "No, I didn't forget Valentine's Day" excuse that got out of hand. The idea is, that maybe a CEO at Google forgot to buy something for their romantic partner for Valentine, and thus tried to suggest that it was not because they forgot, but that at work it was still February 14th. Presumably, in February 2016, they used this excuse to buy 12 extra hours (as the end of a smeared Feb 14 is exactly halfway through the month) to get their partner a present, and then required the company to actually implement "leap day smearing" by 2020 to maintain the illusion.

Randall has some issues with Valentines, see for example 1016: Valentine Dilemma. This comic was released four days before Valentines Day of 2020. It was the first time in 8 years he made any reference to Valentine around this time of year, but the seventh time in total. Randall has since not mentioned Valentine's day.

1481: API also covered leap seconds in its title text.


[Cueball, Ponytail, and Hairy are looking up at a digital clock on a wall. It displays the time in white on a black background, with a logo on the frame beneath the time.]
3:02 AM
Cueball: Why do the clocks say it's 3AM?
Ponytail: Adding an extra day creates too many glitches. Instead, we're just running our clocks 3.4% slower during February, to avoid the irregularity.
[Caption below the panel:]
This year, Google has expanded their leap second "smearing" to cover leap days as well.

comment.png add a comment! ⋅ comment.png add a topic (use sparingly)! ⋅ Icons-mini-action refresh blue.gif refresh comments!


Although to be fair, leap seconds are confusing. Unpopular Opinions (talk) 04:08, 11 February 2020 (UTC)

Leap seconds are idiotic. The only people who care about keeping the Earth tied to the time are astronomers. And no one cares about them.SDSpivey (talk) 04:56, 11 February 2020 (UTC)

Oh, you'll care about leap seconds when your GPS starts failing, i assure you. 07:08, 11 February 2020‎ (UTC)
GPS does NOT have leap seconds. That's why GPS time is drifting away from UTC. It's off by about 19 seconds now, since 1980. However, people would care eventually, when the time on the clock doesn't match up with the solar day (as pointed out by the next comment.) It would take a long time, but why get started off on the wrong foot? 14:39, 12 February 2020 (UTC)
Leap seconds are a mess, but so is changing the definition of UTC and letting it drift away from solar time. There are movements to try to make this change, but there are significant obstacles. (For example, the signatories to the 1884 International Meridian Conference agreed that the civil time everyone should use is based on mean solar time, and US Federal Law indicates that the legal time of the US is based on mean solar time.) Zmatt (talk) 06:30, 11 February 2020 (UTC)
If we don't use leap seconds, then the GPS won't use them either. How many seconds difference before we humans could even notice? A century's worth or more, I'm certain. By then we could just fix the wobble of the Earth. SDSpivey (talk) 07:33, 11 February 2020 (UTC)
1. You use “we humans”, who do you think is studying and correcting with leap seconds? Robots? 2. I don’t think you realize just how quickly that would cause problems. “That Guy from the Netherlands” (talk) 12:52, 11 February 2020 (UTC)
Leap seconds are added rougly every couple of years. If we stopped, it would take about a century to be off by a minute, and 6,000 years to be off by an hour. So maybe we should just plan on every 6K years we skip Daylight Saving Time to recover that hour. Barmar (talk) 16:26, 11 February 2020 (UTC)
For half a year, then we're back to the situation we were ignoring. ;) ((Obviously, what we might need to do is move the Prime Meridian, send it on a very slow "world tour" by passing it onto the next suitable city. But I'm a bit of a conservative when it comes to historic locations, so we should just put Greenwich Observatory on wheels, or rails, if necessary.)) 23:37, 11 February 2020 (UTC)

I believe the actual time would be 11:42am (on the 11th of February). Dakranon (talk) 06:20, 11 February 2020 (UTC)

But the comic was released on 10t February Monday as always, but the date was written wrongly on the comic here. I have treid to calculate the time on February 10th. --Kynde (talk) 08:21, 11 February 2020 (UTC)

I think there is an error in the calculations given in the explanation, but it's possible some bistromathics got involved instead. By my reckoning, 24 hours smeared over 28 "days" make each "day" 24/28 hours (≈ 51 minutes, 26 seconds) longer than a day instead of 24/29. Also, conveniently for my calculations, the end of "14 February" should be exactly halfway through the month, meaning the CEO should have until exactly noon on the 15th to get away with the given excuse (12 extra hours, not 11). 10:27, 11 February 2020 (UTC)

Thanks for correcting my attempt. As I wrote in the incomplete tag I was not sure I did it right.

You guys are all missing the point! We should apply non-leap smearing to the other 11 months so that EVERY month has 28 days. No more crazy calendar day-shifting: if you were born on a Monday(e.g.) your birthday will always be Monday. Cellocgw (talk) 15:06, 11 February 2020 (UTC)

Or go even further... 17:04, 11 February 2020 (UTC)
Actually we should do as the hobbits in Tolkien's Lord of the Rings. They run 28 day months, 13 of them instead of 12 and that gives 364 days. I cannot remember the details correctly, but it is something like they then have a New Year day every year, and a leap day every four years after New Years day. The Year starts on a Monday as do all months. The New Year day (and Leap days) are not given any Weekday, so after Sunday 28th of December (or what the last month would be called) there are one or two days, without a weekday assigned, and the new year begins on Monday. It would all be soooo much more easy, but of course if you where born on a Monday you would always have your birthday on a Monday! ;-) --Kynde (talk) 12:01, 12 February 2020 (UTC)

As of right now, I feel like the explanation is a bit of a mess. I already understand this comic but IMO someone who doesn't would not be able to follow this explanation. I think a better structure would be:

  1. Briefly explain what leap seconds are, since most readers will not know about them.
  2. Explain the "smear second" approach, and mention how the resulting time deviates by only half a second at the worst time.
  3. A line like "This comic suggests taking the smear second approach and applying it to leap days"
  4. Brief explanation/reminder of what leap days are - most readers will be familiar with this concept already, and those that don't can click on a Wikipedia link to read more.
  5. Explanation of how bad the results would be (some math here), the resulting date&time would be off by 24 hours at the worst time (end of Feb 29 will appear as the end of Feb 28). It's not 12 hours because unlike the smear second, the smear period will not be centered around the leap day but rather the leap day will be at the end of the smear period (which is all of February). Also mention exactly what the clock would show on the day of this comic's publication, and what the in-comic time actually is.

--NeatNit (talk) 19:00, 11 February 2020 (UTC)

I guess this has happened more or less now? --Kynde (talk) 12:01, 12 February 2020 (UTC)

This would violate the NTP 500ppm maximum slew rate, right? ;) (talk) (please sign your comments with ~~~~)

I really wish this was an interactive comic, with the Time changing throughout the month... 16:59, 12 February 2020 (UTC) Sam