Save the Leap Second!

I recently stumbled across an Instagram post with an ominous message. It was something like "people are going to decide on whether to switch from leap seconds to leap hours".

At first, I filed it in the back of my mind as something to research, and possibly make a post about, in the next few days, and just kept scrolling. A few days later, I thought back to it. Wait, leap hours? That can't be right. Those wouldn't be needed for around 3000 years. What would even be the point? Surely they were talking about leap minutes instead.

Meanwhile, it's been almost 10 years since the last leap second. The graph of discrepancy between UTC and UT1, which had previously been trending significantly upward for the first time in living memory, has now gone back to hovering steadily around 0:

Still, the next leap second is somewhat more likely to be negative than positive.

Unsurprisingly, this week it was announced that there would be no leap second at the end of 2026. The Hacker News thread is depressing, with people still fully expecting leap seconds to be completely phased out by 2035... or sooner. Wait, sooner? Yes. I had forgotten, but 2035 is actually the upper bound for the date of the change, not the lower bound. The CGPM resolution itself says that

the maximum value for the difference (UT1-UTC) will be increased in, or before, 2035

and the 2023 ITU resolution agrees:

Key outcomes [of the negotiation] included [...] Resolution 4 of the 27th CGPM (2022).

But that's in 9 years, you might say. Almost certainly, we are at least going to have another leap second, positive or negative, by then. Why is today "possibly one of the last days of leap second relevance"? Well...

Remember the Instagram post from the top of the page? It turned out to be for a Scientific American article with the headline:

Yeah.

The article itself (which I am linking to from the web archive because the original article is paywalled, and because Scientific American has been known to publish sussy opinion pieces in the past and I'm not sure if they deserve our money) says that as a negative leap second appears more likely, the BIPM is scrambling to avoid computer problems from some of its "stakeholders"... gee, I wonder if any of those include the big tech companies that are destroying the planet and trying to implement mass surveillance of their users, the same ones who put out an anti-leap second piece a few years ago?

This will be discussed at the 2026 CGPM in October of this year. What's worse, the article says that the plan may be implemented as soon as 2027.

As.

Soon.

As.

20

27

(note: if you're viewing this from the Tumblr dashboard, the above digits should appear really large. I don't know why, and I don't know why it doesn't work on the blog itself, but I couldn't resist the opportunity)

Take a moment to let that sink in. All this time, we were expecting the leap second to be decided on in 2015. Then they put it off until 2023. We expected there to be multiple leap seconds in between, but there was just one. We expected a decision to not be reached until 2023, but CGPM went ahead and decided in 2022 to do something about leap seconds by 2035. We expected that this would give us 13 more years of potential leap seconds, but now, considering that there are no leap seconds in the second half of 2026, that might be reduced to 0 years.

Well, it looks like this might be the end. We had a good 45 year run. I guess we now know the secret ingredient to make the ITU and CGPM stop being so slow and bureaucratic: the interests of billion-dollar companies. Still, the law of leap seconds strikes again.

This is the best article about the 2022 vote to abolish the leap second I've seen so far. Unlike the articles on pop-science magazines, it's clear it's written by a time nerd who knows what he's talking about and goes into the details and subtleties of the process.

First, the author, Randy Au, covers the difference between UTC, UT1, and TAI. I mentioned this in a previous post, but the summary is this:

The length of UT1 seconds comes from rotation of the earth.

The length of TAI seconds follows the SI definition.

UTC seconds are the same length as TAI seconds, but leap seconds are added.

Apparently, UTC was developed as a "compromise" between the other two systems.

The article then goes on to quote the actual wording of CGPM's Resolution 4, and it seems I was mistaken about the outcome being to abolish the leap second by 2035 "or later." In fact, the resolution says:

CGPM [...] decides that the maximum value for the difference (UT1-UTC) will be increased in, or before, 2035,

requests that the CIPM [...] propose a new maximum value for the difference (UT1-UTC) that will ensure the continuity of UTC for at least a century,

So actually, the plan is to replace (the current system of adding) leap seconds (i.e. adding one every time the difference UT1-UTC exceeds 0.9 seconds) in or before 2035, not after.

Randy Au then goes on to say that, even though CGPM hasn't decided yet what the difference will be increased to, people believe that the ultimate goal is to have UTC be based on the SI second while also, somehow, remaining continuous. This seems borderline paradoxical, and the solution may involve previously unseen temporal anomalies such as UTC seconds or longer periods of time running half as fast or following leap smears. This is a take I haven't heard before, but it may have been made obsolete by 2023's discussion on leap minutes.

Randy Au then goes on to talk about the 2023 ITU conference (which the article was written one year before), and has the pessimistic view that the ITU will likely affirm the CGPM's vote. He quotes the New York Times:

Felicitas Arias, the former director of the time department at the B.I.P.M. and now a visiting astronomer at the Paris Observatory, said that negotiations between the two organizations convinced her that the I.T.U. will support the Versailles vote.

In the November 2023 edition of the ITU News magazine (link above) there is an interesting passage about leap seconds on page 11:

Similar questions about global timekeeping came up a decade ago, in an ITU News Magazine edition published in 2013. As the foreword from François Rancy, then-Director of the ITU Radiocommunications Bureau, said: “Modern times — is the leap second history?” Now, 10 years later, it could well be the case.

This is interesting. It implies they haven't externally settled the leap second question yet, and probably haven't internally settled it either.

The magazine was published on November 2, before the conference started.

Another interesting passage:

CGPM, in fact, took a decision on a continuous reference time scale in November 2022, supporting the abolition of the leap second. The remaining work, such as ITU cooperation with international organizations and updates to Recommendation ITU–R TF.460, falls under the responsibility of relevant ITU–R working groups.

This wording is very revealing. It sure sounds like the ITU hasn't fully committed to agreeing with CGPM's vote to abolish the leap second, and could strike it down at any time.

This is an interesting article about some peoples' proposals to turn the leap second into a leap minute, possibly every century or half century. It was proposed by Judah Levine, one of the leading timekeeping experts at NIST. It will be interesting to see if the ITU conference discusses this! However, the article says that the current ITU conference may not decide anything about the leap second, at least according to American scientists, because different countries have such strong opinions on it.

Also, props to the article for giving an accurate summary of BIPM's decision last year (saying they "declared it was ready to explore alternatives to the leap second," rather than just saying they decided to stop having them by 2035 like most articles say).

Yesterday, on November 20, the ITU World Radio Communication conference 2023 began. This year, it is being held in Dubai, United Arab Emirates and it will last until December 15. The 2019 conference was held in Sharm el-Sheikh, Egypt, and long-time readers of this blog may remember the 2015 conference was held in Geneva, Switzerland.

Let’s just say things have changed since I last made a post here. On the weekend of November 19-20, two ominous changes happened to the world of universal standards. For one, four new metric prefixes have been made official: ronna-, quetta-, ronto-, and quecto-, for 10^27, 10^30, 10^-27, and 10^-30 respectively. This work seems to have been accomplished without even considering any of the numerous unofficial proposals that come up when googling “unofficial SI prefixes”, effectively rendering them outdated despite their prevalance in number names.

Well, at least “hella” for 10^27 didn’t become official. That was one of the most popular proposals, but to me it sounds very primitive compared to the Greek and Latin-based roots of the other prefixes, and doesn’t even sound like a word for nine!

But I’m not here to talk about SI prefixes, I’m here to talk about the leap second. At the very same conference that decided the metric prefixes, the CGPM voted to make leap seconds optional starting 2035. [1]

Wait, what? Isn’t the ITU in charge of deciding the fate of leap seconds, you say, not CGPM? And didn’t they defer the decision until their meeting in late 2023?

It turns out that the ITU also gave CGPM permission to decide the fate of the leap second in lieu of them. [2] The reason we didn’t hear about this earlier was beacuse everyone expected CGPM to be as slow and bureaucratic as ITU. As the Nature article says:

The CGPM's involvement is unlikely to mean a decision on whether to scrap the leap second will come sooner than 2023, however: the organization's next chance to even propose a change would not come until 2018.

Haha, that sure aged...

But there’s more. Apparently the wording of the proposal states that UTC “is allowed” to diverge from UT1 (the time standard determined by Earth’s rotation) by more than 0.9 seconds (the currently imposed limit), not that it has to if the earth slows down or speeds up. In fact, the CGPM merely proposes to add no more leap seconds for a century starting 2035. I’m not usually one to end on a pessimistic note, but given the influence of large corporations and other big-ticket donors on the decision, the chance of another leap second happening after 2035 currently seems grim.

Also, even though ITU allowed CGPM to make the decision, there was no formal process of transfer [2], which means that ITU could theoretically override the vote [1] and continue to implement UTC with leap seconds. However, this also seems unlikely.

I think we need a version of Hofstadter’s Law concerning the arrival of leap seconds. Hofstadter’s Law, formulated by computer scientist Douglas Hofstadter, says “It always takes longer than you expect, even when you take into account Hofstadter's Law.” Similarly, we can define the Law of Leap Seconds as “any future prediction related to the leap second is going to be disproven in an unexpected way, even if the predictor understands the Law of Leap Seconds.”

This was the case with the ITU’s decision in 2015, the surprisingly early leap second in 2016, the surprising lack of any leap seconds from then onward, and now the CGPM’s decision one year earlier than planned.

It’s been several years since I last posted here and I wanted to give an update on how things have been going with leap seconds.

First of all, the most surprising development is that no leap seconds have happened since 2016. This is not something anyone could have predicted until just a few years ago; the most recent leap second before 2016 was in 2015, and it looked like the frequency was increasing again after decreasing in the 2000s.

What is even more surprising is that around 2020, the graph showing the offset between the earth’s rotation and UTC (you know the one) actually began turning around so that not only are times between leap seconds getting longer, but individual days are on average lasting less than 86400 seconds. If this trend continues, we may need to add a negative leap second. It would be the first time in history one has been added, and it would involve the clock going from 23:59:58 to 00:00:00. In terms of excitement, a negative leap second doesn’t produce a particular time to celebrate so it isn’t as celebration-inducing as a positive leap second in that regard. On the other hand, a negative leap second may literally be a once-in-a-lifetime event, and so hopefully we can agree that if it happens, it is much more exciting despite there not being a “traditional” way to celebrate the lack of an event.

This all is happening because the earth has been spinning unprecedentedly fast; in fact, June 29, 2022 was the shortest day since day length was first measured in the 1960s (wait, then what is this graph measuring in the 1600s?).

Who knew the world could spin so fast? I didn’t.

I guess that song was really about leap seconds.

Remember though, the ITU World Radio Conference will be meeting to decide the fate of leap seconds in 2023 after they were unable to reach a conclusion in 2015. 7 years ago, I didn’t expect the 2023 debate to be nearly as suspenseful for me as the 2015 debate for two reasons: (1) another leap second would almost certainly have happened by then and (2) they’ve been trying and failing to decide the fate of the leap second since 2005. But lately public criticism of the leap second has been growing, with a number of tech companies calling to put an end to leap seconds, including Meta, Google, Microsoft (which are all hellbent on invading their users’ privacy), and Amazon (which is infamous for its terrible working conditions).

At the current rate, it seems unlikely that the difference between UTC and earth rotation will reach +/- 0.9 seconds before the end of 2023. If the leap second gets abolished next year... well, it looks like that one leap second in 2016, formerly considered a miracle, is the only thing preventing me from being as anxious this time around.

We still don’t know exactly when in 2023 the next meeting will take place, but it will apparently be late in the year according to this source. More interestingly though, the same source says that due to slow bureaucracy it may be several years after the vote that any action to abolish the leap second takes place. I never knew this! All this time, I thought the 2015 debate would lead to immediate removal of the leap second if it passed. Maybe we will see another leap second after all.

Here’s another graph similar to this one. It shows the difference between universal time (presumably without leap seconds) and terrestrial time, which is defined by the earth’s rotation. What’s really interesting about it is just how far it goes back. I have no idea how they were able to measure changes in the length of the solar day that accurately back in the 1600s.

https://soundcloud.com/planet-groucho-records/takitaro-the-leap-second-song-by-fjord-kduggan

https://www.youtube.com/watch?v=0afg9-38GZ0

https://soundcloud.com/hallelujahthehills/leap-second-song

I would never do anything but celebrate it.

(I’ll probably also do other things, like watch “spend your leap second here” videos, but that will be on other seconds of the day.

Also, the article says:

...in 2016, the world will be “gifted” a leap second.

Surprisingly few songs have been written about the leap second. This was the only one I could find that was more than a few seconds long. It’s a nice piano piece by Leo Sestili to listen to when you want to do some quick activities 5 minutes before the leap second.

Also, for people living in Iceland, Ireland, the UK, Portugal, Morocco, Mauritania, Mali, Senegal, Gambia, Guinea-Bissau, Guinea, Sierra Leone, Liberia, Burkina Faso, Cote d’Ivoire, Ghana, and Togo the leap second will be the last second of the year! Just imagine their surprise if their New Years party will consist of watching the time on a UTC-synchronized clock!!!

Oh well, at least they’ll be informed.

Just a reminder, the leap second will only come on December 31 if you live west of Greenwich. Otherwise it will come on January 1.

And if you live in Eucla, Chatham Islands, or Nepal, you can enjoy a unique occurrence of a second added 45 minutes into the hour.

This graph is from the Wikipedia article “leap second”. It is a PNG version of an SVG graphic that plots the deviation of the solar day length from the SI day (86400 seconds) against the absolute time t measured in years. If you want to study it, I suggest you use the original SVG version here.

The gray line, let’s call it gray(t), is the difference, measured in milliseconds on the left side of the chart, between the solar day and the SI day throughout the year. The green line, green(t), is the average of gray(t) over a 365-day long period centered at t. And the red line, red(t), is the accumulation of the total deviation per day, with the beginning of 1972 normalized to 0, measured in seconds on the right side of the chart. The formula for red(t) is ∫(gray(x)*dx/1 day), where x goes from 1972 to t. (I know that it is gray(t) and not green(t) that gets integrated by the way the high values of gray(t) at the endpoints of the years get matched by slightly faster risings in red(t); in the SVG this can be seen if you look closely.)

The points near the red line represent leap seconds inserted into UTC. Each point has a height on the graph which corresponds to the total offset of UTC time, due to the addition of leap seconds, from how it was at the beginning of 1972, minus half a second.

Why are the dots always half a second below the actual offset? Because a leap second is added whenever the solar time is expected to be a half second ahead of UTC, not a whole second. Since UTC and solar time are supposed to be less than a half second apart in either direction, the ideal time to insert a leap second would be when solar time drags half a second behind UTC. If a leap second arrives before this ideal time, its point is above the red line; if it arrives after the ideal time, its point is below the red line. As you can see, the most recent leap seconds arrived after the ideal time. Even though this next leap second is coming way before I thought it would, it seems that it too will arrive before the ideal time.

This is the Reddit thread where I first found out about the new leap second. It was such big news that I immediately wrote the following in a document, which was acting like a diary:

---10:26 PM---

I just found out something amazing. I mean MONUMENTAL. I just wish I had been more ready for it. But I suppose I am okay as it is.

It's still sinking in. It's now 10:27 PM on July 6, 2016 according to Windows's unreliable clock.

Leap seconds sound like the type of event that there could be a lot of misconceptions about (being an event which is occasionally talked about in mainstream culture but not nearly enough for people to completely understand it), and in fact on the Reddit thread there are many people saying things about the leap second that are inaccurate.

I think the most common misconception about leap seconds is that wherever you are, they will always be added right before midnight. In fact, they always occur at midnight UTC. In the case of the next leap second, this can occur from 12:00 PM on December 31 to 2:00 PM on January 1, 2017. I hope that any Redditors who plan to watch the leap second happen will use a clock site that tells them this.

Other things I saw in the comments were people saying:

that it took forever for leap seconds to happen (they actually happen once every few years),

that leap seconds are added to align the rotation of the earth with its revolution around the sun (they are actually added to align Earth’s rotation with normally 86400-second days),

and a link to a Wikipedia article that said that in 50000 years “under the present-day timekeeping system” a leap second would have to be added every day (actually, under the current system leap seconds can only be added to June 30 or December 31 UTC, so there would be about 183 added at once every time those days came around).