When Does the Decade End?

I have seen this question asked (or its fraternal twin, “when does the new decade begin”) in a number of places, and my response is this:

That’s a lousy way to phrase the question.


I will remind folks that I work at the Naval Observatory, but this blog in no way represents the official position of USNO. That said, I am one of the people who might be consulted on such a question, if it were difficult to figure out. But it wouldn’t get that far. This is not a “math is hard” subject.

The question is ambiguous, which is why it’s a lousy way to ask it. There is no “the decade” because there are a number of ways to label decades. A decade is a period of 10 years. 2010-2019 is a decade (we would call that the 2010s), as is 2011-2020 (the 202nd decade). The latter is based on numbering the decades, as we tend to do with centuries and millennia, which started with the year 1. The former is a count of an interval, which is a perfectly cromulent way to keep track of things —if we have a meeting on Wednesday and we say “see you in a week” we start counting from that point, not from Sunday (the equivalent of starting at 1). We can use time labels as an interval. We do it all the time. Almost nobody gets confused by this.

Which means the immediate response to the question in the title should be “to which decade are you referring?”  Without that clarification, you get the mess that I’ve been seeing. People assuming one protocol, and, what’s worse, denying that there is another. Instead they blindly point to an authority they claim will back them up, citing the Naval Observatory and the Farmer’s Almanac, except…

The few people who have provided a link sent me to discussions of when the 2nd millennium/20th century ended; some are leftover from these discussions from 20 years ago. Nothing about decades. No discussion of intervals, because when the 2nd millennium/20th century ended has already defined the discussion in a way that “the decade” has not.

The Farmer’s Almanac citation may be from this NPR piece

We ran a story several years ago. In fact, you know, remember the big celebration in 1999. People thought that the new millennial (sic) was going to start the next year. But really, a decade begins actually with the year ending in the numeral one. There was never a year zero. So when we started counting time way back when, it goes one through 10. So a decade is 10 years.

See the problem? It starts with the millennium discussion and applies it. That last sentence — a decade is 10 years — is true and has nothing to do with the bit that preceded it. The fact that there was no year zero has nothing to do with using decade as an interval of time.

NPR does better here

…the definition of a decade is just any 10-year span. Where it begins is fairly arbitrary, in their view.

Rick Fienberg of the American Astronomical Society says he doesn’t think his group has adopted an official position on the matter — but he adds, “History is clear: Because there was no Year Zero, the first decade of the common era (CE or AD) was years 1 to 10, the second decade was years 11 to 20, and the next decade will be years 2021 to 2030.”

Part of the issue, he and others say, is our use of “decade” as a frame of cultural reference.

“The reason people get confused is because we tend to think of decades as ‘the 20s’ or ‘the 30s,’ Fienberg says. “It’s true that ‘the 20s’ — that is, the period 2020 to 2029 — is a decade, i.e., 10 years

Fienberg lays out both cases for you.

The biggest mistake in all of this is people saying that the teens (2010s) don’t end for another year. They have taken both conventions and mashed them together into a horrible, horrible mess. You can talk about the 2010s decade, which ends (as I write this) tonight, and you can talk about the 2nd decade of the third millennium (or any similar numbering convention) which started in 2011 and doesn’t end for another year.

If the US founding fathers had settled on 5-year terms for presidents, it’s quite likely that we in the US would be referring to presidential decades for two-term presidents. Since Washington was sworn in in 1789, we would have these decades for two-termers starting on 9s and 4s (since not all presidents served two terms). And maybe there would be slightly less confusion about such a relatively simple concept.


Pick one convention or the other, as appropriate, and be consistent. Recognize that the other convention exists. And ask better questions.


This is the Hardest Job a Manager Has …

… but … the organization’s decided to make a change.

I’m here to not apologize for my recent absence. I started blogging a little over 7 years ago; tried it, liked it, and kept going. I had no really clear plan other than I’d do it as long as I was enjoying it.

Lately, I’m not enjoying it. (I think the technical term for it is “being in a funk”). So I’m taking a break. (It’s not you, it’s me. Continue to see other blogs. We were never exclusive)

This isn’t the first time in a funk — motivation wanes and waxes. Each time I eventually found something interesting to blog about, and posting links filled the gaps. Even as things slowed down over time — I went from multiple posts pretty much every day to eventually one post on most weekdays. In the past several years I had a pick-me-up this time of year in the form of the Science Online conference. Getting to see friends and meeting new people was a lot of fun, and there were always new things discussed in the sessions that rejuvenated me. But the organization folded last year, which is a long story, but the result is that there is no conference (which should have been happening this very week). No salvation there. It’s gotten tiresome slogging through feeds and lists looking for interesting things, and my normal fallback — ranting about bad physics reporting — just feels like it’s all been done.

There are bloggers out there who have done this longer, but I think most have not (heavily skewed by a large infant mortality rate). I expect I’ll return — someday — but if and when that happens there are no guarantees as to the frequency of my posting. We will see.

5 Things You Should Know About Light

5 Things Every Human Should Know About Light


All of these are electromagnetic waves and they all travel at the same speed (the speed of light). However, they have different interactions with matter. If you are inside, your mobile phone can still get data from a cell tower since these radio waves pass through most walls. Can you see through the walls? No. Visible light does not pass through most walls. X-rays mostly go through your skin, but you can’t see (with visible light) through skin – that would just be weird.

Technically the interaction with light and matter depends on the frequency of light – but since frequency and wavelength are related, we can just talk about the wavelength.

The System Works

Failure in real science is good – and different from phony controversies

Real scientific controversies play out in the scientific literature, through papers drawing on many other sources of data.

Phony controversies tend to play out in the media, through press releases, stump speeches, and polemical writing reshared via social media.

Somewhat related: something I wrote a while back. Each step along the way of doing the science increases your confidence, but ultimately what you need in any scientific finding is confirmation of a result.

Once the weight of experimental result hits a certain critical mass, the expectations swing away from needing data to confirm a theory to needing exceptional data to disprove it.

I'm Syndrome, Your Nemesis!

Stop Blowhard Syndrome

Understanding my limits and being willing to acknowledge them is, in fact, one of my strengths. I don’t think it should be pathologized alongside the very real problem of “impostor syndrome”.

In fact, it is the opposite behavior—the belief that you can do anything, including things you are blatantly not qualified for or straight up lying about—should be pathologized.

I Want to Say One Word to You. Just One Word: Plastics

Harriss spiral

The Harriss spiral is constructed from rectangles in the ratio of the plastic number (1.3247…), in a similar way to how a Fibonacci spiral is created from rectangles in the related golden ratio (1.6180…). These plastic rectangles can be split into two smaller plastic rectangles, leaving a square. Recursively splitting the rectangles, and drawing curves in the squares gives this fractal spiral.

Another Harriss spiral

It's Always Harder than You Think

An open letter to Gov. Scott Walker: stop perpetuating the myth of the lazy professor

When you say we should work harder, I hear two things: 1) we aren’t working hard, and 2) we don’t think we have to. Professors seem like an easy target. We have good job security, we’re paid well, we often come from privileged backgrounds. We appear to have little to do but teach a class for a few hours a week, and we have extended vacations. It’s easy to see us as cloistered in the Ivory Tower, without much experience with the “real world” and the concerns of average folks.

The picture I’ve painted for you is incomplete, though.

Why Are the Dwarves Seven?

Why Is Snow White?

The whiteness of newly fallen snow is, of course, one of its primary defining characteristics, so it’s tempting to just say that, you know, that’s the way snow is. But it’s actually a pretty good question, because snow is really just frozen water, and frozen water tends to be transparent

The Coin Paradox

The Coin Paradox

A teaser. For the setup, go to the link.

In each case the rolling coin has made one complete rotation. But the red arc at the top is half the length of the red line at the bottom. Why?

I have a more physics-y than a formal math-y explanation of why, which I will post soon.


OK, here’s my answer.

In the rolling case, all you have is rotation. On rotation gives you 2*pi, so it rolls one circumference.

But in the other case you have rotation and revolution (spin and also orbital motion). Going halfway around the coin gives you an equal contribution of each, so the amount of spin only requires pi rotation, and it rolls half of the circumference. If the coin’s point of contact never changed, it would still do a rotation over the course of its revolution. If the orientation stayed fixed, the point of contact would make a complete trip around the coin.

A related example of this is the moon. If viewed from an external inertial frame (where the distant stars appear to be fixed), the moon rotates around the earth every ~4 weeks. But since it’s tidally locked and always has the same part facing the earth, it also rotates once about its axis.