Leap Years: we can do better 

So glad the US were still a colony when that Gregorian Calendar change happened or we'd all have to convert between international dates and US dates.

Pope Gregory was probably thinking “by the time that happens humanity will have found a better way to keep track of time”

*The Parker Calendar* It's not quite perfect, but its very close..

As a leap year baby born on feb. 29, 2000, I have done my research, crunched numbers, and looked at many calendars, and have figured out similar information, but that last part of your equation was a good touch!

Alright, I'll buy a calendar in 3 million years. Gotta put that date on my... oh...

I would have preferred the 0th of March, that way we could all agree that - eventhough it's a day - it's not a day and we can collectively do nothing.

"One great thing about being a pope, I guess, is that you are good at getting a lot of people to change their behavior on seemingly arbitrary reasons." LMAO you right

Who’s here in 2020 when it’s a leap year again?

Even better than binary - write the years in hexadecimal. Then it's just whenever the year ends in 80 or 00.

I've always been in favor of a 13 month calendar. It has the benefit of keeping dates and days of the week synced until the very last day of the year. The first 12 months of the year have exactly 28 days each, making them multiples of the number of days in a week, so for the entire year, you would know that the 1st is always a monday, or that the 27th is always a saturday. The final month of the year has 29 days, so the first 28 are the same as the other months, and then it shifts by one, unless it is a leap year, in which case it has 30 days, and shifts by 2. So for example, in year 1, the first is always a monday. In fact, mondays are always either 1st, 8th, 15th, or 22nd. This trend continues throughout the year, until the final month, when there is also a monday which falls on the 29th. Then the next year starts, and your 1st, 8th, 15th, and 22nd's all fall on Tuesdays now. This might cause some confusion, if you were always used to an 8th being a monday, or a 13th being a saturday. Of course, this could be fixed by making the last one (or two) days of the 13th month a special vacation day, with no assigned week day name. A blank day (or two) if you will. This can significantly simplify scheduling various things, such as doctor appointments, school holidays, vacations, and work days. You'll never have to look up whether the 20th is a week day or not, as it is always a saturday, assuming the blank day is appropriated into this calendar system.

I did a bit of math on my own comparing this proposed calendar to the Gregorian calendar and found something interesting. If every 3200 years we skip a leap year, the calendars become exactly the same in terms of long term drift. Under the Gregorian calendar, we have 776 leap years every 3200 years, while this calendar has 775 in the same period.

Does it bother anyone else there are probably billions of people in this world who think a leap year is every 4 years, and have no idea that 1800, 1900, etc were NOT leap years?

How about altering the Earth's orbit to fit our calendar? Problem fixed!

looks like i gotta mark my calendar for 3.372 million years from now, for when I should buy -- ... another calendar. hmm

Matt Parker: the only person capable of turning the word "binary" into a punchline.

Now imagine that the perfect year with integer number of days turns out to be a leap year...

You and the rest of the numberphile crew have tangibly enriched my life.Thank you for this!

I was going to argue that Matt should have waited 5 days longer to release this video, so that it released on Feb 29. But then I remembered that Feb 24 is the actual leap day, and the remaining days of February just get pushed back.

Britain and its colonies were by no means the last to switch to the Gregorian Calendar. It took becoming defunct for the Russian Empire to switch to the Gregorian Calendar, adopted in 1918

Julius Caeser got it wrong initially, in his new calendar the leap years were every 3rd year. It took Augustus to fix this error and have leap years every 4th year (with the standard exceptions).

What a Parker Square of a system.

I don't believe you went all the way through the whole video without mentioning leap seconds.

Matt: We have to fix the calendar so it drifts every couple of trillion years Also Matt: Give or take a bit

Trivia question: How many Olympic Games have taken place in a non-leap year? Two: Paris 1900 (not a leap year) and Tokyo 2020 (took place in 2021)

I like to think that if the US hadn't switched to the Gregorian calendar before its independence they would still stick to it and defend it like they do with Imperial units.

"that's longer than the sun is gonna last... I think we have this sorted" haha touche

or alternatively, we keep the Gregorian calendar and add extra leap seconds to keep things in sync. Which is, coincidentally, what we are doing since 1972.

Caesar's fella's did a pretty decent job considering. They trusted future smart folks would be able to parse the date if it really mattered. Good on them. And you too pal.

Hearing a mathematician say "give or take a bit" will always crack me up.

So in the absence of a reliable long term answer to the ascribed problem, a series of short term solutions that change with the problem is the best solution.

Nobody: RU-vid in 2020: Since 2020 is a leap year I'll ignore the fact that you've already seen this video and put it in your recommendation section

"The optimal time to buy a calendar" 😂 I love your videos.

One year is 365.2421891 _years_ long ... (1:18).

"Tough luck says the Universe" - CGP Grey.

don't worry, Humanity isn't going to live another 3,216 years

8:54 "The Solar System itself is not so cut and dried" is the most Australian Matt has sounded for years.

At 1:22 he says 5 instead of 4

10:10 This is why I have not purchased ANY calendars and I await for that day, my friend.

So satisfying. As a software dev the first thing I thought when seeing 128 was „thats a nice number“. Glad he made a binary calculation for that heh

It is people like you that make me realize how little I have accomplished in life. Well done video. Educational yet entertaining.

4:40 shots fired

I'm not sure everyone will be on board with calling this the year 11111100000.

I have created my own calendar system called the Yamamoto Calendar. The Yamamoto calendar is the same as the Julian Calendar, except for the fact that there are four 5-year gaps in between XX40 and XX60 every century, and every 500 years we have a super leap year (that is, one where February has 30 days). This means that the years 2045, 2050, and 2055 are leap years instead of the years 2044, 2048, 2052, and 2056. This year (2021), the 21st of March (Gregorian) corresponds to the 1st of March (Yamamoto).

In 1712, in Sweden, February had 30 days. In Alaska, Friday October 6, 1867 was immediately followed by Friday, October 18, 1867.

A thief stole a calender once. He got 12 months.

I find it inappropriately funny when you mention that they both agree that it was Thursday. I can't quite explain why I find it so hilarious, but every time I think of it, I can't contain my giggle reflex.

I'd say the fact a day only increases by a little over a millisecond every century is a testament to the stability of the universe.

I like how he just kept going until he exceeded the Suns lifespan.

This is why we should change to the stardate system.

Your date for 'everyone' adopting the Gregorian calendar is rather Anglocentric. One must remember that the October Revolution started on November 7th, 1917.

I just love the fact that the error in Julian calendar just happens to be almost exactly a power of 2.

I think he means put back a leap day in a year that is a multiple of 625,024 (itself multiple of 128), not take it out. But that is truly a tiny quibble. The 128-year calendar is a great idea. But someone has pointed out that the same net result (a calendar year of 365.2421875 days) can be achieved by modifying our Gregorian calendar to omit the leap day every 3200 years (every 8th 400-year cycle).

You need to roll out the Parkerian calendar now. Don't wait.

I want this guy to be the next Doctor. He reminds me of a mashup of Ten and Eleven.

Parker: This calender is perfect People 5300000000000 years later: Huh we are off by 1 day? Who made this calender? Parker's great great great great ... great great grandson: **Rick Astley of 5300000002016 music plays**

I like how this video is actually very informative - and funny at the same time due to the extreme and very much intended nerdiness.

10:04 i think this video should've been titled "the optimal time to buy a calendar"

1:30 "365.25..." Either you or the video is wrong, I'm going with the assumption that post production Matt is more reliable.

I can't believe Pope Gregory pretty much Parker Squared the calendar. The 128 year fix is so much simpler and is 2 orders of magnitude more accurate than what we got.

Since 1972 we have had a total of 27 leap seconds. They are fixing this, just not in a very structured manner.

sounds good, but if we get around to space travel in the next 90,000 years then im betting the Gregorian Calendar will become obsolete

This power of 2 stuff would make this calendar very intuitive to computers. In a way, the calendars are already stored in binary, so switching to every 128 years would only mean changing a setting in your smartphone.

I don't know how anyone could watch this and not be excited about math. Which probably says a lot more about me than other people.

In the distant future... Mathematicians are wondering if the year 11825792 is a leap year. By the Julian Calendar, it is as it is a multiple of 4. By the Parker Calender... they cant decide, until they write it in binary to: 101101000111001010000000 and realise it shouldn't be a leap year! until they realise it has deviated by 129 days at this point, and they need to redesign another calender.

4:38 There have been others, if I recall, with enough persuasive power to get people to change their minds about seemingly arbitrary things. Henry VIII, for one, comes to mind. Henry persuaded the English population that it made sense for him to be the pope of England. Henry also revised the theory of divorce, whereby one may lop off the head of one's spouse if one is in the mood, provided you are the pope of England. Previously, people had the opinion that made you a homicidal maniac. Henry was persuasive.

Hi there! Nice video. Just an info about calendar drifting: Russia did not adopt the Gregorian Calendar until the sovietic revolution; the result was that the "October Revolution" (as for russian/julian calendar) actually took place in November (as for the gregorian calendar)!

Yeah, I figured it out by myself the same way the guy at the end did: with continued fractions. they are particularly useful for finding the periodicity of the corrections if you want to make the most precise system.

One nice feature of the Gregorian leap cycle is that its 146097 days equal exactly 20871 weeks. Many other cycles, including 128 years, lack this property. 293 years with 71 leap days does work, but would require a more complicated, but potentially also better distributing leap rule.

So Parker has this sorted..............but not quite. PARKER SQUARE BLAST FROM THE PAST

Matt, you missed the best thing about leap time; leap seconds! There is no formula for calculating how many leap seconds there are. They are arbitrarily given out by the leap year wizard who sits atop his magical leap year throne ( we currently have 17 leap seconds). The only rule for leap seconds is that they are either given out in June or December. If you chose to ignore leap seconds because you think the leap second wizard is silly, you will never be able to accurately navigate using GPS.

Sounds like the Gregorian calendar was a real Parker Square of a solution. Glad to see the Parker Calendar o̶v̶e̶r̶-̶e̶n̶g̶i̶n̶e̶e̶r̶i̶n̶g̶ fixing the issue.

I LOVE IT! I love messing with calendars, years, months, weeks and days! Have you ever thought about creating a binary week? (i.e. a week being 4 days long or 8 days long?) We already have a semi-binary calendar with seasons involved. What would a full binary calendar look like? Thoughts?

It would be fun if that one year where the actually year is 365 days was a leap year with the current calendar. If that makes sense.

We're gonna party like it's 2048! To the power of two, even - it''s a digital blast! (New Prince song above)

You know you're in deep with math nerds when they say "it's easier to understand in binary." Good thing I'm a math nerd!

I found out that with the super accurate calendar, there are 15 years every 10,000,000 years that have not only a February 29th, but also a February 30th, which means that they are quote-unquote “double-leap-day years,” where every year that is a multiple of 625,000, but not a multiple of 10,000,000, has two extra days in themselves.

1:22 - screen says ".24" - you say "point two FIVE" :P

So what your saying is that rather than fixing the calendar, it's actually the solar system that needs fixing?

The disparity counter starts at 0 at Year 1. Every year we add 0.24219 to the disparity counter, unless it is above 1. In the case described above, we instead subtract 0.75781 and have a leap year. Solved.

I hope the world will adopt your calendar

From 1:21 to 1:27 is a double epicfail! XD Seriously though, your videos are a really good thing for this world.

Who's still watching this in 2048?

As a person born on the 29th February, I'm grateful to be here around the year 2000, as opposed to the non-leap 1900

**Standsupmaths wakes up from a coma ** Nurse - Sir, do you know what year it is?

How can you honestly say people are not going to want to apply your calendar idea during the power of two year (2048)? Dude, it's the 128-rule, aka the 2^7 rule. The power of two year is EXACTLY the right time to advocate for switching to a power-of-two calendar (2^2 - leap, 2^7 - no leap). As a CS graduate, I find the modified Julian calendar A LOT prettier to look at than the 4/100/400 mess.

They do have these leap seconds every so often. Is that to correct the length of a day?

This video has inspired me to use a "every 4 unless it's divisible by 128" calendar in a bit of fantastical fiction I'm writing. Maybe I should include some folks grumbling how it's not *quite* accurate enough to their tastes...

Im so sad that i wont be alive long enough to flex this knowledge

13 months of 28 days each=364 days, add one day at the end, call it "World Party Day" or something. Every four years, add a second day at the end of the year, and voila! problem solved.

So who's up for a global party starting at 2:22 am on the 2nd of Febuary, 2048!!! ^___^ Wohoo, AMIRITE?!

Thanks. I was just about to go to the store and pick up a calendar, but after watching this video I decided to wait. Gotta catch that optimum time slot!

I’m, personally, waiting for the time, when we get the exact mathematical year of 360 days.

I would pay money for a full version of the song used at 10:40

It is strange that you didn’t mention the Milanković calendar which is also known as the revised Julian calendar. It is a very accurate calendar which is actually used by the Orthodox Church referring to it as “the new calendar”.

Things I never expected in life: listening to a mathematician talking about leap years and being facinated by it.

A calendar that to drift takes longer than the total lifetime of the Sun. Brilliant.

But what if that moment of an integer number of days in a year falls during a leap year?

Why didn't you wait 5 days to post this :(

Sometimes I think that due to this inconsistency the seasons have already drifted at least one month. At least according to the weather.

Thank you. This video showed an incredible revelation. Mathematics is the tool in solving many problems, but there's more yet to come with this resolution. I don't know what it is but I'm all ears. Pi rules! Pi could be the universal language, as infinite as it is.