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.

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

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

"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

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.

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

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!

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

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

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.

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

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

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 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.

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.

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

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

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

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

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.

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

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.

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

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.

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)

Nobody: KZfaq 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

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.

At 1:22 he says 5 instead of 4

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

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

"Tough luck says the Universe" - CGP Grey.

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

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 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).

4:40 shots fired

This is why we should change to the stardate system.

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

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

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.

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

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).

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"

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.

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.

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

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

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.

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

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.

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

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

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?

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)!

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.

Ha. Nice. This reminds me that when I wrote my first science fiction novel I worked out a calendar that included when and how to add leap days. Lots of fun that probably no one else even noticed. Took a while to work out and it occupied a brief paragraph in the appendix.

You're just awesome Matt! Keep it up!

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

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.

Love the continued fraction approach

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

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

My Dad was in favour of making 1 day a year or 2 days in a leap year to not be days of the week - then the calendars for every year would have the dates on the same days of the week so you don't have to change them apart from sometimes adding that 2nd 'unnamed' day. I'm glad you mentioned how variations in the Earth's rotation changes the length of the day - and the orbit changes... I suppose the sun's mass changes over time changing the orbital periods of all the planets -then there's all the precession effects as well moving the equinoxes (seasonal year points) around in about 26,000 years - and that might change. The last data I looked up had the tropical year as 365.2421909 [mean solar] days, so I've been using that as the most accurate. If the mean solar day is fixed as 24 hours, then as the rotation (sidereal day) changes and the year changes, the mean solar day actual time changes so the definition of hours, minutes and seconds will change. If the day length is increasing slightly, then we are aging more per day when we are older than we did when we were younger!! No wonder the days seem to go by faster. !! If we measure light years by calendar years that might change over time too, just as parsec distance would change if the Earth's orbital distance changes. If the fraction of day left over in the number of days in a seasonal year was closer to 1 than 0, wouldn't we have 'skip days' instead of 'leap days'? I mean for example if it was 364.75 days we would have years of 365 days 3 years in 4 and one skip day is 'skipped' in the skip year!! At least that's how the calendar works on my imaginary planet...! They have skip years with one fewer 'celebration day' or whatever you call those extra days that could be left out of some years. I haven't yet worked out or thought about how their calendar year length changes over very long timescales. I don't think it matters over a few centuries or a few millennia!

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

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

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

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.

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**

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

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

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

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

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

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

03:25 - Actually, when Gregory introduced the new calendar, the Julian calendar was 12 days off. However, Gregory wanted the solstices and equinoxes to fall on the same day of the year they did in the year 325, when the Council of Nicaea was held; by this time, the Julian calendar had already lost two days, and so the date only jumped forward 10 days. This is why, if you trace things back, 1 January 1 in the Gregorian calendar is two days after 1 January 1 in the Julian calendar. The Gregorian calendar is impressively accurate, but 500 years before him, Omar Khayyam and colleagues came up with a better one. In Khayyam's calendar, known as the Jalali calendar after sultan Jalaluddin Malik-Shah I of Iran, who introduced it. In the Jalali calendar, years are arranged in 33-year cycles, in which the fifth year and every fourth year thereafter are leap years. The Jalali calendar is accurate to one day in 5,000 years, which is better than the Gregorian's 3,216 years. The Jalali calendar was used in Iran and Afghanistan until 1925, when it was replaced with the Solar Hijri calendar. This calendar, by design, cannot possibly drift, because there is no algorithmic scheme for leap years. Instead, New Year's Day falls on the day whose midnight is closest to the moment the centre of the north ascendant sun crosses the celestial equator; yes, the calendar is observation-based. New Year's Day can be reasonably predicted, but still has to be officially announced rather than calculated arbitrarily far back in time.

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.

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.

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

Ive always wanted to know the optimal time to buy a calendar. Setting a reminder on my phone for 3 million 372 thousand years from now. Cheers mate!

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...

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.

11:35 you make it sound like we want the video to be over

Calander Unboxing videos? Binary based Calanders? I can't wait for that spinoff from the calculator series

Actually in all of that the thing that really gets me is the precision of year length measurement especially back in the days (years? Epochs? You name it). Like, you can not just stick a pin into a fabric of space-time and next year be like «Oh, we reached a pin, stop the timer». If last year there were -15°C on 1st of March and now it's +1°C, there's no way on God's green earth I can tell that exactly one year has passed. And people without any complicated tools were like: «Oh, yeah, it's easy, it's 365.2425 days. Approximately.». That absolutely boggles my brain every time I'm thinking about it.

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

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

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.

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.

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

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

Read about the (unpredictable) leap-second to understand why Gregorian calendar is good enough in accuracy. 27 leap-seconds have been added so far since 1972.

The digits you were saying and what is on the video do not agree at about 1:22 in. I'm guessing it's okay to be a touch pedant in a situation where we're taking things out to seven decimals. Other than that nearly microscopic nit I just picked, this was excellent and will be fun to ponder later. Is there any way to do a rough estimate on the scale of the "irregular drift" part of things,, assuming no rogue gas giants go wandering through our solar system? Would a calendar reform good for over 100 thousand or 600 thousand years be worth doing? And what about the leap seconds we kick into our clocks here and there? Is that going to negate the need for the reforms you discussed?

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”.

Or we could just accept that a date is nothing but a label. And accept the drift. It really doesn't matter whether winter starts in june or december.

YES!!! Someone else who talks about their past self. I'll get to a soda in the fridge, or pack of candy in the cabinet that I had placed there to enjoy at a future date with the announcement, "There ya go, future Mark, hope you enjoy!" and forget it... Once I stumble back onto my 'treasure' this version of Mark often times states aloud, "Thanks past Mark!" every so often with the reply, "No prob. Mark, I got our back!".

OMG...this video is full of so much nerd!!!...I can share with only one or two of my friends :'( Mr. Parker you are the best.