Leap Years: we can do better

2016 is a leap year because it is a multiple of 4 (and not a multiple of 100). The Gregorian Calendar system of leap years gives an average tropical year of 365.2425 days compared to the current true value of 365.2421891, but I think we can do better.
Yes, at the 1:20-ish point it should be "365.2421891 days" as is on the screen, not the "365.2521891 years" I say. Sorry, it's been a busy week and I recored and edited the video a bit too quickly to spot Past Matt's mistakes.
Read Adam Goucher's article here:
cp4space.wordp...
Music by Howard Carter
Design by Simon Wright
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
Book: makeanddo4D.com/
Nerdy maths toys: mathsgear.co.uk/

[@unvergebeneid]

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.

[@standupmaths]

This is almost too true to be funny.

[@DanDart]

+Penny Lane They *sometimes* listen to standards. Not often I'll admit.

[@DanDart]

+Leonardo Cisija that's what I meant by "not often" yeah :p

[@unvergebeneid]

Dan Dart Huh ... I'm not saying you're wrong but I really have a hard time thinking of an example. I mean in an area where the general public is concerned, not some obscure and purely technical ISO standard. UTF-8 maybe but that's compatible with ASCII so I don't think it really counts.

[@DanDart]

+Penny Lane that they're still using the imperial system?

[@deldarel]

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

[@YamamotoTV2021]

Lol first reply I find that funny…

[@YamamotoTV2021]

Also, 117 is the telephone number for the time-broadcasting service in Japan, which they call the _jihō._

[@emirhannecip3258]

Best comment!

[@ilickcatnip]

Cracked me up 😂

[@MilanMilan0000]

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

[@brycebenz5902]

#ParkerCirle

[@david82633]

* #Parkersquare

[@mgsquared5204]

;snop170 there’s a Parker square and a Parker circle. The Parker square came a lot earlier.

[@partynhouse]

Carrot Slice you should check persian/solar hijri calendar

[@otesunki]

Classic Parker Square.

[@QuarioQuario54321]

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

[@pedronunes3063]

Or maybe: "I'd be okay with a week off after 15000 years." That's basically for how much time humanity has existed.

[@acmenipponair]

Or perhabs they noticed, that the earth is becoming slower. I mean, yes, it's only seconds, but we are talking about astrophysics, who only from the movement of the planets accounted that there must be more planets than six... And that displacements were tiny. So perhabs they recognized, that the earth time is not 100% stable and therefore in some thousand years it don't matter anymore

[@qgde3rty8uiojh90]

"...or the rapture will have happened..." 😇

[@pappagamingpoo9766]

@@pedronunes3063 No much longer than that

[@AB-wf8ek]

@@pedronunes3063 Humanity has been around for at least 200,000 years

[@nolansprojects2840]

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!

[@Macrotrophy-mq3wh]

1 in 400 year chance lol

[@flikkie72]

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.

[@kcuhc84]

Agreed, except if you have to be sworn in to office or something like that, it could be reserved for oath day.

[@Patrick94GSR]

Babies born on the 0th? lol a zero day birthday. :-P

[@内田ガネーシュ]

Donuts Dooonuuutttssss!!!!!

[@yashgaikwad7516]

It's a Parker square of a day

[@rafaelrafaelrafael]

@@Patrick94GSR it's a no labour day.

[@dan339dan]

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

[@eveeeon341]

+TheCheungDan Sounds like a very religious way to go about it, and very fitting for our Gregorian calendar.

[@Pattonator14]

+TheCheungDan I'm sure if we did the "everyone in China jump at once" thing we could work out how to adjust our orbit

[@robsbackyardastrophotograp8885]

+Smokestacks actually, if we moved closer, we'd speed up to balance ourselves again, same thing but with slowing if we backed out

[@Pattonator14]

Agustas Stephaunzz you'd just have to get people to keep doing it then ;)

[@dan339dan]

Smokestacks Nope, when you fall down, the process reverts. But everyone walk east or west will do. It has to do with rotational force.

[@reeper147]

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.

[@g.seangourlay2593]

reeper147 I like this calendar, but only if you keep the blank day. and keep the year regular. is it your creation? my personal calendar skips Saturdays, leaving a six day week, with the 1st on a Sunday and the 30th on a Friday with 5 weeks a month, 60 weeks per year, and 5 or 6 saturdays reintroduced on the 31st of every other month, so you have a built in 3 day weekend every other month or so.

[@g.seangourlay2593]

I call it the gordonian regular calendar.

[@reeper147]

I'm not sure if I am the only one who thought of it, I am sure someone else noticed that 365 is divisible by 13 with just a remainder of 1. But I came up with the idea independently, for what it is worth. I like yours too, both are better solutions than what we have now. The two main reasons I advocate for my calendar is 1) The fact that you will always know what day of the week a date is, and 2) Each month has the same number of days. No using your knuckles to check and see if the month has 28, 30, or 31 days. My only question about your calendar, is how you handle February. Do you just treat it like a regular month that ends early?

[@g.seangourlay2593]

February has a 31st day only on leap years. May June august October December always have a 31st.

[@sabinrawr]

The "blank day" has been thought of before, and I'm personally a fan of it. However, there will be a great deal of religious opposition, as many monotheistic faiths consider the unbroken 7-day cycle to be central to their belief system. In order for the "blank day" to work, each year the churches, synagogues, mosques, and temples would have to shift their holy day of rest back one day to account for the shift. Every seven years, the blank day will be a holy day.

[@Blackbird74733]

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.

[@sk8rdman]

His 2800 year rule only works because he ignores any digits beyond the 4th. All it does is takes out 3 leap years every 10,000 years, so if we could apply it to the multiples of any multiple of 4 years that is less than 3333 (1/3 of 10k years), but greater than 2500 (1/4 of 10k years) and it will work just the same. You just have to be careful that the number you use is not a multiple of 100 unless it's also a multiple of 400. Using multiples of 400 gets around this problem, which is what both you and Matt did with 2800 and 3200, but even though it looks the nicest and is easiest to memorize, there's no mathematical reason why it needs to be a multiple of 400. There are no multiples of 4 which can multiply by 2 or 3 to get another multiple of 100, so any other multiple of 4 (that is not a multiple of 100) between 2500 and 3333 will work equally well with this rule. Personally, I prefer your 3200 rule because it means that the removed leap years are more evenly spaced over the course of any given 10,000 year period.

[@funnymyth1827]

"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

[@98cents]

Very few people would take him that serious nowadays. He might spur a world convention to discuss problems, but outright demanding others to comply would be pretty insulting to a lot of nations, and only the most devout, such as Italy (mainly because the Vatican is... in Italy), would give it any credence.

[@yourpalpalmetto979]

The pope is still pretty influencial, a potential war between Argentina and Chile was stopped because of him in the 1980s, pretty good imo.

[@aarontt]

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

[@jacksainthill8974]

+Aaron Traynor And when they don't, add FA.

[@3Ppaatt]

+Aaron Traynor But every four years is every time the year ends in 0,4,8, or B, which is too much to remember.

[@jacksainthill8974]

Ppaatt Er - B is eleven; C is twelve.

[@aarontt]

+Ppaatt why is that any more difficult than remembering 0, 4, 8, 12, and 16?

[@jacksainthill8974]

Aaron Traynor No need to remember a digit for sixteen, because there won't be one. In hexadecimal, a sixteen-multiple terminates in '0', which you had already listed.

[@SoulSukkur]

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

[@fishandchips8813]

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

[@standupmaths]

Our pleasure! Thanks for watching the videos.

[@christinam2805]

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

[@kpaasial]

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).

[@ethanfrank670]

I think it was the priests who misinterpreted what his calendar was, not caesar himself, because of the confusing way romans talked about numbers

[@feynstein1004]

I was looking for this comment lol

[@andyswales3516]

What a Parker Square of a system.

[@matrix9083]

lol good one

[@AirIUnderwater]

How dare you!? xD

[@vincentwilliamrodriguez3572]

Hahaha. nice pfp btw

[@ryantaylor8421]

365th like, how apropos

[@aviralaryal7332]

your comment has 365 likes

[@Boba0514]

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

[@joelsmemes4140]

Internal screaming

[@ahlpym]

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.

[@blue_leader_5756]

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

[@leomoran142]

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

[@mamamheus7751]

Which is why some historians talk about the October/November and February/March revolutions. One month being the Russian date, the other being the Gregorian. I have to stop and try to remember which is which lol

[@XenophonSoulis]

Greece in 1925 I think.

[@696190]

And China in 1949. Plenty of religions and denominations still follow older calendars

[@XenophonSoulis]

@@696190 Israel has found the best solution so far. They are not christians, so there is no point in saying BC and AD, so they use Common Era and Before Common Era, but the years are the same. As an atheist, I can tell that this solution is perfect.

[@jshariff786]

@@XenophonSoulis Merely changing notation doesn't solve the problem at hand -- you're still using the exact same calendar. The problem at hand is that the tropical year is not an integer number of days. Try to keep up.

[@amandaperez3238]

At 1:22 he says 5 instead of 4

[@nevertrustanatom1486]

And he says years instead of days, who cares.

[@connortremblay1259]

a real parker square of word choice that is

[@joelshewmaker3567]

My policy is that if you can still understand his meaning clearly, then it's fine. Not everyone can be perfect. :p

[@brycebenz5902]

And ONE year is apparently 365.242 YEARS long. Well if you say so... ( He says years instead of days)

[@lyrimetacurl0]

It's a Parker 5.

[@Jimpozcan]

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

[@MasterHackerChannel]

Years?

[@Kazmomusic]

+jimpozcaner He dun goofed, what ever. He also said .2[5]2, but who cares :)

[@Jimpozcan]

Mat Kaz I don'T _care_, just pointing his goof out.

[@gasparRaduB]

+Mat Kaz i was looking for this

[@freebite]

+Gaspar Radu Yup didn't wanna repost it if someone already did.

[@doriancostley9075]

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.

[@codys2018]

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.

[@jimdecamp7204]

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

[@forthehunt3335]

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

[@Macconator2010]

"Tough luck says the Universe" - CGP Grey.

[@stevethea5250]

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[@IamGrimalkin]

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

[@standupmaths]

Leap seconds fix a different problem. So as much as I love talking about them, I thought I'd leave them out to keep the video simple.

[@alexcalafuri9201]

What are leap seconds ?

[@stevewood8914]

+Meatloaf Lammer The amount of time it takes for the Earth to spin isn't exactly 24 hours so clocks are getting slowly out of sync with the day/night cycle. Or they would be if it weren't for leap seconds. They are extra seconds added to a day on average once every 18 months (it varies) either on the end of June or December. On these days the last second before midnight is 23:59.60.

[@2Cerealbox]

+Meatloaf Lammer That's a correction you have to add because the Earth's orbit around the sun is not 100% predictable. They're more or less random and have to be added in arbitrarily causing massive headaches for programmers.

[@UlyssesKrunk]

+standupmaths I hope you know this means you now need to make a leap second video.

[@ahmedsyed7241]

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

[@ChristianFS1]

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

[@javierbg1995]

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.

[@SkyrimHod]

+javierbg1995 Not likely. The main reasons the US sticks with imperial units are: 1. It's hard to get everyone to start thinking in the new unit system. Even if people know how to convert between the two, they still start off thinking in feet and then have to figure out how many meters it is. It would only be after a long time of using metric that people would start automatically thinking that way. 2. It would cost a lot of money to switch over all the existing tools, equipment, signs etc,. Neither of those really apply to switching calendars. 1.The years would still be the exact same except for the question of when to have a leap year or not and that would only be an issue at all once every 4 years, not every time you wanted to measure anything. 2. New calendars are printed every year anyway, so it wouldn't cost anything extra to switch to the new ones instead.

[@jangxx]

+SkyrimHod The same is true for every other country that switched (which happens to be almost every country there is) and it worked out for them.

[@8ytan]

+javierbg1995 The US uses metric for most important things anyway.

[@Poldovico]

+SkyrimHod Well, switching to metric was "hard" (but actually not that hard at all) for every other country, but really all it takes is to start teaching both systems at school which will let children understand how much simpler it is to do unit conversion in metric, and then switch to metric only on the next generation. Give it less than a century and you're done.

[@kat369-mine]

Damn straight. It's our God given right to say "F#%& You to the rest of the world if we want to.

[@kennethflorek8532]

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.

[@PopeLando]

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)

[@ChicagoSkyliners]

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

[@pmnt_]

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.

[@limepop340]

just you wait until politicians seize control of leap seconds and start adding/removing them for their own gain

[@jshariff786]

Leap seconds are solving a *different* problem...which is that a day is not a consistent number of SI seconds, due to the variability and slowing of Earth's rotation. Matt is talking about the problem that a tropical year is not an integer number of days...which is the problem that the intercalations of the Gregorian calendar try to solve (albeit imperfectly). This is still the only solution we have to this day.

[@shirou9790]

Exactly what jtron84 said. The goal of leap seconds is to do so that the average solar noon stays at noon (that is, on Greenwich meridian in UTC: the difference between the timezone you are in and your actual longitude* might add a delay but this delay will stay consistent). The thing is that a tropical year isn't a whole number of mean solar days, so you have to make a different correction for that problem (and this is what leap days are about). If you say that you'll divide the tropical year exactly into 365 days no matter what, you might get inconsistencies along the lines of having noon during the night and midnight during the day--because your day defined as 1/365 of the tropical year does not have the correct length. The day/night cycle and the cycle of seasons are two independent cycles hence the two independent corrections

[@Anonymous-df8it]

@@jshariff786 Isn't a second *_defined_* as 1/86400 of a day?!

[@TheMoonRover]

@@Anonymous-df8it Historically, yes. However the modern definition comes from defining the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom to be 9 192 631 770 Hz.

[@AJGoff110]

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

[@glueball0230]

Nobody: KZbin 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

[@zenice1911]

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

[@krzysztofjuszczak906]

Pikachu me

[@mr.goodcat582]

I’m here in 655000 year and it didn’t work.

[@sidewalk__]

Yes and it’s February when there is an extra day which means if there was someone born on the 29th February in my class they would be 4

[@tev5040]

KZbin recommendations are pretty smart

[@Th3Curs3dChild]

What are you talking yet?

[@PopeLando]

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

[@davidfarinaofficial]

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

[@HeavyboxesDIYMaster]

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

[@chentiangemalc]

This is why we should change to the stardate system.

[@heronimousbrapson863]

chentiangemalc Thank you, Mr. Spock.

[@ninjaed13]

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

[@unvergebeneid]

+Debated Nothing Yes he is. He misspoke, not miswrote.

[@Betelgeuse1996]

He also said years instead of days.

[@standupmaths]

If in doubt: always go with Post-Production Matt.

[@brianjuelpedersen6389]

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

[@okamichamploo]

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!

[@joshinils]

4:40 shots fired

[@nickevery5078]

lol

[@lxxwie9407]

I was literally about to comment that.

[@silicalnz3008]

me too xD

[@Somerandomdude-ev2uh]

+SilicalNZ your icon is the same as my iPad lock screen

[@silicalnz3008]

Somerandomdude4.2526 :D

[@mosesramirez6330]

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

[@JesseRaylabrancaro]

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

[@MichaelBerthelsen]

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

[@anirudhsilai5790]

My party would be on February 11th, 2048

[@kevinjohnson4531]

My favorite stupid date trivia fact. 2/22/22 2:22:22 will be a Twosday [sic].

[@louis_cgf9206]

shouldn't it be 2nd of November cause 2^11 is 2048 so the date will be 2/11/48

[@edwardnygma8533]

@@louis_cgf9206 Yours is good too, but the top reply is also 2/11/48 via different formatting.

[@BradenBest]

@@edwardnygma8533 This is why we all need to use ISO 8601 en.wikipedia.org/wiki/ISO_8601 Edit: Oh look, youtube added automatic @/+ back in. And yet they can't implement basic markdown support. C'mon, guys. I want to write things like `this`, $2^(this)$ and [this](example.com) like I can in reddit/stackoverflow/github

[@wombat4191]

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

[@davidepiazzoni]

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)!

[@jeffc5974]

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.

[@sabinrawr]

One of the central problems with trying to fix the calendar is that many monotheistic religions (including the one that the Pope presides over) rely on an unbroken 7-day cycle. So, for religious reasons, the days of the week would still line up, even in the date does not. This is also why adding a "blank" day that is not assigned to a day-of-week label would be difficult to implement.

[@GDNachoo]

"Besides being in war, both powerful nations agreed it was IN FACT... a Thrusday"

[@stevenvanhulle7242]

It might have an impact if the attacked party was on Sunday, and the attacking party wasn't. Given how religious people were back then.

[@juanausensi499]

@@sabinrawr They are a bunch of countries that have 2 calendars, a civil one and a religious one.

[@warmanfuzzy2198]

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.

[@YamamotoTV2021]

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).

[@supervegito2277]

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

[@strongside4565]

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

[@ABaumstumpf]

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

[@TuberTugger]

+ABaumstumpf Maths are hard.

[@drkingschultz2513]

he also says "years" instead of "days" :D

[@itsdox0006]

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

[@bxdanny]

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).

[@Alkis05]

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.

[@RedsBoneStuff]

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

[@DaveScottAggie]

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

[@fede142857]

Indeed, that's what they are added for.

[@DaveScottAggie]

Thanks.

[@razaelll]

+David Scott Yes, but the thing is, it's really hard to keep all analog clocks in sync and nobody actually gives a shit about leap seconds. All computers sync the time anyway and most of analog clocks are off by a minute or two anyway. It's both pointless and very important simultaneously. My brain hurts

[@tedmeisterb]

+David Scott Yes but now that's got me thinking, with these leap seconds that we are adding every so often, won't that end up making the Gregorian system work overall?

[@jeffnarum1373]

+Edward Brightman Wait a second...

[@Holobrine]

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.

[@3Ppaatt]

+Holobrine Intuitive to computers

[@VampireBuddha]

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.

[@TYEDYEGYE1]

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?

[@sebastianpiotrowski5973]

the shortest week is 5 day 365/5=73 weeks

[@MegaLoquendo2000]

It took me years to get it, the .2421 days doesn't refer to hours that we could simply measure by looking at the sunset and sunrise slowly switching places, but rather the additional distance the earth has to move to reach the same spot as the previous year.

[@pokedude583]

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

[@LaPingvino]

+pokédude583 it's the video that needs fixing ;)

[@caseye11is]

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

[@demonking86420]

Casey Ellis Parker Calendar ftw

[@KishoreShenoy1994]

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

[@black_platypus]

+Kishore Shenoy "was the sentence"? Maybe I don't get it, but it seems like there's a missed chance for driving the joke home ^^ ...How about "he got 12 months"? That works on both levels

[@KishoreShenoy1994]

+Benjamin Philipp Altered. Cheers for the correction

[@black_platypus]

Kishore Shenoy Cool ^^ It was more of a suggestion rather than a correction (who am I to say what's right in that situation? It's your joke after all) - but yes, I personally think it works better now :)

[@hurdit]

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.

[@debblez]

128 years is actually VERY unusually close to an integer number of days, being a mere 17-18 seconds off. The next time the year and day line up that closely isn’t until nearly 5 millennia!

[@GDNachoo]

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

[@fritz46]

Reading this in 2022, it sounds quite optimistic...

[@Perririri]

Vesszen az emberiség!!

[@MikeBMW]

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

[@Sahl0]

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**

[@HarmSchelhaas]

Has anybody mentioned Mädler already? That is, Johann Heinrich von Mädler, who proposed the 128-year leap year rule in 1864. [en.wikipedia.org/wiki/Johann_Heinrich_von_M%C3%A4dler]

[@GrimSleepy]

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!".

[@LazerField]

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

[@xxXthekevXxx]

I'm reading this comment in the professor's voice lol

[@abiramn9983]

Enjoy: standupmaths.bandcamp.com/releases

[@Gunbudder]

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.

[@johncochran8497]

+Gunhaver You might want to look again at the current number of leap seconds. There have been 26 leap seconds announced since 1972.

[@Gunbudder]

You are right! I have been working with GPS too much. GPS time is not adjusted to leap seconds, and UTC is. This means GPS is ahead of UTC by 17 seconds (the magic number). GPS-UTC uses the 1980 epoch to begin counting (there wasn't really GPS before then... ok first navstar was 1978 but close enough). Basically 17 seconds is the magic number that gets you from special GPS time to the UTC time that the rest of the world uses. That is, until the IERS wizard creates another leap second!

[@micahgruenwald9321]

They add another leap second if the clocks are off from the rotation of the earth by more than .9 seconds, nothing arbitrary.

[@Gunbudder]

Fair enough. It only seems arbitrary because of the nature of the day length drift. You take all the fun out of the IERS wizard. They could choose not to add a leap second though even if it is passed the threshold. The wizard just promises that he won't...

[@heronimousbrapson863]

Gunhaver Yes. The wizard lives next door to Hogwarts.

[@ironicdutchmoonshade]

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

[@SjurSkur]

The subtitles, my lord they're great

[@darleschickens7106]

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.

[@postbode30]

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

[@robertr7923]

+mike postma its still an integer, cause 1 is an integer, whats the point?

[@robertr7923]

+mike postma its still an integer, cause 1 is an integer, whats the point?

[@Jimpozcan]

+mike postma They'll probably have abolished leap years by then.

[@mahmoudelsharawy5405]

1:24 you say 365.25..... and the screen says 365.24.... which is it?

[@LeoStaley]

+Mahmoud Elsharawy Came here to say this.

[@robinw77]

+Noah Hastings But we'd have one epic summer! (Until we found that 'Winter is coming')

[@pitri_hub]

+Mahmoud Elsharawy When in doubt, I assume that the text is the correct version. The text is added in the video editing, which apparently comes after recording. With the text you can correct some mistakes you did when recording the video.

[@SimulationWithDaniel]

+Mahmoud Elsharawy I think it is what the text says

[@jrdn.lauren]

something tells me you dont REALLY honestly care. BUT, its .25. and you can reason it simply because we get one extra day ecery 4 years. Or average it out (like mathematicians do) to .25 of a day every year.

[@JamiePersaud36]

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

[@feynstein1004]

This is the year of the scorpion.

[@yahccs1]

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!

[@SabrinaXe]

9:00 is where my comment was going to be about until he bursted his own bubble. So, my new comment is about . . . You have my respect for the time it took for all the maths doing

[@chakatfirepaw]

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

[@angelmendez-rivera351]

chakatfirepaw Yes, every global calendar is Eurocentric, really. Most things are

[@XenophonSoulis]

Greece: 1925 I think.

[@joshinils]

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

[@xiaomarou9890]

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”.

[@alanr4447a]

10:09 "That is the optimal time to buy a calendar." I'll set a reminder!

[@Crissov]

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.

[@Markovisch]

The Parker Calender?

[@marxnutz]

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.

[@stevenvanhulle7242]

I'd rather call it "work day", and party the other 364...

[@deproissant]

A part of me really likes that as every single date of the month would line up to be on the same day (January 1 would be on the same day as February 1 and March 1 and so on). The other part of me is feeling uneasy with the rigidity, for lack of a better word, of it.

[@ahsenchaudhry5754]

@@deproissant Imagine if you were on a monday, youd forever have your birthday on a monday. No chance for it to ever ben in the weekend. thats kind of sad.

[@auto_ego]

@@ahsenchaudhry5754 This is why we also switch to the 4-day week. If you were born on Monday, you celebrate the previous weekend. If you were born Friday, you celebrate the following weekend. If you were born Saturday or Sunday, congrats it's already the weekend. You were'nt born Tuesday, Wednesday, or Thursday, because those don't exist.

[@juanausensi499]

@@ahsenchaudhry5754 The Mad Hatter has the solution: celebrate only non-birthdays.

[@B3Band]

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?

[@chriswatson3464]

Yes

[@newcantinacrispychickentac7754]

It would be especially hard for people to notice since 2000 was a leap year They're in for a surprise in 2100

[@Freak80MC]

I know my comment will never be seen, but this video got me thinking of the issue of "long time" like in a million years how would people be writing the year numbers? (assuming civilization still exists lol) I feel like a simple but elegant solution is to just restart the years. So like you have the year 9999 and then the next year is actually 0000 and goes up to 9999 from there. And then you just represent that 10,000 years has passed with a new number in front that would just be used for history classes and such but in day to day life the year would be the regular four digit year the same way we have it now. So 0 2024 would be 2024 AD, 1 2024 would be the years 12,024 AD and you could even extend this backwards, -1 2024 would be the year 2024 BC. (actually wait BC years would be different in this date system vs the AC/BC one... whatever im too tired for this lol) I don't feel like figuring out what the limit of this system would be but maybe you could just continue it on onwards, when the year reaches 9999 9999, you add a new four digit spot in front of it and continue like that. It helps capture the scale of large time while also still being easy to use day to day because day to day dates would be four digits still like it is now, or even just the last two digits.

[@beirirangu]

or... you could use TWO numbers: Years with decimals, and days that reset when the year gets to a whole number and, with the 128 calendar, you could also use hexadecimal: leap year every 0, 4, 8, and C, except 00 and 80

[@ghuegel]

This will all be so much easier once the Earth is tidally locked with the sun.

[@stephensmith5193]

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

[@standupmaths]

So people have time to get ready!

[@stephensmith5193]

+standupmaths Hey, fair enough.

[@Neptutron]

+Stephen Smith I'll allow it

[@anastasissfyrides2919]

change title to "when to buy a calendar"

[@andrasfogarasi5014]

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.

[@as7river]

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