Leap Years: we can do better

2016 is a leap year!

And that makes me very excited

as much as I mourn the loss of Februrary no longer being an integer number of weeks.

Long, I still love leap years

because, frankly, calendar drift is a serious issue.

In 1627, during the Anglo-French war

the English Army invaded a French island on the 12th of July.

The French Army however, were ready to defend on the 22nd of July.

But it doesn't matter! Because those were the same day!

Because the French and the English had different approaches to leap years

and keeping their calendar drift in check,

the 12th of July for one country, was the 22nd of July for the other country.

It was all very confusing.

At the very least both countries agreed, it was a Thursday.

Calendars were born way back in pre-history,

as a way to keep track of the seasons, and to this day

we use them for pretty much the same purpose. Sadly,

it is not exactly 365 days between the start of one season and the start of the same season a year later.

That so-called tropical year is slightly longer than 365 days, specifically, it is an extra

5 hours, 48 minutes, 45 seconds, and a 138 milliseconds longer.

So one year for our calendar is actually 365.2421891 days long.

I like to measure how good or bad a calendar is by calculating the number of years rounded to

the nearest whole year for how long it takes the seasons to drift one day.

If you just use a calendar of 365 days and call it done, then every four years, your seasons would drift by a day.

That is a terrible amount of calendar drift, every, let's say, 28 years, summer will start a week later.

But it seems that civilizations dealt with this by simply inserting extra holidays,

put a bonus festival into your calendar every now and then, and everything lines back up again.

Which brings us to the origins of our current calendar. That's what the Romans did!

Politicians would decide occasionally, "Hey, let's put in a bonus holiday, line everything back up again."

But as should come as no surprise, politicians did not have the need of the calendar as their top priority,

above that were their own needs. And so they would actually add festivals more based on how their

terms were lining up, than on how the calendar was.

Some bit part historical figure called Julius Caesar had enough of this.

In 46 BCE he thought he would fix this one-day drift every four years

by simply putting in an extra day every four years.

There was a bit of administrative complications to get the whole thing rolling,

but by the third year CE we had the Julian calendar, which fixed the previous problem.

Or rather he almost fixed it

is we can calculate that it will now drift one day every hundred and twenty

eight years I mean it's a lot better but it's not perfect how bad is that is one

extra day every hundred and twenty-eight years longer than a century he's gonna

notice that well by the 16th century people would noticing it by then through

the various calendar changes everything was out by around about ten days

Pope Gregory the 13 thought he better get this fixed and so we hired the

mathematicians to look into it and they noticed while going up from three

hundred and sixty-five 265 point 25 days was an improvement we had overshot the

MOT ever so slightly in fact we had three more days every hundred years than

we needed and so a simple plan was concocted well I say simple plan it's

all relative isn't it

this was the new system they come up with they kept the old Julian calendar

approaching the year was a multiple of four you add a limpiar they then added a

sub clause is also almost full of a hundred you don't at the leap year but then

if it's a multiple of four hundred you do put the leap year in any way which is

why I 1800 was not

le bien 1900 was not a leap year 2012 Olympia below 400 problem solved the

problem with this fix is it involves convincing everyone in the world to not

only simultaneously switched calendars to calculate leap year the different way

but on top of that you gotta take off that bonus 10 days that have managed to

creep in to bring everything back into alignment well the one great thing about

being a pope I guess is that you're good at convincing a lot of people to change

their behavior on seemingly arbitrary reasons and so in 1582 in the Gregorian

calendar was rolled out well I think everyone changed in 1582 some of the

less pope friendly countries refused to get on board but with another century or

so it became pretty obvious that the Gregorian calendar was superior to the

Julian calendar and so in 1752 England and all of its colonies including the

soon-to-be United States of America swapped over and everyone finally was on

a new calendar how good is the Gregorian calendar? well because the average

year length is now 65.2425 days long and that is disturbingly close to

the actual tropical year. We only drift

one day every three thousand two hundred and sixteen years that's good I mean

it's so good this is the calendar we continue to use to this very day well

hang on there's still a slight discrepancy surely we can do better than this

I mean sure three thousand two hundred and sixteen years doesn't seem very long

to us but to our distant descendants it's still going to be a problem as life goes on

surely we can add in a few more rules to correct that slight remaining difference

and I worked out we need to take out another three leap year

days every 10,000 years it's ok I've got a system. Current system recap: multiple

full leap year multiple of a hundred not only be a total of 400 again here's what

I'm gonna add London AP ignoring the tens of thousands and above in any given

year he just take the thousands and hundreds of the two digit number of

centuries if there is now a motor pool on 28 instead of having a leap year

which predicted by the Gregorian calendar you don't have a leak and that

takes out three leap years every 10,000 years and they're reasonably spaced

the easy way to remember this is it and then ends 2804 5604 8400 any of those

cases you don't have a leap year otherwise carry on with the Gregorian calendar is

intended how good is my calendar well if we add on the 2800

rule as home now calling it the resulting Caledonia just one day every

ninety 1743 not come on that is a lot better

problem solved their occurred to me maybe fixing the Gregorian calendar is

patching a sinking ship

maybe we have to go back a few more versions roll right back to the Julian

calendar before you try and released an update to fix this bug the Julian

calendar as you remember drifts one day every hundred and twenty eight years but

the creepy thing is it's almost exactly a hundred and twenty eight hundred and

twenty eight points 026 week in nearly completely fix the Julian calendar by

just skipping one day every hundred and twenty eight years is no easy to spot

every mobile device

and 28 how we gonna know when to have not had mediate its very straight

forward from now on we just write all ears in by Nuri the stand it if it's a

multiple of four you have a leap year that easy and the last two digits zeros

if it's a multiple of hundred and twenty eight of the last seven digits zeros you

don't see you just look like 20 unless the last seven digits 0 no leap year 228

calendar is incredibly good only drips one day every six hundred and

twenty-five thousand years over half a million years before you drift one day

and if we choose to fix that

let's say we take out every Leap Day on here which is a multiple of 625,000 and

24 for convenience in this new calendar drips one day every fifty three and a

half trillion years longer than the Sun is gonna last

I think we have this sorted one last tiny insignificant almost you know

trivial slight thing to bear in mind as wonderful as these mathematically

precise calendars I we're very strategically in certainly days exactly

where we need them

the solar system itself is not so cut and dried very sadly everything from the

Earth's orbit to its rotation is constantly changing the solar system is

a slushy mess everything is drifting this way and the other so long term we

have no idea how long it day or a year will be from what we can tell in recent

history the length of a day has actually got 1.7 milliseconds longer every

century so as the day gets longer if the years stays the same we actually need

fewer and fewer days in the calendar which means one day in the distant

possible future

you could actually be an exact integer number of days if probable years they've

exactly where it is at the moment which it won't go with me here and the day

continues to get longer at the same rate which also it won't but again continue

bearing with me here I asked to make a round about 30 million three hundred and

seventy-two how many years from now it will take a bit

the length of the year will go from being slightly over 365 days to being slowly

under 365 days and somewhere in that crossing for a brief instant we will

have an integer number of days per year that is the optimal time to buy a calendar as

much watching my video all about leap years one last thing to mention my

deliverer of research to see if anyone else to come up with a hundred and

twenty eight role of course other people had including mathematician Adam Gutsche

128 row but by a slightly different and I'm prepared to admit nice method he

took the length of a tropical you only he used the measurement from 2000 was I

use the measurement from 2000 attendant of course since then has drifted by

fifty two milliseconds why wouldn't it anyway

65.2 42 1897 as opposed to a 911 and then he turned that into a continued

fraction I love continued fractions that the whole topic for another video

they're brilliant if you haven't seen them and then he looked down the

continued fraction wait a minute at 27 is pretty massive I reckon I can lop off

the continued fraction here and get a good approximation erode that back up

again and found that the bonus amount old yet is about thirty one hundred and

twenty with Julian calendar give you an extra quarter Monday which is 3228

by taking up that extra one day of a hundred and twenty-eight years you go

down to 3128 again a fantastic approximation

ok one final final plan then I swear the video is over what I see is the major

downside 228 room is the first year it deviates from the current Gregorian

calendar will be in the year two thousand and 48 which also happens to be

the first power to you we have had a very long time not since the year 1024

and not again until 4096 well we have a power of two year 1 to year that gonna

be we're gonna be having non stop powers of two parties no one's gonna pay any

attention to a debate about Lee BS in such a fantastic power of two

yes i frankly we might have to wait a while before we can have any lasting

calendar change