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
