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
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