Leap Years: we can do better

Because the Earth's rotation is slowing down at an unpredictable rate, there is no point in devising a calendar with a drift more accurate than about 1 in 50,000 years. Instead let's look at the Herschel Calendar which suppresses a leap year every 3,200 years, and amend it by a discretionary suppression every 1,600 years. If we just make a random choice concerning the suppression, then on average we have the Herschel Calendar. A targetted choice should maximise the number of years on which the vernal equinox falls on March 21st for the next 1,600 years.

I rewatch this video once in a few months. I think this one is one of the best Matt has ever made in terms of content and humour.

i am kind of sad i wont live in a lifetime to witness the 100n rule mean anything. damn 400n.

is that 365.24218 days of sidereal or solar days. is that x 24hrs or x23hrs 56min 4sec?

If we add a leap year every year divisible by four but not 132 with a correction every 4460 years by removing a day we couldn’t we line up our calendar perfectly with the tropical year?

01:25 - he says the number wrong :)

😂😂😂

Wait a minute. The actual seasonal drift for the Julian Calendar is 1 day every 128 years. Since the Gregorian Calendar is built on top of the Julian Calendar but instead of addressing the actual drift waits until enough drift has accumulated to do something, the Gregorian calendar too actually drifts 1 day every 128 years. Then waits 400 years to fix that. Hardly a good system imo. You're basically out of sync for 400 years. Granted it's only a small discrepancy (upto 3 days max) but we can still do better.

i can’t wait to buy a calendar in 389,726!

Do we need a calendar that’s over 3,000 times longer than the universe has existed tough

You should have made the video on Feb 29.

How much longer would a second be if it took earth exactly 360 days to orbit the sun once with there still being 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute?

Take a day out in years divisible by 4000 and 10000. In years divisible by 50000 another day gets omitted (31st January). In years divisible by 100000 31st January gets put back in. In years divisible by 500000 31st January gets omitted. In years divisible by 1000000 31st January gets put back in. In years divisible by 10000000 29th February gets put back in.

1:23 It is actually 365.2421890972 2/9 days.
((5×60×60)+(48×60)+45.138)÷(24×60×60).
That means it would be out by a day every 91719 years (using Matt's rules the average calendar year would be 365.2422 days.)
1÷(0.2422-0.2421890972 2/9)=91719 117/157.
The calendar will probably be different by then anyway.

You can't account for the fact the orbit of the earth is slowing slightly

I am here partially because of Michael Stevens.

The solar system is sloshy, thanks for pointing this out. Earth itself is sloshy. Just do something trivial like building the Three Gorges Dam with its reservoir slowed the Earth by microseconds. Glaciation and de-glaciation moves great gobs of water from the equator to the poles speeding/slowing Earth by some fraction of a second.

Hey Matt!
I think we need a follow-up to this, cause people are claiming that a 13 month calendar would be better, and I need you to show them how that would be a mess, mathematically. lmfao

Didn't know he had hair at some point lol

I'm surprised you didn't mention the "revised Julian calendar" designed by Milankovic (tyes, the one Milankovic cycles are named after)

The revised Julian calendar year lasts 365.242222... days. Compared to the Julian, it has 7 fewer leap days every 900 years.
It drifts one day every 31'000 years or so. Making it more accurate than either the Julian OR the Gregorian calendar!

The rues are:
If the year is divisible by 4, it's a leap year.
But of the years that are also multiples of 100, the only leap years are the ones that leave a remainder 200 or 600 when divided by 900.

6:38 the subtitles say 5604 instead of 5600

A probably much simpler solution is simply to skip the 400 year rule every 3200 years by extending the Gregorian. So

4n leap year
100n not a leap year, unless
400n which is a leap year unless
3200n which is not a leap year

Who's watching in a leap year?

Better use a calendar with 13 months of 28 days each, isn´t? +1 neutral day, being 2 on leap years

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.

HAPPY LEAP DAY 2024!!

leap day in 2 days

Hello from the Future! I'm from 27 December 2023, and Next year is a leap year.
But as for the 128-year calendar, I noticed something fascinating.
If you take away 1 leap year every 128 years, it is self-correcting, meaning every 384 years, the Gregorian Date would be the same as on this new calendar. This phenomenon would only happen until the year 4798 AD, however, because that is 3216 years after the Gregorian calendar was invented.

we would have an integer amount of days in a year, but totally non integer amount of hours in a day

Okay but WHAT IF we have twelve 30 day months that always begins with 01/01 on the Winter Solstice, and the time after 12/30 is a nonspecific number of days until the next Winter Solstice. Also this model has 6 day weeks. Other options are ten 36 day months (six 6 day weeks per month) and thirteen 28 day months (four 7 day weeks per month).

Here's an interesting one I've read about called "the" Standard Calendar: there are 159 leap days inserted every 656 years (a full cycle) of this calendar exactly when (159*year + 522) mod 656 < 159. There are 3 more changes: the leap day is shifted to the end of the year, February gains a day each from July and December, and the algorithm for Easter is slightly different. How bad is it? Assuming 2024, the Wikipedia cubic approximation (which is one part in 43200000 too big- doesn't account in the day length for the extra 2 ms in an actual solar day) says, using the formula Matt describes, it would take about 5268 years for that to drift a day.

And here's the "calendar drift" formula. Call the average year length A for average, and the tropical year at the point y where you're calculating the "drift" T(y) because that's always changing. The drift he mentions will be: abs(A-T(y))^-1. The bigger this is, the closer A is to T, and the more the calendar lines up with the seasons!

2800 is a multiple of 400 so you aren’t adding any leap years

Ah. 25 more years until 2¹¹.

absolutely beautiful math

Binary saves us once again

King Julian calendar.

Russians who're still using the Julian calendar for religion and any events before 1918: 7th of November is October!!!

Didn't Augustus also use the fact of the Julian Calendar being off & so updated them so he can launch an early attack on an enemy in Silicily?

Also, fun fact: July is named is after Julius Caesar, August is named after Augustus (Octavian Caesar), & February has 28 days because Roman superstition (about 2,000 years ago).

Days are longer than they used to be. As the Earth's core continues to cool, it rotates slower. The time it takes to orbit the Sun remains essentially unchanged.

The best calendar reform would be to get rid of weeks and months, and just number the days of each year. Start a new year at each winter solstice.

1000 years was added also?

I recently calculated the desynch between an actual year and a calendar year after 400 yrs. Using 365.242190 as the exact length of a year and approximate lengths of 365 for 303 years and 366 for 97 years, I found that the difference between the average year's exact length and approximate length resulted in a desynch of about +0.124 days per 400 years or +0.00031 days/yr. Although that doesn't sound like much, the result means that after nearly 135 yrs there will be a gain of 1 hour. So in another 2000 yrs, with the current system the time for midnight will be closer to noon or when the sun is at its peak.

If anyone is wondering why such a desynch is not present in our current time it is because Time Zones were established near 1878, which is 145 yrs ago. So, theoretically if that was when clock times were synched closely to the physical time of day, there should only be a discrepancy of an hour from the physical time of day before considering day light savings or other issues such as the length of days being not uniform. Because I don't know if the system was established during day light savings or not nor what season it was, it is impossible to tell if there is a discrepancy of an hour or not. However, the shift would become more obvious in just 3 more centuries. So, no one here will be able to verify if this is true or not in practice. YAY!

TLDR:
We gain an hour every 135 yrs with the current system. I wonder if people are going to know why in the future or be able to competently enact laws to fix the issue. Good thing, the issue doesn't need to be solved by today's people because no one can agree on anything in this current world.

Of course we can do better. First of all, we should stop using 12-based number system for the time units (12h, 24h, 60m/h, 60s/m, etc).

P.S.
Writing from the year 7E7.

ROTFL