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The Math of Leap Days
The Bad Astronomer writes "We have leap days every four years because the Earth's day and year don't divide evenly. But there's more to it than that... a lot more. A year isn't exactly 365.25 days long, and that leads to needing more complicated math and rules for when we do and don't have a leap year. If you've ever wanted to see that math laid out, now's your chance, and it only comes along every four years. Except every hundred years. Except every four hundred years."
There are no leap years. It's a conspiracy to cause IT nightmares and bratty kids who claim their age /= 4.
To offset political mods, replace Flamebait with Insightful.
and it only comes along every for years.
Wow! That really IS rare!
I think we have different definitions of complicated.
On climagic I laid it out in less than 140 characters.
A year is not even exactly 365.2422 days long (if we could actually agree how long a "day" is).
Those who can make you believe absurdities can make you commit atrocities. - Voltaire
One of my first projects in Computing and Algorithms I in college was to make a calendar that would print out in console with days correctly placed on the day of the week. The instructions specified to take special care for leap day; everyone thought they understood leap day, so no one bothered to check on the rules. The fact that round centuries do not include a leap day except when (year mod 400 = 0) meant that every one of our calendars[1] was wrong for certain years (but right for others, IIRC). And our professor docked us points as such. Back then, the entire class (along with myself) felt that we were misled or cheated, but looking back on it now that was an important lesson on project management, specifically researching requirements and checking with the interested party about how things are.
I reckon this lesson was missed by many, which leads to the various issues we see for software on Leap Day, including Microsoft's Azure as mentioned in a recent /. article.
[1] For the half of the class that completed the project, this 101 class was used to weed out those who couldn't actually program for crap and the EEs just needed a C to meet their requirement.
How is this news? It's been in Wikipedia for years!
Have you heard about SoylentNews?
I much prefer the explanation in this video: http://www.youtube.com/watch?feature=player_embedded&v=xX96xng7sAE
The whole 7 day week is rather random too- based on some out-of-date dogma that is probably mistranslated. (the original word in Genesis translated as "day" was more accurately "a period of time" although it was often "day" but not necessarily) - so we force the meaning of "day" onto it and have a 7 day week. Silly number.
Let's make a week 10 days- a much more logical number.
Actually 7-day week makes sense if you have a 28-day month.
did your "Myans" invent the number "for"?
"I disapprove of what you say, but I will defend to the death your right to say it." - Evelyn Beatrice Hall, re Voltaire
The extra, or "bissextile" day is actually inserted immediately after February 23.
The Romans picked up the Egyptians' idea of treating a common year as 360+5 days, since 360 is a highly composite number and all (the Mayans ended up doing the same). But instead of treating the extra 5 days as "epagomenal" (outside any month), they were treated as the last five days before the first month of spring, i. e. the last five days of February.
Treating the five-day block of Feb 24 through Feb 28 as inviolate meant inserting the extra day (previously an extra month) before it.
This is why the Christian feast of Saint Matthias has historically been observed on February 24 in common years and February 25 in leap years; it's always the fifth ("sixth," if you lack an understanding of zero) day before the calends of March.
e.g.; "In Soviet Russia, year leaps you! Ha ha ha." (there's no way to spell Yakov's laugh)
"I disapprove of what you say, but I will defend to the death your right to say it." - Evelyn Beatrice Hall, re Voltaire
http://thedailywtf.com/Articles/DATE_NOT_FOUND.aspx
To give first-time programming students a fun and interesting homework assignment.
"Deinde, ne in posterum a XII kalendas aprilis aequinoctium recedat, statuimus bissextum quarto quoque anno (uti mos est) continuari debere, praeterquam in centesimis annis; qui, quamvis bissextiles antea semper fuerint, qualem etiam esse volumus annum MDC, post eum tamen qui deinceps consequentur centesimi non omnes bissextiles sint, sed in quadringentis quibusque annis primi quique tres centesimi sine bissexto transigantur, quartus vero quisque centesimus bissextilis sit, ita ut annus MDCC, MDCCC, MDCCCC bissextiles non sint. Anno vero MM, more consueto dies bissextus intercaletur, februario dies XXIX continente, idemque ordo intermittendi intercalandique bissextum diem in quadringentis quibusque annis perpetuo conservetur."
This quote should make the algorithm clear to any competent programmer. Note that it contains the explicit example that in the year 2000, February contains 29 days.
Of course, it can be expressed in many fewer characters in most programming languages. But the pope's astronomer didn't have any programming languages available back in 1582.
It can be fun to point out that the above Latin passage is still the "official" definition of the leap year scheme, since no standards body has tried to revise it. As far as I've been able to determine, that is; let me know if this has ever actually happened. It'd be especially fun if some standards body had tried to rephrase this in a modern language, but got it wrong. If so, they were probably shocked to discover that a 16th-century pope's edict trumped their scientific calcuations.
(The /. software guys might be able to block posting in Russian or Chinese or Arabic, but it's a lot harder to prevent people from using Latin. ;-)
Those who do study history are doomed to stand helplessly by while everyone else repeats it.
Exactly my point.
Nobody's going to listen to any ideas of changing this at this point because there is no need, and a lot of pain involved.
If you planned it for 10 years you would still have 50% of our automated infrastructure stuck on old time keepers. Bazillions of contracts, deeds, etc would need rewrite, and virtually all historical texts would need corrections.
The only place where there is anything to gain is in date computations in computers, and we have that solved.
Its a mess, but not a debilitating one.
Converting to any other system would be all pain, and zero gain.
Sig Battery depleted. Reverting to safe mode.
Our whole calendar is messed up. First- Jan 1st is a poor start date.
I suspect the original pioneers intended the year to start on the Winter Solstice-
Yes, but Julius Caesar decided to start it on the first new moon following. And based on the best data available at the time, every 19th year would have started on a new moon (see below).
which is more like Dec 21st most years on our calendar.
More like Dec 25 at the time, hence the date of Christmas.
So- The year should start on Dec21st.
It took almost 2500 years for everyone to agree to start their year with January (instead of March). George Washington himself was fuzzy on what year he was born. Now, after just getting things straightened out (on a relative time scale), you want to fuck with it again?
Then- our months are supposed to be based on cycles of the moon (Approx every 28 days)-
29.5 days. The usual approximation is alternating months of 29 days and 30 days in length.
but because there were 13 and superstitious nitwits didn't like 13 we have 12 months with varying days.
13-month years work for all the cultures with a lunar calendar, e. g. the Jews and the Chinese. The biggest problem is reckoning when the 13th month gets added. If you treat the tropical year as 365 days, you have to add an extra synodic month 7 times in 19 years (Metonic cycle). If you use 365.25 days for a tropical year, it's more accurate to say that 28 are added in 76 years (Callippic cycle). And if you're using the even-more-accurate 365.2425-day approximation... well, go search for the term "epact."
The whole 7 day week is rather random too-
Try counting the number of days between the first visibility of the new crescent moon and first quarter. Only your eyes and your ability to estimate the illumination of the moon are allowed.
based on some out-of-date dogma that is probably mistranslated. (the original word in Genesis translated as "day" was more accurately "a period of time" although it was often "day" but not necessarily)
If you're referring to chapter 1, note that "day" is always paired with "night."
Let's make a week 10 days- a much more logical number.
Revolutionary France called, they want their "decades" back.
Regardless, (365 mod 7) = 1 while (365 mod 10) = 5.
So we have 36 weeks in a year. If we MUST have a bigger break- we can divide these into 9 months of 4 weeks each.
Even Revolutionary France understood the importance of the four seasons, with agriculture being the foundation of modern civilization and all.
We would then have 5 or 6 days at the end- a "half week"
Coptic Egyptians want their "epagomenal days" back.
Not perfect- but based more on logic than our current system and no-silly formulas needed (other than determining the solstice)
And you would once again have devised a calendar system that focuses on rationalism at the expense of pragmatism and utility, using many ideas have have been tried for centuries or even millennia. Here's what you'd be abandoning:
In fact, 2, 4 and 6 above were deliberate design choices on the part of Julius Caesar specifically to keep things simple.
Pff, base 10 logical? I propose we cut off everyones pinky fingers and transition everything to base-8 which is a nice power of 2. We should also probably be working on speeding up the rotation of the earth so that there are 512 days in a year. Once we do all that we can have exactly; 8 months to a year, 8 weeks to a month, and 8 days to a week.
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All start dates are equally arbitrary, so Jan. 1 is as good as anything else.
No, The starting day of the year under the old Roman Republican system (from which our modern system evolved by way of the Julian and Gregorian reforms) was whatever day happened to start the Roman consular term (since years weren't numbered, they were named after the consuls in office), this moved more than once during the life of the Roman Republic and came to rest at January 1 in 153 B.C.
The starting date stuck in most places using the Julian calendar (at least in common usage as to what was "New Years Day"; though lots of places moved the official starting date for the numbered year to some church holiday, and which holiday was chosen varied from place to place) and eventually became a universal norm.
Actually, no, the ancient Roman Calendar had ten months of 30 to 31 days, the months in it were never aligned to cycles of the moon, and there weren't 13 of them. It started on the vernal equinox (not the winter solistice, as you've suggested must be the case), and had a number of days added outside of any month at the end to make sure the next year started on a vernal equinox (and, since it only had 304 days in its 10 months, there were a bunch of those days.)
A later reform brought it up to 12 months, all of which (except February) had an odd number of days (29 or 31) because odd numbers were considered lucky. February was addressed by splitting it into to pieces, each of which had an odd number of days (23 and 5), and whenever a leap month (the basic calendar was 354 days long) was added to align it with the equinoxes, the leap month was added after the first part of February and incorporated the last part of February.
Actually, the 7-day week makes sense as 1/4 of the 28-day lunar cycle; its quite likely that that shaped the creation story you are referring to rather than the other way around.
Its a completely arbitrary number. Matching up with the median number of fingers a human has doesn't make it a "logical number".
Actually, its based on no more logic than the worst of the older calendars -- its just pick some arbitrary numbers as a basis for the basic schedule based on criteria that have no fundamental utility except aesthetic appeal to the designer, and then when it doesn't match to its basic goal (aligning with the cycle of equinoxes) add however many days necessary outside the regular cycles to fix that
I have been ranting about a 13 month year to my coworkers for about a year now. 12 months would have 28 days. The last month would have 29 days. Every leap year the last month would have 30 days. A lot of companies would be giving an extra day of vacation every four years.
The oldest known version of the Roman calendar that became the calendar we have now had its start date fixed to the vernal equinox, actually.
Jan. 1 wasn't reached by the date floating because the calendar wasn't pinned to the solar year, it was reached by Roman Republican practice of naming years after the consuls in office, which resulted in the year (for documentary purposes) starting on whatever date consular terms switched, which eventually got ended up being Jan. 1. This start date then stuck even after Roman consular terms became irrelevant.
Its not like all this isn't well documented, perhaps you should bother to read up on what is known about a topic before trumpeting assumptions as likely-to-be-true that are based on nothing more than your speculation about dates that happen to be near each other.
Let's make a week 10 days- a much more logical number.
So we have 36 weeks in a year. If we MUST have a bigger break- we can divide these into 9 months of 4 weeks each.
The French Republic did exactly that. Their calendar had 10 days in a week, 3 weeks in a month, 12 months in a year. That calendar remained in effect for 12 years, until it was abolished by Napoleon.
They also introduced decimal time (100 seconds in a minute, 100 minutes in an hour, 10 hours in a day).
And, not everyone has changed to the Gregorian calendar yet.
There's a few areas of European that refused to change from the Julian to the Gregorian, not because of any scientific reason, but because of a political reason. You see for quite a while, the main purpose of a complicated calendar was to keep track of when exactly Easter should be celebrated, and the different Orthodox churches quibbled about this. For a while, there was two different Easters, one for people on the Julian calendar, and one for people using the Gregorian.
The whole world changed to Gregorian, so they had to compromise. The compromise is one of the most hilarious developments in time tracking: the Revised Julian Calendar
Those who follow the Revised Julian Calendar never obey the "every 400 years" rule. Instead, they celebrate leap years every 4, unless the year is divisible by 100, unless the year is mod 900 is 200 or 600
The net result is that those countries were in agreemet with us retroactively in 1600, and in 2000, but the system will fall apart in 2400. The designers then get to live knowing that their principles have not been compromised, yet it will leave the fallout of the difference to their descendants.
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What I like to do when people seem confused about leap-year calculation is quote them the text in Pope Gregory's definition in the February 24, 1582 document "Inter Gravissimas":
"Deinde, ne in posterum a XII kalendas aprilis aequinoctium recedat, statuimus bissextum quarto quoque anno (uti mos est) continuari debere, praeterquam in centesimis annis; qui, quamvis bissextiles antea semper fuerint, qualem etiam esse volumus annum MDC, post eum tamen qui deinceps consequentur centesimi non omnes bissextiles sint, sed in quadringentis quibusque annis primi quique tres centesimi sine bissexto transigantur, quartus vero quisque centesimus bissextilis sit, ita ut annus MDCC, MDCCC, MDCCCC bissextiles non sint. Anno vero MM, more consueto dies bissextus intercaletur, februario dies XXIX continente, idemque ordo intermittendi intercalandique bissextum diem in quadringentis quibusque annis perpetuo conservetur."
Yep. That cleared it right up!
When our name is on the back of your car, we're behind you all the way!
I like the Shire Reckoning calendar better. Twelve months of 30 days, with 5 days in the middle of summer that are not assigned to any month. In leap year, there are six. Being in the middle of the summer (and being of hobbit origin), these days are used for parties and feast days.
When our name is on the back of your car, we're behind you all the way!
You seem to have misunderstood the point the GP was making. If the computer internally stores the time as UTC then the stored time will always progress forward (UTC isn't affected by DST like GMT is), and behind the scenes it'll always be searchable. It's also about as future-proof as we can make it; if rules regarding leap years or calendaring in general change, you're screwed regardless of which system you're using. The DST translation should be done for display purposes only, based on the user's preferences for localization etc. Proper separation of content versus display logic should solve all of the problems you brought up. Those problems only become issues for people working with heterogeneous data sets (time stored differently in different data stores), in which case you'd expect to be writing translation routines anyways.
"Space Exploration is not endless circles in low earth orbit." -Buzz Aldrin
We should just have star dates.
Oh wait, it ends in 2012!
No, it doesn't... just most of the digits turn to "0"... in fact, the remaining radial digit of the number representing the year will not be a "1" either, as in when we moved from 99 A.D. to 100 A.D. No, in fact, they were already on the 12th cycle, so the calendar already could express more years than just 2012 A.D. and we never had to add anything to their calendar system to do so...
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