Slashdot Mirror
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.
I'm pretty sure the math doesn't go anywhere. It's not Brigadoon.
In fact I'm going to take the URL and put it in my calendar for next June.
Will report back ....
Slightly disreputable, albeit gregarious
On climagic I laid it out in less than 140 characters.
Does anyone else really dislike the way that font represents numbers, constantly bouncing up and down above and below the rest?
Oh wait, it ends in 2012!
-- By all means let's be open-minded, but not so open-minded that our brains drop out.
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?
In Soviet Russia, leap year comes every time Politburo says it comes.
I much prefer the explanation in this video: http://www.youtube.com/watch?feature=player_embedded&v=xX96xng7sAE
There's an extra working day! Woohoo!
Actually there is more like 5/7 of a working day, right?
I'm a good cook. I'm a fantastic eater. - Steven Brust
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.
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.
Why is it everyone has their own scheme for rebuilding Calendars?
And why so much significance tied to the winter solstice? That hardly matters anymore in a global economy.
Sig Battery depleted. Reverting to safe mode.
http://thedailywtf.com/Articles/DATE_NOT_FOUND.aspx
To give first-time programming students a fun and interesting homework assignment.
Hopefully no time soon, but almost certainly before 2100, when the next leap year doesn't happen. If due to lots of exercise, few pizzas and a whole bunch of luck we do survive that long, then we'll all be too dotty to know what day it is anyway. Glad this is sorted. All we have to know is that it happens every 4 years and will do for the entire rest of ever, so long as we care. Lets get coding and hardwire in a leap year to make the 2100 bug!
We're both on /.
I wouldn't really say we're getting a lot of WORK done.
---
ECHELON is a government program to find words like bomb, jihad, plutonium, assassinate, and anarchy.
Let's just switch to stardates and be done with it!
Whats with all the leap stuff?
Yes, I know it's a leap year, but the only other time I remember seeing so much stuff about it being circulated was in 2000.
Still, why are adults explaining it to other adults? Is this one different? Is the world getting so mellow that a leap year is no an excuse for a lengthy discussion on a reletivly trivial event? Trivial in that the rules are pretty simple. Not trivial as in little impact.
The Kruger Dunning explains most post on
Solstice is significant because it is not an arbitrary day- it is a measurable location on earth's flight. Jan 1 is just arbitrary with no scientific marker. It is very likely when the calendar were first created they intended it to be on the solstice- but human ineptitude made it drift to what is Jan 1 today.
"That's the way to do it" - Punch
The answer to every programming Professor's favorite Intro. to Programming project assignment has now been leaked on the web! What will become of all the students who can now look up the formula to that mind-bending programming challenge of making a calendar application.
~theCzar
Let's make a week 10 days- a much more logical number.
We could call it the metric week, and every country but the US could switch to it. Sweet.
Won't work. The orbital period around the sun isn't constant. We're not (yet) locked in a fractional orbital sync with Jupiter, so its pull affects the nominal year length.
365.2421904 is a good approximation for right now, and the 4*25*4 rule is "good enough" for a while - locking it wouldn't make things better.
Plus, you don't really want the day to be in sync with the orbital year. Midday would not not occur at noon anymore, but shift, because perhelion doesn't happen at the same time of day every year.
There's an extra working day! Woohoo!
Also one more day before you need to pay the monthly mortgages and bills. February can be hard on people who are on a tight budget.
No there's an extra working day.
We get an extra Monday this year - if it wasn't a leap year then Dec 31 would be Sunday and that Monday would be part of next year.
Do you remember the shitstorm when daylight savings time got longer, all the problems with clocks not adjusting properly and meetings being missed, and that was just an hour. Imagine a whole day being removed from the calendar every 4 years, the panic will be worse then Y2K. What about the people that were born on Feb 29, do we just say you no longer get a birthday when the calendars are updated? Will entering your birthday as Feb 29 break the system? Our system sucks but it's our system and there is no going back now.
Knowledge = Power
P= W/t
t=Money
Money = Work/Knowledge so the less you know the more you make
Its already been done, but I think the French ended up killing a bunch of people first.
Gamingmuseum.com: Give your 3D accelerator a rest.
There's a very, very simple solution to this, and that is: At some value UTC, we all light model rocket engines with the exhaust facing east, and slow down the day such that its length goes evenly into a year. Any over/undershoot in the quantity or duration of burns can be adjusted on a much smaller scale. After that we just perform regular burns in the opposite direction to maintain angular momentum. Voila!
https://www.eff.org/https-everywhere
"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.
You jump back and forth between wrong and right.
For someone who pretends to know so much, I'm surprised you don't know that originally there were ten months: Dec{imal,ember). December, according to its name is supposed to be the tenth month.
Correct
But thanks to some caesar named Augustus we have one extra. I'll leave the origin of the other added month as an exercise for you.
Often repeated, but not correct. There had been twelve months long before Augustus was born.
And in early Roman times the year used to start in March, closer to the Vernal equinox,
And back to correct.
They originally had 10 months of roughly 30 days each, plus a period called 'winter' that was just kind of there to fill in the rest of it. Some time around 700BC give or take (pre-Republic, still during the Monarchy) 'winter' was converted to the months of January and February, which were added to the beginning of the year.
The months of July and August were always there, they were simply renamed from what in English would be Quintember and Sextember.
William of Ockham had no beard. The most likely explanation is that it was chewed off by squirrels every morning.
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.
Chose an aribitrary starting time, say the origin of this universe about 8 x 10^60 Plank units ago.
Where do you live that midday occurs at noon. The only guarantee is that midday and noon are within two hours of each other. This is due to timezones (roughly an hour wide) and daylight saving (shifting things off by an hour).
He effected a bored affect.
Although, you're talking about shift, which over time would put it further out of sync than it already is. I view that as a possibly good thing, then we can get rid of the timezones, and everyone uses GMT. That also means no more DST.
He effected a bored affect.
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.
I'll take you up on your rebuilt calendar, after you get all mail servers and mail clients to use a replacement for SMTP, to prevent spam (or at least make it 100% reliably traceable/non-forgeable, and not have to need filters on the client end).
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.
Account -> Discussions -> Disable Sigs
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...
Good guess, but there is not a lot of evidence to support that theory. In pre-Roman cultures, the Vernal Equinox was more commonly selected as the start of the year. The Calendar of Romulus, from about 753 BC, used the Vernal Equinox as the start of the year. It ran for ten months (304 days), followed by a number of days of winter, which were not considered part of any month. The Julian Calendar, starting in 45 BC, used January 1 as the start of the civil calendar year but the calendar was designed with the Vernal Equinox as a reference, so that it would fall on March 25th. Different dates, coinciding with various religious holidays, were used as the beginning of the year during the Middle Ages. For a while, the Anglo-Saxon custom was to use Christmas Day, which is indeed close to the Winter Solstice (and may have been influenced by earlier pagan custom), but that was changed after the Norman Conquest. In Britain and its colonies, from about 1155 until the adoption of the Gregorian Calendar in 1752, the civil calendar year began on March 25th, which coincides with the Annunciation and is close to the Vernal Equinox.
Great, for the 6% of months that are 28 days. Otherwise, not so much.
Actually I'm pretty fond of the 7-day week, but maybe months should be a nice round number of days, like 32. Then we'd get an extra day of weekend.
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.
Every month has 28 days.
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).
When code does not correctly model the problem domain, the error isn't with the domain.
Not in my new scheme; the short month would be down to 13, or 14 on leap years. I don't want February to be short though -- it's been short long enough. Calculations would be a lot simpler all around if the *last* month were the short one.
That's right -- a war on Chistmas!
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.
Free unix account: freeshell.org
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!
A month is 1/12th of a solar cycle, a week is 1/4 of a lunar cycle.
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
Its a completely arbitrary number. Matching up with the median number of fingers a human has doesn't make it a "logical number".
I think you mean the mode. It is highly unlikely the median is exactly 10.
We should just have star dates.
No mention of leap seconds in your Latin text unless it was lost in translation
http://en.wikipedia.org/wiki/Leap_second
Well, I'm puzzled by this. How could it be "lost in translation" when that was the original text? It wasn't (mis)translated from any other language. That's what the pope's astronomer wrote. Actually, the edict was a bit longer than that. The whole thing is online, along with some pretty good translations to French and English, and there seems to be no mention of any time unit smaller than a day.
But I'll have to remember this omission, the next time the all-knowing nature of our religious leaders comes up. "If the bible [or the pope ;-] truly tells us all we need to know about the world, where is the commandment on how to implement leap seconds? Inquiring believers want to know ..."
After all, if God hadn't wanted us to use leap seconds, He would clearly have set things up so that the day, month and year are all integer multiples of the next-smallest unit. And they'd stay that way, not wavering all over the place on the millisecond level like our world's rotation obviously does. So He must have intended that we come to terms with all the incommensurabilities in the solar system's rotations and orbits. Where is this documented in the canon?
Those who do study history are doomed to stand helplessly by while everyone else repeats it.
(the original word in Genesis translated as "day" was more accurately "a period of time" although it was often "day" but not necessarily
Yes, and so Yom Kippur is the "period of time of atonement", rather than the "day" of atonement?
Plus, the first mention of "yom" in the text is "God called the light 'yom' and the darkness he called Night. And there was evening and there was morning, the first 'yom'." ... it's kind of hard to argue against a non-literal interpretation of "yom" as "day", when clearly the first day was a single cycle of evening and morning.
WARNING! This girl exceeds the MAXIMUM SAFE standards established by the FDA for BRATTINESS
Ever wonder why Feb was the catch-all (last) month of the calendar? Because they started the calendar with March before. That's the first month good for warring, so it starts the year. Re-aligning the start to the month start closest to the solstice wasn't until later. Yes, starting the year on the day after the solstice and the year end on the solstice would be self-correcting, but almost incalculable. People prefer consistency to accuracy.
Learn to love Alaska
I will agree here. The upshot is that we get more weekdays than weekends.
I'm a good cook. I'm a fantastic eater. - Steven Brust
if (($yr % 400) == 0) $leapYear = true;
else if (($yr % 100) == 0) $leapYear = false;
else if (($yr %4) == 0) $leapYear = true;
else $leapYear = false;
Oh, and before we congratulate the Pope's astronomer too much, I'll quote the FA:
Of course, the calendar’s still not completely accurate at this point, because now we’re ahead again. We’ve added a day, when we should have added only 0.8762 days, so we’re ahead now by
1 – 0.8762 days = 0.1238 days.
Funny thing is, no one worries about that. There is no official rule for leap days with cycles bigger than 400 years. I think this is extremely ironic, because the amount we are off every 400 years is almost exactly 1/8th of a day! So after 3200 years, we’ve had 8 of those 400 year cycles, so we’re ahead by
8 x 0.1238 days = 0.9904 days.
Maybe we should go a little easy on him since he did have to write in Latin and didn't have access to sophisticated measuring tools. Though, maybe if they'd spent a little less time persecuting others, designing silly hats and talking to an invisible man they might have done.
Actually, both the median and the mode would be 10 unless I'm drastically under/overestimating the incidence of polydactyly and missing digits.
It's the median that is closest to the definition you're asking about, however if less than half the population has 10 digits, the median is exactly ten.
I think part of that comment must have disappeared due to the angled brackets.
I mean if less than half the population has fewer than 10 digits and less than half the population has more than 10 digits, the median is exactly ten.
So we're going to see this every four years? Except every hundred years? Except every four hundred years?
Then, lest the day before the Calends of April 12 from the equinox recede in the future, we establish that every fourth leap year (as is the custom) ought to be continued, in addition to, in the hundred years, who, although he had always bissextile they have been, such as we wish that year 1600, after him, which from that time, however, they are not all in the hundred and bissextile obtain, but in each four hundred years, the first, and those who have no bissextile in the hundred and three, the fourth, however, each one in a hundred is bissextile, so that the year 1700, 1800, 1900 bissextile they are not. In the year of 2000, however, in the manner usual intercalation day of the leap day, February 29 the day of the continent, the same order of intercalations of intermittent leap day in each four hundred years, preserved in perpetuity.
Dropbox drops it like it's hot.
Oh, come on! Why don't you go open another tab in your browser there and google for a lunar calendar? You'll see that a lunar month has between 29 to 30 days. A full lunar year cycle would have about 354 days, give or take a day or two.
Dropbox drops it like it's hot.
Let me clarify - that 354 days refer to a lunar year with 12 lunar months. A year with 13 months would have approx. 384 days.
Dropbox drops it like it's hot.
But how come our libraries aren't smarter about it.
Converting to a datetime shouldn't be so difficult. Neither should handling month short forms (Sept. I'm looking at you!) obviously we should be moving to metric time. (Five fingers FTW!).
Even 20 years ago November and December were winter, now it doesn't really get cold enough for snow until late December (in Canada)...
Screw the Romans, and screw the issues with daylight savings, how about some proper month representation.
365.24219878125
That's all, really.
If a leap year is a year that contains one extra day, then surely a leap day is a day that contains one extra second, as happens from time to time to adjust UTC for the earth's rotation. (The extra second is always added just before midnight.) But then, people call that a 'leap second', even though it is exactly the same length as any other second...
-- Ed Avis ed@membled.com
Naturally I couldn’t let this bit of maths go. I’ve made an overly complicated spreadsheet that generates correctly formatted wall planners. Initially I was happy that this nonsense happens every 4 years and will do for the useful period of the wall planner generator. Then I drank too much coffee and added the correction anyway. Assuming cell A1 contains the year of interest, this formula gives the number of days in February: =IF(MOD(A1,4)=0,IF(MOD(A1,100)=0,IF(MOD(A1,1000)=0,29,28),29),28)
Then- our months are supposed to be based on cycles of the moon (Approx every 28 days)- but because there were 13 and superstitious nitwits didn't like 13 we have 12 months with varying days.
The time between two new moons is approximately 29.5 days. 28 is only used because it is a multiple of 7 (the number of greco-roman planets), and it divides the lunation into nice periods between new, half, full and half.
Basic primary school knowledge in the discovery magazine and slashdot.
I vote for growing 3 extra fingers. Then we can use Base 13. The jokes are better.
Or it was a Dr Who reference ?
oooh an internet hardman with his panties in a wad. I'm scared.
January 1st has no measurable quantity- there it is for all purposes unreliable as a starting point for a year with no significant meaning. Setting the start of the year to an equinox or a solstice would be fine with me. January 1st is just silly- it has no meaning. It is just one factor amongst many that is arbitrary and meaningless about our calendar.
Personally, I think a solstice would make more sense for start of a year- but following the roman example of the equinox with the agricultural reasoning would be better than Jan 1.
"That's the way to do it" - Punch
Can't we just change the orbit of the Earth so one year = 360 days?
First, there's absolutely no reason to have a runt month like February.
365 is the product of two prime numbers. You can either have 5 divisions of 73 days each, or 73 divisions of 5 days each. Otherwise, there is no nice, neat way to divide up the calendar.
EVERY MONTH shall have 30 or 31 days EVERY YEAR.
That breaks the predictability of the seasons. As they are now, both solstices and one equinox are at roughly 11 days before the end of their respective months. The odd man out is September, and that can't be fixed while abiding by your "30 or 31 only" declaration.
Keep in mind that the seasons all have different lengths, owing to the variation in the earth's velocity (faster near perihelion, etc.).
Second, to fix the divisibility issues, we shall shorten the leap days to 23 hours 49 minutes and 17.663 seconds (or whatever the correct length is to account for the not-quite-1/4 extra day per year effect).
First off, that breaks the mean solar day. The entire point of a calendar is to count integer numbers of mean solar days.
Second, the "correct length" varies from year to year, and is typically only known after the fact. In fact, both the mean solar day and the mean tropical year are inconstant and vary wholly independently from each other.
Third, the length of your intercalary day can't be remembered by the average high school graduate. The current system can be reproduced by the average elementary school student to 97% accuracy. Exceptions are once in a lifetime, and not even in our lifetime.
Keep in mind that the Gregorian calendar is accurate for its intended purposes for several more millennia at least.
Third, to minimize disruptions to work schedules and reruns of Leave It To Beaver, leap days, when they occur, shall be on December 31. And it shall be declared a holiday in all jurisdictions.
Good luck with that. Not all governments use the Gregorian Calendar for all purposes as it is.