No account? Create an account

#### « previous entry | next entry » 3rd Oct 2010 | 20:14

"Lots of people are WRONG on the Internet!"

Twitter users have a propensity to retweet, echo and rebroadcast interesting facts and links without very much fact checking. For example,

@_468 This October has 5 Fridays, 5 Saturdays and 5 Sundays all in one month. It happens only once in 823 years. waw.
@bryanthatcher This month has 5 Fridays, 5 Saturdays and 5 Sundays. It happens only once in 823 years.

Those retweet counts do not include the vast numbers of copies that didn't use twitter's retweet mechanism.

If you think about it, this happens whenever the month has 31 days and the first day of the month is a Friday. Because the years cycle through the days of the weeks fairly evenly, you would expect this to happen for a particular month about 1/7th of the time - in fact if you average over the entire Gregorian 400 year cycle it happens 1 in 7.1429 Octobers. Each year has 7 months with 31 days, and if you average over all of them you expect about one month in each year to have this property, and in fact you get precisely this result if you average over the entire Gregorian cycle. There happen to have been two months this year with 5 Fridays, Saturdays, and Sundays because January also started with a Friday.

1 in 7 and 1 in 1 are both rather more frequent than 1 in 823.

#### from:simontdate: 4th Oct 2010 15:30 (UTC)Permalink

And yet, was presumably a complete coincidence.

The only way it could not be a coincidence would be if they considered lots of possible periods (in years) for the Gregorian calendar and picked the one which made the number of days come out to a multiple of 7. (Equivalently, I suppose, look for a good rational approximation to 1/7 of the number of days in a year, and use its denominator as the calendar period.)

I wonder if anyone DID propose any alternatives to the gregorian calendar: obviously you could do something other than the 100-400 exceptions, especially if you're willing to alter the 4-year cycle[1], but I don't know if any would have made equal sense, or had ever been suggested.

At Eastercon 2003 someone gave a talk suggesting a 33-year cycle containing 8 leap years, which he claimed gets an even better approximation to the true length of a year than 97/400. (It appears to be a continued-fraction convergent of the true length.) He also had a very silly conspiracy theory about how some people actually planned to implement that version in the 16th century in order to make the date of Easter work out more sensibly, but I can't remember any of the details.

#### from:fanfdate: 4th Oct 2010 15:38 (UTC)Permalink

"More sensibly"?! The Gregorian rules for Easter are deliberately awkward to minimise the likelihood of coinciding with Passover. Anti-semitism isn't very sensible even in the 16th C...

#### from:simontdate: 4th Oct 2010 15:50 (UTC)Permalink

Oh god, I'd forgotten Passover Sense Multiple Festival / Collision Detect. I don't recall the Eastercon 33-year guy saying how he intended to get round that one...

#### from:cartesiandaemondate: 5th Oct 2010 10:23 (UTC)Permalink

What happened? I learned a lot about the date of passover and easter, but not this.

#### from:fanfdate: 5th Oct 2010 14:42 (UTC)Permalink

I think the details are described in "Calendrical Calculations", and I can't remember them because they are somewhat arcane.

But in essence, Pope Gregory did more than adjust the calendar to match the year more precisely. He also adjusted the rules for Easter, making them more complicated to satisfy various political goals. I can't remember now whether the adjustments also looked to the Eastern (Orthodox) church as well as the Jews- probably not since they continued to use the Julian calendar and the ecclesiastical equinox of 21st March, so their Easter would be unlikely to match the others. Dunno.

#### from:cartesiandaemondate: 5th Oct 2010 15:13 (UTC)Permalink

Thanks. I couldn't see why it would make any difference if Easter remains _normally_ just after passover, but it sounds like the sort of thing I'm not at all surprised happened.

#### from:cartesiandaemondate: 4th Oct 2010 15:42 (UTC)Permalink

The only way it could not be a coincidence would be if they considered lots of possible periods (in years) for the Gregorian calendar and picked the one which made the number of days come out to a multiple of 7.

Well, yes. It seemed unlikely that they WOULD have done, but also, they COULD have done. You could do the 33 year thing, or perhaps something similar but which decides only which normal 4-year leap years to skip. And making the days of the week repeat might be a mild advantage. (I can't see why it would be, but it would be tidy).

I was thinking of the 33-cycle thing. I saw it first invented by Mark Dominus (http://blog.plover.com/calendar/leapday.html) and I don't know if anyone suggested it before that or not. He said ancient persians (?) had something similar but more complicated.

#### from:cartesiandaemondate: 4th Oct 2010 15:43 (UTC)Permalink

I'm sure I heard some people discussing the 33 calendar on LJ. IIRC the advantages are that someone will hopefully remember the last 33-year anomoly, so there won't be any anomolies so rare people will not be ready for them. But the disadvantage is that you can't calculate leap years approximately by testing the year for division by 4, you need to do the division by 33.

#### from:nonameyetdate: 5th Oct 2010 07:05 (UTC)Permalink

http://en.wikipedia.org/wiki/Iranian_calendar

#### from:nonameyetdate: 5th Oct 2010 21:15 (UTC)Permalink

Sorry.
The Iranian calendar seems to have 8 leap days in 33 years: http://en.wikipedia.org/wiki/Iranian_calendar

#### from:pnedate: 2nd Nov 2010 08:03 (UTC)Permalink

This page is all about alternative leap year calculations (and his entire site has quite a lot of information on calendars and variations thereof, including his proposal for two perpetual calendars called "Symmetry 454" and "Symmetry 010").

He mentions the 8/33 rule but prefers a 52/293 one.

Apparently, which rule you choose depends on the length of the year you want to optimise for: time between successive equinoxes or between successive solstices, for example, will produce slight different lengths. (I'm afraid I don't remember details since I've only skimmed his pages - they're long and full of maths.)

Edited at 2010-11-02 08:04 am (UTC)