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Twitter echo chamber fail

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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.
(700+ retweets according to search.twitter.com)
@bryanthatcher This month has 5 Fridays, 5 Saturdays and 5 Sundays. It happens only once in 823 years.
(300+ retweets according to search.twitter.com)

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.

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Comments {33}

M'lisilinaath Thabana

from: naath
date: 3rd Oct 2010 22:13 (UTC)

I wonder where 823 years comes from... surely the rarest possible Interesting Date Thing in the Gregorian calendar would happen once every 400 years or never since the Gregorian calendar has a 400 year cycle. Oh well, I suppose unless you think Easter is Interesting (which it probably is, to be fair).

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cartesiandaemon

from: cartesiandaemon
date: 4th Oct 2010 12:36 (UTC)

I tried googling, but of course, found nothing other than this meme...

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Tony Finch

from: fanf
date: 4th Oct 2010 13:16 (UTC)

Good point about 400 < 823 :-)

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kötturinn

from: kotturinn
date: 4th Oct 2010 07:48 (UTC)

What happens if you just do month=October?

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Tony Finch

from: fanf
date: 4th Oct 2010 08:58 (UTC)

That's the 1/7th case :-)

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kötturinn

from: kotturinn
date: 4th Oct 2010 11:22 (UTC)

Sorry - that'll teach me to wait until I'm awake before trying to read!

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Douglas Spencer

from: dougs
date: 4th Oct 2010 11:57 (UTC)

2010, 2021, 2027, 2032, 2038 ...

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John

from: deliberateblank
date: 1st Nov 2010 19:23 (UTC)

No need for the "...", that's when the world will end.

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Sam Holloway

from: samholloway
date: 2nd Nov 2010 17:02 (UTC)

If the world ends, does the calendar end, too?

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Richard

from: captain_aj
date: 4th Oct 2010 09:12 (UTC)

This is one of the reasons I'm wary of joining Twitter. The urge to exploit reflex retweeters and spread deliberate disinformation around the twittersphere would be way too high. Just take some fears/prejudices that you can wrap up into 140 characters and stand back ...
"OMG the eu is forcing buckingham palace to be demolished to build a mosque. I'm not racist but this is human rights gone mad" or "Amazon.com is rounding up gays and mentals into concentration camps"

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Just a random swede

from: vatine
date: 4th Oct 2010 10:33 (UTC)

Did you know that Friday is the most common "13th of the month"? With one more occurrence over a 400-year cycle than any other weekday being "the 13th" (58 times, as opposed to 57 times).

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Tony Finch

from: fanf
date: 4th Oct 2010 11:45 (UTC)

There are 400x12 months so there are 4800 13ths. Three days of the week fall on the 13th 685 times, three fall 686 times, and Friday falls on the 13th 687 times. (Looks like your error was to count one 13th per year.)

Edited at 2010-10-04 12:37 pm (UTC)

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Just a random swede

from: vatine
date: 4th Oct 2010 12:45 (UTC)

Er, yes.

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cartesiandaemon

from: cartesiandaemon
date: 4th Oct 2010 12:36 (UTC)

I remember I was surprised to learn that "leap days" in the Jewish calendar were carefully tuned to keep certain festivals on the sabbath, or not on the sabbath, or not ADJACENT to the sabbath.

Imagine my surprise when I realised, that I had never realised before, that the gregorian calendar also synchronised with days of the week, because the 400 year cycle was a whole number of weeks.

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Simon Tatham

from: simont
date: 4th Oct 2010 12:56 (UTC)

(Well, even if that hadn't been the case, it'd have synchronised every 2800 years at worst.)

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cartesiandaemon

from: cartesiandaemon
date: 4th Oct 2010 13:13 (UTC)

Oh yes, it'd obviously be quite difficult to design a natural-seeming calendar which DIDN'T eventually repeat. But somehow the two cycles lining up seemed suspiciously neat. And yet, was presumably a complete coincidence.

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.

[1] Although, given the hassle they had getting that going, they were probably wise not to.

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Simon Tatham

from: simont
date: 4th Oct 2010 15:30 (UTC)

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.

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Tony Finch

from: fanf
date: 4th Oct 2010 15:38 (UTC)

"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...

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Simon Tatham

from: simont
date: 4th Oct 2010 15:50 (UTC)

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...

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cartesiandaemon

from: cartesiandaemon
date: 5th Oct 2010 10:23 (UTC)

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

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Tony Finch

from: fanf
date: 5th Oct 2010 14:42 (UTC)

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.

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cartesiandaemon

from: cartesiandaemon
date: 5th Oct 2010 15:13 (UTC)

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.

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cartesiandaemon

from: cartesiandaemon
date: 4th Oct 2010 15:42 (UTC)

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.

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cartesiandaemon

from: cartesiandaemon
date: 4th Oct 2010 15:43 (UTC)

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.

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Andrew

from: nonameyet
date: 5th Oct 2010 21:15 (UTC)

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

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Philip Newton

from: pne
date: 2nd Nov 2010 08:03 (UTC)

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)

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Tony Finch

from: fanf
date: 2nd Nov 2010 09:34 (UTC)

Interesting link, thanks! Re lengths of the year, the Gregorian calendar is intended to match the period between vernal equinoxes, because of the importance of Easter.

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John

from: deliberateblank
date: 2nd Nov 2010 00:51 (UTC)

Which suggests the idea of the Penrose Calendar.

Of course, leap years *ought* to be based on a continually evaluated DDA using real measured year lengths.

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Tony Finch

from: fanf
date: 2nd Nov 2010 01:28 (UTC)

Ugh, no, observational calendars are a serious operational pain.

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Tony Finch

from: fanf
date: 11th Oct 2010 09:20 (UTC)

Ah good :-)

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