The equinox marches on

Spring has officially arrived in the Northern Hemisphere.  Not that you'd notice here in the Western US, where it's unseasonably cold.  Of course, in the East it's unseasonably hot, and in the middle the combination is causing tornadoes.

In fact, spring arrived last night, at 10:14:09 pm my time, Pacific Daylight, on the 19th day of March by the Gregorian calendar (56006.21816).  That's the 20th of March for most of the world, but this is still the earliest equinox in over a century.  Part of the reason for this is that there was a leap day last month, which pushes the date back a day.  The next one, in 2013, will come nearly six hours later, and so on until the next leap year in 2016, when it will again jump back a day.  In fact, it will jump back slightly more than a day.  It continue to slip earlier and earlier every leap year, until 2100, when we will skip a leap year.  The reason we have leap years is to keep the equinox from arriving later and later every year.  The reason we skip leap years is to keep the equinox from arriving too early.  The earliest vernal equinox this century will be in 2096 (86686.5848) after which it will advance nearly six hours each year until 2103 (89243.265).  In 2104 the leap year cycle will start again, so the equinox date will again go back a day, or about 18 hours before 2103 (89608.509). 

For the rest of this century, spring will arrive more and more often on the 19the day of March in Pacific Daylight Time, instead of the 20th.  Then it will arrive on the 20th every year from 2099 to 2135.  Of course, it will always arrive earlier in the Eastern Hemisphere, often on the 21st day of March, as it's supposed to.  The Romans, it's said, originally fixed the equinox on the 25th day of March, as Julius Caesar noted on his calendar, but by the fourth century it had slipped to the 21st, and the latter date is the one that Pope Gregory noted on his calendar, by which time it had slipped by between 9 and 10 days, so he dropped 10 days, although it probably would have been more accurate to have dropped only 9, since it usually falls on the 20th in Europe.  At least it's closer in Asia and Australia.  (I know that doesn't quite add up, since the date should have slipped only 3 days in the first four centuries rather than 4, but I don't know the reason for the discrepancy.)

There is a good graph of the March equinox's wanderings on Wolfram.

MJD 56006.974

Astronomers gone bad

Last week astronomer Phil Plait posted on his Bad Astronomy blog an article about leap day. In it he stated:

The year is not exactly 365.25 days long. Our official day is 86,400 seconds long. I won’t go into details on the length of the year itself (you can read a wee bit about it here), but the year we now use is called a Tropical Year and it is 365.242190419 days long. With malice aforethought — my calculator won’t hold that many digits — let’s round it to 365.2421904... 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...This whole 400-year thingy was started in the year 1582 by Pope Gregory XIII. That’s close enough to the year 1600 (which was a leap year!), so in my book, the year 4800 should not be a leap year.

Except that he's wrong.  He was also wrong when he posted this originally four years ago. I posted a correction in the comments then, and I've done so again now, but obviously he does not read the comments. The reason he is wrong is because he's using the wrong value for the year. The document that Gregory issued establishing his calendar is called the Inter gravissimas.  It clearly states that the reform is intended to fix the date of the vernal equinox, upon which Easter is based.  The year defined by equinoxes is not the same as the Tropical Year mentioned above, but a slightly larger value between 365.24237 and 365.24238.  This is closer to the average Gregorian year of 365.2425 days.  Using the equinoctial figure, it will take about 8000 years before it's off by one day, which would be in the tenth millennium.  Due to the variability of the equinoctial year, we cannot even predict its value that far in the future.  The way it's trending now, I could even be much further in the future.

He is not alone.  This error is often repeated by astronomers.  It is sometimes traced back to John Herschel, but during the Revolution French astronomers calculated that the mean year was between 365.2422 and 365.24225 days and proposed an adjustment after 4000 years.  But none of them were using the vernal equinox, as Gregory did. The correct figure may be found in Wikipedia and others.  Anybody can figure it out themselves simply by taking the average between the equinoxes of any two years.

MJD 55994.238

The Short, Strange History of Decimal Time

In my previous post I linked to an article from the science and sci-fi blog, io9.  There was another post there a couple of weeks ago I wanted to link to, The Short, Strange History of Decimal Time.

MJD 55987.308

Leap Day

I know I haven't posted in a long time, as I've been busy, but I have some time now, and this date happens only once every four years, so I won't let it pass without comment.

The truth is, calling the last day of February "leap day" is a relatively recent practice. Although we today count days from the start of the month, our Gregorian calendar was originally a slight modification of the Julian calendar, itself based by Julius Caesar on the earlier Roman calendar, which counted days backwards.  Thus, the first day of each month was called the Calends or Kalends of that month, so the last day of February would be known as the day before (Latin Pridie) the Calends of March.  (This is where we get the word "calendar".)  The rest of the days in the last half of each month were likewise counted down to the Calends of the following month.  The Romans included the Calends itself as the last day in their countdown.

Caesar did not insert the leap day at the end of February, but on the 24th day, which in Roman counting was the sixth day counting down to the Calends of March.  Thus, in leap years two days were both counted as the sixth day before Calends, which we would now call the 24th and 25th days of the 29-day month.  (Sometimes the 24th was considered the extra day and sometimes the 25th.)

Consequently, someone born on the last day of February in a leap year, i.e. February 29, would not have celebrated only once every four years, but rather every year on the last day of the month, which we call February 28 in common years.  Since the extra day was counted as the same as the 24th, as though it were one 48-hour-long day, anyone born on the leap day, i.e. February 25, would celebrate their birthday in common years on February 24, the sixth day before the Calends of March.  Likewise, the Roman Catholic Church recognized February 24 as the feast of St. Matthias in common years, but February 25 in leap years, up until as recently as 1970.  Other feasts near the end of February were likewise shifted.  I believe that this is still practiced by those using the Julian calendar, i.e. Orthodox churches, although in this century Julian calendar dates fall 13 days behind those in the Gregorian calendar.

Common year:
February                      March
 22  23  24  25  26  27  28   1...
VIII VII VI  V   IV  III II   K


Leap year:

February                          March
 22  23  24  25  26  27  28  29   1...
VIII VII VI  VI  V   IV  III II   K

So in actuality, the leap day occurred on Saturday, February 25, rather than today.  There are a number of articles on the Internet today about leap years, so I'll link to How the Quest for the Perfect Calendar Accidentally Created February 30.

MJD 55987.300

iPhone 4S

I have been broadcasting live video using my iPhone 4. I've been waiting to see if the new iPhone would be worth upgrading to. Now that the iPhone 4S has been released, I can tell you that there have been specific improvements to the camera and video processing:

• 8 megapixels, up from 5
• Wider aperture
• Additional lens (5 instead of 4)
• Faster shutter
• Face detection
• Faster processor
• 1080p HD video
• Video stabilization
• Temporal noise reduction

Hopefully some of those will result in better video broadcasts, with better color, sharper images, less graininess at night, less shakiness and less problems. The download speed is potentially doubled, depending on the network, but the upload speed is unchanged, so that will be of little help.

Another benefit is the integrated Siri voice assistant, which will apparently allow me to do more hands-free while driving, such as getting addresses and directions, sending texts, etc. I'll have to wait to see it in action.

Will it be worth $200 plus $55 tax to upgrade? I guess I'll find out in a week, because I've already ordered one! My wife should be grateful to get my iPhone 4.

It's a shame that Steve Jobs had to pass the day after it came out. This is his legacy.

Bonne année!

The autumnal equinox occurs on MJD 55827.378 (2011 Sept. 23 09:04 UTC) or 9h13 in the morning, Paris mean time. Therefore, according to the rule in effect during the French Revolution, MJD 55827 (23 September in the Gregorian calendar) will be the first day of year CCXX in the Republican Calendar.

According to the rule used by Brumaire, including their iPhone and iPad apps, MJD 55827 is also the first day of the 220th Republican year. The day before, MJD 55826 (22 September), is a leap day according to Brumaire, but not according to the official calendar rule. Dates prior to this are different by one day, but with the start of the new year, dates will be the same by both rules until 2014.

The first month of the Republican calendar is Vendémiaire, so New Year's Day is 1 Vendémiaire. Happy new year!

MJD 55824.627

Metric clock video

I found this video by a guy who actually had a mechanical "metric clock" made for him.


Btw, I'm using the new Blogger app on my iPad to write this. Maybe now I'll post more often. But it leads me to wonder again why anybody makes iPhone apps that aren't formatted for iPads.

MJD 55658.367

Salut et Fraternité app for iPad by Brumaire

Finally, people are starting to make apps formatted for iPad.  Salut et Fraternité for iPad by Brumaire is a port of the Salut et Fraternité app for iPhone, which displays the current French Republican calendar date and decimal time, and allows you to convert between Republican and Gregorian dates. Unfortunately, instead of simply updating the original app for iPad, they made it a separate app, forcing you to pay $1.99 for both.  The iPad version is pretty much the same as the original, but looks better on the bigger screen.  Also, instead of a separate tab for the decimal time watch, you select a setting to have it displayed on the main tab.  However, for some reason the season images don't appear for me on the "Convert" tab after I turn them on.  If you already have the iPhone version, you might want to simply use that on your iPad, rather than pay twice, even if it does look a bit crappy, although another two bucks at least won't set you back much.

MJD 55783.913

Carrigan paper

Richard Carrigan's 1978 paper in the American Scientist, "Decimal Time", is now available online at JSTOR.  Unfortunately, you need an account to read the whole thing, but the first page is available for free.  Here is the complete citation:

Decimal Time: Unlike the metric system of measurements, decimal time did not survive the French Revolution. But is dividing the day by tens a possibility for the future?

Richard A. Carrigan Jr.

American Scientist
Vol. 66, No. 3 (May-June 1978), pp. 305-313
(article consists of 9 pages)

Published by: Sigma Xi, The Scientific Research Society

Stable URL: http://www.jstor.org/stable/27848641

MJD  55770.882

Revol-di app for iPhone by Kodaski.fr

Revol-di 1.0 by Kodaski.fr was released 2011 January 20 (55581) and is the third French Republican Calendar app for the iPhone.  The name is taken from an early proposal for the first day of the décade, better known as Primidi.  Unlike Calendrier and Salut et Fraternité, this one is free.  Unfortunately, like the others, it is formatted only for the iPhone (and iPod Touch) and not the iPad.  (It's been over a year, why doesn't everybody recognize the iPad?)  Also unlike the others, it is targeted at genealogists, so it only converts dates during the revolutionary period when the calendar was in effect, 1792-1805 (JD 2375840-2380688), and does not convert more recent dates, nor does it display decimal time.  At least it does not have to worry about which method to use for determining modern dates.

It does have features the others don't, however.  For one, you can make notes, which are stored under the (Gregorian) date they are made.  This is useful for recording birth dates and such during the Revolution.  The entire notepad may then be shared via email.  Under "Information", facsimiles of the laws relating to the Republican Calendar are available, in French.  (Gregorian dates are also displayed in French.)  "Historical context" gives information about the calendar.  "The calendar months Illustrations" shows period paintings of calendar girls.  There is a "Help" section and four different wallpapers to choose from.

MJD 55710.444

Nonidi 9 Prairial an CCXIX à 4^hd 50^md t.m.P.