Hooptedoodle #138 - All the Rest have 31, except February

"It's weird - you know, I could swear it was a Sunday…"

Yesterday was Sunday, and I was woken early by the sun shining in the window and the birds (no respecters of late night World Cup-viewing schedules) making a racket. As I lay there, it occurred to me that we are close to Waterloo day.

One thing about Waterloo which is important (or seems so) is that it took place on a Sunday. Is there not a reference to the priest at Plancenoit insisting on ringing the bells for morning mass? Whatever, it was a Sunday – you will struggle to find any description of the event which does not mention this.

This year 18^th June is a Wednesday, and next year – the 200^th anniversary – will be a Thursday. So, in my half-awake state, I reasoned that somehow or other I should be able to reconcile the 4-day slippage over two centuries. If I failed, there was always the chance that I would drift off to sleep again, so how could I lose?

Righto – concentrate, I told myself.

Your standard year is 365 days, which is 52 weeks and 1 day, so that gives you a 1 day slip forward each year – and then there’s leap years. OK – no problem – every 4^th year we get an extra day, so on the face of it that’s 5 days forward every 4 years (or 2 days back, if that’s easier – which it probably isn’t). Aha – snag. I was vaguely aware that something funny happens at the end of each century – leap years aren’t so straightforward as this. I realized that this wasn’t going to work until I’d done a little self-education on the nippy question of what happens about extra days at century-end.

[This is a common enough situation – I regularly find that unlocking the window latch requires an expanding series of preliminary jobs until I have to move the entire house four centimetres to the left before I start.]

Not to worry, I reasoned – let’s gloss over the century issue for the time being, and see how far out I am. Then I can check the details and balance everything up. At this stage I wasn’t going to get back to sleep. OK – 100 years is 25 lots of 4 years, which (as I had already decided) means a total slip forward of 25 x 5 days, which is 125 days, which is 17 weeks 6 days, which is a slip forward of 6 days or a slip back of 1 day. That’s not too difficult, though the birds were putting me off a bit. This means that my crude version of the leap year rule gives a backward slip of 2 days in 200 years, which would move the anniversary of our Sunday battle to Friday.

Drat. We already know it’s going to be a Thursday in 2015. I’ve lost a day somewhere – or have I gained a day? At this point I decided

(a) it’s less confusing if I always count the slippage forward

(b) I’d better get up and switch the computer on. Not knowing what happens to leap years at the end of a century is not too pressing a matter if it only affects us once every 100 years, but clearly this is a gap in my toolbox.

First pseudocode rule I found was reasonably simple, even at that time of the morning:

if year is not divisible by 4 then common year


else if year is not divisible by 100 then leap year


else if year is not divisible by 400 then common year


else leap year

But then I found that it isn’t as simple as that – and we get into Gregorian and Julian calendars, and all sorts of alternative calendars, some of which I have never heard of. I think that my world conforms to the Revised Julian, and the full definition for this is:

The Revised Julian calendar adds an extra day to February in years that are integer multiples of four, except for years that are integer multiples of 100 that do not leave a remainder of 200 or 600 when divided by 900. This rule agrees with the rule for the Gregorian calendar until 2799. The first year [in which] dates in the Revised Julian calendar will not agree with those in the Gregorian calendar will be 2800, because it will be a leap year in the Gregorian calendar but not in the Revised Julian calendar.

This rule gives an average year length of 365.242222 days. This is a very good approximation to the mean tropical year, but because the vernal equinox year is slightly longer, the Revised Julian calendar does not do as good a job as the Gregorian calendar of keeping the vernal equinox on or close to March 21.

In fact, I believe these two versions both give the same answer for this particular problem – i.e. 1900 was not a leap year, but 2000 was. So let’s look at this again – 2 x 25 lots of 4 years, each 4 years giving us 5 days slip forward, is 250 days, which is 35 weeks 5 days, but in fact the year 1900 should not have been a leap year, so deduct 1 day, giving 35 weeks 4 days. 4 days forward from Sunday gets us to Thursday for the 200^th anniversary, which is correct.

Thank goodness for that. Since there was no point in going back to bed at this point, I got sidetracked into reading about exactly when centuries end, and I leave you with the following statement from The Times of 26^th December 1799, which does not seem to invite further comment:

We have uniformly rejected all letters and declined all discussion upon the question of when the present century ends, as it is one of the most absurd that can engage the public attention, and we are astonished to find it has been the subject of so much dispute, since it appears plain. The present century will not terminate till January 1, 1801, unless it can be made out that 99 are 100... It is a silly, childish discussion, and only exposes the want of brains of those who maintain a contrary opinion to that we have stated.