I thought I should celebrate the once-in-a-century fact that all of our time/date digits are the same this morning by actually writing another post within a week of the last one (something I don’t think I’ve yet managed on this blog). Of course, the pedants among you might think it improper not to include the “20” in “2011”, but if we were to include those two digits then this occurrence will only ever have happened once before – on this day in 1111 – and will never happen again! Which is a bit upsetting.

Here is a question for you: what day of the week will it be the next time this happens, on 11/11/2111? This is the precisely the kind of question that some “idiot savants” are famously good at answering very quickly. How could they possibly do this, in their heads, in a matter of seconds? It seems very mysterious, until you give it some thought. Not that I have! But John Conway, a highly esteemed mathematician who needs no introduction to any other mathematicians who may be reading this (non-mathematicians might possibly unwittingly know of him through his creation the Game of Life…if you can remember back to the dark old days of Windows 95, this was actually included as a “game” along with Minesweeper et al.)^{*}, has actually invented a method of giving the day of the week on any given date. Why? I don’t know. Perhaps he was bored of competing with mere mortals and decided to take on the savants.

Anyway, his method is called the Doomsday algorithm, and is actually quite simple. It takes advantage of the fact that the “Doomsday” of a given year – that is the last day of February that year – always falls on the same day of the week as the following easy to remember dates: 4/4 , 6/6, 8/8, 10/10, 12/12. So all we need is the Doomsday for a given year; we can then exploit this fact to get to the closest date to the one we want, and then just count mod 7 (which basically means, in this context, go cyclically through the days of the week) until we get to our desired date.

To find the Doomsday for a given year, we just need to start with the Doomsday for this year. Then use the fact that the same date next year will be one day forward (as 365/7 has remainder one), or two if next year is a leap year.

So, given that the Doomsday this year is Monday, in 100 years it will be Monday + [124], as there are 24 leap years between now and then (years divisible by 100 are not leap years! Unless they are divisible by 400). 124/7 has remainder 5, so we get Monday + [5] = Saturday. So Doomsday is Saturday in 2111, hence 10th October is also Saturday, and 11th November is therefore Saturday + [32] (as October has 31 days). 32/7 has remainder 4, so finally we get Saturday+[4]=Wednesday.

Great! Now we know that the next time it will be 11:11:11 11/11/11 will be a Wednesday. Of course we could also have just looked it up on the internet. And this is all assuming that you care, which is quite an assumption to make. But my point is that there is nothing particularly complicated here. Conway is reputed to be able to do this for most dates in just a few seconds, and so the claim that savants are using some mysterious part of their brain, or are somehow hard-wired into the Gregorian calendar system, begins to look a bit unlikely. It is more likely to be the case that they are simply very good at mental arithmetic (especially mental modular arithmetic).

Incidentally, note that the Gregorian calendar “resets” every 400 years, in two senses. Firstly, as I mentioned, years divisible by 4 are leap years, unless they are divisible by 100, in which case they aren’t. Except when they’re divisible by 400, in which case they are! Conveniently, the number of days in 400 years – of which 97 (=24+24+24+25) are leap years – is divisible by 7, which means that the whole days-of-the-week/date correspondence also resets. So we can instantly say that 11th November 2411 will be a Friday.

That’s quite enough days-of-the-week. It may have occurred to you, whilst pondering the Doomsday algorithm, that perhaps the Gregorian Calendar is more complicated than it could be. Also, surely non-Christians are not entirely happy with having the supposed year of Christ’s birth as year zero?

The Islamic calendar is lunar, and has months with the following names (translated from the Arabic):

- “Forbidden”
- “Void”
- “The First Spring”
- “The Second Spring”
- “The first month of parched land”
- “The second month of parched land”
- “Respect”
- “Scattered”
- “Scorched”
- “Raised”
- “Truce”
- “Pilgrimage”

This naming system gives some idea as to how violent and harsh life must have been in the Arabian peninsula at the time. The Forbidden refers to fighting – no fighting allowed in this month. Similarly Respect and Truce. But this still leaves 9 months of fighting time! In fact it will have been necessary in month 2, which is called Void as this was traditionally when the non-Muslims came and robbed everyone, leaving houses empty. Months 5 through 9 generally sound pretty difficult: the “Scattered” of month 8 refers to the necessity of spreading out to look for water after 3 parched months. And then to top it all off, in month 9, which sounds worst of all, they had to fast all day (“Ramadan” means “scorched”). I think the best month, however, is Raised: apparently she-camels raise their tails when they are pregnant. I like that there is a whole month named after camels’ biological cycles. Then again, given the importance of camels if you live in the desert, this is perhaps more sensible and practical than naming months after Roman dictators (July, August) and Gods of War (March), and certainly more interesting than just calling them the 9th month (November), 10th month (December) etc.

However, the lunar system would have led to some problems. Given the fact that 12 lunar months is 11 or 12 days off the time it takes the Earth to travel around the sun, after 20 years or so camels would be raising their tails at entirely the wrong time of year, fighting would be taking place when time would be more practically spent looking for water, and all sorts of other confusion would ensue. I assume they found a way around this, but I’m not sure how.

Most ancient civilisations used lunar calendars…understandable if they had only rudimentary astronomical skills, as the moon provides a regular and easily-observable marker of time. Ironically though, the medieval Islamic astronomers were probably the best in the world at the time, and this was a direct result of having such a calendar. A new month was only declared when certain respected men testified before a committee that they had seen the crescent moon. If it happened to be cloudy that day, then the month would have to start the next day instead. This was, of course, not very satisfactory; it was important to be able to know in advance when the next new moon would occur, as different months meant different religious practices. The search for alternative methods of prediction led to an intensive study of astronomy, and great advances in the subject.

OK, that’s all for today, I’ve got to stop writing now and observe two minutes silence. If you are interested in alternative calendar systems, you’ll be pleased to hear that there is a whole wiki devoted to them! Here. You’d be surprised how many there are.

Finally, as a footnote, I see that, despite a habit of writing rambling, over-long posts with gaps of up to a year in between, I seem to have somehow reached the milestone of 50 Google reader subscribers (if you are interested in how many people subscribe to a given blog through RSS, most of them will be through Google…you can find out by going to Google reader, clicking “subscribe” and searching for that blog).

At the risk of sounding like some kind of customer satisfaction survey: Who are you all? How did you get here? What do you like or dislike about this blog? The more feedback I get, the better your experience might be!

^{* By the way, if you are not a mathematician, can you name any famous mathematicians? I would guess probably not. Can you name any famous physicists? I would guess at least 2 or 3. This has always struck me as exceedingly unfair.}

EDIT: since I posted this (about 5 hours ago), people have landed on this blog through the following searches:

“what day will be 11th november 2111″

“day+of+the+week+of+november+11,+2111″

“what day of the week is 11/11/2111″

“what dayoftheweek will 11112111″

“what day will it be nov 11, 2111″

“what day is november 11th 2111?”

“what day of the week will the next 11/11/11 be”

Why is everyone so interested in what day of the week it will be on 11/11/2111?! How odd. The only possible explanation I have for this is that some teacher somewhere set this as a homework question, and the pupils turned to Google for the answer…

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Hi. Recent Google Reader subscriber here – possibly the 50th, although I doubt it, given my subscription was a few weeks ago. I’m answering the call for feedback.

I am struggling to remember which particular internet search brought me to the first mathematicians blog I read, Irregularity, but it was probably something to do with a curiosity for what mathematicians do – something your ‘Quadratic Equations’ post answered quite well. The blogroll on Irregularity lead me here, and I’m currently trialling a few mathematicians’ blogs to see if I can keep up and retain an interest.

Interests-wise in general, I’m into ‘popular physics’. Many moons ago, having not done as well on my physics A-Level as was hoped, I decided to switch to another strong-ish subject of mine for continued study: languages. This was, for me, the path of least resistance. I now translate for a living and probably have a lot less stressful brain-freezes than I might have done dragging myself backwards through a science course.

But the interest in physics remains. Maths, less so, because of my inability to abstract as well as some, perhaps; but I’ve always suspected that I was missing the point of maths a little. Watching the recent BBC documentary about the young maths ‘genius’ was interesting, especially as the Cambridge professor (apologies for not naming him, he’s probably very well known, but I don’t recall) dismissed and trivialised the importance of A-Level maths so much.

In a wider sense I get kicks from things like reason/logic/answers and dislike posturing/pretention/obfuscation. Advances in understanding in how the natural and physical world work are something I try to keep up on.

I have enjoyed perusing the posts of these maths blogs in recent weeks, and have found an odd mixture of inaccessible encrypted code and deeper insights into the world of the mathematician than I’ve ever come across before.

Why the interest? Because I think the contribution of mathematicians to ‘the answers’ is underestimated, even by myself. However, not being a dinner-table-type subject of discussion, it is almost blindingly obvious why it is underestimated, i.e. it is not very marketable in its current form, from what I can tell.

Do I fit the profile of what you expected from your readership? I suspect you would have been able to have told me my interests, deduced from the very fact that I read your blog.

Thanks for the comment Luke…very interesting, and nice to have a reader de-anonymised! Yes, I would say that you pretty much fit the rough profile I expected . You may have noticed that I am cutting back on the actual mathematics in favour of “interesting scienc-ey things” (with a mathematical slant)…it seemed like these were the things that people wanted to read about. And as you say, while the idea of mathematics is fascinating, unfortunately in practice it often just seem like so much encrypted code (including to other mathematicians who happen to have different specialities)…not really something that keeps people’s interest as they are idly browsing a blog.

Anyway, good for you as a non-scientist keeping up with science. Personally languages are one thing I have always regretted not learning. But there are some quite deep links between mathematics/logic and linguistics, which I have been considering writing a bit about, so perhaps we can find some common ground. in the meantime, I highly recommend the documentary “Fermat’s Last Theorem” if you are interested in what mathematicians do; you can find it here:

http://video.google.com/videoplay?docid=8269328330690408516

That film was fascinating. How Fermat originally proved his theory without modern mathematics seems to beggar belief. If indeed he had proven it without fault.

Thank you for catering to us non-mathematicians and drawing us in that little bit closer to the world of real maths. And it goes without saying that I’d be very keen to hear your thoughts on links between maths and linguistics.

As for regrets of not learning other languages, it’s really just the case of cracking another code, and given that you already have one to use as a base, and that you are quite comfortable cracking codes, I’m sure it wouldn’t take you long to be comfortable in a new one.

To simplify the task, you could pick one with lots of similarities to English (such as French) and you’ll then find that Spanish and Italian suddenly become readable and the snowball effect takes over. Scandinavian languages are also interesting because they are quite simple grammatically and very similar to our own in vocabulary and structure. And as a bonus, learning one opens up the others.

The trouble is the perennial lack of time and necessity. A side project at the back of my mind is to enable people to learn without having to give up much time by encoding the learning process in an easy to digest and memorable package. Easier said than done, but a worthwhile cause. I hope.

Some polyglots use ‘sentence mining’ to pack their memories full of phrases, but it is an extremely labour intensive process. I’ll be working along these lines to offer a simpler method to people who want to become ‘operational’ in a short time.

Thanks again for your reply. This countryman lends you his ear.