I'm going to do the calendar trick with you today, which is a bit of an old mathematician's trick. If you give me a date I can tell you which day of the week it is. I'm hoping to teach you how it's done as well. Okay, well I've got the book of calendars; goes back to 1800, goes up to 2100.
- (Brady: Let's do June 18) Alright, okay so-
- (1976.) All right, June 18 1976. So I'm going to think about this, think about the year first. So 1976- uh-huh. And June you said? And what was the date?
- (18) 18; is it a Friday? (I don't know)
- Let's find out. This is- this is tension now.
- (June 18...) (Yes it is!)
- Oh wow I'm so glad that worked. I tried to look confident but I'm really glad that worked. Yes- now you could test me again to prove that I really know what I'm doing. (January 1) (1901.)
- Going down- so the year 1901, and you're saying January 1- is it a Tuesday?
- (I dunno) (Tuesday!) Wow! Wowee! So I think it's time that I taught you how to do this. So it's a calculation- I haven't memorised every calendar in that book by the way. It's nice to tell people you have but I haven't. There's more than one way of doing this but I'm going to show you something called the Doomsday method which was devised by our friend John Conway in the 1970s. And to do this you need to memorise some special dates. The 4th of the 4th, by which I mean 4th of April; 6th of the 6th, so 6th of June; 8th of the 8th, 8th of August; 10th of the 10th, 10th of October; and 12th of the 12th, 12th of December. And what is quite cool is all these dates are on the same day of the week. And- it's nice fact isn't it? (I didn't know that!)
- I know! It's a lovely little fact, keep that in your pocket, yeah. So that special day of the week we call that the Doomsday because that's going to be special for what we're going to do next. In fact there's more, I can show you some other special dates. The 9th of the 5th, the 5th of the 9th, the 7th of the 11th, the 11th of the 7th also share the same day of the week as all those. Doomsday will change every year but I know that these dates are all sharing the same day of the week. So for example if I know that the 4th of April is a Monday then I know that all of these dates are going to be a Monday for that year. Oh by the way, nice way to remember some of these, I mean the these even ones are quite nice to remember. These ones: I work 9 to 5 at the 7-11, that's sort of a way to remember it. I haven't talked about January, February and March. Slightly trickier because of the leap year problem. For January the special date is the 3rd; or it's a 4th on a leap year. So to remember that it's it's the 3rd of January for 3 years and then it's a 4th on the 4th year. For February it's the last day of February; which is 28th normally but 29th on a leap year. These dates will share the same day of the week as all my other special dates, I've only left out March. And so for March the special date for you to remember is the 14th of March - or as mathematicians like to call it, Pi day! Pi day is Doomsday. So if you know the day of the week, if you happen to know the day of the week for pi day, you will know all these special dates for the rest of the year. Now if the date you want to
know is not one of these special dates, well you just adjust. So all I have to do is find the nearest special date and then I add or subtract a few days. One thing to remember when you're doing that is if you add seven days you end up back to where you started; so if it was a Monday and I add seven days I get back to a Monday again. If I had to add 15 days, then I might add 14 which takes me back to Monday again, and then I'll add one more. Well shall we do a date in the future? What do you want 20th of-
- Christmas! Christmas, lovely. Christmas, let's talk about Christmas in 2021. Now I happen to know that pi day in 2021 was a Sunday. So I know it's a Sunday, I now find the closest date- what's that? Well it's going to be the 12th of the 12th. So I know the 12th of the 12th was a Sunday as well. But I need to add on 13 days? I add 7, takes me back to Sunday, and I add six more days takes me to Saturday. So I now know that Christmas in 2021 is a Saturday. So that's kind of nice as a kind of a life hack. If you happen to know what pi day is for that year, you can work out all the days of the week for the rest of the year. And that's kind of a nice little fact to have in your pocket. Of course if you really want to be impressive about this then you want to be able to do this for any year that you're given; but that involves working out what pi day is or Doomsday is for that year. So let me show you how to do that. Okay, if you want to work out Doomsday for some year in the future - let's do that - then one thing you need to remember is Doomsday for the year 2000. And I will just tell you this as a fact, in the year 2000 Doomsday, you can call it pi day or whatever you want, was a Tuesday. In 2001 our special day was a Wednesday. In 2002 our special day was a Thursday. In 2003 it was a Friday. In 2004 our special day, it was a Sunday. Snd then if I keep going- like 2005 is a Monday, and so on. Hopefully you can see what's going on, so every year goes forwards one day and a leap year it goes forwards an extra day. So if I want to work out Doomsday for a year in the future then what I do: I know 2000 was a Tuesday, I then just add on the year. Because I'm adding as many days as the year, and then I add on how many leap years we've got as well. And that's the calculation I'll be doing in my head. So if I do an example?
- 2020. Okay so if I do 2020: so I know 2000 started on a Tuesday, you actually add on the years, the 20 years, and then I have to add on how many leap years. Which means I take the year and divide by 4. If I divide by 4 here I'm going to get a 5 - don't care about fractions you can throw those away. But in this case there weren't any fractions so I'm going to start with Tuesday, add 25 days. So what's that going to be? I don't care about 7s, so I can- I don't care about 21, it can just disappear, and I would have 4 left over. So it's going to be Tuesday plus 4 more days, so I know doomsday in 2020 is a Saturday. If I then want to work out a date in 2020 I then just do the Doomsday method and find a special date and adjust from there. And that's all there is to- well I say that's all there is to it, that's the calculation I'm doing in my head. You can do this calculation, you get better at it with practice; and I can actually show you some sort of tips and tricks so that you can get really good at this. Okay tips and tricks: one is to convert the days of the week into numbers because then it just turns the calculation into a sum. So I'm not thinking, oh Tuesday plus 25 days, it just becomes a regular sum. So this is a conversion for days of the week: Sunday, think of that as none-day. Monday is one- day, Tuesday to twos-day, and Wednesday is threes-day.
That's a three. Thursday, fours-day. Friday, five-day
- (They almost all work.) I know it's lovely isn't it? It's lovely how they work so nicely. Saturday, six-a-day and that's going to be a 6. So now when I'm doing this calculation it is just a sum, it just works out nicely. And then I convert it back to the day, the last thing I do is convert it back to a day of the week and then you give that answer. Now if you wanted to really show off you could do a century as well, I'll really quickly show you how to do a century. I've shown you how to do the 21st century, so the the 2000s. Because I said that the Doomsday in 2000 was a Tuesday. What about if you wanted to do someone's birth date and they're born in the 1900s? I'll show you how to do that as well. It's really simple actually: Doomsday in 2000 was a Tuesday, 1900 it was a Wednesday. This is just something you remember. If you really want to show off you could do the 1800s - Doomsday was a Friday. And if you want to go back to the 1700s Doomsday was a Sunday. So if you want to do one of those centuries, do the same calculation but you start from those positions. And if you want to do the future that pattern repeats. So I've got a pattern here:
Sunday, Friday, Wednesday, Tuesday; and it keeps going. So the 2100s, that starts with a Sunday and then it would be a Friday, Wednesday, Tuesday and so on. So you can do any century, finally doing the year. Because that's quite hard. We did an example there which was 2020 and that was relatively easy because 2020, the 20 was quite a small number. Now if it's a bigger number it gets quite hard. So imagine if I am doing a date like 90- we started with 1976 and I'll go, okay I've got 1976 and then I've got to work out the leap
years of 19th cent- then I've got add them together and take away the 7s- okay. So I'm going to show you some shortcuts for the year as well. Do you know there's only 28 calendars, and then the pattern repeats every 28 years? Here are some key years to remember: 0 is a 0, but 28 is a 0 as well because the pattern starts again. 56 is a 0 because the pattern starts again, and 84 is a 0 because the pattern starts again. So if you gave me a date, say 1988, what I wouldn't do is think, oh now I have to start at 1900 add 88 years and add the leap years and uh - that's going to be quite hard. What I'm going to do instead is think, okay 1900 starts with a Wednesday, I know 84 is a zero year so then I just start from 84 and add on four more years, so then I add on 4, add one leap year, and I know that that's going to be a 5. So I add on five days after Wednesday, so that's all I would have to do. And also-
- (Which is what? Which is-) And this is why we need those numbers as well: Wednesday is a 3, plus 5 is an 8. 7s disappear so it's a 1, it becomes Monday. That's why those numbers suddenly become useful because you- you stopped there didn't you? You went, okay Wednesday plus a 5 is- and that's why those numbers suddenly become useful. Conway broke it up a little bit more, he broke it up like this way: 0, he started with
12, 24, 36, 48, 60, 72, 84, 96. If you notice there, multiples of 12. And he remembered that 0 is a 0, 12 is a 1, 24 is a 2, 36 is a 3, 48 is a 4, 60 is a 5, 72 is a 6, 84 is a 7 and 96 is an 8. So he memorised that and that kind of breaks up the century a bit more. So when I did the calculation for Brady at the beginning it was - what was it? 18th of June 1976? What I didn't do is go, oh 1976, oh that's a hard calculation. I knew 72 was a 6 and I started there. That's a 6 plus 4 years is now a 10, plus a leap year is an 11, plus the century is a 3 so now I've got 14 - oh 14 disappears! Oh I was really pleased, suddenly disappears suddenly it becomes a 0 again. And then we went and did the Doomsday method on the 18th of June. So the closest special date is 6th of June and then I go, oh well I know the 6th of June is a 0 because that's my Doomsday calculation and I added on 12 more days. So I got a 12, I knew I could ignore the 7s, I went oh the answer is 5 and the last step is going, oh if the answer's 5 I convert that into a Friday - and I can say Friday. (It's my birthday.)
- Oh was it your birthday? You see, I could have prepped this but there, this was live, I actually did it. Yeah, phew. It's a bit Numberwang. Well this is appropriate and a lovely coincidence; I'm building a perpetual calendar. It's the latest box of Genius to arrive from KiwiCo. Everything I need is already in the box and comes with instructions that are not only clear but they're filled with these little extra bits of knowledge. The subscription crates are just a great way to dive into science and technology, engineering, the arts and mathematics; nothing gives you a better feel for how things work, how the world works, than doing the building yourself. I've been sending monthly crates to my nephew down in Australia as you've probably seen before, but let's be honest these are great for people of all ages. You can get 50% off your first box by using our url: KiwiCo.com/Numberphile It's there on screen and in the description if you want to go and have a click. Do it for yourself or do it for the young learners in your life. Don't waste another day. See what I did there with the wasting a day thing? If someone says, are you coming to my birthday, when is it? 18th of June and then you go, uh am I free? Yes it's a Wednesday I am free on that day. Genuinely I think there is something you could do with this but also you can show off at nerdy parties. (Do you ever use this though?
Wouldn't you) (just check your calendar on your phone?) Yeah that's not the fun though! It's all part of the fun, doing the calculation and showing off, it's all part of the fun. Of course you could check on your phone.
What on earth is going on with that thumbnail
This has probably been my favorite thing posted here in forever. You better believe I just spent a good while practicing and I feel like I’ve got it down!
The last step is quite intuitive for those who speak Mandarin/other Chinese dialects, since the days of the week already have numbers in them
Here’s a similar method that I found pretty easy to learn.
https://youtu.be/714LTMNJy5M
For a straightforward way to calculate a year’s doomsday without thinking about it too much, use the odd-add-11 rule.
Take the year modulo 100 (that is, without the century part). If it’s odd, add 11.
Divide by two.
If the result is odd, add 11.
Take the result modulo 7 (remainder after dividing by 7).
Take that and subtract it from 7.
Add the offset for the century (3 for 1900s, 2 for 2000s, 0 for 2100s/1700s, 5 for 2200s/1800s).
That gives you the year’s doomsday.
Then add the day of the month minus the doomsdate for the month, which you can calculate first if you get that part of the date first (eg June 19: 19-6 = 13). If you run into negative numbers just add 7s to make them positive; you can also subtract 7s as you like to keep the numbers wieldy. All that matters is the result modulo 7.
Example: 1971-07-01 (the date voting age in the US was lowered from 21 to 18):
71 is odd, so add 11 to get 82.
82 / 2 is 41.
41 is odd, so add 11 to get 52.
52 mod 7 is 3 (because 52 is 3 more than 49).
3 from 7 is 4.
4 + 3 (for the 1900s) is 7. At this point we know that doomsday for 1971 was Sunday.
Add the date: 7 + 1 = 8.
Subtract the doomsdate, which is 11 (“I go to my 9-to-5 at the 7/11”). I’ll add 7 first to avoid the negative result: 8 + 7 = 15 - 11 = 4 = Thursday.
Love this video!
Freaking love numberphile. The enthusiasm is really infectious even when they’re talking about stuff I barely have enough brain cells to only sort of get this gist