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.