The Doomsday Algorithm - Numberphile

[@mzadro7]

That “wowie” made James sound like the most un-surprised surprised person in the world

[@bryantg8749]

He's always the type of person that makes you go "wow" and you agree with him as you say it to yourself.

[@MarkWatney]

I think Ron said it too during the first train trip in Harry Potter and The Philosopher's Stone.

[@kristianemilkjrgaard531]

Or like Mr. Poopy-Butthole from Rick and Morty

[@spacebusdriver]

sounded exactly like wilburgur ngl

[@oscargill423]

"Oh wow what a surprise I wasn't expecting that at all"

[@minigrok]

John Conway, the mathematician who made up this algorithm, used it as his login for his computer at his office at Princeton. The computer would give him 10 random dates in any century and would not let him log in unless he got them all correctly in under 40 seconds. He managed to do all 10 in about 15 seconds.

[@asterism343]

how do you know

[@charlieangkor8649]

that's not very secure

[@theterribleanimator1793]

@@charlieangkor8649 but it is cool.

[@minigrok]

​@@asterism343 Conway showed me, I'm just relaying first-hand info. His main research assistant also did the same. This was around 1995.

[@minigrok]

@@topherthe11th23 Yes, it was 10 dates not 15. I edited it now.

[@blakehagins3069]

doomsdays: 3:35 calculate doomsday for arbitrary year: 6:21 day of week to number conversion: 8:13 doomsday century landmarks: 9:25

[@Dr.Cassio_Esteves]

Up

[@davidroddini1512]

He shows how to calculate for dates AFTER 2000. I can do that. Trying to go back I have to actually count the leap years 1996, 1992, 1988, etc or I get the dates wrong. What am I missing? Why is it not working doing subtraction instead of addition?

[@collinvanweelden5242]

@@davidroddini1512 you have to subtract a leap year every time you go back by a multiple of 4 but starting at one. That is because 1999 to 2000 is a leap year so going back you have to go back a leap year also

[@jaysonsvan6092]

I don't get the day of week to number conversion... I understand better with examples😅 can anyone help me out?

[@johndododoe1411]

@@jaysonsvan6092 Monday is 1, Tuesday 2. Sunday is 7th and last, reduce mod 7 to get 0.

[@Cubeorithms]

This is crazy, after less than an hour of practice I'm getting it right almost every time. Those leap years are tricky though

[@jasmintoromanovic5975]

Nice

[@PlutosMusic]

bro ur really copying and pasting your comment

[@theevauwu7853]

I still can't get the anchor year to work I keep getting it wrong

[@TheDreamingDriftersStories]

Me too, I can't believe it's so easy

[@mahiiii2112]

i have a doubt, how to know how many leap years to add 10:41.. im really confused please help me

[@renerpho]

9:00 Note this is for the Gregorian Calendar, so be careful with early dates. For England, the calendar change took place in 1752, so this method only works for dates starting in 1753. For Russia, dates prior to 1918 don't work, for the same reason.

[@davidkim6673]

But all you have to do is just to remember a different century date schemes, and you can convert to a Julian calendar!

[@renerpho]

@@davidkim6673 To some extent, yes. But you'll also have to know which calendar applies, and that's highly dependent on where the event in question took place. Especially on the European continent, the time when territories changed calendars can vary by several centuries between neighbouring towns. There are tables that tell you what date which town made the switch, but try to memorize hundreds, if not thousands of entries...

[@cOmAtOrAn]

@@davidkim6673 The real difficulty is memorizing when every country in the world converted to the Gregorian calendar. And it is something that would have to be memorized, there's no pattern to be picked up on.

[@renerpho]

Of course you could circumvent the difficulty, by asking the person whether their date is Julian or Gregorian.

[@TheOneAndOnlyOuuo]

@@renerpho I live in an environment where coming in contact with the Julian calendar is an every day thing even today. You're free to guess where I live ;)

[@Leo-if5tn]

I really apreaciate when this channel presents James, hope he returns more often

[@alistairkentucky-david9344]

“He remembered that 0 is a 0”. Well that just confirms that memorising this whole algorithm is above my pay grade.

[@Kranzio-]

I’ve always loved the little Numberphile thumbnail caricatures that manage to be both recognizable and strangely unsettling.

[@vigilantcosmicpenguin8721]

Whoever the artist is is perfect for the channel.

[@somedudeok1451]

Especially when it has the word "Doomsday" written next to it. I was sure this video was gonna be a lot darker than it turned out to be.

[@ChristainGuyOfAction]

I believe the term is "uncanny valley."

[@drenzine]

And James' caricature is the most uncanny, just starring at me

[@mr.joesterr5359]

The thumbnail for this video is an absolute monstrosity from the darkest trenches of the abyss itself

[@TomRocksMaths]

YES James is back. Mr Numberphile

[@thatguyalex2835]

James is the reason I watch Numberphile, as well as the fact that this channel has pretty informative math content. :)

[@fariesz6786]

the number of people associated with numberphile who i have a man-crush on is improbably high xD

[@ragnkja]

The very first Numberphile presenter is back!

[@Triantalex]

false.

[@davidfalterman8713]

James coming through with the NUMBERWANG reference at the end killed me 💀

[@cloudstrife1983]

Me too

[@ericwiddison7523]

Now let's rotate the board!

[@YourCrazyOverlord]

Don't forget your Numberhosen

[@thetooginator153]

I am proud to be an American who knows what Numberwang is (and Colosson!).

[@atrusx8232]

The comment I was looking for.

[@papafreddy2123]

One of the neatest party tricks I've ever seen, maths being fun as usual

[@somedudeok1451]

Yeah. Had a friend once that would always bust out some intriguing riddles and tricks at parties and I loved that guy. Somehow these tricks are even more impressive when you're drunk. :)

[@ПетърИлков-ч8ц]

Hey can you tell me how to subtract dates? For example they say 8th February. How do I get from 28(doomsday) on a non leap year to the day of the week?

[@mblada4514]

​@@ПетърИлков-ч8ц if the 28th is a doomsday, the 7th will also be a doomsday(because going back 7 days doesnt change the day of the week), so the 8th will be one day after doomsday

[@JonBastian]

I love this one, particularly back in the days of live meetings, because someone might ask a question like, "What day is Halloween this year?" and without checking or hesitating, I'd just answer It only took a few times before people would stop checking on their phones because they knew I was right. I never really mastered the giving the day for a date in a particular year trick, but since is the first clear and concise explanation of that part that I've ever seen, I'm going to start working on being able to do it. Thanks, professor!

[@woutervanr]

I was just looking through the old videos and wondering when James Grime was going to turn up again and then this is posted. What a coincidence!

[@pvandewyngaerde]

30 + 31 + 2 = 63. This is a multiple of 7. This explains why the even month days are the same.

[@msolec2000]

Correct. And those 63 are split into 28 and 35 by the odd dates. :)

[@KaiHenningsen]

The really surprising thing (back when I found out, many decades ago) was that 400 years are a whole number of weeks - this is why an eternal calendar works. Fast check: 1 year = 52 weeks + 1 day, so 400 years makes 400 extra days; every leap year is another extra day, so one per 4 years makes 100, less one per 100 makes 4, plus one per 400 makes 1, add all up makes 497. Which is 7*71. So indeed, 400 years are an exact multiple of one week. I seem to recall that you can also verify that Friday the 13th is happening more than average in some respect based on this, but I've long forgotten the details. Oh, and don't forget that this is only true for the Gregorian calendar, not for the Julian, so make sure you don't go farther in the past than whenever the Gregorian calendar was adopted at that place! ETA: various typos

[@chriswebster24]

Yep, and 26 + 17 + 5 = 48, which is a multiple of 8. This explains absolutely nothing, but if you add 21 you get a fun game that couples sometimes play.

[@therealax6]

Bonus points for showing why it works when July and August, which are consecutive, have 31 days each. (Hint: why doesn't it work for the odd months?)

[@maxono1465]

Where does the +2 come from

[@EnteiFire4]

If you keep track of the day of the week with a number, here are some great mental shortcuts: - When adding the numbers together, you can pre-remove the extraneous 7 (AKA compute the number modulo 7). So for example, 20 + 37 would become 6 + 2 (because 20 = 2*7 + 6 and 37 = 5*7 + 2). - "High" numbers can be converted to negative numbers. For example, a 6 can be replaced by a -1 and a 5 by a -2. It's not that easy to do 6 + 5 modulo 7 quickly, but -1 + 5 = 4 is easier.

[@therealax6]

...and don't be afraid of keeping the extra sevens. It might be easier to add 10 than to add 3. 20 + 37 is instantly 57, and in that case, it's faster to do the modulo once at the end.

[@virenor]

Yes, I just calculated my first date now and my doomsday happened to be 13, so I spontaneously converted it to negative 1 instead of 6.

[@diegotrabanino8970]

This is a great shortcut! Thank you

[@thecalendarninja]

👍 nice, i thought i was the only one who took advantage of using negative numbers to cancel things out faster

[@somerandomweeb4836]

Finally, the return of James Prime

[@TheNasaDude]

James Prime, leader of the MACSYMA, fighter against the Decepticons

[@NoriMori1992]

@@TheNasaDude Also known as OCTOMUS PRIME

[@LouisOnAir]

It's quite nice that after a full 400 year cycle of years and leap years (X is a leap year IF [4 | X & NOT 100 | X] OR 400 | X), Doomsday doesn't change, it's always Tuesday on the multiples of 400.

[@arnaldo8681]

it means the number of days in 400 years is a multiple of 7. I found it to be the most surprising thing in the video

[@gabor6259]

This is true only from the adoption of the Gregorian calendar.

[@d.m.collins1501]

And even if the dates WERE Gregorian, the Romans and their descendant nations didn't adopt the Sunday-Saturday week until 321 a.d. when Constantine was like "okay, let's do what Christians do." Before that, the Romans used an A through G date designation. And a couple hundred years earlier, they actually had 8-Day weeks!

[@KayvanAbbasi]

James Grime, why I originally started watching Numberphile probably 8 years ago. Still, an excited man and exciting to watch. Fun fact: He does not age! Knock on wood! :)

[@ed6213]

@@epsi So THAT"S why he finally came out on October 31!

[@adamschlinker972]

James was the first person i ever saw on Numberphile. Always engaging and entertaining.

[@DavidvanDeijk]

Can we all appreciate how far Brady has come learning maths, like he really gets this and i think even considers this one easy. If you look back at the beginning of the channel that would have been so different.

[@MichaelaBennison]

This was an episode of "Would I Lie to You" - Lee Mack had to convince the opposing panel that he could say the day of the week of any date. He was lying though.

[@FCBanton]

Yeees! I immediately thought of him. Turns out it's actually quite possible!

[@stomponpie]

I sort of like the idea that some producer thought there was a tiny chance Lee could come up with something like this on the show and fool everyone.

[@piguy314159]

2:11 Such a relief those dates all mirror each other so we don't have to worry about which date format to use

[@BakrAli10]

Doomsday method: 4/4 6/6 8/8 10/10 12/12 9/5 5/9 7/11 11/7 3/1 or 4/1 (leap) 28/2 or 29/2 14/3 pi 4/4 9/5 6/6 11/7 8/8 5/9 10/10 7/11 12/12 2000 = Tuesday Add the years Add the leap years (years/4) 7:31 Tips سبت = 0 أحد = 1 إثنين = 2 ثلاثاء = 3 أربعاء = 4 خميس = 5 جمعة = 6 Century: 1700 = Sunday 1800 = Friday 1900 = Wednesday 2000 = Tuesday 2100 = Sunday 2200 = Friday 2300 = Wednesday 2400 = Tuesday 9:53 Shortcuts for years: There are only 28 calendars, and then the pattern repeats every 28 years. 0, 28, 56, 84 0, 0, 0, 0 0, 12, 24, 36, 48, 60, 72, 84, 96 0, 1, 2, 3, 4, 5, 6, 7, 8

[@patrickbrown7438]

4:55 - Only 30 days in December 5:40 - Only 30 days in March I don't know who I can trust anymore.

[@rustycherkas8229]

December musta been an early start to New Year's Eve... And an abbreviated March??? "April Fools!!!" :-) (Maybe the excitement of 'once in 400 years' longer Feb that "quadra-century" led to the ooops...) :-)

[@ed6213]

The removal of the normal last date of the year (December 31), in prime-numbered years divisible by 400, is a new adjustment made by the new Grimian calendar, which now supersedes the Gregorian calendar. (I added a comment about that somewhere in here. ;-)

[@noterictalbott6102]

Great to see James again.

[@Scanlaid]

"It's a bit numberwang" 😂 hilarious. It was, but still such a cool trick

[@Rubrickety]

But can he _prove_ it’s Numberwang?

[@GGoAwayy]

Das ist Numberphile!

[@kenthemaster]

That's Wangernumb!

[@teeweezeven]

Very neat that doomsday only falls on four days every new century. I thought the fact that leap years are every four years, except for every 100 years, EXCEPT for every 400 years brought complications, but in fact it made it easier

[@guteksan]

It is not really easier. The fact that you mention is embraced in the Sun/Fri/Wed/Tue pattern for 1700-2000. Normally, if you would like to count the doomsday for +100 years, it would be 100 + (100 mod 4) = 125, but since every 100 years we are 1 leap year short, it becomes 124. Then, 124 mod 7 = 5. So you should add 5 every 100 years. 2 (Tue) + 5 = 0 (Sun) mod 7 , then 5 (Fri), then 3 (Wed). But every 400 years we get this extra leap year, so now we are adding 6 mod 7. 3 (Wed) + 6 = 2 (Tue) mod 7.

[@Muhahahahaz]

@@guteksan it’s easier because after 400 years, you’ve added (or subtracted, you could say) exactly 7 days. Which is to say, the pattern repeats So 2100-24100 are literally just Sunday, Friday, Wednesday, Tuesday again. There’s no need to do any new calculations :)

[@_rlb]

Nice to see Dr. Grime again! I listened to the Numberphile podcast episode featuring him just yesterday.

[@yashrawat9409]

Can't have enough of Jame's Numberphile videos

[@mollycollins2125]

Came from Mike Boyds channel

[@harrypainter7472]

1:15 Most convincing wow ever

[@pvic6959]

when you do well on a test that you thought you failed lol (im long out of school but that feeling stays with me)

[@blue_tetris]

WoW-wOwEeEe

[@sshuggi]

This should be a drop in future videos as a little Numberphile/Bradyverse meme.

[@_rlb]

That needs to be a gif

[@williamarcor251]

This will be a great video to show when I'm tutoring people on mod arithmetic. Always great to see James Grimes!

[@lukasproper5830]

That was fascinating, I genuinely want to get good at that now.

[@Kevin-yn7ju]

I figured out that all 5 family members mom, dad, brother, sister, me, all of our birthdays fall on the same day of the week every year. Less than .1 percent chance of this happening.

[@__gavin__]

That's numberwang!

[@mina86]

Let’s rotate the board!

[@filipsperl]

It's also nice that the doomsdays work in both M/D/Y and D/M/Y format

[@7636kei]

The big nine only (anything past March), really. Then again we don't really have enough months in a year to make 3/14 ambiguous (unless we're running, idk, Mayan calendar [18 months of 20 days plus five outsiders iirc] for example?), and the mnemonics foe the Jan anchor (the one Prof. Grime spelt out, at least) also pronounces enough of the date to break ambiguities out?

[@MarcoMontaltoMonella]

This one of those videos that remind me when I initially subscribed to Numberphile! Tricks + Math + James = ❤️

[@dexobj]

As strange as this comment will sound, the "Wowee" at 1:16 made me happy! It has been so many years since I've heard someone using it. Other than that, amazing explanation! Thanks for sharing.

[@rosiefay7283]

An appropriate day to upload, considering that 31 Oct, like 10 Oct, is a doomsday.

[@vigilantcosmicpenguin8721]

Halloween is doomsday. How fitting.

[@ed6213]

[sigh] I always get confused between Oct 31 and Dec 25. Aren't they the same? ;-) (Only old computer nerds like me need to answer. ;-)

[@thomaswarriner2344]

John Conway died on the 11th April 2020, a Doomsday itself. RIP Sir.

[@TheZenytram]

calling "Tuesday" as "Twosdays' completely broke my Portuguese brain.

[@shirou9790]

that said the method will of course still work if you choose Sunday = 1 rather than Sunday = 0, which would indeed be way easier in Portuguese

[@lhaviland8602]

Just wait for 2/22/22...

[@harmidis]

Right! In Greek and also in Portuguese Tuesday is the 3rd day, so it is called "Τρίτη" or "terça"

[@therealax6]

@@lhaviland8602 Oh, don't worry. That date doesn't exist in most of the world. :)

[@ignoringearthquakewarnings]

Sometimes at work, I forget what day it is. Thanks for helping me how to figure it out!

[@janAlekantuwa]

I've known a similar algorithm and love using it as a party trick! My birthday also falls on Doomsday The algorithm I know for working out Doomsday grom each year is a bit different: 1. Take the last two digits. If odd, add eleven 2. Divide by two. If quotient is odd, add eleven 3. Take that number mod seven 4. Subtract from 7 5. Add the century anchor day (1700: 0, 1800: 5, 1900: 3, 2000: 2)

[@hijeffhere]

This is the one I know too!

[@SF-cq3lh]

What if it’s even? And you are talking about the year, right? (Ie the last two digits of 1776 would be 76)

[@mahiiii2112]

i have a doubt, how to know how many leap years to add 10:41.. im really confused please help me

[@inari.28]

@@SF-cq3lh in the first step, you'd just divide it by two. if it's even after that, you do nothing. e.g. for 1968: 68/2 = 34. 34 is even, so you do nothing. 34 mod 7 is 6. 7-6 is 1. 1+3 (century shift) is 4. therefore, doomsdays in 1968 were on Thursdays.

[@wyattstevens8574]

@@SF-cq3lh In at least step 1, don't do anything.

[@minaandherchaos]

This is my new favourite KZbin channel now!

[@jansenart0]

2021 has the same calendar as 2077, which is the year the bombs fell in Fallout, so it was weird seeing this October on the walls when I started playing Fallout 4 again this week.

[@tinnderbox3410]

I have an old calendar on the wall currently, it's from 1996. People are surprised that it's actually correct all year!

[@Robi2009]

Every video with Dr Grime is always cheerful and entertaining. I love his enthusiasm ☺️

[@DerrickJolicoeur]

This is something I will definitely practice! I often want to know what day of the week something is on when discussing things with co-workers, and because my workplace has a zero-in zero-out policy I don't always have access to my phone. - Admittedly I could scroll through the calendar on a work computer (without internet), but it's awfully clunky

[@endrehalasz]

tell me more about this: "zero-in zero-out policy" what it exactly means

[@jodlaa5142]

@@endrehalasz I think it means something like when they get to work they have to leave their phones somewhere and they get them only when they leave, as to perhaps not leak some secret information if it's something not yet released they're working on. Basically for security in a sense

[@flikitisideways9953]

thank you very much i look forward to find more delightful math tricks on your channel

[@xX12VincEXx]

Came from Mike Boyd. Very well explained! I will definitely try this out when I have nothing to do 👍🏼

[@Pax1t0]

Me to

[@shiina_mahiru_9067]

I can recall that when I was a little child, I flipped over a brand-new calendar my mom bought (thinking of it as a new toy I supposed?). Then I realized: the date of the week of Jan 1 of that year and the next year (printed on the upper right of December page) was only differ by 1. Then I flipped over the old calendar, the same thing is true! I was amazed of this astonishing discovery. Then when I learn about division in 3rd grade, I realized: it was just because 365/7 has remainder 1.

[@ed6213]

Almost similar experience: I remember when my (now early 30's) son was three or four years old. We were in the kitchen and he studied a muffin tin for a couple of minutes. Then he came out with, "Dad, three times four is twelve, right?" It absolutely floored me!

[@oxwilder]

"It's a bit Numberwang." I love it!

[@TimJim333]

Awesome! Quick correction for those confused at 6:32 - 2000's Doomaday is a Tuesday, not the start of the year. (Was prob just a slip of the tongue!)

[@skakdosmer]

What about taking into account the transition from the now obsolete Julian calendar to the present Gregorian calendar, where several days were “lost” (which funnily enough worried a lot of people at the time), and which, by the way, happened at different times in different countries? In some countries it happened in the fifteen hundreds (I think), but in Russia it didn’t happen until the twentieth century, so the “October Revolution” actually took place in November by the Gregorian calendar.

[@lo1bo2]

Yep, I was looking for this comment. Great Britain and its colonies switched in 1752. But realistically nobody is going to ask about a date that far back.

[@Math.Bandit]

It didn't actually worry people at the time, to be fair. Matt Parker talks about it in his excellent book.

[@erik-ic3tp]

@@Math.Bandit, which book? Lost in Maths?

[@therealax6]

International time is a mess; international dates suffer from much of that mess plus the historical calendar mess. It's almost impossible to do this consistently that far back.

[@aba_dab_o]

James Grime for the win! Thank you for the vid! :)

[@liriodosvales2009]

Mike Boyd brought me here!!

[@theohaywood4199]

Please don't ever delete this video. I think it comes in very handy , and it's a very interesting video.

[@olivertheswimmer976]

I don’t understand the centuries. For example if I go from any doomsday, say 8/8 in 1700, a Sunday, and I want to go to 8/8 in 1800, I would do 100 (years)+25 (leap years)=125. I subtract 119 because it is the smallest multiple of 7 (7x17). And I get 6. So it should be a Saturday not a Friday right? Edit: Okay so I was looking at the calendar and apparently 1700, 1800, and 1900 were all not leap years. I read an article about why. If we did leap years every 4 years, the average year would have 365.25 days. However, the real length is 365.242199. Therefore, to get even closer to the real length, every centurial year is not a leap year except for every fourth centurial year. This means every 400 years, 97 are leap years. This makes our average year 365.2425 days which is a little bit closer. Who knows, maybe one day we will randomly take away another leap year just one time to get closer to the real number of days because we are still a little bit ahead as 365.2425>365.242199. Very interesting and exciting! This means I would only add 100 years + 24 leap years and subtract the 119 to get 5 so it makes sense!

[@tinnderbox3410]

Nope, you only have 24 leap years. 1900 wasn't a leap year.

[@brianh870]

I was wondering when Dr. Grime would be back! I'm only 3 seconds into the video and I'm already excited!

[@lakshaymehta9399]

James: "Wednesday-third day" Joey: "u sure about that though?"🙂

[@adamcetinkent]

Who? What? When-day?

[@vigilantcosmicpenguin8721]

THURSDAY! The _third day!_

[@joeyhardin5903]

who

[@juangonzalez7011]

Saw James on the thumbnail, came in to leave a like, I'll watch the video later.

[@nicosmind3]

Lee Mack is the master of naming days of the year. Seems like he cant do it, but he's a master!

[@chriswyatt9869]

Mike Boyd bought me here

[@nzwakele]

I want to understand this so bad but i hvnt done math in 12 years

[@Piffsnow]

That's funny. A dew days ago, I was rewatching your video on singingbanana from 2008 when you presented another method to find any day after 1900. :)

[@XanderNotZander]

Oh my goodness it's been so long, James actually started my forray into ASMR many years ago lol, helped my insomnia ever since, and the content is fantastic as always

[@jessica-ez9ud]

Thanks!

[@MrSigmaSharp]

"You don't need to memorize the calendar" Gives a whole calendar worth of information to remember Nice job, professor Grime.

[@polygongaming8859]

He is right, though.

[@skhiozier3038]

It’s almost Christmas, 2021. That’s wild

[@xanthe69]

Here after Mike Boyd's vid

[@tryhardr2658]

Just learnt this trick a few days ago. Have been asking my friends to tell me important dates to them and I‘ll tell them what day it is.

[@TheDreamingDriftersStories]

I've seen people do this and i always thought it must take something special to be able to do this. But now with less than and hour of practice I can do it within 30 seconds getting it right 9/10 times

[@sicapanjesis3987]

U Brady Haran, u don't know how deeply satisfied we were by just seeing the thumbnail, pls don't forget James Grime for another 4 years...

[@twincast2005]

The centuries would've been great time to remind people of the 100- and 400-year rules of leap years. I need to see this written down to memorize it, but I love number patterns, so I really should get to it.

[@FiliusPluviae]

5, 3, 2 are the smallest three prime numbers, then there's a 0. there you go.

[@abhinavdiddigam2330]

Actually I knew this when I was 11-12, as they teach this in India for 9th and 10th graders for a widely known Olympiad where one or two questions of this topic are asked

[@Lep_19]

I remember in a high school psychology class we watched a video about autistic savants and some of the incredible things they can do, and one of the things the filmmakers were selling as this "extrasensory, extraordinary talent" was a young boy's ability to immediately tell you the day of the week of any given date. They presented it (as I'm sure he did to them) as some innate function in his head that understood a relationship between the date and the day without any further calculation on his part. In retrospect, how quickly he was able to calculate them still is a pretty incredible skill, but it's funny to realize that he basically fooled these filmmakers into thinking he had what was a essentially a superpower rather than just being really quick at a math trick (and by extension any audience that wasn't familiar with something like Doomsday). Certainly fooled me anyways! Great video, by the way. I tried writing up a guide on this to test my understanding, and I couldn't get anything that wasn't overly verbose and immediately confusing. The way you were able to present this such that I could learn it in an afternoon is pretty remarkable. It really isn't too tricky all told, but there's so many isolated components that are difficult to justify without a deeper understanding of the mechanics (i.e. the 12 year pattern) that it's easy to get lost in the waters. Worth it though - it's a great party trick, as you say!

[@ed6213]

Concerning speed of calculation, the late Dr. Conway (the discoverer/inventor of the algorithm) was able to calculate the day of the week for any given date in the Gregorian or Julian calendar (past or future), within two seconds. He practised by having a log-in script on his computer display a random date, for which he would calculate the DoW.

[@Lep_19]

@@ed6213 That's fascinating! Love the idea of the script, I may have to try that 😆

[@lizs004]

In Portuguese, the days of the working week are numbered by default. Monday is the 'second day', Tuesday is the 'third day', etc... Only Saturday and Sunday have no number associated, but, because of the number system of the working week, I usually consider Saturday as the 7th day and Sunday as the 1st day.

[@musicboy16]

Here from Mike Boyd's Channel!!

[@cbhorxo]

This is an amazing video! After watching it once, I'm now able to do the trick impeccably

[@esquilax5563]

Nice, I remember hearing about this years ago, no idea where anymore. Maybe in _Surely You're Joking, Mr. Feynman?_ Now do one that takes into account the dates of the switch to the Gregorian Calendar in different countries ;)

[@jgg75]

I am watching this for the first time on the 25th of December 2021 and I can indeed confirm it is a Saturday...

[@geckogra1747]

"Monday, one day, Tuesday, two days, Wednesday, when's the day? Thurday! The third day!" Joey Tribbiani knows his stuff :)

[@rayzhang3246]

feels special watching it for the first time on Christmas

[@omri9325]

Finally the Hebrew way of counting the days of the week has benefits.

[@andrewchou3277]

Same in Chinese

[@pierreabbat6157]

Or Portuguese or Greek, but Portuguese says "domingo" instead of "prima-feira" and Greek says "Παρασκευη" instead of "Εκτη".

[@fred_fotch_baseball]

Same in Arabic

[@johannesvanderhorst9778]

That surprises me, as I have learned that the Hebrew word for "saturday" is close to the Hebrew word for "seven."

[@omri9325]

@@johannesvanderhorst9778 It is, it's also close to the world to rest and for the planet Saturn, they all share similarities in sound and origin

[@stevenbechard2242]

As noted elsewhere, this only works with the Gregorian calendar, which began on September 14, 1752 in Great Britain and its colonies (i.e. the United States). From that date forward, the doomsdays are as follows: 1800 = Friday (5) 1900 = Wednesday (3) 2000 = Tuesday (2) 2100 = Sunday (0) Then, they repeat that same pattern. However, prior to the above date, September 14, 1752, we used the Julian calendar. He lists the 1700 doomsday as being a Sunday, but that will NOT work with the Julian calendar and/or any date prior to September 14, 1752. (You still can use it to compute dates from September 14, 1752 to December 31, 1799.) Here's an extremely easy method to compute doomsdays for the Julian calendar, and thus, any dates prior to September 14, 1752: Simply subtract the first two digits of the year from 21. (Then, use modular arithmetic if needed.) 1700 = 21 - 17 = 4 (Thursday) 1600 = 21 - 16 = 5 (Friday) 1500 = 21 - 15 = 6 (Saturday) 1400 = 21 - 14 = 7 mod 7 = 0 (Sunday) 1300 = 21 - 13 = 8 mod 7 = 1 (Monday) You can see the obvious pattern.

[@Einyen]

I previously made my own method, I have to memorize a number for each month and each century: Jan: 6 Feb: 2 Mar: 2 Apr: 5 May: 0 Jun: 3 Jul: 5 Aug: 1 Sep: 4 Oct: 6 Nov: 2 Dec: 4 (I remember them as: 6 2 2 5 0 3 5 1 4 6 2 4, very similar pattern). 1700s: 5, 1800s: 3, 1900s: 1, 2000s: 0, 2100s: 5, 2200s: 3 It might seem hard but you remember them fast with little practice, and then you do not have to remember special (dooms)dates, it just comes down to adding the century + year + leap year + month + date and do all (mod 7). Examples: June 18th 1976: 1 (century) + 76 (year) + 76/4 (leap year) + 3 (June) + 18 (date) but then you do mod 7 as you go: 1 + 6 + 5 + 3 + 4 = 19 = 5 (Friday) Jan 1st 1901: 1 (century) + 1 (year) + 0 (leap year) + 6 (Jan) + 1 (date) = 9 = 2 (Tuesday) Dec 25th 2021: 0 (century) + 21 (year) + 21/4 (leap year) + 4 (Dec) + 25 (date): 0 + 0 + 5 + 4 + 4 = 13 = 6 (Saturday) One small caveat in this method: For year 2000 (and year 1600 and year 2400 etc.) between Jan 1st and Feb 28th: You have to remember doing an extra +6 or -1 (due to the missing leap years in those years every 400 year. For March 1st to Dec 31st it works fine, just the first 2 months is the problem every 400 years.

[@Einyen]

It has been so long since I used this algorithm, I forgot, that I have to skip adding 1 leap year if date is in Jan or Feb and year is a leap year, I was doing this so automatically I forgot: So if for example 2044 in Jan or Feb I would add 10 for leap year instead of 44/4 = 11. So this can be combined with the "caveat" I wrote at the end for year 2000 etc., so the full algorithm is: Century numbers: 1700s: 5, 1800: 3, 1900s: 1, 2000s: 0, 2100s: 5 and then continue the same pattern ...5,3,1,0,5,3,1,0... in each direction Month numbers for JanFebMar AprMayJun JulAugSep OctNovDec: 622 503 514 624 Step1) Add century number (from list) + last 2 digits of year (modulus 7) + leap year which is: (last 2 digits of year / 4) rounded down (modulus 7) Step2) Add month number (from list) + date (modulus 7) Step3) If Month is Jan or Feb and Year is a "divisible by 4" (so both leap years but also years divisible by 100 and not 400) then subtract 1 (or add 6). Step4) Final result mod 7 is the answer with: 0 = Sun, 1 = Mon, 2 = Tue, 3 = Wed, 4 = Thu, 5 = Fri, 6 = Sat Of course step1-3 can be done in any order and since date + month is often provided first, it would often be Step 2, 1, 3, 4 or 2, 3, 1, 4. Example today: Nov 2 2021: Step2) 2 (Nov) + 2 (date) = 4 Step1) 0 (century) + 21 (year) + 21/4 (leap years) = 26 = 5 (mod 7) Step3) does not apply Step4) 4 + 5 = 9 = 2 (mod 7) = Tuesday

[@pasqualethene]

cool

[@mrewan6221]

This has some similarities to a method described by Martin Gardner. His month numbers were 1-4-4 - 0-2-5 - 0-3-6 - 1-4-6, and his suggested way to memorise them was to notice that the first three are squares, and the last is just over a square. These numbers are all 2 (mod 7) more than yours! His day 1 was Sunday (which annoyed me, but I learned it that way and simply adjust at the end. His century values were 0 for 1900-1999, and -1 for 2000-2099. He also gave values for C-19th and C-18th. I think they were 2 and 4, but I'd have to check, though it would be quicker to just Google the date! He also used the Lewis Carrol method for days in a year (int(year/12) + remainder + int(remainder/4)), but I think yours is easier. Then, if Jan or Feb in a leap year, subtract 1. I also worked out a way of calculating his month values using mod 5, mod 2, and some other stuff, but it was no easier to remember! Gardner's intent was that you could do the calculations in your head, and you didn't need to keep track of multiple values at the same time (apart from the month constants). I think your method might do this too. I'll experiment.

[@Einyen]

@@mrewan6221 Interesting thanks, it sounds very similar. I did write a small mistake in "Step3", you only do -1 for Jan/Feb if its a "leap year", so if divisible by 4 or 400. But NOT if only divisible 100 and not 400 like: ...,1500,1700,1800,1900,2100,... so standard leap year rule.

[@pasqualethene]

@@mrewan6221 Who is Martin Gardener

[@niklaskpunkt8335]

Mike Boyd Fam wya?

[@rajnikant_roy]

The more videos I watch of this channel, the more I am intrigued by the beauty of mathematics and the more I regret not taking Mathematics as a major

[@wecantry4393]

Doomsday Algorithm. Monstrous moonshine, Free will theorem, Surreal numbers ; incredible mathematics by an incredible mind. We will never forget you John Conway.

[@demerion]

You forgot the Game of Life!

[@1.4142]

Also note that years are leap years if they are divisible by 4, but not leap years if they are divisible by 100, but are leap years if they are divisible by 400.

[@Tonyswoodshop]

Who is here because of Mike Boyd?

[@kpk1171]

This was such an easy video to follow! I watched this video one time and then practiced for an hour and got it down. Great video guys!

[@macronencer]

I'm really glad someone uploaded this because I used to know this trick and I forgot how to do it, mainly because I didn't practise often enough. Thanks! By the way, the only minor omission here was that you didn't warn people about most century years NOT being leap years. That only affects dates with century not divisible by 4, year ending in 00 and before March 1st of that year - but still, it's important. Did you know that there's a similar trick for knowing the phases of the moon for given dates? I used to be able to do that one as well but again, I forgot how. I seem to remember it was more complicated - perhaps unsurprising!

[@oh-totoro]

This is one thing I'm stuck on at the moment. Did I completely miss it in the video? It didn't seem to explain how we know whether a particular year is a leap year or not. And all the example dates given were easy ones from March onwards, so they didn't have to factor that in at all. If somebody gives me a date in January in the distant future of 3564 or whatever, how do I know whether the doomsday is supposed to be Jan 3rd or 4th?

[@velienne1319]

@@oh-totoro To determine if a year is a leap year or not, you have to see if it's divisible by 4, it's as simple as that. However, if the year ends with 00, it has to be divisible by 400. For example, 1700 is not divisible by 400 so it's not a leap year, but 2000 is a leap year. 3564 is divisible by 4 so it's a leap year.

[@Giofear]

@@velienne1319 exactly this. But just to make it a bit easier, if your year isn't 1700 1900 etc. and you have year like 1956 e.g. you only care about the number 56 in it when determining the leap year you only want to find out whether 56 is divisible by 4 (as the hundreds and thounsands are always divisble by 4)

[@mrjudge3722]

6

[@mufasao6776]

It's not even November and you're bringing Christmas into this? Sheesh!

[@akashachuas]

From Mike Boyd's video

[@LarsB]

This is genuinely the best and most helpful video I have seen in recent years.

[@DavidJSWayne]

who else got sent here by Mike Boyd!

[@hampuslind7546]

Normally find explanations boring but u made this one entertaining! Well done, going to try and learn this now!

[@kieronparr3403]

"It's a bit numberwang. " awesome

[@livedandletdie]

How can one not love the word numberwang. It's truly one of the best things from Mitchell and Webb.

[@ericherde1]

Convenient that 9/5, 5/9, 7/11, and 11/7 are all the same day of the week, so no need to clarify about American vs. European numbering.

[@gregb869]

Yay! Missed James Grime

[@tfofurn]

I read about this calculation decades ago and could only retain the within-the-year part. I think James's mod-28 suggestion will serve me better than the original div-12. Thank you!