As a mathematician and lay pedant I get easily annoyed when people promulgate mistruths. But I try to distinguish between the trivial and the serious and then only get worked-up about the second category. This week though, I cracked under the pressure of something completely frivolous and end-up releasing my own Bad Maths meme onto the internet.
Last August, I noticed people commenting online that October 2010 would have five Fridays, Saturday and Sundays (which is true) and that this wouldn’t happen for another 823 years (which is not true). At the time I was curious about why this annoyed me as deeply as it did, but I was still quickly distracted by other things. Then, just a few days ago, I saw that people were tweeting exactly the same fact about July 2011 having five Fridays, Saturdays and Sunday and that this wouldn’t happen for another 823 years. Now I was seriously annoyed.
But I couldn’t work out why. Surely this was the very quintessential trivial mis-fact that gets spread on the internet but cannot possibly cause any harm. Yet I found it deeply troubling.
After much thought (and asking the hive-mind) I’ve decided that this incorrect meme presses the following of my buttons:
Easy to disprove, but few people did
I got annoyed that so few people bothered to check a fact before they passed it on. If people aren’t checking easily falsifiable facts about trivial matters, can we still hope that they’re checking complex, semi-ambiguous facts when it comes to matters of great importance, such as medical advice?
It takes near-zero thought to flip forward in a calendar and see that March 2013 also has five Fridays, Saturdays and Sunday. Even if you’re July-centric, you’ll find another one of those in 2016.
With slightly more thought, you’ll notice that all 31 day months must have five lots of some group of three days, starting with whatever day the 1st of the month is. As the days drift around the year, eventually they all get equal goes and so 1/7 of all 31 month days will start with a Friday. There are seven 31 days in the year. This will average our rather nicely to happening once a year, not every 823 years.
Actually, this is about as much thought as it needs to realise there are only 14 different possible calendars (seven starting days, leap year or not) and in fact 2011 will repeat itself exactly in 2022.
If you’re prone to over-thinking things through, you can calculate that the sequence of calendars completely repeats itself every 400 years, meaning you can’t have date/day/month special-combination-events more than 400 years apart.
Perpetuates the Maths is Hard and Impenetrable image
I dream of a world not where everyone is better at maths, but where people have the mathematical confidence to use what they already know. Fewer people would be ripped off my banks and insurance companies if they weren’t thrown off by number-chaff and actually checked what the deal was.
This 823-years meme had me suspecting that people saw a fact accompanied by a big number and instantly assumed that they couldn’t think it through for themselves.
It’s a hollow substitute for real mathematical amazement
Blindly accepting all convoluted and possibly-untrue maths facts is like never peeling that semi-transparent protector film off the front of your mobile phone. You’re settling for a blurry approximation of the real thing because of sheer laziness.
There are so many amazing things in maths it’s a shame people spend their curiosity on whatever pseudomaths comes their way.
A once-in-823-years event twice in two years
Is the meme spreading through an entirely untapped demographic who missed it in October 2010 or do people clear out their mental-cache that frequently? Either the internet really does have an endless supply of forwarding-heavy, fact-checking-light users or there are some serious medium-term memory concerns to be had.
Now I knew what was annoying me about the 823 thing; what was I going to do about it? I considered setting up some kind of automated twitter service that would search for tweets featuring “823 years” without also using the key words “false”, “not” or “do you know how to use a calendar” and drop them a little note. But this felt a bit spammy and I was talked out of it by a wise sage of the internet (aka Dave Gorman).
Then this morning I was sent a different calendar fact that also only happens every 823 years! Apparently if you add the age you turn in 2011 to the two-digit year of your birth, the total will be 111. This is indeed true, and I’ll leave it as a quick puzzle to generalise this to any year and spot the ages for which it will not work. Anyhow: I was amazed that the 823 year had attached itself again despite having nothing to do with the factoid. I asked the tweeter of this fact and he said that his Arabic Dad had sent it to him.
This has resulted in my “823 Years Conjecture”: Stating that something happens every 823 years will greatly increase its chances of becoming a meme. Actually, I’m keen to find the earliest citation possible of 823 years; please do let me know if you find one. Maybe there actually is something that occurs every 823 years.
So I decided that my best outlet for my frustration was not a righteous campaign of auto-correcting people, but rather to craft my own 823 meme. This is what I settled on, and release onto the internet:
“Add the digits of your age in 2011. Subtract from age and add digits of answer. eg 31-4=27,2+7=9 It’s always 9! Will work again in 823 years”
I was proud of this tweet because it is technically correct, including the 823 thing. It will indeed work in 823 years, in addition to working every year in between.
It also mentions a year (2011, but as someone rightfully pointed out: I should have used 2012) but is fairly obviously year-invariant. My hope was that this would encourage people to look closer at the maths behind the trick.
In addition, there certain exceptions on ages. If you’re 9 or younger, the answer is zero (technically the final result is always “0 mod 9”). For ages over 100 you require repeated addition of the digits to get to 9 (known as the “digit root” of the number). It’s easy to start unpicking this maths trick and investigate why it actually works.
The response was half what I’d anticipated and half unexpectedly insightful/educational.
It did indeed get forwarded around with a straight face by faithful twitter followers (god I love those guys) and thus landed under the noses of people who had no idea about me and my emotional, mathematical journey of 823 years. Some of these people forwarded it on (no surprise there) and many people spotted the vacuous reference to 823 years (still unsurprised). What caught me off-guard was the barrage of mathematical smack-downs from people who had done just enough research to locate me as the source of the tweet, but not enough to actually read my twitter-page.
And you know what? Us members of the fact-pack can be real dicks when we feel the need to correct people.
I’m used to all sorts of abuse on the internet; it’s part of the game. Some of it is the brownian-motion of anonymous personal abuse, other bits are mathematical quibbles of disproportionate detail. But these tweets were different. There was something cutting about corrections from people who knew they had a superior grasp of very easy concept.
I realised that Past Matt – who wanted to set up an automated twitter account to do just that – was looking like a real jerk right now.
I even knew that I was meta-correct, but it still felt bad to be corrected. I’d gone from not knowing why I was annoyed at something to not being sure why I felt bad when people were correcting it. This brings me to my (recently devised) Inconsequential Mistake Paradox: As the triviality of a mistake online increases, so does both the want of other people to correct it as well as the insensitivity of doing so.
It seems the solution to depress my buttons is not to try and wipe incorrect memes off the face of the internet (with the damp cloth of insensitivity) but rather to flood the internet with valid, accessible nuggets of mathematical amazement. Netizens clearly have an appetite for this sort of stuff; if anything it’s our fault they have to sate themselves with pseudomaths. If there was more playful maths around, maybe people who develop more mathematical confidence and start to question dubious claims of all levels of severity.
None of this makes me any less annoyed when I do a twitter search for “823 years” and look at the relentless references. So if you’ll excuse me, to cheer myself up, I’m off to bait some homeopaths.
UPDATE: I use the word “factoid” incorrectly above. Please consider it to be “factlet” for all intents and purposes.
And thanks to everyone who sent me this xkcd comic: Duty Calls
Excellent stuff, Matt. One (possibly trivial) observation: you misuse the word ‘factoid’. It doesn’t mean a small fact, it means something that *isn’t* true, but looks like it is because it is asserted so often. Coined by Norman Mailer. It’s a good word, and a good idea, but nearly always used wrongly these days, which is a shame. I’m not much of a mathematician, words are my thing, and I tend to get wound up about their misuse in about the same proportions as you do with numbers! Keep it up…
Jeremy, you’re absolutely right and managed to correct me in a manner that left me feeling enlightened, not disheartened. I now have the gentle buzz of someone who learned something new.
You are an asset to the internet. :]
Great insightful piece. Wish there was a ‘like’ button!
Well done Matt. Like Jeremy, words are my thing too and I notice you used ‘court’ instead of ‘caught’! I’m annoyed at myself that I feel the need to correct you but I am compelled by some inner nerd to stand up for the English Language – I can’t even use abbreviations or mis-spellings when texting, – it feels so wrong. Do I suffer from a similar ailment to your good self?
I use “factlet” for a small fact, and avoid “factoid” because of the misunderstanding about its meaning. And you mis-spelt “caught” as “court.”
And here is a factlet: 73 is prime, as is its reverse 37. 73 is the 21st prime, and 37 is the 12th. And 21 is 7 times 3. And all that only happens every 823 years.
Or something.
Amanda, thanks for pointing that out. I’m all about correct spelling and whatnot, it just happens to fall outside my skill-set.
I pride myself on trying to make sure all of my tweets and text messages are grammatically correct with no abreviations. No sentence fragments!
Goodness, what a gracious reply to my comment. You’ve made my day, Matt.
A “friend” of mine posted the following today on Facebook today – “Weird fact of the day! If you take the year you were born and add your age it always adds up to 2011???”
to which I replied the following – “If you take the year you were born and add your age (i.e. the number of years that have passed since you were born) it will get the current year! – not weired at all . . . just basic maths!”
Apparently this “weired fact” was broadcast on Radio 5 Live on Saturday – if true (I can’t verify!) the this is yet another case of a lazy journalistic maths fail!!!
Great article. And now I’m going to dive right in and prove your point…
You say:
Your reasoning isn’t quite correct here – they don’t necessarily get equal goes. The cycle of leap years repeats every 400 years and because this has an exact multiple of 7 days in it; so does the calendar (otherwise it would repeat every 2800 years).
This leads to some interesting (to nerds like me) factlets. Such as, a 31 day month is most likely to start on a Tuesday (402/2800) and least likely to start on a Monday (398/2800). Although a 31 day month starts on a Friday 400/2800 times – and is the only day which exactly 1/7 of 31 day months start with! Did you pick Friday on purpose?
And really sweetly – the 13th (of any month) is more likely to be a Friday (688/4800) than any other day.
A quick check of an online calendar shows that neither October 2833 nor July 2834 has this property!
I wonder if anyone has any idea where this 823 number came from. It is prime, so maybe that’s a start…
Great post. “Factlet” is not necessary as you are talking about “facts”. You might be better off saying “a simple fact” or “a straightforward fact”. The missuse of “factoid” is similar to the missuse of “simplistic” which means simplified so much that the meaning has changed or even reversed, when the user should have used “simple”.
I came across an error on the web that said that chains of regular dodecahedrons never close. This is seriously wrong as there are simple chains of 8, 12, 16, 20… chains of regular dodecahedrons. Should I try and dispel this factoid?
For what it’s worth, a factlet about 823 is that it is the second member of a set of four three-digit prime numbers all of which begin with ’82′. So what if 821, 823, 827 and 829 are all prime? Well, this is a maximum (primes are all odd except 2 and no prime ends in 5 except 5 itself) and something that doesn’t happen all that often. The lesser instances of this are {11,13,17,19} {101,103,107,109} {191,193,197,199} and the irregular {2,3,5,7}. The next is {1481,1483,1487,1489}. Actually it probably happens infinitely many times, although as it is not yet proved that there are infinitely many twin primes, this may be susceptible to being disproved. But maybe, just maybe , it is why these people have picked on 823 although it is worth noting that 7^7 = 823543 …. who knows?
Keep yourself nice.
Loved reading this article, including the comments. Thank you all!
Magnificent indignation, Matt. Much appreciated. I was railing against my mum’s fascination with the 111 thing just the other day – is the meme’s success down to the fact that many people will find it an aesthetically pleasing number? Other than that, so what?! People just don’t think.
As for this thread’s other topic (misused words), may I submit “statuesque”. Always misused in football commentaries.
Ooh. And people using infer when they mean imply, just because they think it makes them sound clever. Does my head in.
And I can’t go without pointing out your misspelling of abbreviation.
I become as obsessively passionate when I hear from people that travel to the southern hemisphere that water drains counterclockwise as opposed to what happens at the northern hemisphere. It is such a rubbish Coriolism AND SO BLATANTLY EASY TO CHECK!
Great article. I got wound up too last August when someone texted it to me. But maybe that was because I was stuck working late in the office on a Friday night and everyone else was down the pub. It seemed so obviously wrong (using your quick calculation) and was so easy to check. So I checked and had to join them in the pub to tell them.
And what a respectful and civilised thread! Riderofgiraffes’ point about 37/73 above was mentioned in a BBC R5 discussion yesterday morning about favourite numbers. And talking about radio 5 – Simon, the “weird fact” only works in the part of the year after your birthday. Before that it’s one less
“Apparently if you add the age you turn in 2011 to the two-digit year of your birth, the total will be 111. This is indeed true …”
Not for anyone under 11.
Oops, sorry, didn’t read the rest of your sentence carefully enough. I would at least have put it “This is indeed true for SOME people…”
You used the word “factoid” correctly in your original post. The meaning of a word isn’t what a dictionary or even the original coiner says that it is, but what people (informally, subconsciously) agree that it is. In American usage, at least, “factoid” is generally understood to mean something like “a small piece of information”, and using it to mean “an incorrect bit of information that is repeated as if it were true” would confuse people.
I understand that you enjoy pedantry, but language-related pedantry is the very worst kind. Language change is an inescapable fact, and people who make claims like “everyone else is using this word wrong, but I know the real meaning” are just engaging in a kind of confused snobbery. One may as well argue that the continents have always been in their current locations and forms, or that the Earth’s climate has always been just like it is today.
Don’t peel the protector film off your phone! Do you want scratches?
But I agree this is a poor approximation of mathematical wonder. I think the Interesting Number Paradox isn’t widely known.
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No, you’re wrong. The pattern will not be repeated again for another 823 years. I think. I didn’t check.