3019: Advent Calendar Advent Calendar

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Advent Calendar Advent Calendar

Title text: The growth rate of items per day may may seem absurd, but it's actually much less than the acceleration in the 12 Days of Christmas song.

Explanation

Advent calendars are a form of countdown to Christmas consisting of a card or structure with one closed "window"/opening for each day. Every day, another "window" is opened (e.g. a cardboard flap is opened along perforations), revealing a small present (traditionally, just a thematic picture or chocolate). While the religious season of Advent traditionally begins four Sundays before Christmas, most Advent calendars begin on December 1st for simplicity. In 2024, when this comic was published, the Advent season coincidentally starts on December 1st. Advent calendars usually have either 24 or 25 doors (ending on either Christmas Eve or Christmas Day), depending on manufacturer's choice and/or local tradition.

In this comic, Randall has devised an Advent calendar that contains multiple smaller Advent calendars, each of which contains the same number of items as there are days left until (and including) Christmas Day. By the time he reaches Christmas, he will have 325 different items, or 350 if counting the sub-calendars. The calendar is shown as it might be on December 2^nd, the date of publication of this strip. The "window" in the upper left, presumed to be for the 1^st of December, has 25 sub-windows, of which two are open. (One would have been opened on December 1^st and the next for the day after.) The "window" 5^th from the left in the bottom row, probably for December 2^nd, has 24 sub-windows, of which one (that for the initial 2^nd) is open.

The title text refers to The Twelve Days of Christmas, a traditional Christmas carol in which the singer receives one set of gifts from their true love for each day of the Twelve Days of Christmas. On day one, they receive one gift, and on day n, they receive again all the gifts they received on day n-1, plus n copies of a new gift. The exact gifts given each day vary by version of the song, receiving 78 gifts on day 12, for a total of 364 gifts. For the Advent calendar Advent calendar, each day a number of items equal to the number of days left until Christmas are added. There are 364 items total in the 12 Days of Christmas, the final day itself having exceeded the gifts of the nested calendars (the sub-gift count being 325, and regardless of the 25 calendars also being included). However the advent calendar uses 25 days rather than just 12, hence the song's acceleration in number of gifts each day is much higher. The title text says “may” twice, either mistakenly, or maybe on purpose since the comic's name has word duplication.

The advent calendar's advent calendar gift total follows the triangular number sequence of all new gifts on a given day being one more than those the day before: on the first day, this is 1 (the first sub-gift of the first sub-calendar); on the second, we now have 3 (add two sub-gifts from two sub-calendars); on the third, we have 6 (three sub-gifts added), etc. The formula for the total on day n is

n(n+1)

2

. For the Twelve Days song (which goes from the 25th of December to 5th of January), each day adds to the total the next triangular number in the sequence: +1=1, +3=4, +6=10, etc... The formula for this tetrahedral number (a 'pyramid of triangular numbers') is

n(n+1)(n+2)

6

, and matches a triple-nested meta-Advent Calendar's non-calendar gift count. This already starts in a more rapid escalation of gift-giving, immediately after the first day where both counts are at one item. However, due to the later start of the Twelve Days, one would have to extend the gift-giving patterns to the 17th Day Of Christmas (and thus the 41st day of Advent) for the number of true love gifts (969) to properly overtake the continuing meta-calendar's ones, with (902) or without (861) counting the sub-calendars as gifts. (The number of ultimate gifts in any quadruple-nested Advent Calendar would be

n(n+1)(n+2)(n+3)

24

, excluding all the calendars themselves.)

It is not clear what is inside each sub-calendar. The typical filling would be chocolate, however it could also be possible that the advent calendar advent calendars had even more advent calendars within. That this is not the case is revealed in the title text as, if they were (and were run concurrently), the number of (sub-sub-)gifts would always equal those in the song.

Transcript

This transcript is incomplete. Please help editing it! Thanks.

[On a grey board, there are 23 Advent calendars behind large "windows", numbered from 3 to 25, plus two open calendars with their covers torn off.]

[From top-left to bottom-right, the boxes are numbered as such: (opened), 14, 23, 16, 11, 3; 5, 24, 18, 7, 21; 10, 17, 4, 9, 22, 15, 12; 8, 20, 13, 25, (opened), 19, 6]

[Each calendar numbered n has 26−n squares in it.]

[The open calendar on the top left has 25 squares, two of which are black. The other open calendar has 24 squares, one of which is black.]

[Caption below the panel:]

I like Advent calendars, so I got an Advent calendar that gives me a new one every day until Christmas.

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Discussion

Would this basically be triangle numbers? So on Christmas Eve you would open 300 windows?Tommyds (talk) 16:01, 2 December 2024 (UTC)

Yes and no. It's not 12 days of Christmas (as mentioned in the title text), so only the overall number of gifts are a triangle number; you open 30 windows on Christmas Day. The 12 days ref is key as the song generates more gifts if taken literally even in 12 days -- 78 on the last day, 66 on the previous day, etc, for a total of 364. Mneme (talk) 16:35, 2 December 2024 (UTC)

Notice that this year The Advent calendars are correct. Normally, Advent calendars start at the 1st of December even if the Advent starts at a different day. But this year the Advent also starts at the 1st of December. 162.158.172.40 16:55, 2 December 2024 (UTC)

Donald Knuth wrote a paper for April 1984 Communications of the ACM that included an analysis of the complexity of 12 Days of Christmas. It's in the CACM archive https://dl.acm.org/doi/pdf/10.1145/358027.358042. 172.70.211.144 (talk) 16:58, 2 December 2024 (UTC) (please sign your comments with ~~~~)

The explanation currently says "each day, he gets another advent calendar, which each contains 24-25 different items". I don't think that's correct; look at the picture: each day's calendar has one fewer item than the previous one. For example, the 24th only has 2 boxes and the 25th only has one. --Itub (talk) 17:25, 2 December 2024 (UTC)

Perhaps each smaller advent calendar might also contain a smaller advent calendar and so on ...? 172.70.90.199 17:51, 2 December 2024 (UTC)

Since the 1st has a calendar with a 1st, that would mean an infinite number of calendars just on the first day, so probably not. 172.71.154.225 18:03, 2 December 2024 (UTC)

It could work out if you don't open the first window of a new advent calendar on the day that it is revealed. So on day 1, you open the first window revealing an advent calendar that starts on day 2. Then on day 2 you open the second window, revealing a second advent calendar and the first window of the day 1 advent calendar, revealing a third advent calendar. ... and so on. If my mental math on that is right, it's doubling every day, so 2^24 =~ 16M calendars in total? (I could be off by a day) 172.71.147.69 19:38, 2 December 2024 (UTC)

Can we just take a moment to appreciate whoever named the bot for this page? They wrote as follows: Created by 4 ENVELOPE BACKS 3 NERDS A-EDITING, 2 TURTLE BOTS, AND A FUNNY NEW XKCD. Willintendo (talk) 23:26, 2 December 2024 (UTC)

That note is hand-edited on the first couple of edits. Not sure why that rule exists, though. Fabian42 (talk) 00:50, 3 December 2024 (UTC)

Honestly, about half the time the "note" is funnier than the comic itself. Apollo11 (talk) 19:31, 4 December 2024 (UTC)

The title text says 'may' twice, "per day may may [sic] seem absurd" --198.41.236.163 00:01, 3 December 2024 (UTC)

The German YouTube channel "Malternativ" has actually done this a couple years: Opening one advent calendar every day. He went more and more insane as December went on… Fabian42 (talk) 00:50, 3 December 2024 (UTC)

Noting that the calendar is entirely correct for the day of publication. Too much to hope for that it is kept correct for each further day of Advent until (or, rather, 'until and including', as noted at least once above) Christmas Day? Maybe worth checking to see if (at an appropriate time, Randall-time, later today on the 3rd) it hasn't been updated. Or some special sub-page appeared with a revised (Time-like) update. Just in case. And, if Randall doesn't, I'm sure it's not beyond our own wit to make adjustments/animate as a fan-copy. 172.70.91.214 01:57, 3 December 2024 (UTC)

Yo Dawg, I herd you like advent calendars, so I put an advent calendar in your advent calendar so you can count down while you count down. Solomon (talk) 03:31, 3 December 2024 (UTC)

Wonder how many chocolates you would get if you did this with the life expectancy advent calendar. N-eh (talk) 04:40, 3 December 2024 (UTC)

At some point, most people would reach the point at which that many chocolates would be a lethal (or at least LD50) quantity, so would be a self-shortening process. For those who reach the end of their LEAC without it actually being the cause of death, there should be a compensatory (or 'condolances') supply hidden on the back, for entirely guilt-free eating. 172.70.162.200 06:01, 3 December 2024 (UTC)

Nobody tell Stuart and Dan about this one... 172.71.183.11 06:56, 3 December 2024 (UTC)

I still don't understand it. Does he not open the first and second door of the second calendar on the second day? If not, does he open the first or the second door of the second calendar. Do the other items stay in the calendar? 162.158.245.162 07:36, 3 December 2024 (UTC)

Each next calendar has one fewer doors. So the second calendar starts with door number 2. On 1 December he opens the number 1 door revealing the first subcalendar, where he opens the number 1 door. On 2 December he opens the number 2 door of the first subcalendar and then the second door of the big calendar, revealing the second subcalendar, where he opens the first door, which is the number 2 door, since it has no number 1 door. Mtcv (talk) 08:12, 3 December 2024 (UTC)

Is the title correct, from a formal language point of view? I would have expected it to be Advent Advent Calendar. OTOH I'm not American and not overtly familiar with this tradition. 172.69.194.19 (talk) 08:49, 3 December 2024 (please sign your comments with ~~~~)

A "<Foo> Advent Calendar" is an Advent Calendar that is themed for <Foo>. A "Dogs Advent Calendar" is probably themed with dog pictures (a "Dogs' Advent Calendar" might be themed for dogs, perhaps with dog-treats/-toys, and the "Dog's Advent Calendar" might be a regular (human) AC that you've gifted to your dog... hopefully one without chocolates!). A "Fine Whiskey Advent Calendar" might have sampler bottles of various fine malts (or just pictures of them... booo!).

An "Advent Advent Calendar" would be just Advent-themed. Which is just a Advent Calendar (i.e. traditional, not particularly rethemed; or even rather pointedly traditionally-themed as a poke back against the commercialist subversion of Advent Calendering). "Advent" is not a modifier to "Calendar" that gives one of them little doors and pictures (and/or gifts), but is a thing for which an object ("Calendar") has been created as an accessory.

This is an Advent Calendar whose schtick is Advent Calendars, thus is an Advent Calendar Advent Calendar. Which seems at least as good as any other theme I've seen. And it's the first time I've seen this. But, if there are at least 24 other examples, then obviously there's now a possibility of an Advent Calendar Advent Calendar Advent Calendar. 172.69.194.185 13:57, 3 December 2024 (UTC)

Thank you, it's very clear. I was indeed wrongly interpreting Advent as a modifier to Calendar. 172.69.194.204 14:04, 3 December 2024 (UTC)

(That was clear? I really should have cut back on everything else once I realised it might just have been the modifier-misunderstanding...)

Slight correction: An AC³ would not require 25 different but functionally identical AC²s. As well as the pictured AC², you'd need an AC² that started with the 2nd day (which holds a 2nd-day-starting AC¹, just as the AC² contains in its 2nd day), one that starts with the 3rd day... etc. Given that there are already a limited number of not-25-(or -24)-day ACs, for the AC to hold, I don't know how many would have to be specially created to fit (we do know of one that covers just 18 days, but otherwise one might sabotage a 'more windows' one by taping over and/or pre-emptying too-early windows ...seems wrong to do that, though), but it's then 8ncreasingly likely the non-primary AC²s would just need to be created just for the purpose of being appropriately installed within the 2nd+ slots of the AC³. Which is probably far simpler. FCVO 'simpler'. 172.69.194.98 14:57, 3 December 2024 (UTC)

Except that every one after the first one isn't a proper advent calendar, because it starts too late.172.70.90.198 09:54, 4 December 2024 (UTC)

Randall clearly thinks that "starting late" doesn't disqualify a pretruncated Advent Calendar from being an Advent Calendar in an Advent Calendar Advent Calendar. Or, perhaps that an Advent Calendar Advent Calendar's requirement is the inclusion of just the one 'true' Advent Calendar (whatever you call all the others, behind flaps beyond the first). If you're not complaining about Randall's interpretation, then this also applies to the AC³ suggestion given above, and over-explained, that it seems you're replying about. 172.71.118.144 01:57, 5 December 2024 (UTC)

Nope - wasn't replying about that. I was replying about the reply. It was a reply reply, not just a reply.141.101.98.107 09:18, 5 December 2024 (UTC)

The singer in The Twelve Days of Christmas receives two gifts on the first day, not one - a partridge, and a pear tree. (Then four on the second day, seven on the third, and so on.) That one item is presented within the other doesn't make them a single gift. Otherwise they would only receive 12 gifts total, with the final day's gift being twelve drummers drumming and eleven pipers piping and ten lords a leaping... 172.70.90.199 09:59, 4 December 2024 (UTC)

Wouldn't that mean twelve drummers drumming would give them at least 36 gifts? Twelve drummers, at least 12 drums, and and least 12 drumsticks? (unless it's twelve drummers around one large drum? ... ) 172.68.186.50 14:43, 4 December 2024 (UTC)

Not necessarily - all you need for drumming is you. Pipers piping might be another matter though...172.69.194.184 15:07, 4 December 2024 (UTC)

The geese-a-laying would complicate matters too. Are these just geese of a laying age and condition (in which case, count 1 each), or are they actually in the act of laying? If the latter, at what stage in the laying process are they at the point of gifting, and are any eggs that have already been laid at that point included in the gift? It would be very difficult to get them to synchronise to lay at exactly the same moment.172.70.90.237 15:15, 4 December 2024 (UTC)

Well it's time for historic pedantry vs. math nerds. The partridge and the pear tree are a package deal (it's not possible to "send" a mature tree somewhere unless you're time travelers anyway.) Would you claim that my true love sent 24 drumsticks, 12 drums, 12 drummers, 12 copies of sheet music,and 12 costumes? But more importantly, even Wikipedia knows that only one set of gifts corresponds to each day. The repetition elides mention of the day numbers because it was poetic license, and no sane listener would assume twelve pear trees or 22 doves. That's ridiculous. If you wanna analyze the progression, at least couch it in hypothetical terms instead of perpetuating myths. Excuse me while I kiss this guy.

[Munroe's use of "acceleration" is a double-entendre, because performers often enjoy starting slow and increasing tempo for each "day" in the style of "Dueling Banjos". Elizium23 (talk) 09:52, 14 December 2024 (UTC)

Wait, isn't it similar to the comic Alignment Chart Alignment Chart? --172.70.110.119 05:06, 7 December 2024 (UTC)

Is anyone going to point out that proper advent calendars only have 24 doors? 172.68.150.90 07:13, 8 December 2024 (UTC)

All of mine have 25 doors? Is the traditional one only have 24? Cause the commercial ones are most 25 Apollo11 (talk) 14:49, 8 December 2024 (UTC)

It is (or was, maybe it got lost in further mass-edits, but I remember it being there and should really have checked before replying...) mentioned that some calendars have 1..25 (to finish with 'big reveal' on Christms Day), others may go 1..24 (given that there's more than enough gifts and distractions expected on the 25th, though that could also be said of the 24th in some cultural traditions).

What wasn't really expounded upon, but hi ted at, was that if you go really traditional, it starts on the 4th Sunday before Christmas Day, which is only on the 1st when the 1st is a Sunday. Regardless of the inclusion of the 25th, a 'proper' one for any given year might have doors all around the mid-20s in number. But chocolate/etc ones probably just settle on starting at the 1st (or cheaper 'fortnight', 'final week' ones, perhaps, as discount gifts for tardy uncles' and aunts' benefits?), whichever day they finish at. 172.70.163.46 15:26, 8 December 2024 (UTC)