Main Page

Welcome to the explain xkcd wiki!
We have an explanation for all 3189 xkcd comics, and only 54 (1.7%) are incomplete. Help us finish them!

 Go to this explanation

Latest comic

Apples

|< < Prev #3180 (December 12, 2025)

Title text: The experimental math department's budget is under scrutiny for how much they've been spending on trains leaving Chicago at 9:00pm traveling at 45 mph.

|< < Prev Random Explanation

Explanation

Three "experimental mathematicians" have experimentally confirmed the answer to a mathematical query that might normally be described to an elementary school class: "If Cueball has seven apples and Hairbun has five, how many apples are there in total?" With everyone having literally brought together their stated number of apples, Cueball counts the two groups of apples and states that the total is twelve. Blondie is very excited that this real world demonstration has perfect agreement with some theory, presumably arithmetic.

The root of the joke is the conflation of mathematics, an abstract framework, with sciences like physics or chemistry that describe real world phenomena and that require experimental confirmation. In the context of the comic, because most sciences have both theoretical and experimental wings, mathematics should as well, with a humorous example of what "experimental mathematics" would look like. In this case Cueball and Hairbun are literally "testing" the concept of addition by reenacting a word problem in a mathematics textbook. This physical experiment itself is humorous because there is no mathematical difference between adding groups of apples or groups of hash marks on a piece of paper, but the characters would likely consider the latter to be "theoretical".

A different take on the joke is that mathematics is inherently experimental, but the "experiments" take the form of rigorously proving concepts, including something as basic as addition, from first principles. From this angle one would find humor in the fact that the three characters are testing math with physical objects instead of referring to the established proofs.

The irony is that some aspects of mathematics are experimental in the manner depicted in the cartoon. Children are often taught that the angles of a triangle sum to 180° by tearing off the points of a paper triangle and using them to construct a straight line. Some aspects of computer science can also be considered "experimental mathematics", especially at the circuit level where binary logic can be physically used to perform mathematical computation.

There are real-world cases where "basic addition" doesn't give the mathematical result, when combining certain items that aren't uniform. Measured volumes of two different substances, combined to make a solution, usually results in a volume of the end solution that differs from the sum of the original volumes. When measured volumes of nearly-freezing and nearly-boiling water are combined, the resulting liquid, at an intermediate temperature, will almost always be measurably different from the sum of the prior values.)

The title text confirms the comic's point of experimentally reenacting mathematics textbook word problems by reference to the "Two Trains Problem", a popular type of question to teach students how to solve simultaneous linear equations. A typical question of this type asks “If a train leaves station A at 9:00 am and travels at 60 miles per hour, and another train leaves station B at 10:00 am and travels at 80 miles per hour, where will the two trains meet if station A and B are 200 miles apart?” This type of problem is so common that it became a pre-internet meme with many references in popular culture, so Randall has to provide only the setup ("trains leaving Chicago at 9 pm traveling at 45 mph") to be reasonably sure that the reader will know what he's talking about.

Unlike apples, chartering real life trains to leave both Chicago and another city to test that class of word problem would present enormous expense to the experimental mathematics department. This expense again implies that the experimental mathematics department is not content with any abstraction, such as using model trains, and must test the word problems as written.

Transcript

[Hairbun and Cueball stand at the left of the panel. Blondie stands at the right. Between them are two piles of apples, one of seven apples (stacked four on the bottom, two in the middle row, and one on top) and the other of five apples (stacked three on the bottom, and two on top).They are all looking at the apples but Blondie has her arms raised high above her head.]

Cueball: Okay, with my seven apples added to your five, we have ... let's see ... twelve apples!

Blondie: Incredible!

Blondie: Perfect agreement with the theory!

[Caption below the panel:]

Experimental mathematicians

---

        View comic discussion

New here?

Last 7 days (Top 10)

Rank Score Pages Changes Username 1 264 262 263 管委会篝火无法解放军“赐额“你去呢管理哦法？ 2 115 103 138 DollarStoreBa'al 3 22 18 22 TheusafBOT 4 12 9 12 Headphones the stickman 5 12 5 17 BunsenH 6 11 8 11 R128 7 10 3 15 Sturmovik 8 9 9 9 Lp0 on fire 9 6 1 8 SammyChips 10 5 3 4 Potatocakethrow

Lots of people contribute to make this wiki a success. Many of the recent contributors above have just joined. You can do it too! Create your account here.

You can read a brief introduction about this wiki at explain xkcd. Feel free to create an account and contribute to the wiki! We need explanations for xkcd comics, characters, What If? articles, and everything in between. If it is referenced in an xkcd comic, it should be here.

• If you're new to wiki editing, see the explain xkcd:Editor FAQ for a specific guidance to this wiki and the more general help on how to edit wiki pages. There's also a handy wikicode cheatsheet.

• Discussion about the wiki itself happens at the Community portal.

• You can browse the comics from the list of all comics or by navigating the category tree at Category:Comics.

• The incomplete explanations are listed here. Feel free to help out by expanding them!

Rules

Don't be a jerk!

There are a lot of comics that don't have set-in-stone explanations; feel free to put multiple interpretations in the wiki page for each comic.

If you want to talk about a specific comic, use its discussion page.

Please only submit material directly related to xkcd and, of course, only submit material that can legally be posted and freely edited. Off-topic or other inappropriate content is subject to removal or modification at admin discretion, and users who repeatedly post such content will be blocked.

If you need assistance from an admin, post a message to the Admin requests board.