Main Page

Explain xkcd: It's 'cause you're dumb.
Jump to: navigation, search

Welcome to the explain xkcd wiki!
We have an explanation for all 2658 xkcd comics, and only 75 (3%) are incomplete. Help us finish them!

Latest comic

Go to this comic explanation

Coffee Cup Holes
Theoretical physicist: At the Planck length, uncountably many.
Title text: Theoretical physicist: At the Planck length, uncountably many.


Ambox notice.png This explanation may be incomplete or incorrect: Created by a CAFFEINE MOLECULE WITH A HOLE DRILLED IN ITS SIDE. Do NOT delete this tag too soon.

This comic depicts people in different fields of study answering the question, "How many holes are there in a coffee cup?" This question can have multiple interpretations, in particular concerning the definition of a hole.

The coffee mug and donut shown in this animation both have topological genus one.

Ponytail, a topologist, states the coffee cup belongs in the genus of one hole. A common joke is that topologists can't tell the difference between a coffee cup and a donut since they're homeomorphic to each other — they have the same genus. From the topologist's point of view, the coffee cup definitely has one hole. See 2625: Field Topology for more information about topology.

Hairy, a normal person, is not sure (the acronym "IDK" stands for "I don't know") and asks for clarification about whether the opening at the top counts as a hole. This shows flaws in the question, which suffers from the mathematically imprecise, ambiguous common usage of the word hole. Topologists would refer to the opening as a concavity, not a hole, and while they consider such geometrical properties generally outside their field, most practical applications of topology do involve geometric components.

A genus two surface

Hairbun, a philosopher, answers the question with an elucidating counter-question, considering a hypothetical scenario. Drilling a new hole should increase the number of holes by one, and after the hole has been drilled, a common teacup or mug has two holes according to topologists. Since drilling a hole increases the number of holes by one,[citation needed] the philosopher's question requires the original questioner to reveal the answer to their own question. (Also, she asks how many holes there are now rather than after we do that, an ambiguity.)

A point cloud of a genus one surface

Cueball, a chemist, looks at the coffee in the cup on a molecular level, which means it has very many holes: 1,000,000,000,000,000,000,000 (1021 or 1 sextillion) “in the caffeine alone.” An implication is that there are more holes in the cup itself, with which normal people and topologists would probably disagree. Also, the coffee itself could have other holes, depending on the type of coffee. For example, espresso contains significant amounts of niacin and riboflavin, each of which has at least one hole in its chemical structure. However, this ignores the fact that bonds are not discrete sticks as portrayed in many molecular models. The "holes" in the middle of a caffeine molecule are not completely empty but instead merely have lower electron densities/probabilities. So the point-cloud duality of electron orbitals and bonds might not satisfy a topologist's, normal person's, or philosopher's criteria for a connected substrate in which holes may be formed.

String theory describes the worldlines of point-like particles as worldsheets of "closed strings," forming topological holes.

In the title text, a theoretical physicist looks even deeper, at the subatomic scale of Planck units. Since fundamental particle interaction is governed by fundamental forces and collision (per the Pauli exclusion principle) instead of tensile or ductile solid connectedness, the theoretical physicist posits that any definition providing for a single hole would also describe a number of holes akin to the factorial of the number of particles in the universe, or at least within the cup's light cone, which is a number impractical to accurately count, but not uncountable in a mathematical sense.

Part of the joke could be that all five methods of inquiry don't discern between a cup (as described) and a mug (as depicted), the cliché being that topologists are unusual because they don't. Or, as many people use the terms interchangeably, Randall may too.


Ambox notice.png This transcript is incomplete. Please help editing it! Thanks.
[The first panel has text only. The "Q:" below is a large letter Q representing a question, not a character name.]
How many holes are there in a coffee cup?
[Each of the next four panels has a caption at the top to indicate the kind of person answering the question.]
Caption: Topologist
[Ponytail stands holding a coffee mug.]
Ponytail: One.
Caption: Normal person
[Hairy stands to the right of Ponytail, holding a coffee mug at an angle to look into it.]
Hairy: IDK, does the opening count as a hole?
Caption: Philosopher
[Hairbun is shown in closeup, with two drawings of coffee mugs to her left.]
Hairbun: To answer that question, consider another: If we drill a hole in the side, how many holes are there now?
Caption: Chemist
[Cueball stands with a drawing of a caffeine molecule above him and to the right.]
Cueball: 1021 in the caffeine alone

Is this out of date? Clicking here will fix that.

New here?

Last 7 days (Top 10)

Lots of people contribute to make this wiki a success. Many of the recent contributors, listed 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 sign up for an account and contribute to the wiki! We need explanations for comics, characters, themes and everything in between. If it is referenced in an xkcd web comic, it should be here.

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


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 (and helping everyone better understand) 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.