Editing 2658: Coffee Cup Holes
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==Explanation== | ==Explanation== | ||
− | + | {{incomplete|Created by a CAFFEINE MOLECULE WITH A HOLE DRILLED IN ITS SIDE. Do NOT delete this tag too soon.}} | |
− | This | + | This comic depicts people in different fields of study answering the question, "How many holes are there in a coffee cup?" This question has different interpretations depending on the definition of a hole. |
− | The | + | [[File:Mug and Torus morph.gif|thumb|200px|The coffee mug and donut shown in this animation both have topological genus one.]] |
− | + | [[Ponytail]], a {{w|topology|topologist}}, states the coffee cup belongs in the {{w|Genus (mathematics)#Topology|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 — meaning they have the same genus. From the topologist's point of view, the coffee cup definitely has one hole, which corresponds to the opening in the cup handle. See [[2625: Field Topology]] for more information about topology. | |
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− | [[Ponytail]], a {{w|topology|topologist}}, states the coffee cup belongs in the {{w|Genus (mathematics)#Topology|genus}} of one hole. From the topologist's point of view, the coffee cup definitely has one hole, which corresponds to the opening | ||
− | + | [[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. | |
− | + | [[File:Double torus illustration.png|thumb|left|200px|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. After the hole has been drilled, a common teacup or mug has two holes according to topologists. Therefore, the philosopher's question requires the original questioner to reveal the answer to their own question. | |
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− | [[Hairbun]], a philosopher, answers the question with an elucidating counter-question, considering a hypothetical scenario. | ||
[[Image:Point cloud torus.gif|thumb|200px|A point cloud of a genus one surface]] | [[Image:Point cloud torus.gif|thumb|200px|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 (10<sup>21</sup> or 1 sextillion) “in the [https://chemapps.stolaf.edu/jmol/jmol.php?model=CN1C%3DNC2%3DC1C%28%3DO%29N%28C%28%3DO%29N2C%29C caffeine] alone.” One molecule of caffeine has two rings of bonds with holes in them, so Cueball is talking about 500 quintillion molecules, or 0.00083 {{w|mole (unit)|moles}}. As the molecular mass of {{w|caffeine}} is about 194 grams per mole, [[Randall]] must think that the mass of caffeine in a typical cup of coffee is 161 milligrams. The coffee could have other holes, depending on the type of coffee; for example, espresso contains significant amounts of niacin and riboflavin, which have one and three rings in their chemical structure, respectively. However, bonds are not sticks as portrayed in many molecular models. The "holes" in the middle of a molecule's rings are not completely empty but instead merely have lower electron probability density through the middle than other parts of the bonds. So the point-cloud duality of {{w|Bonding molecular orbital|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. | |
− | [[Cueball]], a chemist, looks at the coffee in the cup on a molecular level | ||
− | + | [[Image:World lines and world sheet.svg|left|thumb|200px|{{w|String theory}} describes the {{w|worldline}}s of point-like particles as {{w|worldsheet}}s of "closed strings," forming topological holes.]] | |
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In the title text, a theoretical physicist looks even deeper, at the subatomic scale of {{w|Planck units}}. Since fundamental particle interaction is governed by fundamental forces and collision (per the {{w|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,[https://tel.archives-ouvertes.fr/tel-02341882/document] or at least within the cup's {{w|light cone}}, which is a number impractical to accurately count, but not uncountable in a mathematical sense. | In the title text, a theoretical physicist looks even deeper, at the subatomic scale of {{w|Planck units}}. Since fundamental particle interaction is governed by fundamental forces and collision (per the {{w|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,[https://tel.archives-ouvertes.fr/tel-02341882/document] or at least within the cup's {{w|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 {{w|cup}} (as described) and a {{w|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. A cup without a looped handle is topologically equivalent to either a flat disk (if the cup' walls are assumed to have no thickness) or an amorphous sphere (if the cup's walls have thickness). | |
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− | + | ==Transcript== | |
− | + | {{incomplete transcript|Do NOT delete this tag too soon.}} | |
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− | + | :[The first panel has text only. The "Q:" below is a large letter Q representing a question, not a character name.] | |
− | :[The first panel has text only | + | :Q: |
− | : | ||
:How many holes are there in a coffee cup? | :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 | + | :[Each of the next four panels has a caption at the top to indicate the kind of person answering the question.] |
:Caption: Topologist | :Caption: Topologist | ||
+ | :[Ponytail stands holding a coffee mug.] | ||
:Ponytail: One. | :Ponytail: One. | ||
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:Caption: Normal person | :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? | :Hairy: IDK, does the opening count as a hole? | ||
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:Caption: Philosopher | :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? | :Hairbun: To answer that question, consider another: If we drill a hole in the side, how many holes are there now? | ||
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:Caption: Chemist | :Caption: Chemist | ||
+ | :[Cueball stands with a drawing of a caffeine molecule above him and to the right.] | ||
:Cueball: 10<sup>21</sup> in the caffeine alone | :Cueball: 10<sup>21</sup> in the caffeine alone | ||
{{comic discussion}} | {{comic discussion}} | ||
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[[Category:Comics featuring Ponytail]] | [[Category:Comics featuring Ponytail]] | ||
[[Category:Comics featuring Hairy]] | [[Category:Comics featuring Hairy]] | ||
[[Category:Comics featuring Hairbun]] | [[Category:Comics featuring Hairbun]] | ||
[[Category:Comics featuring Cueball]] | [[Category:Comics featuring Cueball]] | ||
+ | [[Category:Math]] | ||
[[Category:Food]] | [[Category:Food]] | ||
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[[Category:Chemistry]] | [[Category:Chemistry]] | ||
[[Category:Philosophy]] | [[Category:Philosophy]] | ||
[[Category:Physics]] | [[Category:Physics]] |