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 comic depicts people in different fields of study answering the question, "How many holes are there in a coffee cup?" and also compares this to what a normal person would say. | This comic depicts people in different fields of study answering the question, "How many holes are there in a coffee cup?" and also compares this to what a normal person would say. | ||
This question has different interpretations, entirely dependent upon the definition of a hole. The type of {{w|coffee cup}} shown in the comic is with a handle (like a {{w|mug}}), but [[Randall]] calls it a cup and there are also cups with handles on the Wikipedia page for coffee cups. Most people would recognize that there is a hole through the handle. | This question has different interpretations, entirely dependent upon the definition of a hole. The type of {{w|coffee cup}} shown in the comic is with a handle (like a {{w|mug}}), but [[Randall]] calls it a cup and there are also cups with handles on the Wikipedia page for coffee cups. Most people would recognize that there is a hole through the handle. | ||
| − | The comic explores the answer to the question through several | + | The comic explores the answer to the question through several avenues of thought: |
| − | === | + | ===Topology=== |
[[File:Mug and Torus morph.gif|thumb|200px|The coffee mug and donut shown in this animation both have topological genus one.]] | [[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. From the topologist's point of view, the coffee cup definitely has one hole, which corresponds to the opening created by the cup handle. A cup without a handle would have zero holes, as it is equivalent to a dinner plate, just an indentation in the surface. See [[2625: Field Topology]] for more information about topology. | [[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 created by the cup handle. A cup without a handle would have zero holes, as it is equivalent to a dinner plate, just an indentation in the surface. See [[2625: Field Topology]] for more information about topology. | ||
| − | The panel as a whole references an academic joke wherein topologists can't tell the difference between a coffee cup with | + | The panel as a whole references an academic joke wherein topologists can't tell the difference between a coffee cup (with handle) and a {{w|doughnut}} since they're {{w|Homeomorphism|homeomorphic}} to each other — meaning they have the same genus (i.e one hole). |
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| + | [[Image:Point cloud torus.gif|thumb|left|200px|A point cloud of a genus one surface]] | ||
===Normal person=== | ===Normal person=== | ||
| − | [[Hairy]], representing 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. By contrast, in everyday usage many concavities are called holes, such as a hole dug into dirt with a shovel. Hairy would say one for the handle, and two if the opening counts as a hole, which he is not certain the one asking the question thinks. | + | [[Hairy]], representing 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. By contrast, in everyday usage many concavities are called holes, such as a hole dug into dirt with a shovel. Hairy would say one for the handle, and two if the opening counts as a hole, which he is not certain the one asking the question thinks. |
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===Philosopher=== | ===Philosopher=== | ||
| − | [[Hairbun]], a philosopher, answers the question with an elucidating counter-question, considering a hypothetical scenario. One might expect that drilling a new hole would also increase the number of holes by one. However, as illustrated, some people would consider that the new arrangement has three holes (in addition to the handle, there is a hole at the top where coffee can be poured in, and one at the bottom where it can run out), while others would consider it to have only two (the new hole forming a continuous hole with the original opening at the top, through which coffee can run) | + | [[Hairbun]], a philosopher, answers the question with an elucidating counter-question, considering a hypothetical scenario. One might expect that drilling a new hole would also increase the number of holes by one. However, as illustrated, some people would consider that the new arrangement has three holes (in addition to the handle, there is a hole at the top where coffee can be poured in, and one at the bottom where it can run out), while others would consider it to have only two (the new hole forming a continuous hole with the original opening at the top, through which coffee can run). In this way she forces her interlocutor to confront the ambiguities and consider what they mean by the word 'hole' in different contexts. |
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| − | === | + | ===Chemistry=== |
[[Cueball]], a chemist, looks at the coffee in the cup on a molecular level. He envisions a {{w|ball-and-stick model}} of the {{w|caffeine}} molecules in the coffee, and estimates a total number of holes of all the coffee molecules. He comes up with a truly massive number: 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, multiplied by 500 quintillion molecules, or 0.00083 {{w|mole (unit)|moles}}. As the molecular mass of 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. | [[Cueball]], a chemist, looks at the coffee in the cup on a molecular level. He envisions a {{w|ball-and-stick model}} of the {{w|caffeine}} molecules in the coffee, and estimates a total number of holes of all the coffee molecules. He comes up with a truly massive number: 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, multiplied by 500 quintillion molecules, or 0.00083 {{w|mole (unit)|moles}}. As the molecular mass of 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. | ||
This estimation depends on taking the ball-and-stick model of molecules somewhat literally. However, real molecular bonds are not solid sticks, but shared electron clouds between atoms. 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. | This estimation depends on taking the ball-and-stick model of molecules somewhat literally. However, real molecular bonds are not solid sticks, but shared electron clouds between atoms. 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. | ||
| − | [[Image:World lines and world sheet.svg|thumb | + | ===Subatomic physics=== |
| − | + | [[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.]] | |
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. | ||
| − | + | The main joke is that the number of holes depends on both the scale and perspective from which you are looking at the world. From a topological standpoint, when someone digs into the ground it should go all the way through (or easier, down and up again another place) before it is considered a hole, since a hole is something that some other thing should be able to pass through. But from a common usage perspective, if people dig in the ground the result is called a hole, because functionally it creates a discontinuity in to which, for example, things can be placed or fall. Similarly, the opening in a coffee cup (without a handle) or a bottle of beer is called a hole, even though they are topologically equivalent to a dinner plate, which normal people would never say had a hole. | |
| − | The main joke is that the number of holes depends on both the scale and perspective from which you are looking at the world. From a topological standpoint, when someone digs into the ground it should go all the way through (or easier, down and up again another place) before it is considered a hole, since a hole is something that some other thing should be able to pass through. But from a common usage perspective, if people dig in the ground the result is called a hole, because functionally it creates a discontinuity in to which, for example, things can be placed or fall. Similarly, the opening in a coffee cup without a handle or a bottle of beer is called a hole, even though they are topologically equivalent to a dinner plate, which normal people would never say had a hole. | ||
| − | A cavity in a surface could also be considered a physical barrier, preventing movement along the surface in certain scenarios (e.g. a {{w|sinkhole}} opening up in the middle of a road) even though it may | + | A cavity in a surface could also be considered a physical barrier, preventing movement along the surface in certain scenarios (e.g. a {{w|sinkhole}} opening up in the middle of a road) even though it may topologically 'flat' in the most general way, and so is very open to context, and such a hole might be considered more a 'thing' than the surface that has been removed to create it. And the 'hole' in a vessel that is functionally useful to hold liquid (or the drilled one that removes that ability) is of a different nature to the holes in various of the molecules that ''are'' the liquid but are neither required nor counter-productive in the general liquid-holding capabilities of the container, as are not the holes in the planck-length model, except insofar as the general physical laws of reality. Conversely, this conceptual confusion over what a hole is or actually means can be seen in the idea of the {{w|portable hole}}, which tends to obey ({{w|Wile E. Coyote and the Road Runner|or defy}}!) the owner's particular preconceptions or needs. |
The topological discussion here regarding cups and doughnuts is related to the question of how many holes there are in a human, which is excellently answered in Vsauce's video | The topological discussion here regarding cups and doughnuts is related to the question of how many holes there are in a human, which is excellently answered in Vsauce's video | ||
| − | [https://www.youtube.com/watch?v=egEraZP9yXQ How Many Holes Does a Human Have?]. This also takes a | + | [https://www.youtube.com/watch?v=egEraZP9yXQ How Many Holes Does a Human Have?]. This also takes a god look at the topological difference between a paper cup and a mug with handle. |
==Transcript== | ==Transcript== | ||
