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. | ||
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[[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). Some might in fact say that the coffee cup now has one hole because it is leaky, disregarding the handle topology at this point. In this way she requires her interlocutor to confront the ambiguities and consider what they mean by the word 'hole' in different contexts. An interesting point about Hairbun's response is that she doesn't actually answer the question, a trope often found in philosophical replies. | [[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). Some might in fact say that the coffee cup now has one hole because it is leaky, disregarding the handle topology at this point. In this way she requires her interlocutor to confront the ambiguities and consider what they mean by the word 'hole' in different contexts. An interesting point about Hairbun's response is that she doesn't actually answer the question, a trope often found in philosophical replies. | ||
| β | [[Image:Point cloud torus.gif|thumb|200px|A point cloud of a genus one surface]] | + | [[Image:Point cloud torus.gif|thumb|left|200px|A point cloud of a genus one surface]] |
===Chemist=== | ===Chemist=== | ||
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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. | ||
| β | |||
===Theoretical physicist=== | ===Theoretical physicist=== | ||
| + | [[Image:World lines and world sheet.svg|thumb|200px|{{w|String theory}} describes the {{w|worldline}}s of point-like particles as {{w|worldsheet}}s of "closed strings," forming topological holes; shown here as a genus two surface.]] | ||
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. | ||
