Difference between revisions of "3125: Snake-in-the-Box Problem"
(→Explanation) |
|||
| Line 14: | Line 14: | ||
The other thought experiment alluded to is {{w|Schrödinger's cat}}, which is used in quantum physics. In this thought experiment, a cat is put in a box which contains poison, a radioactive source and a {{w|Geiger counter}}. This aims to illustrate an apparent paradox in the principle of {{w|quantum superposition}} — a property of quantum mechanics in which objects can exist in two apparently incompatible states simultaneously, so long as no attempt is made to verify which state they are in. If an atom of the radioactive source decays, the poison is released, and the cat dies, tying its fate to the radioactive decay. Since radioactive decay obeys quantum mechanics, so long as the particle is not observed it will exist in a superposition of two states: decayed and not decayed. Therefore, the cat, too, may be considered to exist in a superposition of two states (alive and not alive) which appears to be absurd. The opening of the box collapses the superposition so that only one of those states remains. | The other thought experiment alluded to is {{w|Schrödinger's cat}}, which is used in quantum physics. In this thought experiment, a cat is put in a box which contains poison, a radioactive source and a {{w|Geiger counter}}. This aims to illustrate an apparent paradox in the principle of {{w|quantum superposition}} — a property of quantum mechanics in which objects can exist in two apparently incompatible states simultaneously, so long as no attempt is made to verify which state they are in. If an atom of the radioactive source decays, the poison is released, and the cat dies, tying its fate to the radioactive decay. Since radioactive decay obeys quantum mechanics, so long as the particle is not observed it will exist in a superposition of two states: decayed and not decayed. Therefore, the cat, too, may be considered to exist in a superposition of two states (alive and not alive) which appears to be absurd. The opening of the box collapses the superposition so that only one of those states remains. | ||
| − | The comic jokes that these two "cute animal in a box" thought experiments are instances of a universal rule that applies to every field of study. Other fields have simply yet to "discover" their own analogies. Whether a snake counts as a "cute animal" <!-- Not really. --!>that would satisfy the "rule" is likely to occasion some debate. | + | The comic jokes that these two "cute animal in a box" thought experiments are instances of a universal rule that applies to every field of study. Other fields have simply yet to "discover" their own analogies. Whether a snake counts as a "cute animal" <!-- Not really. --!> that would satisfy the "rule" is likely to occasion some debate. |
The title text takes this further by claiming that chemistry students have been trying to fix the lack of cute-animal-in-box thought experiments in their field by attempting to trap a squirrel with a laundry basket. This is possibly a reference to {{w|Endohedral fullerene}} complexes, where an ion or atom is caged inside a spherical structure of carbon. Those students seem to hope that it will inspire them in some way, maybe similarly to what is depicted in [[1584: Moments of Inspiration]]. | The title text takes this further by claiming that chemistry students have been trying to fix the lack of cute-animal-in-box thought experiments in their field by attempting to trap a squirrel with a laundry basket. This is possibly a reference to {{w|Endohedral fullerene}} complexes, where an ion or atom is caged inside a spherical structure of carbon. Those students seem to hope that it will inspire them in some way, maybe similarly to what is depicted in [[1584: Moments of Inspiration]]. | ||
Revision as of 07:58, 12 August 2025
| Snake-in-the-Box Problem |
 Title text: Chemistry grad students have been spotted trying to lure campus squirrels into laundry hampers in the hope that it sparks inspiration. |
Explanation
This comic makes fun of the fact that many fields of math and science use analogies to help visualize complex problems. One such analogy, drawn in the comic, involves a snake on the edges of an n-dimensional hypercube, which is a real problem in graph theory called snake-in-the-box. In this problem, a snake is coiled around the edges of an n-dimensional hypercube. No two adjacent corners of the cube can be occupied by non-consecutive parts of the snake (i.e., the snake can't come near itself). The problem involves finding the longest snake for a box of a given dimension. This problem has been solved up to an 8-dimensional cube, but remains unsolved for 9 dimensions and up. (The proper name for this problem, as stated in OEIS A099155, is "Maximum length of a simple path with no chords in the n-dimensional hypercube" but, as the entry acknowledges, "snake-in-the-box problem" is the name commonly used for it.) Because a common way to formulate hypercubes is as a graph of N-tuples (each corner has N coordinates, each a 0 or 1 - for example, a 2-cube has vertices (0,0), (0,1), (1,0), (1,1) - and edges are drawn between vertices differing only in one coordinate), and this problem in particular pertains to connecting edges between vertices, this comic considers the problem to be an example of this phenomenon for the mathematical field of graph theory.
The other thought experiment alluded to is Schrödinger's cat, which is used in quantum physics. In this thought experiment, a cat is put in a box which contains poison, a radioactive source and a Geiger counter. This aims to illustrate an apparent paradox in the principle of quantum superposition — a property of quantum mechanics in which objects can exist in two apparently incompatible states simultaneously, so long as no attempt is made to verify which state they are in. If an atom of the radioactive source decays, the poison is released, and the cat dies, tying its fate to the radioactive decay. Since radioactive decay obeys quantum mechanics, so long as the particle is not observed it will exist in a superposition of two states: decayed and not decayed. Therefore, the cat, too, may be considered to exist in a superposition of two states (alive and not alive) which appears to be absurd. The opening of the box collapses the superposition so that only one of those states remains.
The comic jokes that these two "cute animal in a box" thought experiments are instances of a universal rule that applies to every field of study. Other fields have simply yet to "discover" their own analogies. Whether a snake counts as a "cute animal"
