Editing 3125: Snake-in-the-Box Problem

{{comic
| number    = 3125
| date      = August 6, 2025
| title     = Snake-in-the-Box Problem
| image     = snake_in_the_box_problem_2x.png
| imagesize = 359x611px
| noexpand  = true
| titletext = 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 {{w|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 [https://oeis.org/A099155 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 {{w|Square|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 {{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", 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]].

==Transcript==
:[A panel with text both above and below the illustration, with further text outside the panel below.]
:[In the panel, above the illustration:]
:A snake slithers around a hypercube. No two non-consecutive parts of its coils can be on adjacent corners.
:[Three small illustrations of 4-dimensional hypercubes, each with a snake slithering around its edges. Each illustration has a red line or lines indicating an edge or edges where two non-consecutive parts of the snake are on adjacent corners. Below each hypercube is a red X.]
:[A large illustration depicting a 4-dimensional hypercube with a snake slithering around its edges.]
:[Below the large illustration is text printed in green. To the left of the text is a green checkmark.]
:Dimensions=4
:Max length=7
:[The following text is printed in black, except for the last word "UNSOLVED" which is printed in red:]
:Snake(N) = Largest snake that can fit in an N-dimensional hypercube
:Snake(N=1, 2, 3 .. 8) = 1, 2, 4, 7, 13, 26, 50, 98
:Snake(N>8) = UNSOLVED

:[Text outside the panel:]
:It turns out every scientific field has a key thought experiment that involves putting a cute animal in a weird box for no reason.
:So far, quantum mechanics and graph theory have found theirs, but most other fields are still working on it.

{{comic discussion}}<noinclude>

[[Category:Comics with color]]
[[Category:Math]]
[[Category:Physics]]
[[Category:Animals]]
[[Category:Cats]]
[[Category:Squirrels]] <!-- title text mention, only -->