3125: Snake-in-the-Box Problem
| 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"
