MARSHALL PENFIELD in front of a large group of graduate students -- lecturing. Charlie quietly slips in the back. MARSHALL From set theory's inception, some have argued it's a game that includes elements of fantasy. Wittgenstein questioned how Zermelo-Fraenkel set theory handled infinities. Errett Bishop dismissed it as "God's mathematics, which we should leave for God to do." Marshall spies Charlie in the back. MARSHALL (cont'd) Next week's talk will be on the Spectral Theory of non-Hermitian Random Matrices. Thank you. The students file out. Charlie approaches.

Each eigenvalue in the spectrum of a combinatorial graph's adjacency matrix gives rise to a "spectral realization" of the graph. Such a realization is both eigenic (replacing each vertex with the vector sum of its neighbors is equivalent to scaling the figure) and harmonious (each automorphism of the graph is realized by an isometry of the figure). In many cases, they are also just plain fascinating. This Demonstration reveals the spectral realizations of (the skeleton of) each named polyhedron in *Mathematica*'s PolyhedronData[] collection.

AMITA What if it's not just computer code ... but a cipher code? MARSHALL If it is, could take months to figure out. NIKKI They painted this on a wall -- I doubt they made it hard to crack. CHARLIE Maybe a simple Vigenere cipher? MARSHALL With the first 13 alphabet letters matched to these 13 code symbols -- AMITA And the key word is "Vanguard"-- Amita brings up a Vigenere software program on a second screen -- and it translates the computer code into TEXT.

Substitution ciphers are one of the simplest forms of encryption, where replacement rules are provided that map each letter of the alphabet onto a different letter. This tool will generate randomly chosen keys that map the 26 letters of the English alphabet onto themselves. It also generates snippets of sample text from a range of English sources.