Proposition Infinity (generally referred to as "Proposition 8"), which banned same-sex marriage in California in November 2008. The title of the episode is derived from Proposition 8, turning the 8 sideways to create the symbol for infinity (∞), hence "Proposition ∞". Though the episode satirizes arguments for same-sex marriage, it leans favorably toward the idea of allowing same-sex marriage. The theme of the episode revisits the social taboo of robosexual relationships presented in earlier episodes "Space Pilot 3000" and "I Dated a Robot". Openly gay actor George Takei of "Star Trek" fame, who married his partner in California during the debate over
Determining the number of clusters in a data set of "G" "p"-dimensional Gaussian distributions with common covariance. Then for any fixed "K" less than "G", the distortion of a clustering as "p" goes to infinity is infinite. Intuitively, this means that a clustering of less than the correct number of clusters is unable to describe asymptotically high-dimensional data, causing the distortion to increase without limit. If, as described above, "K" is made an increasing function of "p", namely, formula_5, the same result as above is achieved, with the value of the distortion in the limit as "p" goes to infinity being equal to formula_10. Correspondingly, there is the same