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Explore the fascinating concept of a "gauguine" - a probabilistic program that infers its own source code through self-observation and pattern detection in this 39-minute conference presentation from Onward! 2025. Discover how researchers from MIT have created a program that starts with minimal chances of guessing its own code correctly but gradually bootstraps self-knowledge by analyzing its previous guesses and detecting behavioral patterns. Learn about the theoretical foundations combining probabilistic programming with self-reflection, drawing inspiration from Gauguin's artistic introspection, Descartes' philosophical self-examination, and Bayesian inference methods. Examine the technical implementation details of how a program can gain information about its inner workings through repeated self-observation, ultimately achieving the remarkable feat of discovering its own source code. Understand the broader implications of this work for programming language theory, artificial intelligence, and computational self-awareness, as the researchers discuss both the methodology behind constructing such a system and the insights gained from this novel approach to program self-reflection.