2013/01/01 by Joshua Cooper, Aaron Dutle · 2 citations
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Computability, Logic, AI Algorithms #semigroups and automata theory #Interpretation (philosophy) #Sequence (biology) #Morse code #Mathematical economics #Galois theory #Mathematics #A priori and a posteriori #Pure mathematics #Computer science #Epistemology #Philosophy
paper · doi:10.4169/amer.math.monthly.120.05.441
openalex publication_date 2013/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that two duelers with similar, lousy shooting skills (a.k.a. Galois duelers) will choose to take turns firing in accordance with the famous Thue–Morse sequence if they greedily demand their chances to fire as soon as the other's a priori probability of winning exceeds their own. This contrasts with a result from the approximation theory of complex functions, which says what more patient duelers would do, if they really cared about being as fair as possible. We note a consequent interpretation of the Thue–Morse sequence in terms of certain expansions in fractional bases close to, but greater than, 1.