De_Xtra_Whisper (@alternate_distance_reiki)

Received Query on New to Publications, Recursion Monsters Home in Ramsey Theory ---- Historical Mini-Bio of Ramsey Frank Plumpton Ramsey was born on 22 February 1903 in Cambridge, England. Ramsey entered Winchester College in 1915, but left in 1920. Then Ramsey began studying mathematics at Trinity College, Cambridge that same year. Ramsey graduated in 1923 as a Wrangler. [first-class honours with distinction in the Mathematical Tripos] Ramsey married Lettice C. Baker on 21 August 1925. Ramsey was appointed University Lecturer in Mathematics at Cambridge in 1926. Later, Ramsey served as Director of Studies in Mathematics at King’s. Ramsey died on 19 January 1930 in London at the age of only 26. ---- Ramsey theory originated in a paper Frank Plumpton Ramsey wrote in 1928 titled “On a Problem of Formal Logic,” which was published posthumously in 1930. Ramsey proved that in any sufficiently large structure, orderly patterns must appear no matter how the elements are arranged or colored. There were many contributors to the collective Ramsey Theory. Issai Schur proved an early related result in 1916. Bartel van der Waerden published his theorem on arithmetic progressions in 1927. Paul Erdős and George Szekeres gave an important new proof and extension in 1935. Their work helped turn Ramsey’s original insight into a full and rich mathematical theory. The ideas first sketched by Ramsey over 1928–1930 continue to influence combinatorics, graph theory, and computer science today. ---- One thing about the functions in the Tcl/Tk simulations . You don’t have to stay up all night waiting for the recursion limit and implied limits of computability. Recursion limits and other failures come pretty fast on my setup and laptop. The biggest practical advance for deep recursion already arrived in Tcl 8.6 with the Non-Recursive Engine (NRE). NRE moves most of the call stack onto the heap instead of the C stack. This lets Tcl/Tk scripts go much deeper before crashing than older Tcl 8.x versions could. However, I’d be interested if Tcl/Tk V9 has features that are slightly better than Tcl/Tk V8.6+ in tackling Recursion Monsters.... or otherwise caging a lion. ---- The function returns only an upper bound, never the exact Ramsey number. We are using only a tiny fraction of the rich Ramsey Theory to study scalability limits or recursion limits in classical computing. The upper-bound Ramsey number function is the classic recursive inequality R(s, t) ≤ R(s-1, t) + R(s, t-1) The Inequality is turned into a pure recursive procedure. The call tree grows extremely fast, so that the strong depth and call-count guardrails are applied. The recursive procedure produces a number that always sits above the true Ramsey number (R(s,t)). Informally, the function can be called an envelope function for the Ramsey numbers. ---- Figure. Ramsey (1903–1930) ----