Cological Words

Thanks to Walker for letting me use his incredible idea about cological words for a video. Thanks to ‪@potatoyianimations‬ for letting me use the funny ouroboros gif. TIMESTAMPS: 0:00 autological words 0:50 cological words 1:30 trilogical words? 1:49 borromeological words 2:31 E (and strange loops) 4:46 a program that writes itself 7:23 B 9:08 G 11:47 I FOOTNOTES: On Gödel: I simplify the theorem a lot. The big things to note: 1) The Gödel sentence doesn't technically contain an exact copy of itself. It refers to itself indirectly (this is the difference between big G and little g in the original theorem), which I glossed over. But basically, it contains the instructions to reproduce itself, not exactly itself. 2) "Rich enough" has a precise meaning in the theorem. I show it very briefly, but the system needs multiplication as a general operation, not just addition. Arithmetic with only addition (Presburger arithmetic) is complete and consistent. It might seem like multiplication is just repeated addition, but computation and expression are not the same! There is no formula with a variable number of plus signs (“add y, x times” is not expressible with just + and =, without sneaking in multiplication). 3) (Most of) the huge Gödel numbers I showed are really calculated from the encoding shown, but the symbol coding follows the Stanford Encyclopedia of Philosophy's convention, not the OG encoding (which is quite confusing and complicated). Different textbooks assign different codes, so the precise Gödel number of a formula is convention-dependent (the exact encoding doesn’t matter for the argument). SOCIALS: instagram:   / alezhoux   SOURCES: Bach, J. S. (1747). Canon a 2 per tonos, from Musical Offering, BWV 1079 [Rendered by the author with MuseScore/MuseSounds]. Endoh, Y. (n.d.). Quine Relay [Computer software]. GitHub. Retrieved April 12, 2026, from https://github.com/mame/quine-relay Escher, M. C. (1948). Drawing hands [Lithograph]. Wikipedia. Retrieved December 13, 2025, from https://en.wikipedia.org/wiki/File:Dr... Escher, M. C. (1953). Relativity [Lithograph]. BYU Museum of Art. Retrieved December 13, 2025, from https://moa.byu.edu/m-c-eschers-relat... Escher, M. C. (1961). Waterfall [Lithograph]. NHPR. Retrieved December 13, 2025, from https://www.nhpr.org/word-of-mouth/20... Gödel, K. (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik, 38, 173–198. Hofstadter, D. R. (1979). Gödel, Escher, Bach: An eternal golden braid. Basic Books. Hofstadter, D. R. (2007). I am a strange loop. Basic Books. Raatikainen, P. (2025). Gödel's incompleteness theorems (E. N. Zalta & U. Nodelman, Eds.). The Stanford Encyclopedia of Philosophy. Retrieved July 13, 2026, from https://plato.stanford.edu/entries/go... (Symbol coding from the supplement: https://plato.stanford.edu/entries/go...) Searle, J. R. (1984). Minds, brains and science. Harvard University Press. Strange Loop Conference. (2021). "What Is a Strange Loop and What Is It Like To Be One?" by Douglas Hofstadter (2013) [YouTube video].    • "What Is a Strange Loop and What is it Lik...   TodePond. (2023). DEFINE DEFINE [YouTube video].    • DEFINE DEFINE   🎵 Copyrighted music licensed from Lickd. https://lickd.co One Note Samba by Herbie Mann, João Gilberto, Antonio Carlos Jobim, https://t.lickd.co/l/gW6gWkp367k CC ATTRIBUTIONS: Lee Sallows, Lee Sallows, CC BY-SA 3.0 DNA Structure, Zephyris, CC BY-SA 3.0 Structural classification of neurons by polarity, Hariadhi, CC BY-SA 4.0 Shepard Tones spectrum linear scale, Grin, CC BY-SA 4.0