This poem is an exercise on self-reference and diagonalisation in mathematics featuring Turing’s proof of the undecidability of the halting problem, Cantor’s cardinality argument, the Burali-Forti paradox, and Epimenides\u27 liar paradox

Doat, Joël A

English

Scholarship@Claremont

Journal of Humanistic Mathematics Volume 13 | Issue 1 January 2023 Self-Reference and Diagonalisation Joël A. Doat Technische Universität Darmstadt Follow this and additional works at: https://scholarship.claremont.edu/jhm  Part of the Arts and Humanities Commons, and the Logic and Foundations Commons Recommended Citation Joël A. Doat, "Self-Reference and Diagonalisation," Journal of Humanistic Mathematics, Volume 13 Issue 1 (January 2023), pages 297-298. . Available at: https://scholarship.claremont.edu/jhm/vol13/iss1/24 ©2023 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. Self-Reference and DiagonalisationJoël A. Doat1joelandre.doat@gmail.comDo you know when you know everything?Or is knowing the unknown something?Do you know when you know nothing?Or doesn’t this knowledge rely on anything?Thoughts perform acrobaticswhen in self-reference.A look at mathematicsand infinity makes a difference.First example: machine automaticswhere to find evidence.Is it stoppable when encodablein itself as insertion?A problem solvable for some predicableof finite instantiation.Neither haltable nor decidablefor infinite recursion.Because assumable if it’s computablethen look at the version.One is programmable becoming loopablein destructive perversion.An argument undeniable when diagonisableis terminating the motion,while unthinkable also unendable.Therefore a solutionwhich is undisputable turingable.It follows the assertion.Away from machines, back to naturals.Maybe horizontal sequences in vertical sequentials?1 Even though Joël Doat pursued a career in software development after his studies, one ofhis main interests still lies at the intersection of mathematics and art. This poem was written asan exercise in an introductory course on mathematical logic highlighting Epimenides’, Cantor’s,and Turing’s contributions to self-reference.Journal of Humanistic Mathematics Volume 13 Number 1 (January 2023)Now supposeones and zerosplaying the key roles.Align thosein several rows.Then diagonally transpose.Here it goes!When they compose,it showsunwanted weirdosin their outsider pose.A path representswhat uncountably definesCantor’s proof extendsbroader cardinality confinesfinishing his arguments.Look at the last three lines,the respective contentsand word combines.This is how to diagonalise.Get ready,this one is tough.’cause infinityisn’t always enough.Talking about the original Or.D.and no. . . not a speech disorder.His rhymes teach how to well-order.Not only ordinal words, but transitive letters.No one reduces him to a set when he enters.Nobody else containing his skills at this efficiency.For you simply too high classy.He is the only true Or.D.All this rationalisea poem to exercise.Self-reference it memorialise.Paradoxes it implies.Ending with overemphasise:Poems tell lies. . .298

Self-Reference and Diagonalisation

https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1955&context=jhm

Self-Reference and Diagonalisation

Abstract

Similar works

Full text

Available Versions

Scholarship@Claremont