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John Abbe (aka Slow)<p><span class="h-card" translate="no"><a href="https://toolsforthought.social/@billseitz" class="u-url mention" rel="nofollow noopener" target="_blank">@<span>billseitz</span></a></span> Happy to make a connection about connections!</p><p>Here's an upcoming paper about how the IETF makes protocols about protocols: <a href="https://docs.google.com/document/d/1tgZ86ugijXPUOo_lD3kLfQBPbneecUNzZim1GOgkC1M/edit" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">docs.google.com/document/d/1tg</span><span class="invisible">Z86ugijXPUOo_lD3kLfQBPbneecUNzZim1GOgkC1M/edit</span></a> <a href="https://mastodon.social/tags/Internet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Internet</span></a> <a href="https://mastodon.social/tags/protocols" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>protocols</span></a> <a href="https://mastodon.social/tags/meta" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>meta</span></a> <a href="https://mastodon.social/tags/selfreference" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>selfreference</span></a> <a href="https://mastodon.social/tags/strangeloop" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>strangeloop</span></a></p>
Brian Sletten<p>Slow clap. Chef’s kiss. No notes.</p><p>Meme perfection.</p><p><a href="https://mastodon.social/tags/meme" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>meme</span></a> <a href="https://mastodon.social/tags/humor" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>humor</span></a> <a href="https://mastodon.social/tags/dialectic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>dialectic</span></a> <a href="https://mastodon.social/tags/foundontheinternet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>foundontheinternet</span></a> <a href="https://mastodon.social/tags/selfreference" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>selfreference</span></a></p>
Marcel Fröhlich<p>Fernando Rosas (unfortunately not on Mastodon) asked on bsky:</p><p>"Has anyone figured out what exactly is the relation between the ideas of feedback, recurrence, and self-reference?"</p><p>A really interesting question.</p><p>He pointed to this paper for ideas: <a href="https://arxiv.org/abs/1711.02456" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">arxiv.org/abs/1711.02456</span><span class="invisible"></span></a><br>"Self-referential basis of undecidable dynamics: from The Liar Paradox and The Halting Problem to The Edge of Chaos"</p><p>I did some desk research and found this cool paper:<br><a href="https://arxiv.org/abs/1112.2141" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">arxiv.org/abs/1112.2141</span><span class="invisible"></span></a><br>"Resolving Gödel's Incompleteness Myth: Polynomial Equations and Dynamical Systems for Algebraic Logic"<br>that argues there is no essential incompleteness in formal reasoning systems if you look closely enough (using a more elaborate formalism based on polynomial equations to represent and evaluate logical proposition).</p><p>I wonder if analogous construction could be created for related theorems like the halting problem in computability theory.</p><p><a href="https://mathstodon.xyz/tags/DynamicalSystems" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>DynamicalSystems</span></a> <a href="https://mathstodon.xyz/tags/IncompletenessTheorem" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>IncompletenessTheorem</span></a> <a href="https://mathstodon.xyz/tags/PolynomialEquations" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PolynomialEquations</span></a> <a href="https://mathstodon.xyz/tags/HaltingProblem" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>HaltingProblem</span></a> <a href="https://mathstodon.xyz/tags/Undecidability" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Undecidability</span></a> <a href="https://mathstodon.xyz/tags/SelfReference" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>SelfReference</span></a> <a href="https://mathstodon.xyz/tags/Recurrence" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Recurrence</span></a></p>
Catherine Berry<p>I finally found time to read Douglas Hofstadter's blisteringly critical essay on large language models. As usual, he makes excellent points, and supports them with precise and well thought out arguments. </p><p>It is, then, merely a wonderful bonus that the essay is centered around Hofstadter critiquing an AI which is in turn pretending to be Hofstadter writing about GEB. There are at least two interwoven levels of self-reference here. Bravo!</p><p><a href="https://mastodon.sdf.org/tags/AI" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>AI</span></a> <a href="https://mastodon.sdf.org/tags/SelfReference" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>SelfReference</span></a> <a href="https://mastodon.sdf.org/tags/HashTag" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>HashTag</span></a></p><p><a href="https://www.theatlantic.com/ideas/archive/2023/07/godel-escher-bach-geb-ai/674589/" rel="nofollow noopener" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">theatlantic.com/ideas/archive/</span><span class="invisible">2023/07/godel-escher-bach-geb-ai/674589/</span></a></p>
Jim Donegan 🎵 ✅<p><a href="https://mastodon.scot/tags/JeffreyKaplan" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>JeffreyKaplan</span></a> - The <a href="https://mastodon.scot/tags/LiarParadox" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>LiarParadox</span></a> - an explanation of the <a href="https://mastodon.scot/tags/Paradox" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Paradox</span></a> from 400 BCE </p><p><a href="https://www.youtube.com/watch?v=in4u2i9v4vg&amp;ab_channel=JeffreyKaplan" rel="nofollow noopener" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">youtube.com/watch?v=in4u2i9v4v</span><span class="invisible">g&amp;ab_channel=JeffreyKaplan</span></a> </p><p><a href="https://mastodon.scot/tags/Philosophy" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Philosophy</span></a> <a href="https://mastodon.scot/tags/PhilosophyOfLogic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhilosophyOfLogic</span></a> <a href="https://mastodon.scot/tags/Logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Logic</span></a> <a href="https://mastodon.scot/tags/Language" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Language</span></a> <a href="https://mastodon.scot/tags/Math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Math</span></a> <a href="https://mastodon.scot/tags/Maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Maths</span></a> <a href="https://mastodon.scot/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Mathematics</span></a> <a href="https://mastodon.scot/tags/Truth" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Truth</span></a> <a href="https://mastodon.scot/tags/SelfReference" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>SelfReference</span></a> <a href="https://mastodon.scot/tags/Completeness" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Completeness</span></a> <a href="https://mastodon.scot/tags/Incompleteness" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Incompleteness</span></a> <a href="https://mastodon.scot/tags/StarTrek" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>StarTrek</span></a> <a href="https://mastodon.scot/tags/Kirk" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Kirk</span></a> <a href="https://mastodon.scot/tags/CaptainKirk" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>CaptainKirk</span></a> <a href="https://mastodon.scot/tags/Picard" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Picard</span></a> <a href="https://mastodon.scot/tags/CaptainPicard" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>CaptainPicard</span></a></p>
Oscar Cunningham<p><span class="h-card"><a href="https://mastodon.mit.edu/@eirikbakke" class="u-url mention" rel="nofollow noopener" target="_blank">@<span>eirikbakke</span></a></span> I saw on Twitter you were saying about how Tupper's formula isn't really self-referential. I thought you might like this page: <a href="https://jtra.cz/stuff/essays/math-self-reference-smooth/index.html" rel="nofollow noopener" target="_blank"><span class="invisible">https://</span><span class="ellipsis">jtra.cz/stuff/essays/math-self</span><span class="invisible">-reference-smooth/index.html</span></a></p><p>It turns out that Tupper went on to make a formula that really was self-referential. And then Jakub Trávník made a self-referential formula which uses smooth functions to implement a nice typeface.</p><p><a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Math</span></a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Mathematics</span></a> <a href="https://mathstodon.xyz/tags/Maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Maths</span></a> <a href="https://mathstodon.xyz/tags/SelfReference" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>SelfReference</span></a></p>