Domenico Cacozza<p>👉 Bottom line:<br>Some problems are decidable.<br>Others are fundamentally undecidable.<br>This is a mathematical boundary, not a technological one.</p><p><a href="https://mastodon.social/tags/Computability" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Computability</span></a> <a href="https://mastodon.social/tags/algorithms" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>algorithms</span></a></p><p>5/🧵</p>
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#computability
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Domenico Cacozza<p>🧵 Alan Turing showed that not everything logically definable is also computable.</p><p>Using a diagonalization method like Cantor’s, we can build a set D:<br>the set of Turing machine codes that don’t belong to their own halting set.</p><p>🔁 Here’s the twist:<br>No Turing machine can generate D without causing a contradiction.</p><p><a href="https://mastodon.social/tags/Turing" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Turing</span></a> <a href="https://mastodon.social/tags/computability" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>computability</span></a></p><p>1/🧵</p>
Counting Is Hard<p>Thanks to the work of <span class="h-card" translate="no"><a href="https://mastodon.acm.org/@mspstrath" class="u-url mention" rel="nofollow noopener" target="_blank">@<span>mspstrath</span></a></span> all the TYPES 2025 talks are available (including mine)</p><p><a href="https://www.youtube.com/watch?v=W-lYwG3E_x4&list=PLjPpkiIsfkBP2Iarv-Zvd7QS7WrGcDqem&index=80" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">youtube.com/watch?v=W-lYwG3E_x</span><span class="invisible">4&list=PLjPpkiIsfkBP2Iarv-Zvd7QS7WrGcDqem&index=80</span></a></p><p>Like comment and subscribe, ring the bell, all that stuff</p><p><a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>categorytheory</span></a> <a href="https://mathstodon.xyz/tags/computability" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>computability</span></a></p>
Counting Is Hard<p>As promised. Here is the sequel to my Weihrauch reductions are Containers post, this time relating strong reductions to dependent adaptors. Enjoy!</p><p><a href="https://www.countingishard.org/blog/strong-reducibility-as-an-adaptor" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">countingishard.org/blog/strong</span><span class="invisible">-reducibility-as-an-adaptor</span></a></p><p><a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>categorytheory</span></a> <a href="https://mathstodon.xyz/tags/computability" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>computability</span></a></p>
Richard Zach<p>I'm a logician and historian and philosopher of <a href="https://mathstodon.xyz/tags/logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>logic</span></a>, <a href="https://mathstodon.xyz/tags/computability" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>computability</span></a>, and analytic philosophy. I run <a href="https://openlogicproject.org/" rel="nofollow noopener" target="_blank"><span class="invisible">https://</span><span class="">openlogicproject.org/</span><span class="invisible"></span></a> <a href="https://mathstodon.xyz/tags/Introduction" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Introduction</span></a> <a href="https://mathstodon.xyz/tags/philosophy" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>philosophy</span></a></p>
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