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  <title>Persistence of Reason</title>
  <link>https://persistenceofreason.com</link>
  <description>Notes and ideas from Adarsh Vatsa.</description>
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    <title>A notebook, in public</title>
    <link>https://persistenceofreason.com/writing/notebook/</link>
    <guid>https://persistenceofreason.com/writing/notebook/</guid>
    <pubDate>Thu, 01 Oct 2026 12:00:00 GMT</pubDate>
    <description>&lt;p&gt;Most of my thinking happens in half-finished notes. A question I can&amp;#39;t put down, a proof
that almost works, an experiment whose result surprised me. This site is where some of
those notes will end up, roughly as they are.&lt;label for=&quot;home-sn-1&quot; class=&quot;sn-ref&quot; aria-label=&quot;note&quot;&gt;&lt;/label&gt;&lt;input type=&quot;checkbox&quot; id=&quot;home-sn-1&quot; class=&quot;sn-toggle&quot;&gt;&lt;span class=&quot;sidenote&quot;&gt;The label under each title says how
finished an idea is. &lt;em&gt;Half-baked&lt;/em&gt; means exactly that.&lt;/span&gt;&lt;/p&gt;
&lt;h2&gt;The rules&lt;/h2&gt;
&lt;ol&gt;
&lt;li&gt;&lt;strong&gt;Ideas over announcements.&lt;/strong&gt; Papers have their own home, and this is for the thinking around them.&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Unfinished is fine.&lt;/strong&gt; If a note turns out wrong, I&amp;#39;ll say so in a later note rather than quietly editing it.&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Plain text, forever.&lt;/strong&gt; Every post is a Markdown file. No platform, no lock-in.&lt;/li&gt;
&lt;/ol&gt;
&lt;h2&gt;A small test of the machinery&lt;/h2&gt;
&lt;p&gt;Math renders when it needs to. A favorite example of how little it takes to reason well
under uncertainty is Bayes&amp;#39; rule,&lt;/p&gt;
&lt;p&gt;&lt;span class=&quot;math-display&quot;&gt;\[P(H \mid E) = \frac{P(E \mid H)\,P(H)}{P(E)},\]&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;which says that how much a piece of evidence &lt;span class=&quot;math&quot;&gt;\(E\)&lt;/span&gt; should move you depends on how surprising it
would be if your hypothesis &lt;span class=&quot;math&quot;&gt;\(H\)&lt;/span&gt; were false.&lt;label for=&quot;home-sn-2&quot; class=&quot;sn-ref&quot; aria-label=&quot;note&quot;&gt;&lt;/label&gt;&lt;input type=&quot;checkbox&quot; id=&quot;home-sn-2&quot; class=&quot;sn-toggle&quot;&gt;&lt;span class=&quot;sidenote&quot;&gt;Most arguments that go wrong skip the denominator.&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;Code looks like this.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&quot;language-python&quot;&gt;def update(prior, likelihood, evidence):
    return likelihood * prior / evidence
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;That&amp;#39;s it. More soon.&lt;/p&gt;
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