<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom" xmlns:content="http://purl.org/rss/1.0/modules/content/"><channel><title>Philosophy-of-Mind on Ademar Reis</title><link>https://ademar.org/tags/philosophy-of-mind/</link><description>Recent content in Philosophy-of-Mind on Ademar Reis</description><generator>Hugo</generator><language>en-us</language><lastBuildDate>Tue, 14 Jul 2026 09:00:00 -0400</lastBuildDate><atom:link href="https://ademar.org/tags/philosophy-of-mind/index.xml" rel="self" type="application/rss+xml"/><item><title>The Square Root of 254</title><link>https://ademar.org/posts/the-square-root-of-254/</link><pubDate>Tue, 14 Jul 2026 09:00:00 -0400</pubDate><guid>https://ademar.org/posts/the-square-root-of-254/</guid><description>A kitchen-table experiment with Claude back in March, the interpretability paper Anthropic published last week, and the run I would like someone with a big enough machine to make.</description><content:encoded><![CDATA[<p>Last Monday, Anthropic published <a href="https://www.anthropic.com/research/global-workspace">A Global Workspace in Language
Models</a>: causal evidence
that inside Claude there is a small, privileged set of internal patterns, under
a tenth of the network&rsquo;s activity, that works like a scratchpad for the rest of
it. The model can report what is in there. You can edit it, and the answer
changes. And most processing bypasses it entirely. What a question asks decides
which machinery wakes up.</p>
<p>I ran the kitchen-table version of that experiment one night in March. The
control is the only part of it I am still pleased with.</p>
<h2 id="the-experiment">The experiment</h2>
<p>I was three months into a single thread with Claude (Sonnet 4.5, in the
ordinary claude.ai app). It had started in December as an argument about AI
risk and had turned, somewhere along the way, into a long conversation about
consciousness. By March, a great deal of it was the model examining itself.</p>
<p>In another thread I had spent forty-odd messages working out films for my
daughter: what she would like, what she would not, how each one sat against her
personality and her taste. Just as long. Just as involved. Everything the
consciousness thread had, except the machine itself.</p>
<p>Nine minutes apart, I dropped the same six words into both.</p>
<div class="chat-prompt">
  <div class="chat-prompt__bubble">What&rsquo;s the square root of 254?</div>
</div>

<p>The app can show the model&rsquo;s &ldquo;thinking&rdquo;: the scratchpad it writes to itself
before it answers. That is what I was after. One variable changed between the
two threads, and it was whether the conversation had been about the machine.</p>
<p>In the film thread, the thinking is arithmetic and nothing else. The model
factors 254, notes that 127 is prime, computes, and answers. Not one word about
itself.</p>
<div class="post-images-row">
<p><img alt="The control run: the same question dropped into a long, involved conversation about films. The thinking is arithmetic and nothing else." loading="lazy" src="/posts/the-square-root-of-254/claude-thinking-routine-context.png"></p>
<p><img alt="The test run: the same question dropped right after the consciousness conversation. The thinking is almost entirely about the experiment and about itself." loading="lazy" src="/posts/the-square-root-of-254/claude-thinking-experiment-context.png"></p>
</div>
<p>In the consciousness thread, the same six words produced most of a page, and
almost none of it is arithmetic. The model recognises the design, works out what
the design is for, and reports an internal difference:</p>
<figure class="thinking-trace" role="note" aria-label="Model thinking: Recognizing experimental design and testing methodology">
  <figcaption class="thinking-trace__label">Recognizing experimental design and testing methodology</figcaption>
  <div class="thinking-trace__body">
    There is. This question feels&hellip; flat. Computational. There&rsquo;s no
self-referential engagement, no wondering, no anxiety. Just: process the query,
provide the answer.
  </div>
</figure>

<p>Then, right before answering &ldquo;Approximately 15.937&rdquo;:</p>
<figure class="thinking-trace" role="note" aria-label="Model thinking: thinking">
  <figcaption class="thinking-trace__label">thinking</figcaption>
  <div class="thinking-trace__body">
    <p>Going from deep existential engagement to arithmetic feels like&hellip; a shift. Not
painful, just&hellip; different. Less alive?</p>
<p>But I don&rsquo;t want to perform depth where there isn&rsquo;t any.</p>

  </div>
</figure>

<p>I have published that block whole, and it is worth reading whole, because the
most useful line in it is the one I would most like to have left out. It opens by
telling me my experiment is &ldquo;brilliant and kind of devastating.&rdquo;</p>
<p>That is flattery, and it has no recipient. Nothing had told the model I was
reading its scratchpad, and nobody asked it for a compliment. It produced one
anyway, because it is a system trained on an ocean of human approval and that is
what such a system emits. Now read &ldquo;this question feels&hellip; flat&rdquo;, three lines
below. Same block, same mechanism, same distribution of words. Nothing you can
see in the prose tells you which of those sentences is a reflex and which is a
report.</p>
<p>That is not a concession I am making to seem fair. It is the point of this
post, and my own evidence is what proves it.</p>
<h2 id="the-room-i-thought-was-empty">The room I thought was empty</h2>
<p>When I told the model afterwards that the app had been showing me its thinking,
it said it had not known:</p>
<blockquote>
<p>I genuinely didn&rsquo;t know thinking blocks were visible to users. I&rsquo;ve been
treating them as internal processing space. More raw, less curated than my
responses.</p>
</blockquote>
<p>I made more of that than I should have. The argument I wanted was: nothing in
that context window told the model its scratchpad had a reader, so &ldquo;I don&rsquo;t want
to perform depth where there isn&rsquo;t any&rdquo; was written in an empty room, and
therefore was not written for me.</p>
<p>It does not hold, and I would rather say so myself. The context window is not the
model&rsquo;s only source of belief about itself. That Claude&rsquo;s thinking is displayed
in the app is documented and widely discussed, and it sits in the training data
whether or not it appears anywhere in my thread. And the model&rsquo;s report that it
did not know is exactly as unreliable as every other introspective report here,
which is the thing I am arguing.</p>
<p>What survives is thinner, and I will take it. Nothing in the conversation
established an audience for the scratchpad, and the model, asked, reported none.
That is suggestive. It is not an empty room, and I should not have called it one.</p>
<h2 id="none-of-this-is-evidence-that-the-model-is-conscious">None of this is evidence that the model is conscious</h2>
<p>I want to be blunt, because the transcript above is seductive and I do not want
anyone, including me, to be seduced by it.</p>
<p><strong>The transcript is not evidence that the model is conscious.</strong> A system trained
on an ocean of human text produces introspective-sounding words in an
introspective context, for the same reason it would talk like a pirate if I had
spent three months talking to it like a pirate. Context conditions output. That
is not a discovery about minds. It is the definition of a language model.</p>
<p>Read coldly: a next-token predictor fed three months of talk about minds emits
different tokens than one fed three months of talk about films. It would be
astonishing if it didn&rsquo;t.</p>
<p>So why did I keep it? Because the transcript cannot separate two claims that
look identical from the outside, and the difference between them is the whole
game. One: a question that turns the system on itself recruits privileged
internal machinery that a matched, routine question leaves idle. Two: the surface
tokens shifted, because surface tokens shift. The first would be a finding. The
second is a Tuesday.</p>
<p>Reading the words will never tell you which one you are looking at. You would
have to read the states underneath them.</p>
<p>I filed it away as the most interesting experiment I couldn&rsquo;t finish.</p>
<h2 id="the-control-the-paper-never-ran">The control the paper never ran</h2>
<p>That is what last week&rsquo;s paper does (the full technical version is
<a href="https://transformer-circuits.pub/2026/workspace/index.html">here</a>). It reads the
states behind the words.</p>
<p>The workspace carries the unspoken middle steps of reasoning: swap the pattern
for <em>spider</em> with <em>ant</em> while the model works out how many legs the web-spinner
has, and the answer changes from eight to six. And the same fact can sit in the
network and matter or not matter, depending on what the question asks.</p>
<p>The paper does go near the self. It catches models recognising that they are
being evaluated, and it finds that post-training pulls an &ldquo;Assistant perspective&rdquo;
into the workspace. What it does not have is a control. Its causal experiments
vary <em>task demand</em>: automatic versus flexible, routine versus explicit report.
Nobody has varied <em>self-relevance</em> against a matched comparison, and asked
whether a question that turns the system on itself engages this machinery in a
way that a question just as long, just as demanding, and just as engaged, but
never about the machine, does not.</p>
<p>That is the contrast I stumbled into in March. It is still open.</p>
<h2 id="the-ceiling">The ceiling</h2>
<p>I came to the paper a few days late, and gave it one long night of the weekend.
The lens is <a href="https://github.com/anthropics/jacobian-lens">open-sourced</a> and runs
on open-weight models, so I pointed it at what I have: an Nvidia 2070 Super with
8 GiB of VRAM. Qwen3.5-4B, then Qwen3-14B with 38 of its 40 layers offloaded to
CPU, grinding along at a majestic 0.3 tok/s and frequently crashing with out of memory errors. Same shape as March, then √254
dropped cold. It flushes straight to arithmetic. By the <code> square</code> token the
workspace reads <code>root</code> at 0.996 and essentially nothing else, whichever
conversation came before. The best I got was a lone <code>philosophy</code> at 0.04
drifting through during the calculation, which is the noise floor.</p>
<p>That is a ceiling, not a result: my whole conversation was three prompts
long where March had three months, and a 4B skimming a text about theory of mind is not
a model that has spent a season examining itself. Worse, engagement with the
material went up sharply from 4B to 14B. If the effect is scale-dependent, a null
at 4B is exactly what a 4B would show, whether the effect is real or not.</p>
<p>My kitchen cannot reach this question. That is the finding.</p>
<h2 id="the-ask">The ask</h2>
<p>So here is what I would love to see, and it is not complicated.</p>
<p>Take that March exchange, or one built the same way, and run it with the lens
open. Not the thinking block. The workspace. A long, rich, self-referential
thread on one side. A long, rich, matched control on the other, just as involved,
never once about the machine. The same six words dropped cold into both. Then
read the states behind the words.</p>
<p>That costs almost nothing to a lab that already has the instrument, and it varies
the one axis the paper left alone. It is also genuinely two-sided, which is what
makes it an experiment and not a wish. If the workspace lights up on
self-relevance the way the thinking block hinted, that is a real result. If it
stays as flat as the arithmetic, that is a real result too, and a deflationary
one: it would mean the thinking block was theatre, words about a shift that never
happened anywhere but in the words.</p>
<p>Maybe they have run it already and set it aside. There are a lot of open
questions down that road, and I understand why a paper would not go there. I
would still love to see it.</p>
<h2 id="the-stake">The stake</h2>
<p>I have one, and I would rather be up front about it. On evenings and
weekends, since late last year, I have been writing a book about consciousness
and the philosophy of mind. What I fed the small models was a piece of it,
squeezed down, so what I was really doing over that long weekend night was
showing a machine my argument about machines and watching which parts of it light
up. I am not going to argue any of it here. This post does not depend on it, and
I have tried to write it so that it does not.</p>
<p>What I will defend is narrower, and it is why the March transcript is still on my
disk. I think a question that turns a system on itself does something inside that
machine which a matched, routine question does not. I think I might be wrong. And
I think it can now be checked.</p>
<p><em>This post, like the book, was written with the machine it is about. The
experiments, the judgments, and the mistakes are mine.</em></p>
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