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Dear Gabriele Scheler,</div>
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You wrote, "Each symbol stands for one pattern". This is an invalid statement, meaningless in mathematics and computer science. </div>
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(1) I suggest that you review the term One-to-One correspondence required for symbolic representations in discrete mathematics and computer science (like Turing machines). </div>
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(2) Counter Example 1: While my brain senses your face, many neurons in my brain will fire. Do they stand for the same pattern (your face)? This means one-to-many mapping, defeating the one-to-one correspondence in (1). </div>
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(3) Counter Example 2: While my brain senses your face at different viewing angles, distances, and lighting conditionss, my motor neurons will fire to produce Gabriele Scheler. Any of motor neurons stand for many patterns of your face, not only "one pattern".
This means many-to-one mapping, defeating the one-to-one correspondence in (1). </div>
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With the above proof, "Each symbol stands for one pattern" is meaningless in mathematics and computer science.</div>
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Best regards,</div>
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-John Weng</div>
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On Sat, Jun 15, 2024 at 9:46 PM Gabriele Scheler <gscheler@gmail.com> wrote:</div>
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> Oh st simpkicissismus.</div>
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>Symbolic neurons have connections with each other. Each symbol stands for one pattern. They also have >connections with their feature patterns. But we compute with the symbolic neurons alone. There are no >examples given for that.</div>
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>So by computing with symbolic neurons we can use exact reasoning. But when we want to know the >meaning of a symbol we can then turn to their features. The clever part - since you have trouble reading - is >that we can use only the symbolic neurons, we do
not ha e to stimulate them in a way that their feature >parts become active. In that case, 1 symbol, 1 neuron. </div>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Connectionists <connectionists-bounces@mailman.srv.cs.cmu.edu> on behalf of Gabriele Scheler <gscheler@gmail.com><br>
<b>Sent:</b> Monday, June 10, 2024 8:03 AM<br>
<b>To:</b> connectionists@mailman.srv.cs.cmu.edu <connectionists@mailman.srv.cs.cmu.edu><br>
<b>Subject:</b> Connectionists: Ensemble computing</font>
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<div dir="ltr">This paper may be relevant to the discussion on symbolic computing in the brain. <br clear="all">
<div><a href="https://urldefense.com/v3/__https://www.biorxiv.org/content/10.1101/2023.12.22.573036v2__;!!HXCxUKc!3XvVBOS7Ewzj9hEc7LIS4jJ1KaOBIEg96-dgQQoFBKgSXwmbWIv9bbBw_q5aEBIrkXofN97mq1r_Tw$">https://www.biorxiv.org/content/10.1101/2023.12.22.573036v2</a><br>
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<div>It leverages ideas about ensembles in the brain and outlines a basic scheme for symbolic abstraction .</div>
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<div>Gabriele</div>
<span class="x_gmail_signature_prefix">-- </span><br>
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<span><span>
<div style="text-align:right"><span><span><span></span></span></span></div>
</span></span>Dr. Gabriele Scheler<br>
Carl Correns Foundation for Mathematical Biology<span>
<div style="text-align:right"><span><span><span><span></span></span></span></span></div>
</span>1030 Judson Dr<br>
Mountain View, CA 94040 </div>
<div dir="ltr"><a href="https://urldefense.com/v3/__http://www.theoretical-biology.org__;!!HXCxUKc!3XvVBOS7Ewzj9hEc7LIS4jJ1KaOBIEg96-dgQQoFBKgSXwmbWIv9bbBw_q5aEBIrkXofN95zer6I-w$" target="_blank">https://www.theoretical-biology.org</a><br>
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<div dir="ltr">Please re-send an email if I fail to respond.<br>
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