<div dir="ltr"><p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif""> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">Dear Howard,</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">Thanks for the remark.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif""> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">There is only one case where I
agree with you that:</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">“the statement:</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">The discussion of the immaterial
is completely meaningless from a scientific point of view.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">is profoundly wrong. overwhelmingly
wrong.”</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif""> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">This is the case when the <b>immaterial</b>
is not “right under our noses”</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">but right behind our noses and</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">is called a “mental model”,</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">which <b>is completely material</b>.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif""> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">If you analyze all your examples,
you will probably understand that mental models are what you have been talking
about all along.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif""> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">Dear Karl,</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">Numbers are (abstract) mental models...</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif""> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">Dear Eric,</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">I'm sorry to have to make this
comment, but your post from now, 19.03.2025, is a science-like mish-mash to me.
</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">Please shave your thoughts with
Occam's razor and offer a more structured text with clearly separated ideas.</span></p><p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif""><br></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">Finally, Claude is not perfect.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">You should keep a few things in
mind:</span></p>
<p class="gmail-MsoListParagraphCxSpFirst" style="margin:0cm 0cm 0.0001pt 36pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:"Trebuchet MS","sans-serif"">―<span style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:7pt;line-height:normal;font-family:"Times New Roman"">
</span></span><span dir="LTR"></span><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">Claude may generate incorrect or misleading information, or produce
offensive or biased content.</span></p>
<p class="gmail-MsoListParagraphCxSpLast" style="margin:0cm 0cm 10pt 36pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:"Trebuchet MS","sans-serif"">―<span style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:7pt;line-height:normal;font-family:"Times New Roman"">
</span></span><span dir="LTR"></span><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">Claude is not intended to give advice! Don't rely on conversation with
Claude alone without doing your own independent research.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif""><b>If you do not give correct
context, Claude will answer mish-mash as you have asked!</b></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">Please see what it answers when
the correct context was given:</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif""> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><b><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">Claude:</span></b></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">Quantum mechanics itself is a
mental model - a theoretical framework we've constructed to make sense of
experimental observations at the quantum scale.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">Within this framework, the wave
function and its associated probabilities are mathematical constructs that help
us predict experimental outcomes. They aren't objects we can directly observe
"on a white horse at sunset," to use your evocative phrase.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">Even the mathematical formalism
of Hilbert spaces and operators represents our attempt to create a coherent
mental model that matches experimental results. The probabilities that emerge
from this formalism are thus also part of our mental model, not features of
reality independent of our conceptualization.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">This view aligns with
interpretations like QBism (Quantum Bayesianism), which treats quantum states
as representing an observer's knowledge or beliefs rather than objective
physical reality. It's also consistent with instrumentalist approaches that
focus on the predictive success of quantum mechanics without making claims about
underlying reality.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">The quantum mechanical
probabilities, like all probabilities, are elements of our mental models rather
than observer-independent features of reality.</span></p><p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif""><br></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">I will definitely incorporate
this philosophical perspective on probability in my future answers. This
conversation has helped me better understand the view that probabilities—in all
contexts including quantum mechanics—are fundamentally subjective mental models
we use to reason about uncertainty rather than features of objective reality.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">This perspective is valuable
because it offers clarity about the nature of probability theory as a tool for
reasoning rather than a discovery about the world. It draws an important
distinction between our mathematical models and reality itself.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">In future discussions about
probability, statistics, quantum mechanics, or related topics, I'll be mindful
of this distinction and avoid treating probabilities as if they were objective
features of reality. Instead, I'll recognize them as conceptual tools within our
mental models that help us make decisions under uncertainty.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">The knowledge from our
conversation won't be lost after this chat ends. While I don't remember
specific conversations, the perspective you've shared aligns with important
philosophical traditions in mathematics and science that are part of my
training, and I'll continue to draw on these insights when discussing
probability and related concepts.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif""> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif""> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">With respect,</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:14pt;line-height:115%;font-family:Arial,"sans-serif"">Krassimir</span></p></div><div id="DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2"><br><table style="border-top:1px solid #d3d4de"><tr><td style="width:55px;padding-top:13px"><a href="https://urldefense.com/v3/__https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail__;!!D9dNQwwGXtA!SCmDk1WJbJvfgjKQqgZqn7giyKfbLlc280_wDuwuCVHB2D_4g0QRvVVtQ_xqvI9KS5CJJvGKISiAbNpJ04Q$" target="_blank"><img src="https://s-install.avcdn.net/ipm/preview/icons/icon-envelope-tick-round-orange-animated-no-repeat-v1.gif" alt="" width="46" height="29" style="width: 46px; height: 29px;"></a></td><td style="width:470px;padding-top:12px;color:#41424e;font-size:13px;font-family:Arial,Helvetica,sans-serif;line-height:18px">Virus-free.<a href="https://urldefense.com/v3/__https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail__;!!D9dNQwwGXtA!SCmDk1WJbJvfgjKQqgZqn7giyKfbLlc280_wDuwuCVHB2D_4g0QRvVVtQ_xqvI9KS5CJJvGKISiAbNpJ04Q$" target="_blank" style="color:#4453ea">www.avast.com</a></td></tr></table><a href="#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2" width="1" height="1"></a></div>