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<p><font size="+1"><i>(clean posting: delete all the accumulated
stuff below your message, otherwise it won't pass--P.)</i></font><br>
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-------- Mensaje reenviado --------
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<th valign="BASELINE" nowrap="nowrap" align="RIGHT">Asunto:
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<td>Re: [Fis] Fis Digest, Vol 113, Issue 17</td>
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<th valign="BASELINE" nowrap="nowrap" align="RIGHT">Fecha: </th>
<td>Mon, 8 Jul 2024 16:31:25 +0100</td>
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<th valign="BASELINE" nowrap="nowrap" align="RIGHT">De: </th>
<td>Mark Johnson <a class="moz-txt-link-rfc2396E" href="mailto:johnsonmwj1@gmail.com"><johnsonmwj1@gmail.com></a></td>
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<th valign="BASELINE" nowrap="nowrap" align="RIGHT">Para: </th>
<td>Louis Kauffman <a class="moz-txt-link-rfc2396E" href="mailto:loukau@gmail.com"><loukau@gmail.com></a>, fis
<a class="moz-txt-link-rfc2396E" href="mailto:fis@listas.unizar.es"><fis@listas.unizar.es></a></td>
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<br>
<br>
<div dir="ltr">
<div dir="ltr">
<div dir="ltr">Dear Lou, all,
<div><br>
</div>
<div>
<p class="MsoNormal">Apologies for taking ages to reply –
I’ve had a busy couple
of weeks travelling. <span></span></p>
<p class="MsoNormal"><br>
</p>
<p class="MsoNormal">I wonder if I might address your
question about measurement and the
representation of wholes by using the wonderful cartoon
that you sent me a few months
ago (attached)</p>
<p class="MsoNormal"><br>
</p>
<p class="MsoNormal">In a way, there is some similarity to
the “blind men and the
elephant”, but in that story we observers of the
situation see there is an “elephant”
and laugh at the story of the restricted perception of
the blind men. With your
cartoon, we observers are as much in the dark as the two
people arguing.</p>
<p class="MsoNormal">The two people: <span></span></p>
<p class="gmail-MsoListParagraphCxSpFirst">a.<span
style="font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;font-size:7pt;line-height:normal;font-family:"Times
New Roman"">
</span>Are perturbed by what they see;<span></span></p>
<p class="gmail-MsoListParagraphCxSpMiddle">b.<span
style="font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;font-size:7pt;line-height:normal;font-family:"Times
New Roman"">
</span>Make a distinction;<span></span></p>
<p class="gmail-MsoListParagraphCxSpMiddle">c.<span
style="font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;font-size:7pt;line-height:normal;font-family:"Times
New Roman"">
</span>Utter a word which has meaning to them;<span></span></p>
<p class="gmail-MsoListParagraphCxSpLast">d.<span
style="font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;font-size:7pt;line-height:normal;font-family:"Times
New Roman"">
</span>Disagree with each other.<span></span></p>
<p class="MsoNormal">I think it is the dynamics between a,
b, c and d which is the
whole. More abstractly, there is:<span></span></p>
<p class="gmail-MsoListParagraphCxSpFirst">a.<span
style="font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;font-size:7pt;line-height:normal;font-family:"Times
New Roman"">
</span>Noise or disturbance;<span></span></p>
<p class="gmail-MsoListParagraphCxSpMiddle">b.<span
style="font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;font-size:7pt;line-height:normal;font-family:"Times
New Roman"">
</span>A selection;<span></span></p>
<p class="gmail-MsoListParagraphCxSpMiddle">c.<span
style="font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;font-size:7pt;line-height:normal;font-family:"Times
New Roman"">
</span>An utterance of a word relating to that
selection whose meaning is contextualised within a
shared culture</p>
<p class="gmail-MsoListParagraphCxSpLast">d.<span
style="font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;font-size:7pt;line-height:normal;font-family:"Times
New Roman"">
</span>An appreciation that there is a difference
between their selection and the other person’s, and that
this awareness may
even reinforce the selection and the utterance. <span></span></p>
<p class="MsoNormal">It's similar, it seems to me, in your
knot paper the abstract representation of the knot
is the result of distinction-making, and the associated
formal representation.
And there might be argument (among mathematicians) as to
the particular
formalisation. This means that the formal representation
on its own is not a
representation of the whole. Seen in isolation from the
original knot, it loses
the dynamics between a, b, c and d. The formalism is a
reduction which attenuates - rather like a measurement.
Is it drained of meaning? I think it might be more
accurate to say that it is divorced from the dynamics
which connect "disturbance" with "distinction",
"utterance" and shared expectation. </p>
<p class="MsoNormal"><br>
</p>
<p class="MsoNormal">But I think we can have “reduction”
which doesn’t attenuate –
a "non-reductive reduction" as Alex was puzzled by. This
isn’t a new idea – David Bohm particularly
talked a lot about “holomovements” and so on. I'm
thinking particularly about Peter Rowlands’s
physics as a compelling example - and indeed, your own
work on time, commutators and imaginary numbers, from
which you arrive at quaternions and Clifford algebra. If
you go backwards from Clifford algebra back to
commutators, distinctions and imaginary numbers have you
performed a reduction? </p>
<p class="MsoNormal"><br>
</p>
<p class="MsoNormal">When I first encountered Peter’s
“Rewrite system” I was
confused that each group of terms expressing the
quaternion variables do not
use i, j, and k. He does explain it in his “Foundations
of Physical Law) that he
just uses i and j: <span></span></p>
<p class="MsoNormal" style="margin-left:36pt">“It may be
significant that the
rules A → B and B → AB seem to be suggesting the
structure of 3-dimensional
(quaternion) algebra: <span></span></p>
<p class="MsoNormal" style="margin-left:36pt">i → j <span></span></p>
<p class="MsoNormal" style="margin-left:36pt">j → ij (“ =
k”) <span></span></p>
<p class="MsoNormal" style="margin-left:36pt">and that a
string like
BABABBABABBABBABABBAB appears to be creating a
fractal-like structure in
3-dimensional space, but situated in the AB or ij plane,
as in holography. The
logarithmic spiral then becomes a way of expressing
3-dimensionality in the
plane with the increasing length of the intervals
substituting for penetration
into the third dimension”. <span></span></p>
<p class="MsoNormal"><br>
</p>
<p class="MsoNormal">It was obvious when he explained it –
but this is precisely
the kind of non-reductive reductionism that I am
concerned with. I think we agree that non-commutativity
is the key to make it work. Non-commutativity creates a
spiral leading to ever-deeper
recursions, which obviates the need for more than three
dimensions. (Do we need
n-dimensional Hilbert spaces?? – Peter blames Eddington
for that)<span></span></p>
<p class="MsoNormal">(1, –1) <span></span></p>
<p class="MsoNormal">(1, –1) × (1, i) <span></span></p>
<p class="MsoNormal">(1, –1) × (1, i) × (1, j) <span></span></p>
<p class="MsoNormal">(1, –1) × (1, i) × (1, j) × (1, i) <span></span></p>
<p class="MsoNormal">(1, –1) × (1, i) × (1, j) × (1, i) ×
(1, j) <span></span></p>
<p class="MsoNormal">(1, –1) × (1, i) × (1, j) × (1, i) ×
(1, j) × (1, i) ...<span></span></p>
<p class="MsoNormal"><br>
</p>
<p class="MsoNormal">The perception of wholes entails
apprehension of this spiral.
Your cartoon exemplifies this: the perturbation is a
kind of “noise” – a scalar;
the distinction is a vector; the utterance is a chosen
in the context of
language and culture – it is reliant on redundancy which
is a higher order than
a vector (a bivector probably); and the mutual
understanding is a higher order
still. <span></span></p>
<p class="MsoNormal"><br>
</p>
<p class="MsoNormal">So to come to music, the “swing” is
in the spiral. There is
dimensionality in making any sound – it involves noise,
notes (signals),
redundancy (repetition/pattern) and expectation. And
most importantly, once we start “swinging”, we
have to find a way to stop: music has to reach a point
where the next thing
that happens is silence. <span></span></p>
<p class="MsoNormal"><br>
</p>
<p class="MsoNormal">With regard to AI, I am no zealot.
But it raises fascinating
questions – I really recommend playing with Google’s
Teachable Machine (<a
href="https://urldefense.com/v3/__https://teachablemachine.withgoogle.com/__;!!D9dNQwwGXtA!UsPK2SRbiXBsfUCVImOrMm7fPKKNuBbKeVeR7v6-AmTt7BCvZVrKGYKDIRzLOAqwbokC90rmAhTGK6Hkf8MZ_pw$"
moz-do-not-send="true">https://teachablemachine.withgoogle.com</a>)
– it’s good to experiment with this stuff. But there
are structural similarities to how
it performs its selections to what I’ve described above.
It is noisy (and this
is significant in driving its development further); it
selects signals as
predictions of the likely categories of data it hasn’t
seen before; it both
requires redundancy for training, and exhibits
redundancy in the structuring of
its output; and it must meet our expectations otherwise
we would not see any
good or use in it. Is it a practical non-reductive
reduction? That’s the
question. If it is then we have a very important new
kind of scientific instrument
on our hands which, like all previous scientific
instruments, helps us perceive
deeper order in nature. <span></span></p>
<p class="MsoNormal"><br>
</p>
<p class="MsoNormal">Measurement, I think, is how we
encode our perception of that deeper order. While the
encoding of measurement drains the meaning from any
specific perception, it creates a new meaning through
the shared understanding. Isn't it another level in the
spiral? So we move from perception to measurement with
each having commensurable dynamics. Musical notation
provides another example of this: written notes are not
music, but they are part of a complex set of
inter-relationships which connect noise with signal,
pattern and mutual expectation.</p>
<p class="MsoNormal"><br>
</p>
<p class="MsoNormal">Best wishes,</p>
<p class="MsoNormal"><br>
</p>
<p class="MsoNormal">Mark </p>
</div>
</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Sun, 23 Jun 2024 at
16:23, Louis Kauffman <<a href="mailto:loukau@gmail.com"
moz-do-not-send="true">loukau@gmail.com</a>> wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px
0.8ex;border-left:1px solid
rgb(204,204,204);padding-left:1ex">
<div style="overflow-wrap: break-word;">Dear Mark,
<div>I am writing privately since I have to rights on fis
until tomorrow.</div>
<div>When we use the word measurement in the usual
scientific context, we mean making a record that can be
viewed without disturbance by anyone.</div>
<div>Thus the measurement is drained of all meaning that
might be supplied by a given observer.</div>
<div>It takes a very concentrated effort to produce
measurements of this kind and they are the subject of
engineering practice.</div>
<div>Think of vinyl records. The track is an accurate
transform of the sound. The track is in itself
meaningless. The track can be transformed back into
sound and </div>
<div>observed/ heard by a sensitive human at which point
the meaning can arise in the interaction of the human
with the sound.</div>
<div>Best,</div>
<div>Lou</div>
<div><br>
<div><br>
<br>
<br>
<br>
<blockquote type="cite">
<div
style="line-height:1.7;font-size:14px;font-family:Arial">
<pre>>Isn't meaning "part" of any measurement? How could it not be? But perhaps
>the difficulty lies in what one might mean by "part"... Reductionism - as
>in the attenuation of "dimensions" of experience - lies in wait for any
>trivial identification of a "part". But there is a kind of "reduction"
>which does not attenuate... Holograms are reductions, for example.</pre>
</div>
</blockquote>
<div><br>
</div>
<span class="gmail_signature_prefix">-- </span><br>
</div>
</div>
</div>
</blockquote>
</div>
<br>
<div dir="ltr" class="gmail_signature">
<div dir="ltr">Dr. Mark William Johnson<br>
<div dir="ltr" style="color:rgb(34,34,34)">Faculty of
Biology, Medicine and Health</div>
<div dir="ltr" style="color:rgb(34,34,34)">University of
Manchester</div>
<div dir="ltr" style="color:rgb(34,34,34)"><br>
</div>
<div style="color:rgb(34,34,34)">Department of Science
Education</div>
<div style="color:rgb(34,34,34)">University of Copenhagen</div>
<div style="color:rgb(34,34,34)"><br>
</div>
<div style="color:rgb(34,34,34)">Department of Eye and
Vision Science (honorary)</div>
<div style="color:rgb(34,34,34)">University of Liverpool</div>
Phone: 07786 064505<br>
Email: <a href="mailto:johnsonmwj1@gmail.com"
target="_blank" moz-do-not-send="true">johnsonmwj1@gmail.com</a><br>
Blog: <a
href="https://urldefense.com/v3/__http://dailyimprovisation.blogspot.com__;!!D9dNQwwGXtA!UsPK2SRbiXBsfUCVImOrMm7fPKKNuBbKeVeR7v6-AmTt7BCvZVrKGYKDIRzLOAqwbokC90rmAhTGK6HkIVeDeaY$"
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