<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Dear Mark,<div class="">I just came back from a trip, so will first just reply to part of your letter, but it does pertain to all of it.</div><div class="">In the case of a diagram that represents a knotted curve in the space, there is a dialogue that is carried our that will bring most people into agreement about the meaning of the diagram. Different aspects of the dialogue will be emphasized by different groups. For example, imagine that I am working with weavers who will make actual versions of the diagrams. Then they need to know how to interpret the diagram as an instruction or recipe for making an actual woven knot from rope. And I would discuss with them not just the rules for making the weave, but also the kinds of rope we might use and how the actual knots would be displayed or otherwise used. Look at a book on knot tying and you will see various levels of such discussions. For mathematicians, the same interpretations are needed but also they need to see that the diagrams can be interpreted in terms of mathematical curves in space and they need to understand the combinatorial moves on the diagrams that we use to do topology and a number of other things. So the mathematical discussion is more complex. There is no controversy here since there seems to be no one who disputes the use of the diagrams. Some mathematicians prefer to use methods that are not diagrammatic, but this really is not a dispute.</div><div class=""><br class=""></div><div class="">In the case of the bars which look like “3” at one end and look like “4” at the other end, I am interested in the possibility that the disputants could be led by a friendly mediator to see that there are the “bars” and how they lead to two different points of view and indeed to “3” or to “4” depending on the viewpoint. I would like the disputants to find a place from which each could see what the other sees. Some disputes can be settled this way. I do not claim that all can.</div><div class=""><br class=""></div><div class="">An interesting contemporary example of a dispute is the argument between orthodox quantum mechanics and Bohmian quantum physics. Adherents to the orthodox mechanics tend to say that they see the Bohmian point of view but that it does not add anything new to quantum physics. While adherents to Bohemian view tend to believe that eventually this point of view will lead to new physics. The difference between the groups lies in their ontologies and how much they want to work with the reality of possibility versus the actuality of physical objects. It is a very interesting and complex argument.</div><div class="">Best,</div><div class="">Lou</div><div class=""><br class=""></div><div class=""><div><br class=""><blockquote type="cite" class=""><div class="">On Jul 8, 2024, at 11:29 AM, Pedro C. Marijuán <<a href="mailto:pedroc.marijuan@gmail.com" class="">pedroc.marijuan@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class="">
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<div class=""><p class=""><font size="+1" class=""><i class="">(clean posting: delete all the accumulated
stuff below your message, otherwise it won't pass--P.)</i></font><br class="">
</p>
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<th valign="BASELINE" nowrap="nowrap" align="RIGHT" class="">Asunto:
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<td class="">Re: [Fis] Fis Digest, Vol 113, Issue 17</td>
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<th valign="BASELINE" nowrap="nowrap" align="RIGHT" class="">Fecha: </th>
<td class="">Mon, 8 Jul 2024 16:31:25 +0100</td>
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<th valign="BASELINE" nowrap="nowrap" align="RIGHT" class="">De: </th>
<td class="">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" class="">Para: </th>
<td class="">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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<div dir="ltr" class="">Dear Lou, all,
<div class=""><br class="">
</div>
<div class=""><p class="MsoNormal">Apologies for taking ages to reply –
I’ve had a busy couple
of weeks travelling. <span class=""></span></p><p class="MsoNormal"><br class="">
</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 class="">
</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 class=""></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"" class="">
</span>Are perturbed by what they see;<span class=""></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"" class="">
</span>Make a distinction;<span class=""></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"" class="">
</span>Utter a word which has meaning to them;<span class=""></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"" class="">
</span>Disagree with each other.<span class=""></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 class=""></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"" class="">
</span>Noise or disturbance;<span class=""></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"" class="">
</span>A selection;<span class=""></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"" class="">
</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"" class="">
</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 class=""></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 class="">
</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 class="">
</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 class=""></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 class=""></span></p><p class="MsoNormal" style="margin-left:36pt">i → j <span class=""></span></p><p class="MsoNormal" style="margin-left:36pt">j → ij (“ =
k”) <span class=""></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 class=""></span></p><p class="MsoNormal"><br class="">
</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 class=""></span></p><p class="MsoNormal">(1, –1) <span class=""></span></p><p class="MsoNormal">(1, –1) × (1, i) <span class=""></span></p><p class="MsoNormal">(1, –1) × (1, i) × (1, j) <span class=""></span></p><p class="MsoNormal">(1, –1) × (1, i) × (1, j) × (1, i) <span class=""></span></p><p class="MsoNormal">(1, –1) × (1, i) × (1, j) × (1, i) ×
(1, j) <span class=""></span></p><p class="MsoNormal">(1, –1) × (1, i) × (1, j) × (1, i) ×
(1, j) × (1, i) ...<span class=""></span></p><p class="MsoNormal"><br class="">
</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 class=""></span></p><p class="MsoNormal"><br class="">
</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 class=""></span></p><p class="MsoNormal"><br class="">
</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" class="">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 class=""></span></p><p class="MsoNormal"><br class="">
</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 class="">
</p><p class="MsoNormal">Best wishes,</p><p class="MsoNormal"><br class="">
</p><p class="MsoNormal">Mark </p>
</div>
</div>
</div>
<br class="">
<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" class="">loukau@gmail.com</a>> wrote:<br class="">
</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;" class="">Dear Mark,
<div class="">I am writing privately since I have to rights on fis
until tomorrow.</div>
<div class="">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 class="">Thus the measurement is drained of all meaning that
might be supplied by a given observer.</div>
<div class="">It takes a very concentrated effort to produce
measurements of this kind and they are the subject of
engineering practice.</div>
<div class="">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 class="">observed/ heard by a sensitive human at which point
the meaning can arise in the interaction of the human
with the sound.</div>
<div class="">Best,</div>
<div class="">Lou</div>
<div class=""><br class="">
<div class=""><br class="">
<br class="">
<br class="">
<br class="">
<blockquote type="cite" class="">
<div style="line-height:1.7;font-size:14px;font-family:Arial" class="">
<pre class="">>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 class=""><br class="">
</div>
<span class="gmail_signature_prefix">-- </span><br class="">
</div>
</div>
</div>
</blockquote>
</div>
<br class="">
<div dir="ltr" class="gmail_signature">
<div dir="ltr" class="">Dr. Mark William Johnson<br class="">
<div dir="ltr" style="color:rgb(34,34,34)" class="">Faculty of
Biology, Medicine and Health</div>
<div dir="ltr" style="color:rgb(34,34,34)" class="">University of
Manchester</div>
<div dir="ltr" style="color:rgb(34,34,34)" class=""><br class="">
</div>
<div style="color:rgb(34,34,34)" class="">Department of Science
Education</div>
<div style="color:rgb(34,34,34)" class="">University of Copenhagen</div>
<div style="color:rgb(34,34,34)" class=""><br class="">
</div>
<div style="color:rgb(34,34,34)" class="">Department of Eye and
Vision Science (honorary)</div>
<div style="color:rgb(34,34,34)" class="">University of Liverpool</div>
Phone: 07786 064505<br class="">
Email: <a href="mailto:johnsonmwj1@gmail.com" target="_blank" moz-do-not-send="true" class="">johnsonmwj1@gmail.com</a><br class="">
Blog: <a href="https://urldefense.com/v3/__http://dailyimprovisation.blogspot.com__;!!D9dNQwwGXtA!UsPK2SRbiXBsfUCVImOrMm7fPKKNuBbKeVeR7v6-AmTt7BCvZVrKGYKDIRzLOAqwbokC90rmAhTGK6HkIVeDeaY$" target="_blank" moz-do-not-send="true" class="">http://dailyimprovisation.blogspot.com</a></div>
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