[Fis] Fis Digest, Vol 113, Issue 17. From Mark

Tue Jul 9 06:49:25 CEST 2024

Dear Mark,
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.
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.

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.

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.
Best,
Lou

> On Jul 8, 2024, at 11:29 AM, Pedro C. Marijuán <pedroc.marijuan at gmail.com> wrote:
> 
> (clean posting: delete all the accumulated stuff below your message, otherwise it won't pass--P.)
> 
> 
> 
> -------- Mensaje reenviado --------
> Asunto:	Re: [Fis] Fis Digest, Vol 113, Issue 17
> Fecha:	Mon, 8 Jul 2024 16:31:25 +0100
> De:	Mark Johnson <johnsonmwj1 at gmail.com> <mailto:johnsonmwj1 at gmail.com>
> Para:	Louis Kauffman <loukau at gmail.com> <mailto:loukau at gmail.com>, fis <fis at listas.unizar.es> <mailto:fis at listas.unizar.es>
> 
> Dear Lou, all,
> 
> Apologies for taking ages to reply – I’ve had a busy couple of weeks travelling.
> 
> 
> 
> 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)
> 
> 
> 
> 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.
> 
> The two people:
> 
> a.      Are perturbed by what they see;
> 
> b.      Make a distinction;
> 
> c.      Utter a word which has meaning to them;
> 
> d.      Disagree with each other.
> 
> I think it is the dynamics between a, b, c and d which is the whole.  More abstractly, there is:
> 
> a.      Noise or disturbance;
> 
> b.      A selection;
> 
> c.      An utterance of a word relating to that selection whose meaning is contextualised within a shared culture
> 
> d.      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.
> 
> 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. 
> 
> 
> 
> 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?  
> 
> 
> 
> 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:
> 
> “It may be significant that the rules A → B and B → AB seem to be suggesting the structure of 3-dimensional (quaternion) algebra:
> 
> i → j
> 
> j → ij (“ = k”)
> 
> 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”.
> 
> 
> 
> 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)
> 
> (1, –1)
> 
> (1, –1) × (1, i)
> 
> (1, –1) × (1, i) × (1, j)
> 
> (1, –1) × (1, i) × (1, j) × (1, i)
> 
> (1, –1) × (1, i) × (1, j) × (1, i) × (1, j)
> 
> (1, –1) × (1, i) × (1, j) × (1, i) × (1, j) × (1, i) ...
> 
> 
> 
> 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.
> 
> 
> 
> 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.
> 
> 
> 
> With regard to AI, I am no zealot. But it raises fascinating questions – I really recommend playing with Google’s Teachable Machine (https://urldefense.com/v3/__https://teachablemachine.withgoogle.com__;!!D9dNQwwGXtA!VigefKGT9EQ0qbQStRw1CtoijqU3tnPPNISD0rhPYOK8JvhVfvUujhDZXVnBoABZpoIj__myBqtCv2sQ$  <https://urldefense.com/v3/__https://teachablemachine.withgoogle.com/__;!!D9dNQwwGXtA!UsPK2SRbiXBsfUCVImOrMm7fPKKNuBbKeVeR7v6-AmTt7BCvZVrKGYKDIRzLOAqwbokC90rmAhTGK6Hkf8MZ_pw$>) – 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. 
> 
> 
> 
> 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.
> 
> 
> 
> Best wishes,
> 
> 
> 
> Mark  
> 
> 
> On Sun, 23 Jun 2024 at 16:23, Louis Kauffman <loukau at gmail.com <mailto:loukau at gmail.com>> wrote:
> Dear Mark,
> I am writing privately since I have to rights on fis until tomorrow.
> When we use the word measurement in the usual scientific context, we mean making a record that can be viewed without disturbance by anyone.
> Thus the measurement is drained of all meaning that might be supplied by a given observer.
> It takes a very concentrated effort to produce measurements of this kind and they are the subject of engineering practice.
> 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 
> observed/ heard by a sensitive human at which point the meaning can arise in the interaction of the human with the sound.
> Best,
> Lou
> 
> 
> 
> 
> 
>> >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.
> 
> -- 
> 
> Dr. Mark William Johnson
> Faculty of Biology, Medicine and Health
> University of Manchester
> 
> Department of Science Education
> University of Copenhagen
> 
> Department of Eye and Vision Science (honorary)
> University of Liverpool
> Phone: 07786 064505
> Email: johnsonmwj1 at gmail.com <mailto:johnsonmwj1 at gmail.com>
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