Spooky Christmas!

Here are some improvisations I did this Christmas. I'm finding myself increasingly drawn to the creativity that the Seaboard offers me than to what I can do with the piano. This feels like a real change for 2019...

Communicative Musicality and Entropy

An activity which I've done a few times now is to invite people to simulate conversation in music using my Roli Seaboard. The result sounds a bit like the Clangers, but people enjoy it (and I get something much more expressive out of them than I would if I tried to get them to vocalise "talk"). What's interesting is that it's obvious when its done well - the musical conversation has a kind of coherence about it - which raises a fundamental question about the coherence of any shared "musicking" between people, and the prosody of language.

This coherence is, I think, a fractal structure, and another aspect of this analysis is to consider how the fractal might emerge. Any musical communication involves an "emergent alphabet" of utterances, which invites the suggestion that a fractal must express the emergence of this alphabet. The emergent alphabet issue also presents a problem when trying to apply analytical techniques like information theory to music: information theory relies on the fact that the alphabet is known at the outset, so it knows what to count. If the alphabet is emergent, it doesn't know what to count until (possibly) the end. However, it is a possibility that an alphabet at time t1 has a similar structure in terms of entropy as a larger alphabet at t2. This is where the fractal likely resides.

The critical question is at what point is it necessary to expand the alphabet? This is closely related to the question as to "at what point is a new concept introduced into a learning conversation?" My answer to this draws on the relations between entropies of basic elements.

Consider that a "basic" alphabet in sound contains four elements: pitch, rhythm, intervals and volume. They can be A, B, C, D. Over time, the entropies for each of these values can be calculated, and at different times the entropy for each  will either increase or decrease. For example, a note which is sung typically has an "attack" - which is an increase in volume, and hence an increase in the entropy of volume. It may then have a "sustain" period where the volume is constant: that gives a entropy closer to zero. Finally the note is released, which results in a rapid decrease in volume to nothing, which is also an increase in entropy. Every dimension is like this, having a period of increase and decrease, so for each of A, B, C, D there is a corresponding A*, B*, C*, D* for its inverse. This means that AA*, BB* CC*, etc are all effectively zero. In drawing the attack and decay of a note and encoding  an increase in entropy as 1, and a decrease as 0, we might see:

A   A*
1    0
0    1
0    1
1    0

Sometimes it may seem that the entropy of A oscillates very quickly with the entropy of A* (e.g. vibrato), or even that it is difficult over a period of time to determine whether on average there is an increase or a decrease: both seem to be simultaneously present. If we draw this then we might see:

A   A*
1    0
1    0
0    1
1    1
1    0
0    1
1    0
1    0

taken over a longer period of time, we would basically see:

A   A*
1    1
1    1
1    1

This means that the AA* pair is complete and in total is zero. The question is whether this is the trigger for the production of a new element in the alphabet. I think it is. Intuitively, what is described is the point at which a gesture or idea is thoroughly familiar to the point of being boring, and this requires something new. It is a way of describing the satiety of the alphabet.

Now what happens in communicative musicality? When two people are in musical conversation, there is in each person a different idea of what the alphabet might be. So person x might articulate an alphabet which is A,A*,B,B* and person y might articulate an alphabet which is A, A*, C, C*. The conversation articulates a combined alphabet: A, A*, B, B*, C, C*, AC, AC*. At what point does this alphabet become sated, where each element is 1?

In a conversation that "doesn't work", what will happen is that the communication breaks down. This means that the utterance of one person is not met by a corresponding utterance by the other. Equally, the other person might simply keep on repeating the same behaviour (the same alphabet) irrespective of the attempts of the other person to elicit a different response. Both these situations result in restrictions to the growth of the alphabet.

But when it does work, there is adaptation in the utterances of both parties, which eventually results in an expanded alphabet that is shared between the people.

"Sunday evening": My Roli Seaboard is fantastic...

A little over 10 years ago, I did my first post on this blog called "Sunday afternoon", with a video of me playing the piano.

So here's "Sunday Evening" 10 years later, but it's not a piano, but a Roli Seaboard. What an amazing musical instrument this is. I am growing into it more all the time. I have never had this experience with any digital technology before...

The Digital Computer and the Implicate Order

All living things "compute" (literally, "com-putare"... they "contemplate with"). The human-digital computer system (the whole system of humans and machines), is a system where the computations in people are constrained by the logic circuits in a machine. Since we are allergic to the uncertainty that is produced within our human "computing system", the constraints of the digital computer are welcomed - they provide ways of attenuating our uncertainty and giving us "answers".

But if we look at living things as computers, and seek to contemplate with them, we would, I think, look at the world in a very different way. It is not the attenuation of uncertainty that we should seek from our contemplation. It is instead guidance on how to act to maintain the coherence of life.

This "acting to maintain coherence" is essentially a process of understanding when and how to generate redundancies in our human system. The digital computer can be used to generate redundancies, but a lot of the time it is used to attenuate reality and to generate "information", which is the opposite of redundancy.

What I mean by coherence is, at its most basic level, a hologram, or a fractal. It is a fundamental process which encapsulates totality. When things fall apart, the fractal loses its internal coherence. When this happens, it is necessary to generate new redundancies, and sometimes new variety. But we need to know what to do and how to do it.

The fundamental question we should ask ourselves is how we might apprehend this hologram. It is close to what David Bohm called the "implicate order". Essentially it is unknowable, but some features can be perceived - particularly in the growth of living things, and especially music.

Music is a kind of computation. Music specifically shows the ways in which redundancies are required to be generated to maintain coherent life: a new accompaniment, a new melody, a modulation, are all ways in which music computes the nature of perception. Each new moment is not an accident. It is an expression of the whole, or an intervention to reveal the whole.

Digital computers are powerful enough to give a glimpse into the computations of nature. It is the latter computations which are our best guide for making collective decisions.

From Topology to Holograms

There's a missing link in my thinking. On the one hand I am seeing holistic approaches to organisation as in Beer's work (in fact most cybernetic approaches are holistic) in a topological way. On the other hand, I am concerned with the fractal encoding of nature in things like holograms, where time and space are enfolded (this comes from Bohm).

The topology side reveals forms like the Mobius strip, trefoil knot, hexaflexagon, etc, where re-entry (which is something I'd not properly understood until quite recently) is a feature of a whole form. The connection with eroticism which I mentioned in my last post is something that puts a new dimension on this - a connection to lived experience, and perhaps psychological dynamics such as the double-bind. More than anything, I find this a productive way of thinking about profound questions such as "what drives the bee towards the flower, or the sperm towards the egg?"

Topologies enfold time in a peculiar way. We have to pass over them to understand them. They are structured space (synchronic), but the time of diachronic exploration is implicit in them.

But a topology is not an encoding - it is a manifest space. However, a topology can be encoded as a hologram.

Whilst a geometric form like a trefoil knot plays with space, music plays with time. The way in which music's playing with time might be encoded is the critical issue. I think this works according to the same principle as an object's encoding of space. Actually, in the case of a hologram, space and time are implicated in both, because a hologram is formed through the interference patterns of light, which implicates frequency, and in turn, time.

Music's interference pattern involves the interactions of redundancies or constraints. It's not just music - it's any diachronic process which involves this... learning and conversation are exactly the same. But where is the connection between the hologram's encoding of space and music's encoding of time?

A holographic encoding combines not only all dimensions - time and space are two of them (but we should also consider mass and charge since these also participate in the interference in light) - but is also able to represent the relation between these different dimensions in different ways. Aesthetic experience relies on this multiplicity of decodings of a hologram: we can be moved in similar ways by Beethoven, Shakespeare and Picasso. They all express something fundamental about the universe.

Seeing systems whole (and topology in Bataille's "Eroticism")

I've been giving a few seminars on the work of Stafford Beer recently. I've tended to concentrate on the work from Platform for Change, working backwards to the viable system model, and forwards to syntegration. One of the things which has really struck me is the topological coherence of Beer's thinking. If I can sum it up in a nutshell, it is simply that every whole system has "undecidables" which require a metasystem whose job it is to maintain the whole. This means that we make a mistake if we conceive of any "whole" as simply a boundary around a system (i.e. a circle). The undecidables are the hole within the whole. To put it most simply, "Every whole has a hole" (this is probably another way of expressing the Conant-Ashby theorem)

Another way of thinking about it is to see a whole as a Möbius strip. One side of the strip is the system and the other is the metasystem. The hole is (obviously) in the middle. If you flatten a Möbius strip, you get a trihexaflexagon which is also a trefoil knot. That's three arms which constrain each other: system, metasystem, environment. But maybe that's stretching things a bit.

A three-dimensional Möbius strip produces a Möbius snail. What a fascinating thing that is!

There are similar objects like "klein bottles", but in each case there is a hole in the whole.

I was looking up a book cover for Bataille's "eroticism" the other day and came across this erotic image which is used as a cover for one of his other books:

There's a strong similarity in these images, isn't there? And in fact there are holes in wholes everywhere we look... Here's one I've spent a lot of time looking at over the last year...

Is the optic nerve a hole within the whole? It certainly connects to the metasystem (the brain)...

Returning to Bataille for a second, he says something in the introduction to Eroticism which is very similar to Beer:

By seeking to present a coherent whole, I am working in contradiction to scientific method. Science studies one question by itself. It accumulates the results of specialised research. Eroticism cannot be discussed unless man too is discussed in the process. 

Bataille is in the hole in more ways than one!

Why has my blogging slowed down? (Some thoughts on holograms, music and machine learning)

I realise that I haven't blogged very much recently. Partly it's because I've been very busy and a bit exhausted. But also I think it's because I've got so much in my head at the moment, I don't know how to get anything out.

What I have been doing is a bit of cybernetic evangelism. It's been great to take people to the Stafford Beer archive and watch their heads explode! It's quite a predictable thing...

But I'm also thinking about Beer's holism, and the way that his approach unfolds from nothing. It's this "unfolding from nothing" which really fascinates me. It's rather like my friend Peter Rowlands's work on physics which expands from the idea of nothing (or his 'nilpotent' formulae). Is everything really nothing? What's real about nothing?

I have some good friends visiting me at the end of the week who also know about this stuff. We're going to do a session in the Beer archive. I'm hoping some colleagues from Liverpool also come along.

It's weird how things start to fit together. I suppose my biggest interest in cybernetics at the moment is coherence: how do things fit together? The mechanistic/stochastic approach of cybernetics doesn't address this question well. But David Bohm's idea of the hologram (which Beer was at least aware of because he had a book on it), does.

All the things that fascinate me most, such as music, or conversation, or narrative, or biological form, are all coherent. Are they all holographic?

This question about holograms - particularly in music - has taken on a new dimension for me. I am also working with machine learning tools for a big medical project. We have a problem: how to adjust the judgement of a trained network without screwing up all the other judgements of the network. It's not really how machine learning is meant to work.

We have a brute-force fix for the problem, but it's rather unsatisfactory (and probably not reliable). It would be much better to have a better understanding of what is happening in a convolutional neural network (CNN)

It turns out that current thinking is that it is a kind of hologram. CNNs encode differences and orders of things in a fractal structure. That means that the nature of the problem we want to solve is "where to change the fractal/hologram so that a specific change in its ordering may be made".

This is rather like asking "where to change the  fractal holographic image so that the hologram changes shape in a particular way". The nature of the challenge can be seen by examining a holographic plate:

What it encodes is the interference pattern of light. That means actually that it encodes distance and time (time because interference involves frequency). Now if we can understand how the interference pattern arises, we might be able to understand where to manipulate it. 

Music, I suspect has a holographic structure. I'm writing a paper at the moment where this structure is considered using the fractal images of anticipatory systems which were developed by Daniel Dubois. His images look like this:

In music's hologram, I think what is encoded is the interference between different redundancies. Like light, this interference means that the hologram encodes time and difference. Because we can play with music in a very practical way, maybe there is a way in which insight gained from music can help with the practical problem of machine learning. 

Let's see. 

In the meantime, I've felt the need to shake up my metasystem...