Problem solving in math and music – what is the connection?

Take a look at these two series of numbers:

6-4-4-3-3-2 5-3-3-2-2-X

What number would you put at X’s place? Would it be 1? I think most people would come to that conclusion. What if you were asked to find the series of six numbers before the 644332 sequence? Wouldn’t you choose 7-5-5-4-4-3? And after the 533221 series, you would probably expect the combination: 4-2-2-1-1-0, right?

Now you have solved a mathematical problem. Does that feel good?

If I told you, that the two series of numbers are from a piece of music, do you think, you can guess which (hint: you probably would have to be Danish to know 🙂 )?

OK, you guessed correctly! They are from the Danish children’s tune, “Jeg ved en lærkerede” (“The lark’s nest“) by Carl Nielsen. It’s a very simple tune, and as a composition, it is brilliantly done. Here you can here the melody, made in Google Song Maker:

In the melody, the two series of numbers appear in the middle of the song, in note names: C-E-C-F-D-G- -E-A-F-F-E-E-D- – -G-E-E-D-D-C– -A-F-E-E-D-D-C- – –

Looking at the melody in midi notation, we can see, that the logic of the two series can also be immediately grasped, when represented as geometric patterns:

Why does it feel good to solve a math problem? You found that the missing number was 1. And you came to that conclusion via a process of looking for a pattern in the number series, and through logical thinking coming to a conclusion. How is this gratifying? Is it the fact of experiencing a confirmation that the world turned out to be, what you would expected it to be?

When you listen to or sing the melody of ‘The Lark’s Nest’, and you experience the tone C at the end of series two, was this what you expected? And if so: was the feeling of experiencing something in the world that turned out as expected gratifying? Was the feeling related, somehow to the feeling, when solving a math problem? Is listening to and playing music (also) some kind of problem solving?

Sudoku and music

I have a habit. When I need to relax my brain, I play Sudokus. I actually play a version called ‘Killer Sudoku’. In math terms, solving a killer sudoku means using basic adding/subtracting, which is of cours good training, but the satisfying part is the part where it’s actually about solving equations. I’ve been doing this for quite some time, and contrary to other time killer apps, I seem to stick to this one. It means predictability, since I know I will always solve the Sudoku, eventually; I know some tricks that will help me crack the problems; but what is more is, that it means discovering new tricks.

At a session with my composition mentor, Jexper Holmen, we talked about musical form. I am working on a series of variations for piano, and Holmen suggested that I ‘coded’ the variations with certain formal elements, something in the beginning, in the middle, and in the end, that could be easily recognized. These elements should help build a ‘contract’ with the listener, setting up something to expect; once there is expectation, expectation can be fulfilled or not, and in this way there is ‘something at play’.

In the children’s tune ‘The Lark’s Nest’, there is a build up of expectation, within the melody itself, and the fulfilling of this expectation is what makes it a good melody.

The sound of sudoku

Now, with the ideas from my mentor in the back of my head, and sitting, as usual, killing time with my killer sudoku, an idea struck me. This is what I knew:

• solving a sudoku is basically about solving equations
• solving equations is a gratifying thing
• music can be build as series of numbers
• series that follow a logical sequence, thus fulfilling the listeners expectations, it can be gratifying to listen to

So my idea was of course: What if I turned a (Killer) Sudoku into music? What kind of music would that be? As is the case with turning DNA code into music, the fact that the system used for generating music is foreign to the sound itself, makes the connection between sound and system arbitrary. Just like with letters and phonemes in language. The letters H-O-R-S-E are supposed to sound in a specific way, when spoken. In language, the relation between spoken and written words is arbitrary. However, once established, the system makes sense to the reader.

So, if I want to make a sudoku into music, I need to choose a way of translating the sudoku’s math problems and their solutions into sound. And the choice of a translation system will necessarily be arbitrary. However, there might be a chance, and this is indeed my purpose, that the audible result will make sense in a way similar to the sudoku.

Here is a sudoku, I’ve solved.

How can this mathematical problem solving become a piece of music?

First, let’s establish some points. Solving a Sudoku takes time. For me, this makes a ‘translation’ into music meaningful, since music is a time based art form. The sequence, and maybe duration, of the problem solving in the sudoku could be used as the outset for the unfolding of the composition.

Secondly, a sudoku is based on numbers. In music, sounds and rhythms can be thought of as numbers. The sudoku uses the numbers 1 – 9 in a variety of combinations. In music, I think, it makes sense to use these combinations to generate patterns of pitch (melody, chord, interval) and rhythm. As we saw in the children’s tune, a simple sequence of numbers can generate musically meaningful sequences of pitch.

Thirdly, in a sudoku, you solve one problem at a time, but all problems are ultimately connected; solving one problems makes it possible to solve the next; in some cases, there will be an intermediary situation, where there are 2 – 3 possible solutions to a problem; reducing the problem to that, can help finding the final solution to another problem. In other words: Solving a sudoku means untangling a web of connections between connections. How can this be translated into music?

Experiments

In order to answer this question, we need to conduct some experiments. Here is a setup, I’m working on.

First of all, I think more instruments are needed. In order to establish a ‘solution’ to a problem, there is a need for something recognizable, and distributing different solutions to different instruments might do the job. The sudoku consists of 9 fields, nine vertical, and 9 horisontal lines, each with the numbers 1 – 9. A single number solution therefore affects a field, and two lines. In order to ‘translate’ this problem solving grid into musical timbre, I suggest that we divide the instruments in groups. In order to cover the whole field of problems, we need a certain number of instruments. How about a sinfonietta*?

Since the occurrence of a solved problem, in a sudoku, is represented in the space of the grid, my idea is to allocate different instruments to different parts of the grid. In order to further enhance the ‘formatting’ of the spatial distribution of the sudoku’s math problem solving, I also coded the grid with pitch differences, going from deep pitches in the bottom left, to high pitches in the top right.

Each instrument would ‘account’ for a problem solving in a certain region, and groups of instruments would gestalt the vertical and horisontal connections.

From here to a final result: a lot of hard work….!

* A sinfonietta is a kind of ensemble , typically, consists of 1 of each instrument from the symphony orchestra. In a sinfonietta, we typically have a flute, an oboe, a clarinet, a bassoon, a French horn, a trumpet, a trombone, two percussion players, a piano, a harp, two violins, a viola, a cello and a double bass.

Has musical composition influenced the discovery of the DNA?

I am working with composition as a kind of ecosystem, and one of the central aspects of this approach is to regard the musical score as a kind of DNA. In the musical score, the notes are the code to be interpreted or translated by the musician into sounding music. This music is what the community around the music need to thrive. In the living cell, the DNA is the code for the living organism, which, once translated or interpreted, form proteins that the organism need to persevere.

From this perspective, music and organic life is basically about scripture, interpretation and communication. Genetics and musical composition have these things in common, and when I compose, I take this connection a step further, you might say, and work specifically with musical expression in a way that is parallel to how living organisms interact with eachother and the environment.

Read more about my approach in this blogpost: “Music as an ecosystem“.

Of course, the fact of setting up this relation is purely cultural. It is a product of human activity through and through. In any case, science itself can be said to be a cultural phenomenon. At least, this idea about a cultural connection between genetics and composition makes me want to ask the question if there is a deeper connection, in cultural/scientific history between these to fields.

Music as a representation of genetic data

My initial research brought a rather big amount of results where musical composition is used as a means to illustrate or conceptualise genetic code.

In 1986, a japanese scientist, Susumu Ohno translated genetic code, with the help from his wife, a professional singer, into musical scores.

As you can hear, the result is a rather conventionally sounding piece in a kind of classical style.

Ohno’s experiments are described in this article: “The Ohnos and Genetic Music”, where the author, genetics professor Manuel Ruiz Rejon also mentions other examples of a musical representation of genetic codes, that are more elaborated. The basic idea is, as I understand it, to make an auditive representation of data. In this case genetic code. The thing about genetic code is, that it implies a lot of repetition. The same can be said about (certain types) of music. What these scientists have done is to represent genetic code data in sound, thus “combining this type of tool, which works “by ear” with existing visual and analytical tools to study the nucleotide sequences of genes and genomes found in the enormous databases that are currently available, where the main difficulty is to sort and make sense of them.” I did something similar, 9 months ago, when I explored how the occurence of prime numbers might sound.

In science, the most common way of representation is through visual means, and I think it makes sense to ask what we might miss? In fact, I can’t help thinking what would happen if we used sound as a means of representation in working with scientific facts.

Composition as a prerequisite for thinking genetic code

I’ve looked a little at how musical composition has been used to illustrate genetic code. How about the other way around? To which degree can it be said, that the development of the pentagram, ie. the Western representation of musical sounds in writing, might have contributed to the idea of code in living organisms?

After an initial search, I came to realize, that this is not an easy question to answer. I started by checking out who actually ‘discovered’ genetic code, and if these persons might have had some sort of epiphany by thinking musical composition. Or maybe they simply had had a musical upbringing. I had to rapidly discard this thought as too far fetched.

In order to answer the question about a possible relationship between the music notation and the ‘discovery’ of the DNA code, it makes sense to look for their respective roots.

The roots of the notational system

How did the notational system come into being in the first place? What were the prerequisites? What kind of thinking, what epistemology was needed for it to be conceived?

Well, musical notation seems to have been developed out of a necessity in the Church to streamline musical practises over large geographic distances. Put in the words of Wikipedia: “Christian monks developed the first forms of modern European musical notation in order to standardize liturgy throughout the worldwide Church”.

It also seem that musical notation was closely linked to written text, where some extra symbols, originally, were added to the text of the songs used in liturgy. I think that the close relationship to written text accounts for the left-to-right linearity of the musical score. Actually, it might be argued that music is not necessarily linear.

When I use one of my compositions as a ‘map’ for improvisation, I ‘read’ the score non-linearly; I jump from one ‘musical event’ to the other without regard to where they are in the score’s temporal logic.

In addition, it is certain, that some basic mathematical principles had to be in place before the notational system as we know it could be developed. To take one example, the idea of a fraction is behind the way that we divide the composition into bars, the bar into beats, and the beat into quarters, eights, etc., and triplets, quintuplets and so on.

The musical score has made it possible, similar to written text, to store and manipulate musical thinking in a non-temporal medium. Life is an ongoing, temporal process. The DNA is a way of conceptualising this process in a non-temporal manner. Is this a possible link?

The roots of the discovery of DNA code

What were the prerequisites for discovering DNA code? What technological development was needed? What kind of thinking, what epistemology was needed for it to be conceived?

These are, you might say, really heavy weight questions, that I am not at all in a position to answer; my guess is, that research in the line of Science and Technology Studies (STS), in the style of Bruno Latour and others would be an interesting place to look for answers. In other words, people who research into science with the assumption that they are not only looking into something which is (also) a cultural phenomenon.

Coming to understand the genealogy of the musical notational system seems much more straightforward than the genealogy of genetic science. This still doesn’t answer the question about a possible connection.

Since going for a directly observable connection has proven, as I have mentioned in the beginning of this blogpost, to be a complete failure, how would it be possible to answer this question?

I think it would require that we take quite a few steps backwards, in order to look at the musical notational system in a broader cultural-technical perspective. And ask if there might have been, throughout history, examples of a cultural environment, where the explorations into what kinds of thinking the musical notational system might offer, and how these kinds of thinking might have influenced thinking within the realm of natural sciences.

A possible place to look, I think, would be in the periods of time, where composers and scientists engaged in exploring and experimenting in their respective fields, interacted somehow, and exchanged ideas. Where composers explored and experimented with the possibilities offered by the musical score, in conjunction with the cultural-technological developments in musical instruments, and the the interaction between composer and his/her public, and society in a broader sense. And where natural scientists, for their part, explored their field, while taking advantage of the cultural-technological developments of the time, and – of course – the interaction with society in a broader sense.

Which periods to look into?

Even though we, in our time, have environments, where specialists of all kinds explore their own field to a detail, which in a historical perspective must seem extreme, I am not sure that own time is the best place to look for the kind of connection I am looking for. The problem is, I think, that artists, and scientists, and other specialists in our time, are too deeply dedicated to the intricacies of their little field of specialty, and that it takes too much knowledge about what others are into, in order to start to see possible connections between the fields.

What does these thoughts make you think of? Am I wrong if I say “the Renaissance man”? You know, the Leonardo da Vinci type of person?

Actually, I am thinking about two other historical periods/places. My knowledge is primarily as a composer, and from this perspective, I come to think of two historical places/periods, where musical composition were taking radically new places. One is the socalled Enlightnment (roughly 1750-1815, according to this article). My first place to look would be into Beethoven, and the environment where his musical thinking was nurtured and influential.

A rapid search online gave this result: A book about the concept of heredity, where one of the central points is, that “the concept of heredity came of age during the Enlightenment”. This makes sense, in a political sense, since it was a time where people started to question the idea, that certain people, ie kings, nobles etc., were born with certain privileges. The German composer Ludvig van Beethoven (1770 – 1827) was very preoccupied with these questions.

“Freedom and progress are our true aim in the world of art, just as in the great creation at large.” Beethoven, in a personal letter (source, cited here).

The other time and place would be Vienna in the beginning of the 20th century. Here, the music of Schoenberg and his pupils would be the place to start. A central characteristic of this school was the concept of dodecaphony, ie, the use of all twelve halfnotes in the musical system, each in their own right. Dodecaphony is an early example of what has become known as serialism, where the idea that musical parameters can be broken down into discreet entities, ie numbers (for rhythm and pitch), and terms (for dynamics, timbre etc), and that these entities can be combined in various ways, that are not necessarily fitting within the general idea of what music is supposed to sound like. This way of thinking music is, I would argue, very similar to the way of thinking needed to work with genetics, where discreet elements, ie aminoacids etc., are combined en various ways in order to generate different kinds of organisms.

The Enlightenment and early 20th century Vienna, would, I think, be two fruitful places to look for a crossover effects between musical composition and life sciences. In musicology, by the way, these two periods/places are being referred to as the first respectively second Viennese School. What happened in these places/times within the field of genetics? Well, maybe some of you have an answer, out there?

While you are thinking about these questions, I would like to invite you to listen to one of my latest improvisations, “Epilogue #0113000”; it is a (‘genetic’) spinoff of the composition “Last Dream” (#000000*)

How to keep track of my artistic research?

Since I started working with music as an ecosystem, I ran into a problem: How can I keep track of all the different variations/spinoffs/mutations?

I needed a kind of coding system, and after some thought, I came up with the following.

Color codes as a naming system

The thought of giving the improvisations a number seemed unelegant – and boring, so I decided to use the hexadecimal system, in a way similar to the way digital colors are coded.

In the hexadecimal color code system a color is represented by 6 numbers/letters. Choosing at random, let’s take the code #11FFA6. This would give a greenish color like the one you see here :

I needed a system, where I could give a unique code to each improvisation/composition that would make it possible to

1. Track where it comes from. IE which composition does this improvisation stem from?
2. Tell it apart from other improvisations with the same source. IE the ‘sibling’ level.

In order to do so, I ended up with something similar to the way names are given in human societies.

The first to ciphers represent the generation. First generation is ’00’. The compositions based on anything from a generation ads a number here, and becomes next generation. Second generation thus has ’01’ here. There are 256 possible numbers in 2 hexadecimals (16×16), and that makes up for quite a few ‘generations’. In each generation, further, there are 256 possible ‘members’. Hopefully 65.536 (256×256) possible improvisations is enough for my lifetime 🙂

The next two ciphers are there to give each improvisation it’s own id, for its generation Let’s call it the ‘first name’. And the last two ciphers take the ‘first name’ from the composition it is based on, and it becomes its ‘last name’.

This naming system results in a kind of genealogical tree, as you can see here:

Here, you see four ‘generations’ of improvisations, where three impros are derived from one ‘mother’ composition, and each of the three have two ‘offsprings’ each with their unique generational ‘first name’ (00 – 06). In the last row, “generation 03”, I have put an improvisation, which is supposed to be the hexadecimal 11th, ie 17th improvisation over the composition #020100.

If you look VERY closely, you might see, that the boxes are shaded differently; I wanted to make this post just A LITTLE entertaining, so I made the boxes the color that their name would give, were it a color code. (This is why I added the 17th generation 03 impro…, so it would be just A LITTLE different in its greenness 🙂 )

This system allows me to identify

• which composition an improvisation is based on (its ‘parenthood’),
• when it is done (generation combined with ‘first name’)

Creating a system, a format, to order different elements in a practice, like I am trying to do here, will inevitably also influence the way these elements are being created.

There are aspects of the practice that are not taken into account in the naming/ordering system. In my case, what the system doesn’t allow to know, is for example which part(s) of a composition has been used for the impro, and to what extend. This can however be shed light upon through an analysis of the involved compositions.

What it also doesn’t allow to know, implicitly, is if an improvisation has more than one parent. This is somewhat more problematic, since it will nudge me to NOT use different compositions, side by side, for example, as a basis for one improvisation. I actually had the idea of taking only endings of various compositions, and use for an improvisation. I think the naming problem sort of deterred my from going forward with this idea. A possible workaround would be to give 1 impro more than one name, that is one, for each ‘parent’.

What this naming system DOES allow is for a practice, where I relate compositions to each other in way, that I have described here, and it thus helps me stay faithful to the conceptual framework of music as an ecosystem, an organic, interdependent, developmental, experimental, and at the same time open, improvised and free approach.

Invitation – explore with us*!

I would like to invite you to a place. It is a place, I have invented. It’s a musical composition called “Last Dream”. I made this composition by improvising on the piano.

Listen to the improvisation here:

Regarding this improvisation as an ecosystem, a landscape, I made made it into a score. I use the score as a map. I put the map/score in front of me, at the piano, and explore the lanscape/ecosystem, improvising, regrouping, repurposing the elements of the landscape. Here is one of my explorations/variations:

As you might hear, I am exploring mostly the first part of the ecosystem/landscape/composition “Last Dream”. The variations/explorations seems to add new dimensions, new organisms, new connections.

Please listen to these variations/field studies, and ask yourself: How can I contribute? Where shall we go from here? Maybe we should explore one of the variations? Make a map/composition/score from it, and use this map as a place to explore? We can have a chain or branchings of such sequences: [exploration –> map of exploration –> exploration of map of exploration –> mapping of exploration of map of exploration], etc.

Maybe you can make an improvisation, using the score as a map? Or you can improvise over the improvisations? And share it with us?

Come with your ideas. Put them in words, sound, video, or whatever format suits you… Looking forward to receiving your contributions 🙂

Upload sound on Soundcloud, and share the link. Or send us an email: caspcordes@gmail.com

* “us” – well to be honest, sofar ‘us’ are me, my hands, mind, the piano.

Music as an ecosystem?

What happens if we create and experience music as a kind of ecosystem?

Improvising on the piano, using what I would call intuitive intelligence, I am developing a method for using my body, hands, arms, and mind to create a kind of sound ecosystem.

This is how this improvisation came into existence:

Next step is to make a score, a transcription of the improvisation. Check it out here.

The score as a map of the ecosystem. A map that can be explored, researched, studied, expanded, etc. Putting the score in front of me on the piano, I made ‘journeys’ into the ecosystem, resulting in a number of variations on the composition.

A traditional format – theme and variations. In nature, we are talking organisms interacting in an ecosystem, and evolving, mutating, adjusting, etc.

Listen to the variations here:

Please share your thoughts about the variations. Help me decide which (parts) to develop further. Comment on the tracks, in the tracks. Thanks! 🙂

Does hierarchy kill nature?

After reading Freya Mathews’ article “A deeper Philosophy of Biomimicry”, (see my summary here)  – which I find very inspirational – I feel the need to further investigate some of the paths she’s laying out. Particularly I would like to dig more into her framework for a ‘deeper philosophy’ based on the two concepts conativity and least resistance. However, I also sense some internal contradictions in her arguments. Before addressing her conceptual framework in more detail, I would like to clean up my thoughts, by dealing with these latter.

The thing I can’t quite get to fit, when reading (and hearing) Mathews, is what I perceive as an inherent contradiction in her argumentation. On the one hand, she stresses the problems with modern civilization’s ‘impose and control’ behavior, that “effectively places us ‘outside nature’”, and has made us “ravage the living constituency of the biosphere”. On the other, she professes a “setting of optimal ecological targets for human population.” My point is that Mathews equates the coercive behavior of a collective with negative impact on the environment, while at the same time advocating for population degrowth, in a language that implies large scale coercion on human societies.

This raises two questions. First of all: Can we take for granted that a given society (human or not) which is organised according to hierarchical principles will necessarily have a negative impact on it’s surroundings? In the article “Social Ecology Versus Deep Ecology” from 1987, Murray Bookchin writes:

“Decentralism, small- scale communities, local autonomy, even mutual aid and communalism are not intrinsically ecological or emancipatory. Few societies were more decentralized than European feudalism, which in fact was structured around small-scale communities, mutual aid, and the communal use of land. Local autonomy was highly prized and autarchy formed the economic key to feudal communities. Yet few societies were more hierarchical.”

Following Bookchin, there doesn’t seem to be a direct correlation between a society’s degree of authoritarianism, and it’s negative impact on its environments. This brings to mind our current situation, where China – a country which we Westeners like to consider as authoritarian – seems to take the front as a green super power, leaving far behind the US, (formerly?) seen as ‘the leader of the free world’

This bridges to the second question that Mathews’ argument raises, which has to do with “setting a target for human population”. Bookchin writes – rather bluntly – about “the mistakes of the early 1970s with their hoopla about ‘population control’, their latent antifeminism, their elitism, their arrogance, and their ugly authoritarian tendencies”. Again, China comes to mind with its one child policy (1979 – 2015).

Since Mathews subscribes to “targets for human population”, is it fair to count her among the authoritarian, antifeminism, elitist etc. stances, Bookchin is rallying against? That Mathews is concerned with environmental as well as social issues, shines through in her comparison between the impose-and-control mode of our modern times with their extensive use of energy supplies, external to our own life-force, and earlier civilizations’ use of slaves “who have been treated as external to the social corpus”. However, reading Mathews, I haven’t sofar come across any particular spelled out strategy of hers for the implementation of a policy for population degrowth. Her focus seems to be on the ways in which we can educate ourselves to become attentive to nature. The implementation of these educational strategies seems to have to do with small scale endeavours, based in communities or educational institutions. In this way, Mathews’ thinking is leaning more towards panpsychism than ideology critique. Mathews’ panpsychism is inspired by Norwegian deep ecologist Arne Næss, and can be describes as a thinking , “in which the world (not just nature) contains many kinds of consciousness and sentience. For [Mathews], there is an underlying unity of mind and matter in that the world is a “self-realizing” system containing a multiplicity of other such systems”. (The Stanford Encyclopedia of Philosophy).

Mathews is building on Næss and through him, Spinoza, but she doesn’t make this connection very explicit, at least not in the text I am referring to here. The problem with Mathews’ argumentation is, as I see it, that she doesn’t manage to apply Spinoza’s thinking to its fullest, and thereby, she lands in some middle ground, where her effort ends in a kind of spiritualistic impasse. And the problem with that, is that in order to have an impact on the current dominant ideas about ecology, nature, climate etc., a vague spiritualism doesn’t speak with a very efficient voice. If I suggest a typical Dane that we solve our current ecological crisis through a ‘musical encounter’ with birds or whales, he would probably at its best have a good laugh.

The rhetorics of deep ecology with its insistence on humans’ parasitic abuse of Nature, as well as discussions of invasive species, etc. comes dangerously close to the imagery of right wing populism. The difference being that whereas the latter refers to specific ethnic or religious groups, and use natural science as a repertoire of metaphors for the unwanted ethnic group’s behavior (“jews/muslims multiply like rats”), the former refers to humanity as a whole (“we are a cancer to the planet”), and their reference to natural sciences is literal. What is common to both, is the expression of hatred. Hatred towards the other or to one self. In the end of the day, it’s no wonder that some people have a hard time telling the difference.

An argumentation that would have a much stronger impact is Bookchin’s assessment, that “throughout most of the nineteenth and twentieth centuries in Europe, [improvements in the quality of life and the status of women] reduced rates of population increase, in some cases leading to negative population growth rates.”

This is a pretty straight forward argument for how people’s taking care of each other can have a positive impact on their environment. Whether intended or not. In this sense, Bookchin seems to be giving a much stronger argument about a possible correlation between how we as humans treat each other and how we treat our surroundings.

To return to the somewhat primitive question in the title, I might conclude by saying that hierarchy does not in it self kill nature, or sustain it for that matter. On the one hand there is the Chinese model of population degrowth, imposed on the population through a top-down, authoritarian strategy and on the other hand there is a, let’s say, Italian or Japanese (non-)strategy based on cultural, socio-economic factors with the consequence that people do not (want to) reproduce. Does welfare lead to sustainable living? Well, in the West we might have a declining population growth, but it wouldn’t make sense to assert that our way of life is sustainable for the planet. In other words: hierarchy or not, welfare or not, at the end of the day, an ecological, economical and social sustainability must be based on cultural sustainability.

References

Bookchin, M. (1987). Social Ecology versus Deep Ecology: A Challenge for the Ecology Movement. In Green Perspectives: Newsletter of the Green Program Project, nos. 4-5

Brennan, Andrew and Lo, Yeuk-Sze, “Environmental Ethics”, The Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/win2016/entries/ethics-environmental/&gt;.

Mathews, F. (2011) A deeper Philosophy of Biomimicry. Organization and Environment. Volume: 24 issue: 4, page(s): 364-387

Sharp, H. (2011). Spinoza and the politics of renaturalization. Chicago: University of Chicago Press.

Uddrag fra mit speciale: Om handlingsvalutaer

[uddrag fra mit speciale, s. 90ff]

“Handlingsvaluta -­ et begreb til at begribe mellemrummenes mellemrum

Centralt i begrebet handlingsvaluta er det, som jeg med Deleuze kalder affektøkonomien. Det er en meget enkel model, som Deleuze har fra Spinoza. Iflg denne model udgøres en krop127 af en række forbindelser, rapports, og disse forbindelser er det, som konstituerer kroppen. Idet to kroppe møder hinanden, præsenterer de sig på forskellige måder for hinanden. Visse af de måder ­ de facetter under hvilke en krop præsenterer sig for en anden, virker til at svække den andens konstituerende forbindelser (Deleuze 1980). Andre til at forstærke dem. Denne vekslen mellem styrkelse og svækkelse af de konstituerende forbindelser kan beskrives som affektøkonomi. Med dette begreb kan jeg beskrive en række af de processer, jeg har observeret, som fx i det forløb med de to børn der hopper i vandpytter, fra de møder kvartetten til de råber “Casper, Casper” (se afsnit 6.0). Her er affektøkonomien kommet ud af balance. Men det er ikke sket fra det ene øjeblik til det næste. Der er en lang række små styrkelser og svækkelser der er gået forud. Derfor kan affektøkonomi som konceptuelt værktøj bruges til at fange nuancerne i samspillet, på en anden måde end fx en tilgang, der fokuserer på kategoriseringer af adfærd (Olesen 2015 op.cit).

Jeg har endvidere bemærket, hvordan børnene, når de mødes med én slags måde at præsentere kroppen, en facet, har en tendens til at reagere tilbage med den samme slags facet. Når nogen tysser, tysser de andre. Når én spytter, spytter de andre, osv. Disse mønstre kan beskrives som mimesis, forstået som “the public (motoric) display of perceived or remembered episodes” (Hurley and Chater se fodnote 99). Børnene giver tilbage af samme mønt, så at sige, ­ og det er bla. med udgangspunkt i denne etymologiske pointe, at jeg har valgt begrebet valuta. Den gangbare mønt, valutaen, kan forstås som “what has been sanctioned by custom or usage”. Når jeg kobler valuta til handling, er det for at kunne sætte fokus på, hvordan visse slags handlinger i en given situation tæller, imens andre lades ude af billedet. I det lærerorganiserede er det således primært verbalsproglige ytringer der tæller. Imens de handlinger, det tæller i børnenes indbyrdes samspil, kommer til udtryk gennem en lang række modaliteter, som udover verbalsproglige også gælder kropslige, nonverbale, og materielle udtryksformer. Og når jeg siger, at en handling tæller, mener jeg, at det er en handling, med hvilken det er muligt i en given kontekst at konstituere forbindelser. Når Mathias (7 år) argumenterer (i en situation, hvor gårdvagten griber ind) med, at hans gruppe havde vandpytten først, indgår hans talehandling som et led i konstitueringen af en ny social virkelighed: i det her tilfælde én, hvor børnenes leg bliver udparcelleret (gårdvagten deler børnene op, så den ene gruppe får én vandpyt, og den anden en anden). Havde han i stedet spyttet eller sparket ud efter gårdvagten, ville det ikke kunne indgå som konstituerende, men ville blive opfattet som en forstyrrelse, som støj. Her er der altså tale om, at verbalsproget er den gældende handlingsvaluta. Mellem børnene, derimod, indgår nonverbale handlinger, herunder bla. sparken og spytten, som mulige elementer i konstitueringen af sociale virkeligheder. I vandpyt­legen er det at sparke med vand på hinanden således et element, som medvirker til at konstituere den sociale virkelighed.

Begrebet handlingsvaluta bidrager til analysen på to måder. For det første muliggør det en analyse af, hvilke slags interaktionsformer, som indgår i konstitueringen af (nye) sociale virkeligheder. For at begribe hvad disse (nye) sociale virkeligheder indebærer for dem, som er del af dem, handler det, med et affektøkonomisk blik, om at undersøge, hvordan de konkrete handlinger påvirker de medvirkendes konstituerende forbindelser. Dermed skal en given handlingsvaluta ikke forstås som noget, som har en bestemt værdi, i sig selv, men det er hvordan den bliver brugt 128, som er afgørende.

For det andet gør handlingsvaluta som analytisk værktøj det muligt at have at gøre med ting, som ofte ikke tænkes sammen, idet begrebet dækker over en bred vifte af former, der kommer til udtryk gennem lyd, gestik, mimik, materialer, mm. Det er således ikke handlingens beskaffenhed, men snarere, hvordan den indgår i en given kontekst som er i fokus. Dermed kan analysen skærpe blikket for, hvilke slags handlinger, der tæller, og hvilke slags der ikke tæller. Dette er vigtigt ifm analysen af, hvad der går for sig i mellemrummene, i det upåagtede børneliv, hvor jeg med handlingsvaluta som konceptuelt værktøj kan identificere en stadig kodning og omkodning af, hvad
der tæller.

Movement, sound and people – a transnordic dialogue in progress

At the seminar The Role of Culture in a Sustainable Society – Sustainability in Art and Cultural Projects, composer Casper Hernández Cordes did a workshop, and choreographer Kenneth Flak had the role of reflecting on the workshop. This started a really interesting discussion, that we would like to continue, this time in a ‘plugged’, online version, for everyone to join, commentate and share.

Welcome!!!

Casper:  “Hi Kenneth, thanks a lot for a great collaboration / confrontation at the seminar on culture, art and sustainability. I felt we embarked on some really relevant issues, and I would like to invite you for a further development of some of the topics.

You said you liked the fact of a composer (me) choosing to only use gesture as a means of expression, as I did in the workshop/experiment. Usually I get the opposite reaction, people saying: “but what about sound??”. In fact my choice is based on the assumption that you can’t have sound without movement, so somehow movement is something more fundamental to human expression. At least, I have this idea, that non-artists are more comfortable in general using gesture as a means of expression than sound. What are your thoughts?”

Kenneth: “Hi Casper, I thoroughly enjoyed your intervention in the seminar, and, as you mentioned, a lot of it had to do with the use of compositional principles applied on different areas. Obviously, the principles you used in the seminar (mainly to do with mimicry, repetition and variation) are as fundamental to choreographic composition as they are to the organization of sound. For me as a kind of dual creature, working both as a choreographer and a composer, I am always looking for these kinds of principles that can be applied to both areas.

It is actually becoming more and more of a challenge for me finding principles that are exclusive to one domain. Right now I can’t really think of any. Obviously, dance probably has a stronger spatial component than sound, in the way that it moves around the space, but this is an advantage that has largely been obliterated by the development of music technology, with the advent of different surround sound formats. And of course, live music on actual instruments has always had this strong spatial component, especially when there are no microphones or cables around to hinder movement.

Of course, I totally agree with you that sound is impossible without movement, but then we still need to think a bit about what kind of movement we are dealing with: is it movement of the human body or for example the movement of your home stereo speakers that do what your computer tells it to? Both represent physical movement, but the difference in perception is enormous. When it comes to sound that is produced by the human body, there is absolutely no question that movement precedes sound, and then merges entirely with it for as long as the sound is produced. It is a very intimate connection, to the point where it becomes impossible to separate. And the really interesting thing (which was demonstrated very clearly in your workshop) was that even when the sound is absent, we tend to “fill in” sound where there is none. I think every dancer does this intuitively, “singing” the movement as s/he performs it, sometimes out loud. This was actually becoming a bit of a problem for me at some point, so I had to consciously unlearn it. It just didn’t look very good on stage, me hopping around providing my own soundtrack to the movement with various crappy sound effects, not even aware that I was doing it.

For the average non-artist I certainly think gesture is a slightly more comfortable area to explore than sound, but I think this depends very much on the kind of sound and movement we are talking about. I could easily picture non-artists happily whacking two sticks together, but once you ask them to use the voice things get much, much more difficult. Vocal sound abstracted from any meaning is a very tricky area for a lot of people (many artists included), somehow there are so many taboos, conventions and emotions connected with the use of the voice that most people are very careful about how they use it. This is, of course, also the case with movement. I think this is why it is important to start out with ways of moving that are socially acceptable, like the use of simple, pantomimic gestures. And even this is very difficult to deal with for people that have no training in contemporary dance or performance, as was evidenced in the seminar: there was this running commentary going, trying verbally to make sense of what was happening, what was expected of them.”

Non-verbal cacophonia in the North

As for Jamie, it seems he has two possible faces. He has a neutral, expressionless face, that he puts on, when he is somehow taken aback (which seems to take a lot). The other – which he puts on here – is this shrewd fox-like smile, which is saying something along the lines: “I know what you are trying to do, and I do have my own thoughts about it, but don’t you think I will reveal them to you. (Ha!)” The fact that the actor behind Jamie Lannister, Nikolaj Coster-Waldau, is a Dane might shed some light this binary facial language.

It is no wonder newcomers to Denmark have such a hard time adjusting to the culture. One thing is the language itself. The phonetics are so complex, that the language is a hobby horse for many linguists around the world. Danish kids seem to learn the Danish words later than other kids growing up with other languages learn their words. In consequence, learning Danish as an adult is a major challenge. On top of that, as I was saying, we have this arbitrary relationship with non-verbal interaction, where we are cautious to let as little as possible slip through.

The Danish language use, the pragmatics of spoken and written language, can be really efficient, when it comes to collaborating, and getting things done. In Danish, we have a rather small vocabulary – maybe because of the work it takes to learn the words – and a single word usually has a very limited range of meanings. Her is here. Der is there. No mistakes. A culture of efficiency, of accountability and of getting things done.

When it comes to emotional content, to person-to-person interaction, it’s another story. It is as if we had a radio jammer implanted in our bodies, that will obstruct the appropriate coding of our inner states and bodily emotions, washing the other person over with a rain of non-verbal white noise.

Danes are experts in reformatting whatever happens inside them into something unrecognizable, when it reaches the outside world. This is a culture of irony, sarcasm, and non-verbal cacophonia.

No wonder that the Danes’ divorce rate is among the highest in the world.

The un-toast – or how “the social stomach” can save humanity

Doran brings out a toast for Tommen, to which Ellaria gloomily reacts by emptying her glass on the floor, sending a defying look to Jamie Lannister, creating in the teenage lovers, Myrcella and Trystane, one of these wtf-moments about the adults being SO embarrassing.

The non-verbal element is of course very strong here, very brutal, very simple, and completely on the symbolic level. Drinking together means: we are in on this together. Refusing to drink is a very strong protest reaction.

I can’t help thinking about the role that consumption plays in our society, in Denmark particularly, it is very strong, at least. Not wanting to share a meal means you can really piss off the host. This is of course particularly accentuated when the reason for not eating or drinking is based on religious, cultural, health related, ethical or political reasons.

This is why I suggest we invent “the social stomach”. This is an implant in the body that includes

• a valve in the throat, controlled by our thoughts (or to begin with, an iPhone with the new app “iSwallow”)
• a plastic tube, parallel to our gullet
• a plastic bag, next to our stomach, and finally
• a second valve, in a hidden place, accessible while at the toilet

This way, we wouldn’t have to create these awkward situations, when with the family, where we’d have to remind them for the hundredth time that we don’t eat this or that. We can simply swallow it, and with a big fat smile on our face let the bad, unhealthy, unethical stuff pass through the body without and side effects. Then at an appropriate moment  simply going to the bathroom and flush it out. Completely acceptable and legitimate behavior. Or better: find an excuse to get a lonely moment in the kitchen, find a clean tupperware container, drop the completely untouched food there, and place it safely in the fridge. Now that is recycling!!

A positive side effect from the social stomach implant – aside from the extremely beneficial effect on the social balance in our society – is of course that we can do our duty as citizens and consume more and more, without having any impact on the health system. What with our innate digestive system, we can simply use our for what it’s there for: nutrition.