This web-page documents my final project for the Transvergence Studio+Seminar Winter 2005 course [UCSB MAT 594C/D W05], subtitled 'Virtual Environments as Spatial Music', along with thoughts, ideas and lateral paths of investigation.
The stated course objectives were to create a project that engages with:
I began by engaging with the idea of organised sound generation according to genetically inspired algorithms.
Inspired by Strogatz' description of organic synchronisation in SYNC, my first practical study consisted of networks of oscillators that spontaneously self organize. Using the poly~ parallel processing framework in Max/MSP, I instantiated a set of oscillators each with randomly distributed starting frequency & phase. Each oscillator voice (in the example image below, there were 18 voices) listens to a combination of the two neighbouring voices, creating a daisy-chain circular network. Each voice compares the differential of its audio with that of the sum of the two inputs in a simplistic attempt to monitor phase differences, then adjusts its own frequency up or down according to the phase differences detected. Though crude, synchronisation does frequently occur.
The system is made more complex by introducing a variable delay in the network, slowing down the emergence of synchronisation, and by using more complex waveforms that simple sine-waves. More complex waveforms make radical differences to the terminal steady states of the system; some evolving towards particular frequencies (perhaps some kind of Nyquist foldover is causing this), some evolving towards pairs of frequencies, some towards very slow oscillations of system state. Interestingly, some of the terminal frequency states appear to hold harmonic relationships between themselves, however this is not universally the case.
The screenshot above is from the fourth version of the author's oscillator
synchronisation patch (source code here), showing
18 parallel oscillators using a waveform with complex harmonics. It is interesting
to note the four similarly sized humps in the FFT spectrogram. Below is an
mp3 recording of the patch, in which I switch between different waveform
shapes every 20 seconds or so.
Though it is fascinating that the waveform shape has such a strong effect upon the terminal stable states, it is not clear how phenomena and behaviour are emerging in this non-linear system, and so I resolved to begin again from the most simple ideas.
During
discussions of genetic algorithms and the search for genuinely new territory
rather than the algorithmic exploration of existing territory (i.e. speciation
as opposed to hybridization), I was reminded of the concept of 'strange loops'
I had encountered in reading Douglas Hofstadter's 'Godel,
Escher Bach'. A strange loop exists
in a system when there are several layers of operation, the higher layers
being built upon the lower, but in which the higher layers are capable of reaching
down and changing the structure or rules (i.e. the topology) of the lower
levels. Hofstadter elegantly points to Escher's Drawing Hands as a graphic
metaphor. Barring the most simplistic implementations, such a system is nonlinear
and unpredictable, and is capable of producing emergent phenomena such as
speciation.
Part of my aim was to avoid simply creating an interesting algorithm and mapping it arbitrarily to some pre-defined synthesis architecture or MIDI data, an approach common in 'algorithmic composition', but to rather find an interesting algorithm that directly generates organised sound (in the form of digital samples) as an integrated process.
One way to consider composition is as a large-scale organisation of sound (e.g. from phrase to form), whilst synthesis is normally concerned with the organisation of sound at a much smaller scale (usually individual samples). Curtis Roads' discussion (UCSB Composers' Forum, Spring 05) of a multi-scale approach to composition echoed Stockhausen's notion (in the 'Four Criteria of Electonic Music') of the continuity of time-scales in Music. Thus from the atomic (for computer music, digital samples) as time expands, sonic process result in timbre, pitch, rhythm, note-form etc through to phrase, section and movement and beyond, exemplified in Stockhausen's electronic music composition 'Kontakte'.
What I find interesting is that phenomena at different time-scales can be superimposed (using signal addition, or mixing) in a single stream, just as waves can superpose each other without interfering in each others' structure. Alternatively, phenomena at different time scales can be applied to each other (using signal multiplication, or amplitude modulation). What would be more interesting would be the possibility of exploring the region between complete independence of addition and complete interdependence of multiplication, in a time-variant manner.
Any feedback process with some interdependent properties at different time-scales can be described as a strange loop, as macro scale (high level) changes are dependent upon micro scale (low level) changes, yet the macro scale changes can change the nature of future micro scale phenomena. A strange loop feedback system would therefore constitute my core process for the project.
By analogy, a strange loop feedback system is somewhat akin to a resonant model in which the shape and material of the resonator changes over time as a result of the resonant sounds it produces. An idea might be to represent the system as a virtual model shape that might have that kind of resonant response, and which changes over time with the system. The kind of deconvolution math for an accurate model is beyond the scope of this project, but I could attempt a simplistic model based upon pipe lengths or vibrating taut strings for example.
Of course, a strange loop is no garauntee of interesting results. In fact it is no garauntee of results at all - a feedback system may tend to terminal states of zero or unity gain, or indeed white noise, which are all (certainly from a musical point of view) the least interesting results possible. The system described so far could be implemented in many different ways; there are still many decisions to be made.
We have dealt with issues of poetic constraint in our class discussions. A poetic constraint (often associated with the Oulipo) is an aesthetic yet systematic constraint on a modality (beyond the convential and inherent constraints of that modality) made voluntarily before commencing a work. I couldn't help but fancifully consider writing a program to ask the computer to give me rules to follow, perhaps using the structure of metaphor (what is to click as 3 is to green etc). Marjorie Perloff describes a constraint as a commodious way to move from language to writing.
As wasn't sure that I even had a language yet, the constraints I made were relatively concrete. The aims, most simply, are as follows:
Viability was discussed in the seminars as the true fitness judge in evolution. No matter how powerful a new development may be, if it cannot persist over time it is irrelevant. Regarding viabilty for a feedback system, one apparently simple solution is to track the audio output level of the system and scale it up/down accordingly (i.e. a filter driven by an envelope follower) in the feedback to maintain a healthy signal level.
In practice this turns out to be not so simple - there are many different algorithms to track a signal level (absolute value, RMS, etc), and all envelope followers must have an response curvature with respect to time. If the response resolution is a single sample, the output waveform will be a flat DC line, i.e. silent! By lengthening the response durations, harmonic distortion of the signal descends from the Nyquist frequency down, eventually to the inaudible frequencies, whereupon the classic 'pumping' sound of audio compression can heard. The curvature of the response with respect to amplitude and also to time will also shape the resultant sound.
When inserted into a nonlinear feedback system, small changes in the sensitivities and behaviours of these correcting level filters may drastically change the behaviour of the system itself. For coherence therefore I have included the parameterisation of these corrective feedback level filters within the system evolution algorithm itself. Thus the corrective filter parameters themselves are changing and yet also subject to the viability rule. Put another way, they are included in the organism, not a feature of the environment.
I tried assigning parallel processing and using a parameter to control spatial position (usually stereo pan). Spatial pan may be easier to extend to many more speakers without requiring more computing power. I also implemented prototypes using parallel processing at full stereo separation with crossover in the feedback loop, which suprisingly resulted in more interesting moving spatial images than using stereo pan, and furthermore avoided the additional complexity of driving a third parameter type in the system.
Regarding the generation of changing results, I have explored parameterisation of different delay & envelope following systems in the feedback loop, mainly comb filter delays, granular delays and flange delays. These delays may shape the sound at different time scales (from micro through to phrase, depending on the maximum length of the delay) according to the parameters controlling them. Where possible I have used algorithms with a minimum of parameterisation.
The reason for choosing comb delays in the final project was that they offer a simple model for many DSP functions, and are therefore generalised and expressive. The balance between delay length, feedforward ratio and feedback ratio parameters mean that a comb filter may act as a generalised FIR or IIR filter or as a single-tap delay line, or anywhere in between. By modulating these parameters they can recreate chorus, phasing and flanging effects (as well as the typical comb-filter sound). By placing several in parallel or series, comb filters can generate reverberation and short series convolution.
Regarding
the generation of interesting results, I have attempted several different approaches.
First I begain searching for interesting harmonic relationships between properties,
on a test program in Java (source code here and here).
This was in part inspired by the class discussion regarding harmonic ratios
in design and architecture. Pairs of geometric lines are compared for divisions
with negligible remainder between their respective angles, lengths etc. What
was suprising is that for a set of 50 randomly placed lines, and a maximum
harmonic ratio of 10, a harmonic relationship could be found between most lines
with a tolerance as low as 0.1% (see example to right; similar relationships
are represented by the same colour). The aim was to develop an algorithm that
retained the strong relationships and removed the weaker ones, as a kind of
hill-climbing algorithm in 2D that could then be diagrammed and translated
to 1D (for audio) and 3D (for OpenGL). However I found that the results tended
not to parry with perceptually interesting relationships, a considerably more
complex problem. There are many other graphic features to search for, such
as whether n points can fit on an arc or bezier spline, or the ratios of areas
enclosed by sets of points, in a seemingly endless rise in complexity. I believe
this might be a fruitful area to explore in the future (the bold attempts to
create a theory and taxonomy in Kandinsky's 'Point and Line to Plane' might
be an inspiration to follow). There is a further problem, in that this method
assumes that similar harmonic structures are perceivable in sound. Simple harmonic
relationships are clearly perceivable in pitch relationships, however there
is much debate over whether the famous Golden Section for example is actually
perceivable in macro form or not. Our sensations of passing time are far from
uniform, and are not traversable, in contrast to our sensations of space!
In
a similar way I also looked at using correlation and autocorrelation to measure
the similarity of signals and use this as a source of control data. Correlation
can compare two data arrays or signals and return an index of simliarity at
a particular instant; comparing a series of instants can indicate the periodicity
and stability of a signal. Autocorrelation can also be used to separate the
steady and noisy components of a signal. These are usefully abstract properties
to be working with! Having built a simple Java/Max/MSP example to test correlation
(and in the process also convolution) as an analysis technique, several problems
became apparent. Firstly, the process is computationally expensive, too much
so for real-time use in my development environment. In addition to expensively
long summing (e.g. at least 2210 samples to detect a 20hz period at a 44100khz
sampling rate), correlation would need to be normalised for comparison (requiring
expensive square root calculations). Furthermore, it would require interpolated
resampling to compare signals at different time scales, which is specifically
what I would be interested in doing. Thirdly, I am not sure how effective correlation
would be on dynamic signals, bearing in mind the potential problems of phase
difference (ignored in correlation) and edge boundary windowing distortion.
I
also looked at the fascinating phenomena arising from simple systems in Valentino
Braitenberg's 'Vehicles:
Experiments in Synthetic Psychology', in which simple algorithmic vehicles
in a plane can suggest very complex behaviour. I implemented the ideas suggested
in the first two chapters of the book as scripts in the Processing environment
(source code here). Although these experiments
showed early promise in generating interesting results, this direction was
taking me away from the original idea of an algorithm that directly generates
audio, rather than an algorithm mapping. Furthermore the ideas in the Vehicles
book are a complex field in themselves that warrant more time and attention
possible for this project.
Following
a suggestion by Marcos Novak,
I tried making an algorithm that simply aims for diversity in values. This
was implemented using JavaScript in Max/MSP (source code here).
A matrix of parameters is compared on a per column and then a per row basis,
and a randomly chosen parameter is then transformed to increase the entropy
of the matrix as a whole. Parameters begin with a value of 0.5, and gradually
all tend towards the limits of 0 or 1. When a parameter hits either limit,
it is reset at 0.5. The net result is a matrix of complex data which is continually
changing by gradual diversification and occasional abrupt changes, and when
applied to synthesis control paramters, produced dynamic sounds. The diversification
algorithm is used in the final project to control the delay lengths of the
parallel comb filters.
Whether these results are interesting is of course to some degree subjective, and the reader is invited to listen to some of the audio excerpts below to judge for his or her self. I am not sure whether the phenomena can be said to include evolution and speciation. There are certainly events that occured in some of my recordings of the algorithm that exceeded my predictions of the system behaviour; and frequently the progression into such events can be heard as coherent. On the other hand, the system at present remains quite volatile, so phenomena rarely persist for extended periods of time.
Example 1: (4 stereo separated pairs of comb filters, up to 4 seconds of delay):
Example 2: (granular delay of up to 20 simultaneous grains, stereo pan on each grain, some reverberation added afterwards):
Having a system that satisfies my constraints to a reasonable degree within the time available, I began to consider how it may be coherently extended to a multi-modal system relating to the course topic of virtual worlds as spatial music.
Building a correlation between an audio and spatiovisual process, whilst maintaining topological similarity, is not trivial. The aural domain has a parameter space of n dimensions - but the nature of nonlinear feedback is that the system is not completely described by these n dimensions, the audio stream itself is required. The ideal system would therefore be a complex feedback network with strange loops apparent in delays and corrective filters operating through a spatial audio-visual world of three or more dimensions.
The path I chose to follow was to embed a transformation of the audio data into a visual domain, perform analysis on this video data, and use this to feedback into the audio chain. By embedding the audio - video translation as a step within the strange loop feedback process, the system fundamentally becomes a unified whole rather than two modally distinct systems glommed together.
The low level incompatibility between audio and data matrix (for video and/or geometry) is that audio is a one dimensional stream (or several one dimensional streams) at a fixed clock rate, while data matrices may be N * M dimensional, but operate at an asynchronous clock rate several degrees of magnitude slower than the audio rate. Thus finding the means to exchange data between these two domains with minimal loss is a serious challenge indeed. I should clarify, when I say minimal loss, I mean that the matrix representation maintains qualities important to the sonic diversity and feedback behaviour (such as loudness, spectral weighting, noisiness, stability, extent of sudden change, etc).
The approach I took was to have three triplets of audio delays with distinct delay ranges for each, and to write out the contents of each delay line as a single row of a video matrix, where each of the triplet delays is mapped to red, green and blue planes. More planes could have been used, but at the loss of easy visual appreciation of the system behaviour. Thus the longer range delays are represented by red, the shortest by blue, and each RGB row represents the contents of the triplet delays at different rates. A square 128 * 3 matrix was chosen where the contents of the top row represent the contents of the first delay triplet, the middle row represent the second delay triplet, and the bottom represent the third. When interpolated to a 128 * 128 matrix, it looks as in the following examples:
Analysis of the distinct colour planes & rows is performed to track the median and the range. The inverse of the median is then used to calculate the parameter controlling audio feedback amplitude (thus maintaining a viable stream by suppressing loud events and amplifying quiet events), whilst the inverse of the range is used to calculate the curvature of changes to feedback delay length (thus homogenous signals with narrow ranges are transitioned away from quickly, whilst diverse signals with broad ranges are transitioned away from more gradually). Upon hearing the results I was happy that this achieves a satisfying balance of interesting change whilst maintaining viability of the audio delay signals; however there remains a great deal of scope to apply distinct analysis procedures to the video matrix which could be used to drive other synthesis parameters.
To continue in the trans-modal development from the audio feedback chain, I then further process this video matrix into a three-dimensional geometry. As a first step, and in order to mirror the model of a feedback system within a feedback system, I applied a convolution feedback process to the video matrix data. At present this involves fixed parameters of feedback, feedforward and spatial bleed on the matrix (performed at the system video framerate of approximately 30 fps); ideal further extensions of the system would allow these parameters to be driven by analysis of the resultant signals.
The RGB matrix is remapped to an ARGB matrix to be used as a texture map in an OpenGL render space, mapping the blue plane to the alpha channel, the green plane to the red, and the red plane to green and blue (the choices here were based on experimentation with different mappings, with the above mapping providing the most aesthetically pleasing result for the author).
This texture map is applied to a complex geometrical shape also constructed from the video matrix data, based upon a spherical model of 128*128 triangles, whose radial displacement is mapped to the luminance of the input matrix. Further mathematical processing of the input and output data lead to a pleasing effect of the shape folding back upon itself, and smoothened transitions.
Total 1:39" [4.4Mb]
At present, there is no further feedback from the resultant geometric shape to the audio and video feedback processes, though this would be the ideal for the achievement of the author's intention regarding the realisation of a virtual environment as spatial music.
I propose that an interesting implementation of spatial analysis for control data would benefit greatly from taking into account the represented point of view, that is to say, the location and direction of the virtual camera within the geometric shape. Not only would this make a consistent tie between user experience in spatial and sonic modalities, but may also aid the sense of presence within the space through the sense of affordance. However, not only would this be a complex problem to tackle, I also wonder whether the level complexity already present in the underlying system would obscure such relationships and affordances; I suspect that revision of lower and earlier levels would be necessary first.
In this way the development reminds me of counterpoint composition, in which the composer must bear in mind and revise many simultaneous levels (parts) at many different scales of time, and will often progress forward in fits and starts at all levels together. Intuition suggests to me that drawing from the spatial form and viewed representation certain harmonic and categorised relationships and using these as the targets in the diversification algorithm (rather than simply aiming for diversity) might be an wonderfully strange loop to try.
Navigation in the world was considered vital to promote the sensation of presence. In practice, the capacity to move around the world lead to confusing and disorienting movement (partly due to incorrect application of quaternion functions), but also partly due to the ease in which one can leave the world entirely. Instead I mapped navigation onto a polar sphere within the world boundary, and orientation being a delayed average perpendicular to location, such that you may move around, but may not leave, and are always looking towards a point near to the centre.
As suggested above, I considered the role of navigation in changing the behaviour of the system beyond the choice of viewpoint represented; I thought it was important to consider the role of a navigating user in the fitness function of the developing world. One other possibility considered but not implemented in my project was to link user navigation control to the maximum step size in the diversification algorithm (including the interesting possibilty to map diversification into reverse, i.e. to ba able to homogenize the system state).
Within the wider context of the Transvergence class group, all projects were intended to be able to stand alone independently, or interact with the other projects, providing both inputs and outputs. Primarily this was considered to be implemented using the OpenSoundControl protocol, though taking into account the nature of my project, I also considered audio and/or video streams as possible points of exchange.
For the final presentation, my project is able to take audio input from the other projects in the moment of transition from other projects to my own; this audio is taken as a kind of seed input to the delay feedback processing, thus the world transitions may occur in a somewhat organic manner. My project is also able to broadcast the current feedback control parameters (delay length, feedback level, rate of change) for each of the 9 delay lines using the OpenSoundControl protocol, for the interpretation thereof by other participant projects.
As a later development in the group project, it was suggested that we embed each participant's world into a larger universe framework, with the possibility of moving from one world to another, and with objects or phenomena in one world having a related impact in another. The realisation of a universe system with the facility to transition from one virtual world to another proved a significant technical hurdle, and in the time available cross-world causality was not implemented.
Download the Max/MSP/Jitter source files of the project here (20kb).
During the course we have dealt with a number of fascinating ideas in the form of seminar discussion, which have been partly inspirational for the project and also partly inspired by our work. Rather than present the material covered and my own thoughts and work upon these topics, I have embedded those thoughts that relate more directly to the practical elements of the studio project description above, and included some of the more outward reaching results and ideas in the sections below.
A few of the ideas in the project developed from the material found after being asked to research upon three MacArthur prize winners.
Jill Banfield pioneered a new field of science called geomicrobiology, studying the role of micro-organisms in the development of geological and environmental phenomena; which resonated with my initial idea to inter-relate microsonic processes with macroscopic form in electronic music.
Stephen Wolfram is a renowned scientist and mathemetician, author of Mathematica, and a pioneer of complex systems and cellular automata research. The relationship to my project work is fundamental, though I have not been acquainted enough with his own work to find a particular interface with the Transvergence project yet.
Stephen Jay Gould's theory of Punctuated Equilibrium states that organism development is stiff and unyielding yet with have sudden large breaks at the point of speciation. I find in this a suggestion of a truly interesting development for my project would be to merge the material and the grammar. At present, the formal rules of the system are relatively fixed, all that changes are the parameters, and the audio content itself. If it were possible to derive the formal rules from the audio content as well as the parameters, then a genuine kind of speciation might emerge. Of course, this will be an enormously difficult idea to put into practice!
Regarding the MacArthur system itself, it suggests to me a kind of altruistic demi-god figure, with the power to shape the process of history and the evolution of our ideas by carefully choosing particularly potentialised nodes (i.e. the winners) to empower. Of course it isn't really playing God as such, since the MacArthur system is as much a part of nature as the 'flu bug and pop music is; however it does slightly shift the environment or rules of the system in which we exist. Broadening a view in this manner makes the strange loops evident in life easier to appreciate.
In seeking to produce a work of impact, the group discussed what we mean by rarity, by interestingness, and by beauty (in terms of form, or sound). Constructing a simple algorithm to generate complex, interesting audio is not easy. Looking back over the process of deriving my project, I can see it now as a kind of sculpting method. As the project was derived, the various forces in the algorithms are modulated in order to prevent them from becoming overbearing, until a complex balance is achieved. From a stream of audio to a persistent stream of audio to a constantly changing multi-channel stream to a stream with change at many different time scales to a stream with emergent harmonic properties (this ocurred as a natural byproduct of resonance in parallel delay lines) and onward towards achieving something musical. From the musical perspective, the next sculptural steps I would suggest are to include longer macro-formal harmony and momentary silences.
Of course this ties into the idea of beauty as 'that which by adding or taking away would make it worse' suggested by Micael Reese, which in turn suggests the peak-finding in evolutionary phase space. In my opinion Reese's idea presupposes that you know all the dimensions and transformations possible to be applied (assuming those perceivable to not be infinite), or at least that we are capable of appreciating these dimensions and transformations (even if we don't understand them). Whether this is a tenable presupposition or not I have no way of knowing.
A breakthrough in development came when I thought of mapping the contents of the delay to a row of a matrix, rather than mapping audio as it occurs to the row of the matrix. That is to say, the rate of movement of the 'writing head' across the row is scaled to match the duration of the delay, or put another way, the notion of time in the matrix row is relative to the delay scale, not an absolute sample rate. Doing this allows many kinds of analysis to be performed on the row contents that relate strongly to the contents of the delay rather than to some arbitrary rate; this is particularly appropriate as the future behaviour of the system is much more closely tied to the contents of the delay lines at any moment. There is ample scope for applying further analysis and feedback at this layer, such as subsequent frame correlation to track variability, colour processing to find relationships at different delay scales, etc.
The breakthough was suggested by considering a delay line as a memory containing data to be communicated; and in turn suggests further development towards the audio signal as grammar approach. A delay line cannot maintain more information than can fit in the delay length, and usually will actually lose information over time through any shaping process recursively applied as the delay repeats. However, if information is being piped in from another network (e.g. a different delay line) then this might not necessarily occur. When delay lines are paired one will tend to dominate the other, however if the lengths and/or feedback ratios are dynamically changing, then the rules of the system are variant and no terminal solution (i.e. steady state) can be found - in fact the network may jump from one qualitative state to another. At this point there is genuine content creation occuring, i.e. emergence.
Emergence was originally proposed by Morgan to describe evolutionary development, and expresses the way in which knowing the material form of a thing may not tell you everything about how that thing might behave, for example. Emergence is holistic and anti-mechanistic in the claim that not all that exists can be deduced from a single unified theory; higher level perspectives may be necessary to understand important secondary qualities.
A fractal can be modelled using less information that chaotic noise, but only by virtue of using different levels of modelling (the strange loop). Consider the simple sinewave tone, a balance between two forces with time separation. Like any waveform, the sine contains information even at the moments when it is at zero amplitude, because at this point its derivative is at a maxima. In fact the derivative of a sine function is itself a sine (and so on ad infinitum); an example of fractal self-similarity in a non-structural dimension. Creative work involves shifting perspectives. Strange loops permit non-orthogonal dimensions, scale-relative dimensions, non-homogenous dimensions, exactly the kind of dimensions to be dealt with in multimodal composition.
An idea suggested in the course of a distinction between topology and geometry. Topology is that which is invariant under rotation and translation, and it was suggested that this embodies the primary form or character of an entity, whilst geometry is the quantifiable, perceived phenomenon. The distinction is repeated by analogy as qualia and quantity, and as discrete and continuous. In fact the distinction can be seen in all aspects of life, and yet these apprently separated concepts are always intertwined, both actually and causally. The causal intertwining is the kind of strange loop phenomena I had studied in undergraduate Philosophy, and which I was interested in exploring in practice for this current project.
During development I noticed that distinctions between continuous and discrete signals can be highly relative. At the level of the sample, digital audio is discrete, however in practical terms it can be considered a continuous signal; we cannot hear at the sample rate (excepting esoteric counter-examples). In contrast, the rate of update in video processing has normally three to four orders of magnitude less temporal discretion, and is furthermore not a stable rate.
When different scales are close, highly unpredictable results can ensue. When different scales are distant enough, the phenomena at the larger scale can be taken almost as a fixed environment (i.e. using discrete concepts) at the smaller scale, whilst phenomena at the smaller scale can be understood and predicted statistically (i.e. using continuous concepts) at the larger scale. Having relationships where the scales relationships can change is perhaps the most fruitful area to explore of all the ideas touched upon in this project.
Another metaphor for the distinction is that between solid and liquid states, yet these can also be relative (glass is a slow moving liquid). Between solid and liquid lies the interesting region of phase transition, which is both discrete and continuous, stable yet evanescent.
The conclusion I am drawing is that what may appear to be a topology, a discrete fact, a fixed rule under transformation, is only so from a particular set of perspectives. Broaden the perspective (change the scale), and the invariance becomes less consistent. By analogy consider theoretical physics - what applies at one scale (of space or time) breaks down at another. The reason is that any perspective taken involves modelling, which in turn demands an abstraction; and an abstraction by its very nature involves cutting the continuity between chosen elements. The distinction between a good and bad abstraction is simply how irrelevant the cut in continuity will be at the scale at which you are working. What at one time was considered a constant may later be considered part of a relationship. Thus the model of gravity in Newtonian physics is a good abstraction for many practical purposes, but useless at the level of the quark.
Fluidity in the choice of perspective/model/abstraction/scale enables the creative movement between levels, systems, dimensions etc, and the scope to understand and make use of complexity and strange loop causality; and to find ways to discover new fields from those that are currently known.
That there is no simple correspondence between form and function in much of life's complexity leads us to construct abstracted generalisations labelled with symbols. The scientific project is a temporal phenomenon, building upon and revising its historical foundations - even the axioms are historical, moderated in a temporal strange loop (the parallel to Gould & Kuhn's evolutionary evolutions may help clarify this). My belief is that the objective and subjective are never orthogonal, because the supposed inviolate rule that divides them is never complete.
I found the challenge to not simply pair up but to genuinly inter-penetrate different modalities complex but highly rewarding, and it has led to insights and understanding of inter-relationships of scale, dimension and discretion. I don't know if my project is objectively useful to the world as such, but I do think that the ideas touched upon and suggestions made may help indicate productive directions for future development. Though it is of course impossible to predict, it seems likely that these directions may lead to important knowledge about our condition in the future, and not just engaging artwork. I find the potential for this kind of interface between philosophy and practice vital.
Is coherence in structure autonomously recurrent because it is meaningful, truth-bearing, beautiful etc, or simply because it is simple?
Why should we seek explanations in ever smaller particles? Why do we usually assume that logical causality is only bottom-up?
Can agents in a complex strange loop network be used productively, and can they learn to use us?
Bossomaier and Green, 2000: Complex Systems. UK: Cambridge University Press.
Braitenburg, Valentino 1986: Vehicles: Experiments in Synthetic Psychology. Cambridge, MIT Press.
Escher, M. C., 1948: Drawing Hands.
Gardner, James, 2003: Biocosm. Canada: Transcontinental.
Hofstadter, Douglas, 1979: Godel, Escher, Bach: An Eternal Golden Braid. UK: Penguin.
Roads, Curtis, 2001: Microsound. Cambridge: MIT Press.
Stockhausen, Karlheinz, 1989: "Four Criteria of Electronic Music", in Stockhausen on Music, Maconie, R.. UK: Marion Boyers.
Strogatz, Steven, 2003: SYNC. USA: Hyperion.