Weinberg (2005) discusses musical networks, the concept of performance as an interdependent art form. Electronics expands the range of possible interdependencies in musical performance: ‘Although acoustic-interdependent models provide an infrastructure for a variety of approaches for interconnections and interdependencies among players, they do not allow for actual manipulation and control of each other’s explicit musical voices. Only by constructing electronic (or mechanical) communication channels among players can participants take an active role in determining and influencing not only their own musical output but also that of their peers’ (Weinberg, 2005, p. 23).

Viewing musical networks with an ecological metaphor, Weinberg says that ’the network serves as a habitat that supports its inhabitants (players) through a topology of interconnections and mutual responses that can, when successful, lead to new breeds of musical life forms’ (Weinberg, 2005, p. 23). Weinberg gives historical examples of musical networks: Cage’s 1951 piece Imaginary Landscape No. 4 for twelve radios (Cage, 1951), Bischoff et al. (1978)’s ‘Network Computer Music,’ a variety of internet-based musical networks (including Whalley (2004)), and local, real-time interactive musical projects that include novel player interfaces, such as the reacTable (Jorda, 2003).

Weinberg also classifies interactive musical networks by the nature of their interconnectedness, the centrality of their control and the placement of the participants actions in time (sequential or synchronous). ‘Process centered musical networks’ can be based on social experience, creative experience or learning experience; they can also be exploratory in their interaction or goal oriented, with either collaborative or competitive goals. ‘In sequential systems ... the interdependent interactions occur in an ordered manner by turn-taking procedures. This approach is more tolerant to latency, can be easily supported by remote online networks, and is usually simpler to follow for the individual player’ (Weinberg, 2005, p. 35, emphasis mine).

I am interested in musical networks made partially or entirely of machine controlled participants. If the network participants can control how they interact, or in Weinberg’s terms, they can control the weight of their connections, they may be able to dynamically change their network between synchronous and sequential. Naturally, many sets of connection weights will result in ‘anarchy,’ while only a few will result in ordered behaviour. How can the agents learn the necessary turn-taking behaviours for ordered interaction in a sequential system? How can centralised control emerge? Weinberg’s classification of ‘process centered musical networks’ is useful in considering different situations which may or may not have the possibility of having emergent turn-taking.

Peter

References:
Bischoff, J., Gold, R., and Horton, J. (1978). Microcomputer network music. Computer Music Journal, 2(3):24–29.
Cage, J. (1951). Imaginary landscape no. 4 (March no. 2). Musical composition for twelve radios, 24 performers and conductor.
Jorda, S. (2003). Sonigraphical instruments: from FMOL to the reacTable. In Proceedings of the 2003 conference on New interfaces for musical expression, page 76.
Weinberg, G. (2005). Interconnected musical networks: Toward a theoretical framework. Computer Music Journal, 29(2):23–39.
Whalley, I. (2004). Adding machine cognition to Web-Based interactive composition. In Proceedings of the 2004 International Computer Music Conference, pages 196–200.

Sacks explores the neurology of music and gives examples of patients who have various unusual responses to music. Told in a wonderful, person-focused, story-telling manner, Musicophilia expounds on music as the wonderful back door to our minds. One man gained a sudden appreciation of piano music after being struck by lightning. Some people get seizures from music or hear music in their seizures. Most people experience getting music stuck in their head, but some have more intense musical hallucinations.

Sacks considers musicality and how musicality is actually a number of related skills. Sacks describes various cases of amusia. Interestingly, he points out that ‘forms of rhythm deafness are rarely total, because rhythm is represented widely in the brain’ (p. 99). Sacks describes neurological aspects of absolute pitch, its prevalence and origins. The effect of losing hearing in one ear is considered for two patents’ cases. Sacks relates music to vision, describing the effect that blindness can have on people’s musical abilities and also several cases of music → vision synesthesia.

Sacks tells the story of Clive Wearing, a man with severe amnesia and complete loss of all but the most transient memory. Clive experiences every moment as if he just woke up, except that he still remembers his wife and he can still play music! Music must be remembered differently to other experiences. Sacks describes the interactions between speech and music and how some people can lose the ability to understand or produce speech, but still be able to sing songs with words. Some aphasic people can be taught to speak again with the help of singing. It seems to me that the brain has two complicated systems, one for language and thought, one for music and feeling.

Some people with Tourette syndrome can channel the explosive energy of their ticcing into rhythm. Sacks describes a drum circle of people with Tourette syndrome who tic out of time naturally, but come together in controlled musical expression when they play. Sacks talks about how music therapy can help people regain motion of their limbs. Sacks speculates about the biological importance of music:

The embedding of words, skills or sequences in melody and meter is uniquely human. The usefulness of such ability to recall large amounts of information, especially in a preliterate culture, is surely one reason why musical abilities have flourished in our species. (p. 239)

Speaking of the importance of rhythm particularly, Sacks says:

What enables us, for example, to bind together the sight, sound, smell and emotions aroused by the sight of a jaguar? Such binding in the nervous system is accomplished by rapid, synchronized firing of nerve cells in different parts of the brain. Just as rapid neuronal oscillations bind together different functional parts within the brain and nervous system, so rhythm binds together the individual nervous systems of a human community. (p. 247)

People with parkinsonism struggle to initiate motion and to move in natural time and rhythm, but music and music therapy can sometimes help them to move more naturally. ‘It is music that the parkinsonian needs, for only music, which is rigorous yet spacious, sinuous and alive, can evoke responses that are equally so.’ (p. 258)

Music appears to some people in dreams, frequently in more detail than their waking musical imaginations can afford. On a personal note, I have had dreams with detailed music similar to what Sacks describes. Some people can understand musical structure but do not emotionally appreciate music, while others connect with music emotionally while having amusia otherwise. With regard to the power of music to connect in moments of grief, Sacks says:

Music, uniquely among the arts, is both completely abstract and profoundly emotional. It has no power to represent anything particular or external, but it has as unique power to express inner states or feelings. Music can pierce the heart directly; it needs no mediation. (p. 300)

Sacks describes a man who lost all ability to feel emotion in an accident who can sing with apparent emotion, and another man with autism who wrote ‘AUTISM DISAPPEARS’ in Sacks’ notebook while he was singing. Some people with frontotemporal dementia display increased musical or other artistic behaviours. People with Williams syndrome are frequently moved strongly by music and can be articulate and musically talented while being disabled in other ways. Music can cheer up people with dementia, affecting patients’ moods even after the music has stopped.

Peter

You can connect up audio signals using the ChucK operator, =>, then when time advances, you get sound. For example, this program will play a sine wave for 10 seconds:
SinOsc => dac;
10::second => now;

So in some ways, ChucK resembles VHDL you are building up a set of connections and rules for those connections. Also similar to VHDL, you can adjust time.

The really mind-bending part comes with the concurrency though. You can run multiple 'shreds' at once, where time is independently controlled in each shred. ChucK schedules all the times right down to the sample so that they all happen at the times you specify.

I'm a bit disappointed to see some of the bread-and-butter programming language features are still in development: there are no asserts, you have to use a command line option to import/#include a file.

But it's fun!

Peter

Of course, I'm in the business of building better and more algorithms for music and other purposes, but this is the kind of hardware platform that I'd be keen to demo algorithms on.

You can read more on the artist's website.

Peter

Towards the end of the talk he makes the interesting point that in absence of a particular reward, a heterogeneous population of simulated robots ends up favouring those kinds of robots that can self-replicate.

Peter

The Unreasonable Effectiveness of Mathematics by Richard. W. Hamming (of Hamming distance and Hamming window fame). Originally this article appeared in The American Mathematical Monthly Volume 87 Number 2 February 1980.

It's a bit of a long read, but here are some highlights:

Just as there are odors that dogs can smell and we cannot, as well as
sounds that dogs can hear and we cannot, so too there are wavelengths
of light we cannot see and flavors we cannot taste. Why then, given
our brains wired the way they are, does the remark "Perhaps there are
thoughts we cannot think," surprise you? Evolution, so far, may
possibly have blocked us from being able to think in some directions;
there could be unthinkable thoughts.

Having given four widely different examples of nontrivial situations
where it turns out that the original phenomenon arises from the
mathematical tools we use and not from the real world, I am ready to
strongly suggest that a lot of what we see comes from the glasses we
put on.

Mathematics has been made by man and therefore is apt to be altered
rather continuously by him. Perhaps the original sources of
mathematics were forced on us, but as in the example I have used we
see that in the development of so simple a concept as number we have
made choices for the extensions that were only partly controlled by
necessity and often, it seems to me, more by aesthetics. We have tried
to make mathematics a consistent, beautiful thing, and by so doing we
have had an amazing number of successful applications to the real
world.

Science in fact answers comparatively few problems. We have the
illusion that science has answers to most of our questions, but this
is not so. From the earliest of times man must have pondered over what
Truth, Beauty, and Justice are. But so far as I can see science has
contributed nothing to the answers, nor does it seem to me that
science will do much in the near future. So long as we use a
mathematics in which the whole is the sum of the parts we are not
likely to have mathematics as a major tool in examining these famous
three questions.

It makes me feel slightly less of a complete nutcase for holding some less-than-conventional ideas on the philosophy of science and mathematics. On the other hand, maybe Richard Hamming was a nutcase too.

Peter

So the question is: does the channel length affect the turn taking?

If you're totally up to scratch on statistical tests, then you probably won't learn much from this post. It's actually mostly a reminder to my future self for when I need to remember how to do this same thing agin.

The first statistical test that I employed was drawing a graph:

For that it looks kinda like maybe turn taking is not related to the channel length. But even averaging 30 independent runs for each channel length has left me with means that are still slightly different. How worried about those small differences should I be?

There are two different analytical statistical tests that I could use: the Mann-Whitney U test, or Student's t-test. Student's t-test assumes the data are normally distributed, which is usually not exactly the case. But for large sample sizes, a t-test is robust to small-ish deviations from a normal distribution.

The Mann-Whitney U test has the advantage of not assuming a normal distribution, but it the downside that it assumes the variances in the two groups are approximately equal. For some varieties of the t-test, the same assumption is made. The Mann-Whitney U test also has the significant pragmatic downside in that it's less common, and so it's less likely that people will be able to follow your paper if you use it.

With a t-test, you start with the null hypothesis that two distributions are the same. Then you calculate a t statistic value and a number of degrees of freedom using the equations from Wikipedia. I fooled around with the different possible assumption sets, but I settled on assuming that my equally sized samples had equal variance, mostly because Python's scipy.stats.ttest_ind() function made those assumptions.

Once you have a t value and n degrees of freedom, you calculate a one-sided p-value. A one-sided p-value is taken by integrating the t distribution probability density (with n degrees of freedom) from the t value you calculated until infinity. You can do this in Python with scipy.stats.t.sf(t, degrees_of_freedom). If you want a two-sided p-value, multiply the one-sided p-value by two. You'd use a one-sided p-value if you wanted to know if one of the distributions had a greater mean than the other, but use a two-sided p-value if you just want to know if they're different. scipy.stats.ttest_ind() will actually calculate a two-sided p-value for your along with a t-value.

I computed the t-test two-sided p-values comparing the sample with a channel length of 1 to the other 7 channel lengths in the graph:
1 vs 2: 0.07
1 vs 3: 0.11
1 vs 4: 0.15
1 vs 5: 0.13
1 vs 6: 0.17
1 vs 7: 0.18
1 vs 8: 0.01

The p-values are the chance that you would get values at least as different as you did if you assume the null hypothesis is true. So it's reasonably likely that the data for a channel length of 1 come from a different distribution than the data for a channel length of 8. But there is a 1% chance that they do both have the same mean.

In this case, even if the channel length makes a little difference, I'm going to get rid of it. But maybe not in another case.

Peter

Distributed Fading Memory for Stimulus Properties in the Primary Visual Cortex - actual data from cat neocortex showing reservoir computing sort of responses.

State-dependent computations: spatiotemporal processing in cortical networks - fascinating review of a large body of research including nice discussions of high-dimensional trajectories.

After discussing the goal of boiling down a problem to its minimal required complexity with Phil Bones and Allan McInnes, I was reminded of the following paper comparing selection mechanism in GA. The point of the paper contains some survey-like discussion, but I admire the simplicity of the system they study. The system choice makes the selection behavior easy to illustrate without extra complexity.

A Game-Theoretic Investigation of Selection Methods Used in Evolutionary Algorithms -- Ficici, Melnik, and Pollack

I guess it's always more impressive to demonstrate learning algorithms on big expensive hardware. But having big hardware is not essential for having great algorithms. I'm sure there are ways to demonstrate great algorithms using relatively primitive hardware.

Peter