Matrix Alignment
Ron Pellegrino, February 6, 2002

What follows is a set of three of my posts to the Metaesthetics List on the subject of matrix alignment, an approach to thinking about relational possibilities for complex multidimensional matrices. It's an approach to communication that's central to my work in the electronic arts. To dig deeper into what was happening on the METALIST at the time of these posts you can access the archives of the list by clicking here.

Post One:

From: Ron Pellegrino <>
Subject: METALIST: Matrix alignment
Date: Wed, 20 Feb 2002 22:42:11 -0800

In the Pribram thread:

Carl Edwards wrote:

>>It's obvious to us all (partly due to Pribram) that the signal processing
>>centers of the brain have similarities in the way they decode their inputs
>>and encode for memory/processing (how could it be otherwise). That they
>>share resources/have overlap is, these days, common sense. We refer
>>to both bandwidths (sound and visible light) as spectra and we use the
>>same basic tools to analyze events in them (in our brain or in our

Pellegrino responded:

>I'm not sure what you mean by "the same basic tools". Do you mean
>frequency, amplitude, phase, and envelope analysis? Or matrix
>alignment? Or what?

Carl Edwards wrote:

>Hmm, what's matrix alignment? I'm going to have to look that up. =)

Pellegrino's response: Some thoughts on matrix alignment:

The quotation is from Bob Seiple's post on Harmonics and Receptive Fields [that's in reference to Karl H. Pribram's work]:

"[the internal architecture] of the receptive fields of visual cortical neurons can be described in terms of spatial frequency. Recordings of axonal impulse responses of the cortical neuron show that the stimulus that best engages these cortical neurons is a (sine wave) grating (composed of regularly spaced bars of widths equal to those of the spaces), which is drifted across the visual field. The spatial frequency of the gratings that engages the spatial frequency of the receptive field is determined by the width of the bars making up the grating and the spacings between them. The range of spatial frequencies to which the cortical neuron responds determines the bandwidth of the tuning curve. This bandwidth is approximately an octave (+/- 1/2 octave) (see review by DeValois and Devalois, 1980)."

When I read the above I envision multidimensional matrices falling into alignments that generate significant information physically, intellectually, and emotionally - a grating drifting across a field generating responses. That's shorthand but if you read the quotation above, what I'm saying should make sense. That's the easy part.

Thoughts of multidimensional matrices swirled in my mind almost constantly for years during the late 70s and early 80s. I was teaching composition at Texas Tech at the time and my experiments (especially the social experiments) with multidimensional matrices got to the point where it was unnerving my students ;-)

A brief as possible explanation of what I mean:

Standard definitions of matrix from The American Heritage Dictionary:

Mathematics: A rectangular array of numeric or algebraic quantities subject to mathematical operations.

Computer Science: The network of intersections between input and output leads in a computer.

So normally when people use the term matrix they're referring to a two dimensional system - rows and columns along the horizontal (x) and vertical (y) axes. Add the orthogonal axis (z) and you have a three dimensional system. Imagine a cube (a three dimensional matrix) of 100 rows and 100 columns 100 units deep. Imagine curves going through the cube at varying rates and intensities; when that happens those curves begin to take on their own dimensionality because they involve unique time, direction, and energy variations. Imagine many curves going through the cube each with their own rate, direction, and intensity changes so that each curve becomes a dimension in its own right yet is related to other curves through induction and intersection. The curves can ebb and flow like they're alive, so that the number of dimensions in the system changes from moment to moment; what you finally have is a complex field bordering on chaos which is why it seems like chaos/complexity theory is a good fit for studying sensory and memory systems. Some of the curves (also possibly subject to influences from outside the matrix) will intersect at one point or another to create points or regions of special importance/emphasis similar to organic nodes that swell, blossom, or light up. By matrix alignment I mean the sort of analysis that clarifies the nature and the meaning formed by the intersections of one or more multidimensional matrices. On one hand matrix alignment seems like a tall order but on the other hand it's a relatively simple notion that grows out of common sense. It is not extraordinary to talk about "chemistry" between people, to search for "common ground", to get "in tune" with something or someone, to be on the same "wavelength", or to get on the same "page"; all of these are simple expressions of matrix alignment.

Think of the above paragraph as a metaphor. It's meant to create a picture in your mind that makes it easier to understand the mechanics of matrix alignment. To make the picture more lifelike (and complex) try morphing the cube into a sphere. Then morph the sphere into a flexible globular field with multiple appendages (regions capable of achieving higher stimulus levels or of projecting stimulants) going both in and out and both growing and shrinking. Just think of the globular field as a highly complex multidimensional matrix capable of communicating, affecting, and merging with other such fields. When you extend the notion in this way it begins to sound somewhat like chemistry and somewhat like biology. It's really both and a whole lot more (as they say in advertising ;-)).

The fact is that when I think about matrix alignment I don't think about cubes or spheres very often, instead I think about fields like weather fronts, raging rivers, swirling flocks of birds, or what's involved in influencing anything living including people. I also think about people and how their multidimensionality is a function of what they've inherited, what they've experienced, and what they desire. One of the beauties of the arts of performing sound and light is that you can explore and experiment with processes that lead to the most fruitful intersections of multidimensional matrices (matrix alignments) - in other words you can play together searching for what you might agree to be the best intersections. It's one of those games that has no losers, only winners, whatever may happen via the search. The social experiments with the Texas Tech people that I was referring to earlier had to do with combining individuals in various mixes (real-time sound and light ensembles) including combining people who had poorly functioning verbal communication chemistry. The experimental point was to put them in a nonverbal (real-time music and/or light) situation for the purpose of finding common ground (fruitful intersections); thrown into the mix was the added pressure of performing their discoveries in public performance. Need I mention again that it was somewhat unnerving to them ;-)

When I think about the human memory system I think of it as a dynamic field that's a multidimensional matrix that's very close to, but a lot more complicated than, that computer science definition of matrix found earlier in this post. Because the human memory system is organic, new dimensions, formed by experiences either external (actions) or internal (thoughts), can create new leads or reinforce older ones. The hardware is soft and malleable (it's actually a field) so it can take on new wrinkles from newly created leads (like ripples on water about to freeze) or can hold onto old wrinkles based on reinforcement of older leads. The system has to be capable of being massively parallel with every lead subject to variation; no lead is ever fixed for very long. Leads are subject to dimming and need to be recharged and that's achieved by either external or internal matrix alignments (physical or imaginary practice/repetition). Fields overlap and influence each other so a matrix alignment with one field will effect those related to it more or less depending upon the order of the relationship. Information flowing into the system is surrounded and followed by an inductive wake so although the information may be targeted by nature (sound or sight) it leaves broad trails in the memory, trails that become two-way streets (mini-loops).

I'll just stop now ;-) Does any of that make any sense Carl? Or does that sound like raving to you? Strangely enough when I left Texas in 1981 I just stopped using the expressions multidimensional matrix and matrix alignment. It may have been that because the notions seemed so clear to me at the time that I didn't think I could do much else with them so I just integrated that thinking into my life and that's become the perspective from which I explore related issues.

Ron Pellegrino

Post Two:

From: Ron Pellegrino <>
Subject: METALIST: A path to matrix alignment
Date: Mon, 25 Feb 2002 21:48:58 -0800

To get a clearer sense of how I'm using the expression matrix alignment I thought it might be worth a walk through the path that led me to the notion.

During 1967/68, as a third of my dissertation project, I designed 108 instruments using various combinations of the modular electronic wave generating, processing, and control functions on the Moog synthesizer. My instruments were to be used in a multi-track music realization of another third of that project, a composition of a multimedia music drama. Those 108 instruments were modeled on the general principles of traditional western orchestral instruments, all of which I had learned to play to a certain degree over a period of 18 years previous to 1967. Compared to what I might do today in instrument design, those 108 instruments were relatively simple systems that set the stage for the next step.

Beginning in 1969 I began designing instrument sets that I could use in live performance with other musicians, dancers, light artists, and other performers. Usually the sets had five or more different individual instruments (still relatively simple systems) that I could call up separately with the turn of a potentiometer - in other words the instruments were routed through sub-mixers and mixers that I could in a sense conduct in performance while I was also keying, sliding, and using other controllers to play the instruments. Often serendipitously, during the process of changing from one instrument to another, I came across sonic material that I found more musically interesting than the instrument that I was leaving or the one I was about to play. Soon I was analyzing what it was that made the transitional states so attractive to me. That analysis led to the abstraction of principles for designing more complex instruments that both shared functionality and cross-modulated each other. During the late 60s/early 70s systems analysis was a prevalent conceptual tool in the world of emerging technology; it fit my studies perfectly so nested flowcharts with accompanying notations became a way of life for me. To keep the whole business manageable I'd make flowcharts of all the individual instruments of the set and then fit them into a larger flowchart, the performance set. Taking the complex flowchart step made it easier to understand what it was that made some systems work so well together musically in their transitional states. (In this paragraph you could just as well substitute the word matrix for the word system.)

During the early 70s the compositional process of systems design led me to integrate music with other dynamic systems such as air currents, audience movement, circuit design, and flowing light - I began to think of other dynamic systems as higher level modules that could relate to each other in ways similar to the modular functions of electronic music synthesizers but on higher and more complex levels. At that time I called those compositions "environments"; today they're more likely to be called installations. Throughout the 70s and beyond I continued to explore experimentally the systems approach to composition while at the same time working to understand physics, psycho-physics, cybernetics, metaphysics, biology, and social systems. Early during the course of those explorations it became clear to me that, for freeing up the thinking process, it might be helpful to think of all those highly complex systems as multidimensional matrices. When designs really got complex I found that the flowcharts I was making with a systems analysis approach were so full of multi-leveled feedback loops and nested functions that, as an analytical technique, systems analysis recorded as complex flowcharts was reaching the point of being counterproductive for me.

The fact is that today I'll use whatever analytical technique makes sense in the context - one, the other, or both. Flowcharts and notes make good records and good springboards but for complex systems flowcharts tend to be too reductive. However matrix alignment seems a whole lot closer to the way things actually work so when I brainstorm away from the sources of electronic synthesis (on a walk, in the woods, at the beach, etc.) my thinking leans more toward matrix alignment - it makes it easier for me to visualize relationships. Now, as far as I know, a notational system for aligning multidimensional matrices doesn't yet exist other than prose which tends to dance around the intersections. But that's no reason not to use matrix alignment as a conceptual creative/analytical tool - notational systems and flowcharts are great tools for keeping records but matrix alignment makes a far better real-time scope.

One example before I stop. The laser animation/projection system that I designed in 1975 has three different galvo/mirror units, one each for x (horizontal deflection), y (vertical deflection), and z (chopping the laser beam). Each galvo/mirror has its own particular frequency response curve and predominant resonant frequencies. As a set, those galvo/mirrors can be viewed as a matrix with multiple highly sensitive frequency regions. Taken together I think of that system as having a personality, as being one example of what I think of as a cyberspirit. To create laser animations with that system I use an electronic wave system (hardware or software synthesizer) to design instruments that generate audio waveforms/frequencies that go in (visual consonance) and out (visual dissonance) of alignment with the personality quirks (matrix features) of my laser animation/projection system. Simply put, to create laser animations I design a matrices on a synthesizer that are capable of being tuned (being aligned with) on the fly to the prominent features of another matrix, my laser animation/projection system - the process can be considered an exercise in matrix alignment.

What I find so attractive about the notion of matrix alignment is that it's very valuable as a metaphor for how living systems communicate with each other. Some of what I was say in my previous post on matrix alignment dealt with a few of my performance art communication experiments.

A side note: in a previous post Sergio was expressing his concern for maintaining mystery as a value. On that account I think there's nothing for us to worry about. The history of science is one generation after another debunking the theories and "truths" of the previous generation. What's amusing about it is that the current established generation always knows that they're absolutely correct and that's because western science is really a religion - the current scientist pope and his bishops are infallible, whatever the established generation. And that includes the latest love affair with the genome. As the old priests were tying up their genome project along came the next generation screaming that proteins hadn't been properly taken into account ;-)

My personal search is for springboards and portals - motivational keys and glimpses of the infinite - the sphere of the Wizard. Simple needs.

Ron Pellegrino

Post Three:

From: Ron Pellegrino <>
Subject: METALIST: dancing around the intersections
Date: Sat, 2 Mar 2002 22:16:48 -0800

I used the expression "dancing around the intersections" in my recent post with the subject line of "A path to matrix alignment" and it's been bouncing around in my thoughts for days.

The quote from that post:

"The fact is that today I'll use whatever analytical technique makes sense in the context - one, the other, or both. Flowcharts and notes make good records and good springboards but for complex systems flowcharts tend to be too reductive. However matrix alignment seems a whole lot closer to the way things actually work so when I brainstorm away from the sources of electronic synthesis (on a walk, in the woods, at the beach, etc.) my thinking leans more toward matrix alignment - it makes it easier for me to visualize relationships. Now, as far as I know, a notational system for aligning multidimensional matrices doesn't yet exist other than prose which tends to dance around the intersections. But that's no reason not to use matrix alignment as a conceptual creative/analytical tool - notational systems and flowcharts are great tools for keeping records but matrix alignment makes a far better real-time scope."

First, I don't mean to denigrate prose as a notational system - no surprise I find it an especially valuable mnemonic alone as well as with other symbols. Neither do I mean to devalue the idea of dancing around the intersections. It's actually essential because it's what breathes life into harmonically based dynamic art - it's what provides the dynamism along with the onsets, the transitions, and the decays. In the compositional designs that I use to generate my laser animations I move through a series of harmonic relationships that can be reduced to whole number ratios. When the whole number ratios are perfect, a state of stasis sets in, which of course means there is no motion - no motion for very long in dynamic art is not all that interesting. So dancing around the intersections (the whole number ratios) is a crucial aspect of that performance art form - I never do the dance the same way twice even though the sound/light image created by any particular whole number ratio is the same from performance to performance (in a sense it's a constant that, unlike the dance, can actually be notated). What I practice before a performance is the dancing around intersections, the onsets, the transitions, and the decays.

So the whole number ratios chosen for sequences (conceptually similar to chord progressions in straight music) are important compositionally as the substructure of the real-time aspect (the dancing, the transitional states, etc.) of the visual music piece. What needs to be noted is that the whole number ratios are based on the fundamentals of the wavetrains at x, y, and z. Matters are complicated considerably (and what happens in sound/sight gets a whole lot more interesting too) when the wavetrains are complex waveforms with envelopes on frequency, amplitude, and timbre. What that means is that the intersections of the whole number ratios are actually intersections of three evolving multidimensional matrices with additional ratios occurring with the partials that accompany the involved fundamentals. (Harmonic partials have whole number relationships to their fundamentals.)

Add all of that to the electro-mechanical galvo/mirrors for x, y, and z (multidimensional matrices as well) and you end up with six multidimensional matrices in search of alignment. Add to the six a small performance group of three - not long ago I worked with another musician and a dancer - and that makes 9 multidimensional matrices not to mention the instruments the musician was playing, the work of the person lighting the stage, the audience, the context for the event, and...(probably because it's too much like infinite regression, this is where Bob Seiple didn't want to go in one of his recent posts ;-)). In that complex there are multilevels of alignment - the whole number ratios of the fundamentals, the whole number ratios of the partials of the waveforms, the wavetrains and the galvo/mirrors, the performers, and all of the other matrices in search of alignment, convergence, and right tuning.

What stirred this pot was Mark's recent reference to Pythagoras and Diana's reply to my "A path to matrix alignment" post. Though I didn't refer directly to what Diana said, reading it everyday since she posted it was the big stirring spoon. I'm hoping the above helps to clarify what I mean by the alignment of multidimensional matrices but I'm not entirely sure it does ;-)

Ron Pellegrino

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