A rough and slightly rambling essay on beauty, number, and the intangible.

On Mathematics and Metaphysics

Western culture is of two minds when it comes to deep ontological questions, if it's not downright schizophrenic.

On one hand, there is a dominant Materialist perspective in the sciences and the cognitive disciplines. Unless something can be touched and measured it has no validity. This mindset has undoubtedly worked well in scientific endeavors, and over time it has been extended to cover increasing dominion. It has been taken so far as to lead to what can at times seem to be bizarre positions, even in more liberal domains. In some schools of philosophy and psychology, for example, it is not even permissible to speak of subjective phenomena; subjectivity can only be spoken of insofar as it leads to objective interactions and measurement. Qualia are dismissed as meaningless speculation, unworthy of serious consideration. At its extreme, subjective phenomena are not only considered unworthy of discussion: they are dismissed outright, seen at best as naive illusions.

On the other hand western culture has developed and flowered from religious and cultural traditions that adopt the opposite extreme. The transcendent is seen as the good, with manifest experiences seen as at best flawed and fallen, if not downright evil. Nature must be beat into submission, the body must be denied, desires repressed. This also leads to bizarre positions and behaviors.

Both of these positions spend more time and effort denying their opposites than they do affirming their insights.

Of course, whenever such extremes are encountered it is usually best to look for more expansive and inclusive perspectives. Experience is often centrist in its character. To maintain any extreme position one usually has to pursue it with religious fervor, denying those things which contradict its deeply held (and cherished) positions.

Personally, I don't feel that much time needs to be spent to argue for the existence of manifest experience. Sure, some people deny existence to all external phenomena (usually westerners who have adopted naive understanding of eastern metaphysics, taking--for example--the doctrine of maya in isolation of its containing non-dual perspective). Such opinions are not widespread but they are held with the power of self-validating conviction.

On the other hand extreme Materialist perspectives hold great purchase in western, intellectual circles, and appear to be gaining ground. Materialism (like Subjectivism) has important things to say, but it is not the only game in town. But these perspectives are also self-validating; they are not falsifiable in any formal sense. What's more, when a position is willing to deny things as seemingly self-evident as subjectivity and consciousness itself, what can be said?

Probably nothing.

Regardless, I feel moved to say something.

There are objects in common experience which are non-material. And I think the best example is that of mathematics.

Mathematics and That Which Can Not Be Touched

In a scientific review of the cosmology of reality (Parallel Universes, Scientific American, May 2003), Max Tegmark offers the following observations on the potential mathematical structure of being:

As children, long before we had even heard of mathematics, we were all indoctrinated with the Aristotelian paradigm. The Platonic view is an acquired taste. Modern theoretical physicists tend to be Platonists, suspecting that mathematics describes the universe so well because the universe is inherently mathematical. Then all of physics is ultimately a mathematics problem: a mathematician with unlimited intelligence and resources could in principle compute the frog perspective—that is, compute what self-aware observers the universe contains, what they perceive, and what languages they invent to describe their perceptions to one another.

A mathematical structure is an abstract, immutable entity existing outside of space and time. If history were a movie, the structure would correspond not to a single frame of it but to the entire videotape.

Even ignoring for the nonce the Deterministic bias of the proceeding (a bias I do not share), many people would probably be somewhat taken aback by such pronouncements. Mathematics is offered as a metaphysical entity, existing outside of time and space but proving the ground to them. This conflicts deeply with the Materialist world-views that currently pervade modern attitudes. In areas as diverse as philosophy and cultural studies it has become downright blasphemous to speak of metaphysical objects, and one is considered slightly daft to even speculate on anything that lies outside of direct, physical instantiation.

Perhaps it comes from my formal training in physics and mathematics or perhaps it comes merely from my own propensities, but in some ways I have acquired that taste for the Platonic view. And that taste informs and directs the work documented on this site.

But even if mathematics is an intangible that exists outside space and time, just how deep does it go? Does it provide the ultimate ground? What, if anything, lies at the base of experience and existence?

Deep Structure and Ground

In their idle moments, people often speculate as the ultimate ground of being (if they're given to such speculations at all). One commonly given answer to such musings is energy, at least if the muser has a passing familiarity to either quantum physics or eastern metaphysics. Everything is seen as "energy" or "vibration," even if just what is vibrating is never made clear. But from my perspective, this answer suffers from many limitations, even beyond those of loosely defined concepts and ambiguously delivered communication.

Most importantly, energy is a precisely defined concept, and by appropriating it from the physical sciences certain subtle tyrannies come with it. Energy is defined as the ability to do something (in the case of physics the something called "work"), so it presupposes that there are things and things to do. In other words, it presupposes a negation of metaphysics in the first place. One can do this is one wants, but it should be done consciously. If one accepts this bias as axiomatic then one would at least expect to find a subtle materialism at the end of one's questioning. And such a subtle materialism is often found in systems based upon some nebulously defied concept of energy or vibration, even if those who engage in such systems often don't notice this. I think this is a good example of the subtle grip that Materialism holds on so many aspects of thought for we "moderns."

From my perspective, the universe's ontological onion goes deeper than energy, and I think that mathematics is one of those deeper layers.

Form. Relationship. These are all "things" which, like the mathematics by which they are described, exist apart from time and space but provide basis for them. Take, for example, one of the simplest patterning structures: number.

So ingrained in us is the pattern of number that we take it for granted. We teach children to count even before they've mastered simple speech. But from whence comes number? Did it arise from the universe, or does the universe arise from it? Or do they both exist, independently?

In the beginning (if we can speak of beginnings) is a void. The void gives way to a unity, which in turn descends into multiplicity. Form arises.

One. Two. Three....

It matters not if there are no beginnings. Sequence exists anyway, even if not embedded in a stream of time. (In fact, perhaps it is more profound and insightful to look at it in a non-temporal way).

These metaphysical objects may not be the ultimate ground from which all experience arises (and I suspect that they are not), but it is, perhaps, the deepest level about which we can say anything. Life contains a mystery, but the contemplation of emergence, bubbling up from the deepest layers of being, can at times provide us with a glimpse of that mystery.

Pattern and Configuration

Like number, pattern and configuration exist deeply within the structure of our experience. They are the mathematics of relationship.

I have written often on emergence in these pages. But even knowing what emergence is, one can still ask the why of it. What guides the spontaneous complexity that arises from emergent interactions? That order arises in the universe in this way is all but a given; why this is the case can't help but draw our attention.

The simplest answer is because the universe is that way.

Some things are so ingrained in our experience that we have a hard time seeing them as anything other than a given, axiomatic and not open to further inquiry. The processes of evolution is one such example. Scientists may argue to finer points of how evolutionary processes take place, but no serious student of the world can deny that it does take place. Competition and changing environments apply pressure to change and adapt. Those changes can confer benefit and are passed on when they do. Over time species will drift to more successful forms. It all seems so infused with common sense that we can't imagine it being any other way, unless we reject it on philosophical or religious grounds. It is that way because, well, that's the way it is.

When a series of whys leads to an axiomatic because, this can be a clue that we're looking at a deep pattern of reality. But being what we are, we internalize these patterns so completely that we cease to see the wonder, beauty, and divinity within them. They cease being miracles and become mere facts.

Order, pattern, and beauty arise spontaneously from certain types of interactions. They are a fundamental aspect of the reality in which we live, and they provide a tangible instantiation of the deepest teleologies of physical existence. Experiencing those teleologies can provide a glimpse into the chain of manifestation, provided that our eyes don't become jaded and the mysteries of emergent form don't become collapsed into mere facts.

Music, Immanence, and Transcendence

The relationship between mathematics and music has fascinated man since at least the 5th century BC, in which Pythagoras created his theories on the subject. In the time of the Greeks the mathematics were simple, being based upon the ratios of simple, whole numbers. Even given such simple mathematics, Pythagoras and his followers saw these maths and musics to be a reflection of divine principle. He conceived the universe as an immense string, upon which the vibrations of creation resounded. Through contemplation of mathematics and music they attempted to touch the beauty of the divine, the creative spark at the ground of being. In speaking of music, one cannot ignore the geometries and mathematics that give rise to it. And when we speak of mathematics, of necessity our discussion will wander into the realm of metaphysics.

Music is an interesting art form, for it straddles the space between the latent and the manifest, between the immanent and the transcendent. On one level it is manifest, with structured sound comprising its body. It is real and tangible. On another level it exists in pattern and form as an intangible, metaphysical object. The beauty we experience in music can come from the apprehension of that form and pattern. It is not so much that music can be inspired or based upon mathematical constructs; music is a higher mathematics. Notes and sounds illuminate the deep structure of this mathematics, in much the same way that number functions in other forms of mathematical expression. Number doesn't create mathematics; it is what is used to express and convey the truths of mathematics. Likewise, at its deepest level sound does not comprise a music, but it is what is used to convey and illustrate the truths and teleologies that give rise to it.

On a personal level I undertook this work as a deep meditation on form and emergence, on pattern and beauty. The work is a tangible expression of some of the experiences, insights, and visions I've had in these areas. As an artistic or philosophical expression it may be somewhat idiosyncratic, but what expression isn't? The work (and music) in an attempt to go as deeply as possible into these waters.

At its deepest level reality is not things. It is configuration and form, relationship and pattern and number. It is little wonder that, when the conditions are right, the apprehension of a musical truth can be one of the most sublimely beautiful experiences we can have as conscious, aware beings.

Closing Remarks

Is the view I present here just another example of a transcendent view of reality, denying (or making subservient) form?

Hopefully not.

While I do see non-physicality at the ground of being (at least to the levels to which we can speak), and I hope this music in some way gives voice to this vision of reality, this in no way renders the manifest in any way flawed or fallen or "less." The manifest and the latent are not necessarily different. They may be different aspects of the same whole, but they are part of that one whole.