The first half of Digital Mantras creates an historical backdrop upon which the author splashes his vision of the next wave of art and knowledge and, in the end, of reality. It weaves together discussions of language, philosophy, music, and visual art, both in theory and in practice. The second half of the book delves into the present age of computer-assisted art, which the author presents as the way forward (I believe this shows his bias as a computer scientist) and then veers off on how to chart a course through the nature of reality (using computers, of course).

The author presents reasonably clear and concise introductions to all the topics he touches on, which include musical serialists (e.g., Boulez, Schoenberg), a few abstract artists (most notably Kandinsky, highlighted by beautiful color plates), philosophers, and linguists (e.g., Saussure, Chomsky). For example, Holtzman’s discussion of music theory includes an overview of the Circle of 5ths, illlustrated with good diagrams. His discussions of Chomsky’s transformational grammars also use examples. However, these discussions are necessarily brief, and structured to support his theme.

I am sure many readers will at least be experientially familiar with some of the main themes of the book, having come across moments in their lives where they felt the pull of cosmologic double or triple entendres. Where, through intensely investigating something (or the connections between things) — for example, your face in the mirror, random snippets of conversation around you that form a coherent meta-dialog, or the colour purple — you stumble across a link, a gate, where the microcosm becomes a metaphor, analogy, or isomorphism to the macrocosm. This is what the author calls the result of “deep structures,” those things underlying the surface level of reality that we interact with every day (well, at least most of us).

The author suggests that a new wave of computer-generated virtual realities will allow us to peek into deep structures by uncovering patterns that, he believes, we cannot intellectually discern without electronic assistance. I personally think that the knowledge gained through such a digital filter is more likely to resemble a map. It may spur us into exciting paths of discovery while visiting a country, but is not a replacement for the trip.

Another issue I have with the book is the idea that all meaning emanates from within the system, and can be understood simply by figuring out its potential structures, hierarchies, and transformations. The philosophical underpinning of this viewpoint (Structuralism) is a good tool to have in your metaprogramming toolbox, but one size does not fit all datasets.

I do not believe that gnosis can be achieved strictly through an intellectual study of structure. I agree that deep structures do exist, and that multiplicities of their emanations occur all around us. I also agree that finding the isomorphisms between seemingly disparate structures can create moments of enlightenment and that studying things with a structuralist viewpoint can help because it provides a set of investigative tools. But intellectual study of structure alone is insufficient to fully grok the deeper meaning — some things must be experienced. I also believe that merely breaking things down into elements does not lead to a full comprehension of the interrelationships and deeper meanings.

I am not certain that “deep structures” are revealed in all structural similarities. I have certainly found cases, as I play games in my mind, where the similarities I come up with don’t seem all that meaningful. One example from the book is to map the integers 1 to 12 to the 12 notes of the musical scale and then to twelve colours. Look, the colours and notes have the same structure! Woo Hoo! Except I could replace those twelve colours with differing shades of grey and still have equality. Or I could replace the twelve notes with the corresponding hertz tones of the numbers… or the twelve chairs around my dining room table. The deep structure revealed by this exercise escapes me at the moment.

I find that not everything is quite so arbitrary, in the structuralist sense. One example from the book is the statement that the circle of 5ths is no better than any other arbitrary map of sounds, even though the elements of the structure as it stands produces pleasing (to many people) harmonies. Perhaps the very reason we find it pleasing is due to some meaning that has more to do with the contents, the texture, and shape of the reality of a C Major chord compared to the “chord” created by a chainsaw, gong, and door squeaking.

As an example of this difference of opinion, the author uses Kandinsky to support his points. I find this a glaring misreading of Kandinsky’s efforts. While Kandinsky did create structured works, going so far as to define correspondences between colours, shapes, spatial references, emotions, spirituality, and more esoteric vibrations, the author takes these at face value, seeing the structure and declaring victory. However, to Kandinsky, a colour emanates in itself the quality he ascribed, and paints a symphony of vibrations that affects the viewer. To Kandinsky, the effect would not have been the same with different colours or if spheres were replaced by triangles, and I concur.

What you gain by looking at the world through a structuralist filter is insight into certain types of synchronicities. What you lose is the inherent qualities of the elements. Structure is not the whole story, merely a map to certain parts of it.

Or so it seems to me now.