Art and Computing : a Marriage Made in Mathematics

The art and computing dichotomy became deeply ingrained in post-Enlightenment culture. It was not just different perspectives, priorities, interests and political expressions: the information age, with its new computational understandings, has brought us both a reinforcement of the rationalist world view, while at the same time an emergent understanding of the role of different models of computation. Of course, computability as a theory is a very young development, and it is only recently that the importance, and real world relevance, of higher order computation has become better understood. But this higher order has increasingly become the 'elephant in the room' manifesting itself via emergent phenomena in nature; via neuroscience and the persistence of conceptual consciousness and mental autonomy; through quantum ambiguity and non-locality; and the omnipresent computational inconveniences of turbulence, chaotic settings supporting strange attractors, and phase transitions working against the reversibility of computation and time. Most importantly, we have the persistent usefulness and sense of real significance of natural language shared in the arts, humanities and science which was discovered in the 1930s to take us far beyond the computable world. On the computational side, we have the dominance of the Turing model, accompanied by less well-known work of Alan Turing and others relating to higher type computation, morphogenesis, and the underpinnings of artificial intelligence see [4]. In this short sketch, we look at how the mathematics of different computational models appears to be embodied in the structure of the human brain. And how the conceptual clarification arising can be carried into the wider context, bringing both direction and optimism to the future of art and computing. 1 ART VERSUS COMPUTING Why should we be so interested in the future of art and computing? Surely the argument goes art is best pursued in visceral autonomy, with computing at best a useful tool for materialising the creativity of the human mind and body? The algorithmic drive associated with the information age is anathema to those who still value humanity per se, and who see normalising rules as ones to be broken. On the other hand adopting a different standpoint computing is the pursuit of clarity, offering freedom from mistakes, a project devoted to something a little more serious than entertainment and the indulgence of human weakness and fallibility? Nothing less than the survival of the species is at stake, and it is scientific understanding that will give us direction and a new found harmony of utilitarian achievement! Clearly, both these rather crudely outlined viewpoints have very different, and very valid roles to play in our complex world. And in an age where marriage itself is in question, what is to be gained from the mixing of such different perspectives? And the ages of the partners! The birth of the former is seen as being lost in prehistory, and the latter having arrived in the world less than 70 years ago. In fact, it is the human brain itself and new eyes provided by early pioneers of the computer age which turns all this from pumpkin into golden coach. And it is the mathematics that so informatively accommodates our intuitions, and provides the basis for a truly magical marriage contract. We see how the magic and materialism may combine, as it does so powerfully in Turing A Staged Case History, delivered to a packed Milanese theatre for a week in November 2012. Created and embodied by artists who worked with the technology, and spent many hours researching, and visiting Bletchley Park the unique workspace of so many early computing pioneers nothing could have demonstrated more immediately the rewards of the new burgeoning synergies. Figure 1. Drawing of Alan Turing by his mother, at his preparatory school, Hazelhurst, Sussex. Annotated by Mrs Turing ‘sent to Miss Dunwall, matron at Hazelhurst. Date Spring term 1923. ’ Courtesy of Sherborne School. The complexity and intimacy of the relationship is illustrated by Sara Turing’s sketch of her son ‘Watching the Daisies Grow’ (Figure 1). A clear dichotomy between ‘art’ and ‘computation’: Hockey, social, interactive, distinctively human, and creative at its best, being determinedly ignored by the geekish Alan with his studious botanical interests. But look again. The hockey is of course a faltering application of rules of the game, a game pursued according to learned, stereotypical (programmed) procedures. While it is rule-breaker Alan we observe, focussed on the mysteries of emergent patterns in nature, a mystery he would immerse himself in and clarify so creatively thirty years later at the University of Manchester. And what about our role as observers? We are certainly computing in some sense a description of Mrs Turing observing her son. But the computation has different levels, assisted by mental framings previously applied in different contexts. The process is partly learned, partly experimental application of conceptual tools successfully applied previously, and partly bringing together of contextual observation, from inside and out, in a formative and informative manner. We are handling the syntactics and semantics of a complex world with an aplomb born of different Levels of Abstraction (as outlined in Luciano Floridi’s recent book [5] on The Philosophy of Information) within which we can apply what we know. What becomes clear is that it is what happens in the cracks between these epistemological/ontological stepping stones that is important to our understanding. And that the relationships we need to deal with involve computation of a scientifically problematic nature. Paradoxically, we do not recognise much of this as computational, even though it provides a familiar and invaluable part of our everyday mental activity. Specially important is the computational role played by natural language, generating a fragmented and troublesome informational terrain, and at the same time reducing the uncertainties to a form which can be handled within the classical computational setting. 2 THE COMPUTATIONAL BRAIN In his 2009 Yale University Press book [9] The Master and his Emissary: The Divided Brain and the Making of the Western World, Iain McGilchrist describes how: The world of the left hemisphere, dependent on denotative language and abstraction, yields clarity and power to manipulate things that are known, fixed, static, isolated, decontextualised, explicit, disembodied, general in nature, but ultimately lifeless. The right hemisphere by contrast, yields a world of individual, changing, evolving, interconnected, implicit, incarnate, living beings within the context of the lived world, but in the nature of things never fully graspable, always imperfectly known ― and to this world it exists in a relationship of care. The knowledge that is mediated by the left hemisphere is knowledge within a closed system. It has the advantage of perfection, but such perfection is bought ultimately at the price of emptiness, of selfreference. It can mediate knowledge only in terms of a mechanical rearrangement of other things already known. It can never really ‘break out’ to know anything new, because its knowledge is of its own representations only. Where the thing itself is present to the right hemisphere, it is only ‘represented’ by the left hemisphere, now become an idea of a thing. Where the right hemisphere is conscious of the Other, whatever it may be, the left hemisphere’s consciousness is of itself. A key aspect of the brain architecture of placental mammals, such as humans, is the corpus callosum, connecting and mediating the functionality of the separate hemispheres. McGilchrist comments (pp. 18-19): . the evidence is that the primary effect of callosal transmission is to produce functional inhibition. it turns out that the evolution both of brain size and of hemisphere asymmetry went hand in hand with a reduction in interhemispheric connectivity. And, in the ultimate case of the modern human brain, its twin hemispheres have been characterised as two autonomous systems. Figure 2. Corpus Callosum, from 20th U.S. edition of Gray's Anatomy of the Human Body, originally published in 1918. So is there actually some purpose in the division of neuronal, and therefore, mental processes? If so, what could that be? We might further ask: Given this division, to be found in animals generally, what is the benefit of the moderated reconnection via the corpus callosum? Left brain-right brain features commonly in popular writings. The point of mentioning it here is that there is a huge body of reputable work pointing to contrasting types of thinking, the types (a term we shall see, with relevant mathematical meaning) broadly corresponding to those in the folk culture. And that these types do correspond, on one hand, to differing computational frameworks: and on the other, to how we view the sorts of thinking predominating in the arts and humanities on one side, and in mathematics and the sciences on the other. Part of the more serious literature is a basket of terminology relating to what is problematic for the classical Turing model of computation, and its embodiment in today’s computing machines. In particular, the notion of emergence, without a clear definition of what it is, brings with it terms from many different fields. Listing in no special order, and with no hope of comprehensiveness, we have: morphogenesis, phase transition, self-organisation, supervenience, synergetics, chaos, strange attractors, randomness, turbulence, non-locality, decoherence, intuition, commonsense, creativity, semantics, inspiration, imagination, intelligence, fractal, wave collapse, entropy, downward causation, incomputability, consciousness, qualia, free will, strong determinism, networks, complexity, etc. Most of the literature is either technically concerned with microanalysis of particular as