{∞}= [-∞…-π...-3…-e… -2… -√2...

-1….Ø…1/2…1…2…e…3..π…99 …+∞]

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Contents:

Research question: What are the consequences of applying set theory to artistic practice? 1.Introducing set theory to art practice. Chapter I; ‘Absolutus realitas’.

i. ‘Absolutus realitas’ as Oneness. ii. ‘Absolutus realitas’ is dual or binary iii. ‘Absolute realitas’ is the empty set Ø.

Chapter II. The empty set {}/ Ø as pure empiricism.

i. The empty set {} as pure empiricism. ii. ‘I am Kia; the feral child’. iii. Set theory.

Chapter III; the empty {}/ø as a subset of the Infinite Set{∞}.

i. The infinite set {∞} and the empty subset {}/ø. ii. The conceptual experiment. iii. The Infinite Set {∞} becomes real. iv. Assemblage.

Chapter IV; {∞} numerous properties.

i. The whole {∞} is not greater than some of its parts. ii. {∞} God or Substance is not pure but the subset Ø is pure. iii. {∞} U ø; the union of {∞} and Ø. iv. {∞} ∩ Ø; the intersection infinite-empty/empty-infinite. v. N.

Chapter V the infinite set {∞} revealed.

i. A conception. ii. An oscillation. iii. A union (U). iv. {∞} is Ganzfeld.

Chapter V+1; a few conclusions.

i. {∞} and Ø exist. ii. {∞} is totality. iii. ‘Recovering artist freedom’. iv. The aesthetics of {∞}. v. Beyond {∞}.

*Appendix *Bibliograph

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1. Introducing set theory to art practice. This thesis introduces the mathematical instrument set theory to art practice. Set theory is a mathematical theory that deals with the properties of sets. ‘Sets’ can be understood as a collection, group or conglomerate, such as the set of all human beings. The thesis also looks into the consequences this might have in practice, which broadly divides into two:

1) A trans-disciplinary thesis operating across science and art disciplines, and in particular mathematical set theory and fine art practice.

2) Two immaterial sublime objects, systems or more precisely sets. The notation for these two sets is: {∞}= infinite and {}/ø=empty.

These sets – which share unions, relations, operations and properties – can be described as: {∞}: An impure pre-conceptual numeral system or structure composed of subsets and abstract elements. The Infinite set {∞} can also be described as God or Substance; a limit-less and sublime Substance conceived through itself that does not depend on the conception of another thing from which it must be formed. {}/ø: The empty set is a finite and pure set. It is also the realm of sublime and pure potential, similar to an empty space prior to the conception of a form. It is also a subset of {∞}. The impossibility of representing these two sets in their totality is latent in art practice, yet if the modeling tools and materials are changed to set theory, the impossible becomes real and great revelations take place. As a result I have realized that for too long, art praxis has been subject to the laws of materiality, bureaucracy, empiricism, and the phenomena of space and time. A practice which in my opinion undermines artistic freedom. In order to find the answers to the most fundamental metaphysical questions, achieve artistic freedom, reveal paradoxes, uncover unhealthy bureaucratic practices, promote learning and nurture flux in the arts, we need to let go of these laws and find new ground. This task is seemingly possible with the aid of the mathematical instrument set theory. A praxis I term: ‘sets art’.

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‘Sets art’ departs from the commodified theoretical views so predominant in the fine arts proposing an infinite and holistic malleable praxis. This sublime immaterial practice is composed of pure potential and truth. As a result of such properties the practice reveals limitations, rigidity, hierarchies, a priori & a posteriori knowledge, fixed methodologies and fragmentations. Hence, there are constant opportunities for the artists using set theory to learn and grow. In this process I have decided to use the first person pronoun ‘I’ for three reasons: 1) This thesis is mainly self reflective of my own praxis so the first person pronoun ‘I’ seems the most appropriate. 2) In the field of humanities the first person pronoun is permissible. 3) There is a strong element of anecdote, introspection and subjectivity in the thesis. Research question: What are the consequences of applying set theory to artistic practice?

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Chapter I; ‘Absolutus realitas’.

iv. ‘Absolutus realitas’ as Oneness. v. ‘Absolutus realitas’ is dual or binary vi. ‘Absolute realitas’ is the empty set Ø.

i. ‘Absolutus realitas’ as Oneness; Through out the history of modern philosophy some of their key exponents such as: Gottfried Wilhelm Leibniz or Benedict Spinoza, have understood reality as a: ‘One or Oneness’. A being which exists without being dependent on anything else, it is self-contained and independent, embodying unity rather than disunity. The above definition of ‘Oneness’ was the inaugural axiom of German philosopher and mathematician Gottfried Wilhelm Leibniz’s ‘Monadology’1where he states: ‘the object of this discourse, the monad, is nothing else than a simple substance’ (Leibniz 1966: 148). This Monad or single substance which Leibniz’s Monadology refers to is in itself and is conceived through itself; so its conception does not depend on the conception of another thing from which it must be formed. It is an absolutely infinite being, a substance consisting of infinite attributes, each of which express an eternal and infinite essence; a similar description to the Abrahamic concept of God. A similar axiom was also the inaugural claim of Benedict Spinoza’s philosophy; for the Dutch thinker ‘One/Oneness’ was a substance with its attributes or essences, modes or modifications. It is God present everywhere, timeless, limitless and which remains the same in spite of varieties and changes that occur in the world; an independent and objective substance, robust and solid (Spinoza 1910:10). For both philosophers, absolute reality was understood as a Oneness and this Oneness was understood as God, so God was Oneness. That absolute reality is Oneness and God is Oneness is also the inaugural claim of many monotheist theologies. For instance: the prophet Mohammed described the God Allah as a substance present everywhere, in everyplace. Whereas in the Hebraic tradition of Kabbalah, God is the limitless ‘En Soph’ from where the 10 Sephiroth (categories or spheres) emanate into a unity, a One which manifests itself as light, both un-discernable and discernable to the human.

1 Monadology is the study of the metaphysical unit or atom also knwon as monad.

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ii. ‘Absolute reality’ is dual or binary. At this stage I began to wonder, if the concept of God is understood semantically as One and numerically as 1, what happens with the negative of that One; the -1 or the ‘One which is not’? What could this -1 be? Numerically, the -1 is simply the negative value of 1, by operating it exists yet it cannot present itself. In other words, it semantically and numerically exists yet it cannot present itself physically, for example I cannot present to somebody -1 apple. Therefore, the ‘One which is Not’ may not present itself; perhaps it can only operate; perhaps it can only be understood as a creation of the imaginary resulting from our human ability to abstract. So it seems that -1 or ‘one which is not’ is the essence of ‘Oneness’, the potential of Oneness. A claim which clashes with the view held by English philosopher John Locke that ‘The real essence of substances is forever unknowable’ (Sir James Jeans 1931: 351-354). However in my opinion this essence is the imagination, the virtual, where endless possibilities, pure contemplation and thinking feeling takes place. A potential which strikes with great force; a momentum operating on multiple registers of sensation. At this stage I realized that the absolute reality I was describing as a Oneness had morphed into a dual or binary reality composed of a 1 and a -1. Such binary reality can be presented physically in the form of a simple exercise whereby you ask people to go from A to B at particular set times. This exercise2 creates a conceptual rhythm whilst mimicking our behaviour in contemporary thought: that is how we forcefully draw from one extreme to the other at all times.

2 Exercise carried out in winter 2005 at a sound workshop (UoP) with other students.

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iii. ‘Absolutus realitas’ is the empty set Ø. Once aware of the potential of ‘physical exercise’ in representing the bipolar reality formed by -1 and 1, I begin to wonder whether I can synthesize this pair of opposites by deducting -1 from 1, or add -1 to 1 hence arriving at 0, being this 0 the synthesis and also emptiness. This makes me wonder whether the ‘absolute reality’ I have previously described as binary or as a ‘Oneness’is in fact the empty set {}/ø. Therefore if absolute reality exists this is the sublime empty set {}/Ø3, a unique and finite set full of the purest of potentials. It is this view that this thesis subscribes to.

3 Go to appendix reference 1 for: ‘Empty Set {}/ø’ diagram.

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Chapter II. The empty set {}/Ø as pure empiricism.

i. The empty set {} as pure empiricism. ii. ‘I am Kia; the feral child’. iii. Set theory.

i. The empty set {} as pure empiricism: In the previous chapter I commented that if absolute reality exists through syllogistic4 argument, it is not binary or a Oneness but rather the sublime empty set: {}/Ø. This reality I speak of is similar to a blank mind or an empty space prior to the emergence of an object. An empty space full of pure potential, which will be filled by lived experiences and events throughout our lives. The empiricist John Locke shared this view and continuously suggested that there is nothing in the mind that was not previously in the senses, speaking of the mind at birth as ‘white paper’ awaiting ideas from experience; similar to the blankness of an infant child, a tabula rasa full of the purest of potentials after conception. Locke thought that knowledge could be gained through both traditional and not so traditional perception, i.e. paranormal or esoteric experiences. Yet it is important to remember that humans are also born with innate physical and mental abilities and that our experiences might help in the eventual evolution or devolution of such dormant abilities. Historically empiricism has its roots in the idea that all I can know about the world is what the world cares to tell me; I must observe it neutrally and dispassionately, and any attempt on my part to mould or interfere with the process of receiving this information can only lead to distortion and arbitrary imagining. This gives me a picture of the mind as a ‘blank tablet’ on which information can be imprinted by the senses in the form of ‘sense-data’. This sense data is the ‘given’ prior to all interpretations, active manipulations or abstractions which take place in the mind; and from where we eventually create the great bulk of our ideas and concepts. A classical view analogous in my opinion, of a mechanistic model which immediately leads to problems, for if the mind is limited in this way and must entirely rely on sense-data, how can we know anything beyond them? Where does subjectivity fit in? How can the mind distinguish between inner and outer experiences? And if it cannot distinguish, how does it know there exists such a thing as an ‘outer world’?

4 A conclusion drawn from two given or assumed propositions.

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Scepticism aside, empiricism becomes rather interesting when it abandons the claim to know an ‘outer world’ at all. Insisting that what we call an ‘outer world’ is simply a construction by our minds, different in each human and indistinguishable from a real ‘outer world’ in practice, and therefore to worry about how things really look is an illusory goal to seek, yet a fascinating, mysterious and endless one to pursue. By embracing the idea that we know everything from experience solely fed by human and social interaction, I can begin to experiment with the possibilities of depriving myself of such common experiences and position myself in a less common scenario such as a relocation into a state of semi total or total isolation from the world; a world located on an island surrounded by oceans and seas, where it becomes miraculous to escape and where I am alone. What form will the knowledge acquired through my experiences take? Will it be different from the knowledge acquired by common everyday experience? Possibly; yet what seems obvious is that at this stage some of my most basic and fundamental abilities will surface; I will be able to have an introspective look at myself and get to understand my most basic animal and human instincts. But what if instead of being relocated I was born on that island? How would my mind and intellect develop away from human language, care and contact? How would I develop from birth to adulthood in a state of complete isolation? Well let’s imagine this case scenario by depicting the mental and cognitive development of myself as a feral child from the supposed blankness of birth to adulthood, in complete isolation from society, that is on a desert island in the middle of a vast ocean.

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ii. ‘I am Kia; the feral child’: My name is Kia. The story I am about to tell you is a recollection of my past memories and what others have cared to tell me. In early intrauterine experience I was sailing with my young parents in Northern seas when a gale came by surprise capsizing the boat in the middle of the storm. My mother, five months pregnant managed to survive and eventually found land after 14 days of drifting at sea. My father, tricked by the storm, was unable to survive... After drifting at sea, land was found; a rugged island somewhere in the Northern Seas where gales, rough seas and fogs are usual yet summers and springs are warm and calm. There are fresh water springs all over the island and spring is a month away, so the wild fruits will blossom and maybe the game will come from hibernation, yet the safety boat has supplies for over two months and the emergency radio signal seems to be working, so a rescue mission will surely arrive soon. However, after a month, nobody has rescued my mother and to make matters worse she starts to have labour pains: my birth seems imminent. Alone and cold Ana gives birth on an early, crisp morning to Kia, a premature infant with vivid blue eyes. Unable to recover, my mother dies a few hours after giving birth. I am left alone and with the smallest chance of survival…the smell that my newly born body emanates does not go unnoticed by all the predators and carrion-eaters of the island who are delighted to find a sudden effortless lunch in front of their eyes. Miraculously a group of seals notices the commotion and a mother seal, leader of the pack, rescues me from the hungry predators. Fed on seal’s milk and raw fish I grow into an amazing swimmer in an environment away from the distractions and diversions of human society. My early years are fed by the seal’s kindness, gentleness, and nurturing. Upon the death of my adopted mother, I begin to suffer the attacks of other animals until I decide to move onto drier land, a cave by the water where one day, I discover fire. A fire I see as a symbol of the inner warmth that animates living things, the inner life-source. Propelled by curiosity I begin to dissect with a piece of sharp slate the dead animals I find ashore, beginning with my dead seal mother, out of a desire and curiosity for knowledge. Such procedures eventually lead me to conclude that warmth is an animating spirit and that all animals, despite their diversity into species, are ‘one in reality’ being all bodies. Continuing this logic, I progress from animating factors to the existence of the soul that is superior to corporeality; seeing the whole universe as one great being, hence uniting all its many parts in my mind by the same sort of reasoning that lead me to see the oneness of all bodies in the

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world of generation and decay. Eventually I begin to wonder where all this had come from? Could it not have always existed? What was causing this cycle of death and renewal? At this stage I had reached the non-corporeal consideration, where I learned that ultimate happiness and triumph over misery would be won only if I could make my awareness of the non-corporeal cause so continuous that nothing could distract me from it for an instant. Attaining as a result, pure beatific experience, submersion and inner concentration, an experience I found at the time necessary. In this experience, my ‘self’ vanishes, extinguishes and obliterates along with other subjectivities. I have obtained a mystical experience – probably the highest form of knowledge – through reason and disposition. Yet there is also a key factor in the successful quest for understanding: self-discipline. To cultivate and maintain self-discipline, the naturalness of the state of solitude is requisite. Reason (both in its limits and its compelling logic) together with nature lead to the culmination of individual purpose: the mystical union. My self-discipline unfolds self-discovery, a discovering of what weakens and distracts spirit, what worsens vices; hence I limit myself to actions that gain food and physical safety, eating only what is sufficient to stave off hunger, attempting to control appetite, inhabiting a meagre dwelling. I spend a minimum of time on the appearance of this dwelling, and find positive experience in never allowing myself to see any plant or animal hurt, sick, encumbered, or in need without helping if I could; concluding that cleanliness matters. One clear night I decide to imitate the non-corporeal cause by mimicking the behavior of the celestial beings or bodies rotating in the night sky. Seeking to cut off sensory experience in order to pursue mystic ecstasy I make wide circular motions with my body until I lose the senses and imagination. I eventually master non-corporeal experience in the stillness and silence of my cave. A cave model of a new kind of learning, a crossroads between Mohammed and Platonic conceptions; not the social womb but the sacred solitude of a man and his creator. A space not for public recognition but private enlightenment where salvation is achieved by the intellectual approach to God. The cave is not darkness and ignorance but inner solitude and reflection, and coming out of this womb-like symbol is not to embrace public and social life or enlightenment but for one's self-knowledge and understanding. As adulthood approached I was one day meditating in my beloved cave when a giant bird with a metallic skeleton landed on my beach; I had come into contact with humans, who took me to ‘safe land’. After some

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DNA testing in a cold white room, I was reunited with my ‘real family’ and introduced to the ‘pleasures’ and ‘commodities’ of Contemporary Culture. Ten years have gone by since I left the island, and I have been introduced to the language of humans, Western Culture and their history just to realize that: ‘Civilization and religion offer a trap to the multitudes, mainly caused by the dependence on material goods which humanity has; distractions from truth which ought to be abandoned by those whose reason recognises them as distractions’. I am Kia, the feral child.

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iii. Set theory: It is to be noted that in the XIIth century Andalusian-Islamic polymath, novelist and philosopher Ibn Tufail in his novel ‘Havy ibn Yaqzan’5 also depicted the development of the mind of a feral child from blankness or tabula rasa to adulthood, in complete isolation from society on a desert island, through experience alone. In this case the protagonist is Hayy ibn Yaqzan rather than Kia, who grows up from infancy to adulthood nurtured by a doe, fed on doe's milk. By presenting this prototype of the human being as solitary, a social tabula rasa, Ibn Tufayl can show us how reason – an innate ability – guides the human intellect naturally and that learning follows the same logical path. Moreover, the solitude of the uninhabited island is a model of the natural development of the mind in the absence of the distractions and diversions of society. Moral observations aside, it seems obvious that my experiences, what I am and what I become in life is largely determined by my environment and the foundations of my knowledge reside in an empty place or blank note book where I write chapters of my life as my experience dictates them. A blank paper or empty set Ø/{} pure of potentiality that is built through education and experience; a knowledge I attained through empirical familiarity with objects in my world from which I abstract universal concepts through a syllogistic6 method of reasoning. Hence observations lead to prepositional statements which when compounded lead to further abstract concepts, objects or groups. Abstract objects or groups that eventually share relations, properties and operations and lead to the creation of further objects, all part of a complex apparatus, axiomatic structure or matrix which is born from what set theory calls the Empty Set Ø/{}. In other words the empty set Ø/{} is the foundation stone on which our empirical experience is built. 5 English translation: ‘Alive, son of the Awake, the Vigilant’. 6 A conclusion drawn from two given or assumed propositions.

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Chapter III; the empty {}/ø as a subset of the Infinite Set{∞}.

v. The infinite set {∞} and the empty subset {}/ø. vi. The conceptual experiment. vii. The Infinite Set {∞} becomes real. viii. Assemblage.

i. The infinite set {∞} and the subset {}/ø: In the previous chapters I have gradually introduced set theory in my art practice and the results have been revelatory. I have identified the foundations of reality as residing in a sublime empty set Ø/{} as opposed to a Oneness or a duality. A blank or empty set, full of the purest of potentials which is not actualized through education and phenomenological experience and which remains the same despite observations and despite the knowledge I attained through empirical familiarity with the objects of my reality. In other words the empty set {}/Ø is being. Further understanding of my new instrumentary reveals that the empty set {}/Ø is part of a larger set called the Infinite Set {∞}7 a sublime set composed by an infinite number of axioms or elements where the empty set {}/ Ø is a subset. These axioms or elements are the infinite sequence of the real numbers8 and can be described as the linear formula: {∞}= [-∞…-π...-3…-e… -2… -√2, -1….ø…1/2…1…2…e…3..π…99

…+∞]

7 Go to appendix reference 2 for diagram of the Infinite Set{∞} 8 The real numbers are: natural, integer, rational, real algebraic or irrational and trancendental or irrational.

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ii. The experiment. Once aware of the Infinite set {∞}and the elements which form it, that is the subset Ø/{} and the sequence of all real numbers. I decide to carry on a simple experiment whereby I equate some members of the Infinite Set {∞}to an imaginative description. The results are revelatory. 1: An axiom formed by a single unit, i.e. a substance. Let us equate this single unit to the ontological and psychoanalytic experience that what is presented – reality – is essentially the Absolute and indivisible: ‘One/Oneness’. In other words all reality is Oneness. Since Hellenistic thought, ontology has been built on this postulate and it has been presented by the following Pythagorean symbol:

-1: The negative of the single unit, it can be understood as the shadow or the self-reflection of the 1. It is also immaterial and equitable to the virtual, a virtual which I describe as the imagination, the thinking feeling, the potential which operates on multiple registers of sensation beyond rhetoric and semiotic models. If we wish to equate the -1 to an act or object there is a possibility in the analogy of the mirror, as self-reflection is the -1 and self-reflection is the visualization of subtraction. 2: I think of two as a conceptual structure formed by two objects which can be either similar or opposites; a dual and binary structure which can be presented by the following diagram:

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Ø: This Nordic letter represents zero, no objects and the empty set. It has no objects to present, besides presenting itself. Which is to say Ø will never adopt the form of an object according to mathematical rigour. It is when we look into physics that we enter representation. Ø is to be understood not as an object, neither as a generator of objects but rather as a sole discourse or act of presentation. An act which needs a medium to present itself; a medium which is the being: a being finite, pure and unique. 3: Three can be easily vizualised as a structure formed by three objects or elements of endless interactions: a trichotomy or triad; i.e. the Christian Godhead with the Father, Son and the Holy Spirit. This experiment can carry on forever, since our Infinite Set {∞} has infinite members and attributes. Yet our revelations are not just concealed to equating some members to an imaginary description. The infinite set {∞} has other properties, for instance:

1) The real numbers which form the infinite Set {∞} share logical relations other than numerical, for instance: 1 is related to 3 in that the holy trinity (3) is the representation of the Christian Godhead as one (1).

2) Or each member of the Infinite Set {∞} can be equated to a

point in geometrical space and the union of these points through lines, planes or surfaces could create an endless matrix.

It seems obvious that this infinite conceptual exercise will eventually reveal the endless attributes and properties of the Infinite Set {∞} has, if I was given an infinite amount of time. However this is not the case and my curiosity makes me wonder about a different issue instead, which is what the physical manifestation the Infinite Set {∞} might be.

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iii. {∞} becomes real: It was in the mid morning of autumn 2009 when the dream of the Infinite Set {∞} being materialized in the form of a magical object able to see and hear infinite possibility became real. It was nine o’clock in the morning and I was seated in the back on the bus heading to my workshop in Goonhavern. Half way into the journey the bus stopped in an odd place, somewhere between Threemilestone and Chiverton Cross. A middle aged man dressed in farming clothing boarded the bus, bought his ticket and sat in front of me; he said good morning and I replied. Nothing much happened until the bus arrived in Perranporth, when the man turned around, looked at me in the eyes and asked: “Where are you from?” “Spain”, I replied. “Where are you going to?” “Goonhavern” “Well I have something for you” he said “And what is it?” “The magical technology you have been thinking about recently.” “How do you know what I think about?” “I just know.” “Really?” “Open your hand boy!” he told me. As I opened my hand he gave me this odd looking object – it felt like plasticine – it was malleable, transparent and really shiny. “ It is yours now.” he said. The bus stopped as it reached Goonhavern, and just before I got out he said to me: “Keep it safe and keep it secret and don’t be troubled, as one day someone will come into your life – like you did today in mine – and you will know they are the right person to give it to. Then you will pass it on.” “Ok”, I replied. It was twenty to ten, so I had twenty minutes before everyone came to the workshop. I went into the washroom and locked myself in. All of a sudden this object levitated from my hand and started to produce colours, shapes and tones. I turned the light off to see better and to my surprise I saw my friend having his breakfast in his local café in Madrid, heard the

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waiter complain about Real Madrid’s performance last night, saw my mother walking by the sea on a beautiful windless morning. Saw a young boy running in the olive fields of south Portugal and heard the Levante wind blow hard across the moor. I saw ‘Saturno’ by Francisco Goya in the Prado. I heard a gale in the middle of the ocean and saw a boat struggling through it. I heard a guitar and a voice of a lady basking in the streets of Porto, it sounded like Fado. I heard laughter; a few boys were celebrating in a far away land, with a man looking at them in the corner of a bar. I saw a young girl praying by her bedside. I saw a boy walking in a dry plateau and heard the noise of rumbling pebbles. I saw and heard a group of men praying in a Muslim country. I heard a beautiful chant inside a big cathedral. I saw a planet in a far away galaxy which had two suns and three moons. I saw my self looking and listening. Everything was seen and heard in this malleable shape; a shape which looked similar to a nebula in outer space. To activate it, it seemed that all I had to do was look into it and I would hear and see an infinity of events in full clarity, and as soon as my eyes moved I would see and hear another event – this formless shape was tracking my eyes moving so that there was no overlapping in the imagery – and the transitions between events were very smooth. It was ten o’clock now and everyone was about to arrive so I decided to stop looking and listening. The magical object was returned to my pocket. The day carried on as normal – I finished the sculpture classes and left for home. I was completely overwhelmed by such a magical gift but I knew I could not share it out loud, even though I had an exhibition coming later in November where I was supposed to present the infinite Set {∞} in public. Just for a minute I imagined what the consequences of sharing such a gift might have on the audience. It was too risky so I kept it as a quiet secret. I had to be discreet and secretive about the whole experience.

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ix. Assemblage. November had arrived and I still had my magical object {∞} able to see and hear infinite possibility. I was really tempted to present it to the public at the exhibition, which I was going to do at the Peninsula Art Gallery in Plymouth, but instead I kept the object secret and presented an installation of my own composition, which informed the audience about the sublime Infinite set {∞}. What this installation9 explained is that the Infinite set {∞} is born from applying set theory to artistic practice and that by applying this mathematical theory to my praxis a pre-conceptual system, structure or whole is revealed whose subsets and elements are all abstract beings and entities. This infinite set {∞} could also be described as God or Substance; a Substance conceived through itself that does not depend on the conception of another thing from which it must be formed. This system or structure was made accessible to the viewer in both visual and tangible manner through the use of a Venn diagram10, a manifesto and seven blank Russian dolls. The short manifesto was addressed to all practitioners across art and design disciplines and it read: ‘For too long, arts praxis has been subject to the laws of bureaucracy, materiality, empiricism, and the phenomena of space and time. This praxis undermines artistic freedom. In order to find the answers to the most fundamental metaphysical questions, achieve artistic freedom, reveal paradoxes, uncover unhealthy bureaucratic practices, promote learning and nurture flux in the arts, we need to let go of these laws and find new ground. This task is seemingly possible with the aid of the mathematical instrument of set theory; a praxis that I call ‘sets art’. Sets art departs from the commodified theoretical views so predominant in the fine arts. In contrast, sets art is an infinite and holistic, malleable praxis composed of pure potential where limitations, rigidity, hierarchies, a priori & a posteriori knowledge, fixed methodologies and fragmentations are revealed and sublime immaterial expressions communicated. Hence, there are constant opportunities for the artist’s learning and growth. I term the pre-conceptual system or structure, this critical practice reveals, the infinite set {∞} whose subsets and elements are all abstract

9 Go to appendix reference 9. 10 A diagram representing mathematical and logical sets pictorially as circles.

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beings and entities. The infinite set {∞} could also be described as God or Substance; a Substance conceived through itself that does not depend on the conception of another thing from which it must be formed…[to be continued]’ Success and discreetness had been achieved – my magical object {∞} had been kept secret and the audience who attended the Assemblage exhibition in Plymouth Peninsula Art Gallery had been introduced and informed about some of the basic consequences of applying set theory to art practice.

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Chapter IV; {∞} numerous properties.

i. The whole {∞} is not greater than some of its parts. ii. {∞} God or Substance is not pure but the subset Ø is pure. iii. {∞} U ø; the union of {∞} and Ø. iv. {∞} ∩ Ø; the intersection infinite-empty/empty-infinite. v. N.

i. The whole {∞} is not greater than some of its parts. At this stage, deeply immersed in the study of set theory and its application to art practice, I must highlight that some of the properties of the Infinite Set {∞} were not entirely revealed at Assemblage. This was due to the complexity the diagram would have acquired if more properties had been added and the difficulty this would have posed to the viewer; particularly as the aim of the installation was to communicate simplicity and sublimity. For this reason I decided not to mention some of the properties of {∞} but to reveal them in this thesis. As explained earlier, the Infinite set {∞} suffers from an inability to present itself physically. Basically {∞} and the sublime immaterial aesthetic which accompanies it are physically indiscernible to human beings. So if I wish to represent the Infinite Set {∞} I need to present it linearly as the infinite sequence of real numbers11 and the finite set ø: {∞}= [-∞…-π...-3…-e… -2… -√2, -1….ø…1/2…1…2…e…3..π…99 …+∞] At this stage, a basic property of the Infinite Set {∞} is revealed, which is that if the infinite set is composed of the infinite sequence of real numbers, then the whole of {∞} is no greater than some of its parts. A statement not applicable to the finite empty set Ø, which is obviously smaller than {∞}.

11 The real numbers are: natural, integer, rational, real algebraic or irrational and trancendental or irrational.

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ii. {∞} God or Substance is not pure but the subset Ø is pure. Further reading into set theory reveals another property, that is the heredity or purity of sets. For a set to be pure all its elements must be hereditary sets. That is; all elements of the set are themselves sets, as are all elements of the elements, and so on. Now if we apply this property to the Infinite set we find that {∞} has one member which is a set, that is the empty set Ø and the other elements are the infinite sequence of real numbers, for this reason {∞} is not a pure set. However it is true that the empty set Ø is a pure or hereditary set because it only contains itself. The consequences of this claim are devastating. Earlier in this thesis I described the infinite set {∞} as God or Substance; a God or Substance which according to set theory, is not pure {∞}; it has been adulterated with every other substance. So the sublimity which accompanies the infinite set {∞} is not a pure sublimity but rather a corrupted one. Such a claim inevitably reframes our consciousness and our aesthetic preconceptions, by saying: God or Substance is not pure: a blasphemy I subscribe to.

iii. {∞} U Ø; the union of {∞} and Ø. As my reading and understanding of set theory develops I find that as a result of the previous operation the infinite set has split into an impure set and a pure set, {∞} and Ø respectively. With this split in mind I realize that if I wish to unite these two sets, I can by the binary operation Union (U): {∞} U Ø So the split encountered earlier, is solved by the union of the two opposites. Opposites whose inherent properties are united by the binary operation: Union (U), creating an intersection (denoted as ∩) formed by the purity Ø and the impurity {∞} which can be defined as: infinite-empty or empty-infinite. The result from the union of the infinite set {∞} with the empty set Ø equals the infinte set. This formula is written in numerical terms: {∞} U Ø= {∞} This means that the union of the infinite set {∞} with the empty set Ø equals the infinite set {∞}, since the infinite set {∞} contains the empty

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set Ø.

iv. {∞} ∩ Ø; the intersection infinite-empty/empty-infinite. The intersection (denoted ∩) of the Infinite set{∞} and the Empty Set Ø is the set that contains all elements of the Infinite set {∞} it also belongs to the Empty Set Ø and vice versa, but no other elements. In numerical terms it is presented as: {∞} ∩ Ø= Ø From this it can be understood that the intersection of the Infinite set {∞} and Empty set Ø equals the empty set Ø since the only element which belongs to both sets is the empty set Ø.

v. N. Within the Infinite Set {∞} we have the infinite sequence of the natural numbers, these naturals are part of an infinite space we call N. This is a space of infinite possibility and potential but only for all natural numbers with a topology12. It is a space of endless variation and combination, a space of endless permutation. From this descriptive chapter, this thesis will now move into a stage where the Infinite Set {∞} and its subset the Empty Set Ø are presented differently, that is physically rather than numerically.

12 Geometric properties and spatial relations unaffected by the continuous change of shape or size of figures.

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Chapter V the infinite set {∞} revealed.

i. A conception. ii. An oscillation. iii. A union (U). iv. {∞} is Ganzfeld.

In the previous chapter I have shown that when I apply set theory to artistic practice the result are two conceptual objects: the Empty Set Ø & the Infinite Set {∞}, being the Empty Set Ø a subset of the Infinite Set {∞}. These immaterial and sublime objects have in my opinion the property of partly revealing themselves physically and virtually. An opinion contrary to mathematical rigour.

i. A conception. The Infinite Set {∞}(God, Substance) is in my opinion analogous of the limitless ‘Ein Sof’. Let me explain – the ‘Ein Sof’ or the ‘Supreme whole’ in the ancient Jewish tradition of the Kabbalah13is what we can describe as God or Substance before giving any shape to the world, before producing any form, when the infinite set {∞} was alone, without form and without resemblance to anything else. It is the source from which the light of creation flows and emanates giving birth to the ten spheres of the ‘Sephiroth’ which make the ‘Tree of life’, also known as the unity and perfection of Divine nature. The ‘Ein Sof’ – just like the infinite set {∞} – is not a being, since it is self-contained and self-sufficient and not limited to its own existence. It is limitless. In some doctrines or secret societies such as Freemasonry it is understood as the ‘Supreme God’ – superior even to the ‘Great Architect of the Universe’ or ‘the Creator’. This non-being is a principle, which remains without manifestation, it is imperceptible and is apparently incomprehensible to human intellect. Yet a glimpse of such ‘non-being’ was achieved in one sculpture part of the series: ‘Conceptions into material space’ made earlier 2009, this object was inspired by research into the ancient knowledge of Kabbalah. A research which was heavily influenced by the conceptual structure present in the ‘Sephiroth’14. A structure which was then mimicked and used as the armature for the construction of the experimental piece: ‘Conception into material space num I’15.

13 Mystical interpretation of the Bible. 14 Go to Appendix reference 3 piece G. 15 Go to Appendix reference 4.

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ii. An oscillation. The source of light from which the infinite set {∞}, God or Substance flows is according to the ancient Jewish tradition of the Kabbalah pure white light indiscernible to the human eye; this source is electromagnetic radiation, part of an infinite and continuous electromagnetic spectrum. There are analogue signals apparently indiscernible to us humans which reside beyond our human perception, yet they are emitted by the source {∞}. I understand this to be similar to long distance analogue, electrical or digital transmissions of written messages without physical transport of letters, i.e. the telegraph or recent forms of data transmissions such as fax, email, telephone and computer networks in general. So I wonder: Is there any form of analogue technology capable of identifying manifestations such as this for later decoding and communication to human beings? Or is there any existing technology capable of mimicking the manifestations of the Substance or God {∞}? The answer to these speculative thoughts was revealed on mid November 2009 as I was returning from a journey abroad. While seated on the passengers seat and immersed in thoughts and questions about the Infinite Set {∞} God, Substance and its manifestations, thunder and lightning struck, followed by a car registration ‘ELF’ pulling into the motorway from the left side. On arrival at my destination and urged by curiosity I ran upstairs to the attic, turned the computer on and examined such coincidences and symbolism on the Internet. The solution to the apophenic16 mystery was eventually solved: light, which emanates form the Infinite Set {∞}, God or Substance is to be found in ELF 17; electromagnetic radiation and frequencies naturally present in lighting strikes. As the mystery was revealed and the needle in the haystack found I began to wonder which analogue technology would be most suited to make this manifestation accessible to our limited perception. The most economical answer arrived in no time: an analogue oscillator. This device generates oscillating extremely low frequency electric currents or voltages by non-mechanical means, currents which can go as low as 0.5 Hz. With this limited creative spectrum in mind 30 to 0.5 Hz and the device available, I decided to create five sound compositions18 based on oscillations, progression and drones, which in my opinion, mimic the imaginary

16 Aphopenia is the experience of seeing patterns or connections in random or meaningless data. 17 Extremely low frequency 3 to 30 Hz. 18 Go to appendix reference 5.

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manifestation and experience of God or Substance {∞} in the human perceptual and cognitive spectrums. These manifestations are present in the deepest states of meditation and ecstasy of sacred humans; a dominant theme of religious imagery in the Golden Century19 of Spanish sculpture and painting which represented the theme of God {∞} and its manifestations in a hierarchical illustration. Amongst this XVII century magna oeuvre20 there are two craftsmen worthy of mention for the relation their oeuvre has to my personal interest. They are:

• Francisco de Zurbaran for his: ‘Saint Francis in Meditation’ 1635-39 and

• Pedro de la Mena for his: ‘Saint Francis standing in Ecstasy’, 1663. It is worth acknowledging that this period in art history, dominated by the theme of God or Substance {∞} is unique since the dialogue between painting and sculpture, eventually lead to the creation of the technique: ‘Imagineria’21 which blended both disciplines into three dimensional mixed media hyperealistic works of art, such as the work of Pedro de la Mena. However I would like to highlight my deepest disagreement with the bottom up narrative so predominant and latent in art history (as it distracts the human for its natural surroundings) and gives an impression of an un-reachable God and Substance {∞}. We need to understand the infinite set, God or Substance {∞} not as an external or internal being but rather as a substance present everywhere in everything: ubiquitous. So the dialogue between the infinite set {∞} and its members is not one of hierarchy, interiority/exteriority but rather one of evenness, totality and flux.

19 XVII century (1600 to 1700) in Spain. 20 Go to Appendix reference 6. 21 Religious sculptural image-making or imaging in Spain.

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iii. A Union (U). Previously I have shown the physical manifestations of the infinite set {∞}, God or Substance. In this subchapter, I will begin to wonder about what manifestations that the operations between the Empty set Ø and the Infinite Set {∞} will present? What physical or virtual appearance will the union of these two sets have? I decided to use video 22for this task and to equate the infinite set {∞} to all the sound frequencies audible to humans as well as white light and the empty set Ø to silence and darkness. In set theory the union of the infinite set {∞} with the empty set Ø will equal the infinite set {∞} whose subset is the empty set Ø. This mathematical operation is translated to video as: the Union of the two sets. This is presented by sound and white light being played at once with one interval of silence and darkness. Digital video seems to illustrate quite well the actual operation but fails to present the union of the infinite set {∞} and the empty set Ø in their totality. Therefore I have to conform to a merely perceptual glimpse: a movement, which translates into a small, yet beautiful, audiovisual representation f the union.

22 Go to appendix reference 7.

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iv. {∞} is Ganzfeld. The infinite set {∞} God or Substance is in my opinion analogous to a total field of perception or Ganzfeld (Massumi 2002: 144-148). From the late 1920’s to the mid-1960’s researchers in the field of scientific psychology became fascinated by the term Ganzfeld, which was described as a total field of perception and in particular a total field of vision. Their research lead them to speculate that if you could experimentally isolate the physical and the physiological conditions of vision at their purest and simplest you would discover the elementary foundations of vision. From that point scientists could build in levels of complexity until visual perception was reconstituted. A classical scientific method based in reduction and reconstitution. The first simple revelation is that vision is produced by light striking the retina and that white light is the simultaneous presentation of the full spectrum of colour. Numerous devices were invented to achieve this; the most typical were goggles that were made of ping-pong balls cut in half, which were then fitted over the eye sockets and illuminated. These experiments were carried on for quite a long time and the devices were improved over the years, yet scientist failed to discover the most fundamental and primitive foundations of vision since the results gained through their experiments lead them to anomalous results. Researchers did not know what to do with this empirical data – they had arrived at an inhospitable ground for scientific reconstitution (Massumi 2002: 145). One of the most interesting anomalies was that some of the tested subjects – in whom pure vision was produced – found it extremely difficult to express, in terms of associated phenomena, what they saw. This happened predominantly in subjects who were tested for long exposures (ten or twenty minutes). Some subjects even reported difficulty in sensing whether their eyes were open or closed, their vision would blank out, it seems that when exposed to a pure visual experience a complete absence of seeing will accompany. This visual un-experience was reported to extend beyond the eyes and various after effects were found such as fatigue and/or a feeling of great lightness in the body. The motor coordination of some subjects was poor and some even found it difficult to maintain balance after a long exposure. Their time perception was disturbed and dizziness as well as an appearance of intoxication also became predominant side effects of the subjects who undertook the visual experiment. Some of the subjects even reported temporary states of depersonalization (Massumi 2002: 145). Scientific psychology during these 30 years was capable of activating the simplest physiological and physical conditions of vision, that is the most

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objective conditions of pure vision. This resulted in the cancellation not just of seeing but of motor-sensory perception, subjects will literally float out of their bodies and lose themselves into an hallucinogenic experience where vision was (to the embarrassment of scientists) non existent. This lead scientists to understand vision as an impure form of perception which co-functions with other senses from which it receives a continuous feed and itself feeds into, i.e. propriaception23, hearing, or touch to name some. These conclusions gave scientific researchers the idea of adding some form of stimulation to the controlled experiments, as they thought that by restoring it to its naturally multimodal nexus would bring it back into a form of experience. But again the results were not what they expected: subjects reported extensive hallucinations accompanied by an even more remote hold on reality: they were experiencing pure flux, a departure from the body, time and space. Most subjects described the experiments as an out of focus cloud, which looked like fog of no determinate shape or measurable distance from the eyes. Some subjects reported seeing nothing and another subject reported seeing levels of nothingness (Massumi 2002: 146). This variability in description puzzled the researchers, who found common agreement on the fogginess and milky white tone of the visualizations reported by the subjects. Scientists were also determined to find whether there was any perception of texture and of form in the experiments, but the participants did not report any objects, edges, forms or textures. The research was proving both unpredictable and variable according to subjects – however, there was one thing where the subjects were unanimous – in that the experiment was ambiguous, indeterminate and indefinite and that there was nothing of definite size, illuminated or shadowed; so nothing could be built as an object from the results obtained in the experiments. Which is to say that the objective condition of vision excluded the visualization of an object, instead the participants could only visualize object-like impressions such as edges and slant, indeterminate with respect to depth and neither two nor three dimensional, but not flat. This fog of pure vision was vaguely surface like. Participants in these experiments were describing without knowing a vacuum of vision. In physics a vacuum is understood as the random coming in and out of existence of all possible particles – it is chaos –which is to say that pure vision, that is the simplest and fullest empirical condition of vision, is a visual chaos, an abstract space or space-like abstraction (Massumi 2002: 147). So the experiments into the total field of vision were producing a visual experience of the visually un-experienceable: a self-abstraction of vision. Vision at its simplest and

23 Is the sense of the relative position of neighbouring parts of the body.

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most concrete, that is when white light is projected into the retina as a complex presentation of its own abstraction, so the closer you get to the physical, physiological and objective basis of vision, the more vision abstracts. What the experiments accomplished, rather than distilling vision to an elementary unit, was to approach a limit, a limit field or limit point for the total field of vision or Ganzfeld were the common feature of the participants’ descriptions was motion. As some participants reported: ‘a white you could go into...a fog coming up where you might wander for hours’, ‘just like a high altitude flight in which the body loses all orientation’, in other words pure kinesis. It is at this stage where discordance occurs – if the infinite set {∞} God or Substance is analogous to a total field of perception (and in particular a total field of vision or Ganzfeld) then this field must be infinite rather than have a limit or confinement. So ideally this experiment will need to include the infinite and continuous electromagnetic spectrum, not just white light projected into the retina. The consequences of this experiment would be are unknown, but probably if the infinite totality of electromagnetic radiation was to be projected onto a participant, I believe that he or she would probably die.

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Chapter V+1; a few conclusions.

i. {∞} and Ø exist. ii. {∞} is totality. iii. ‘Recovering artist freedom’. iv. The aesthetics of {∞} v. Beyond {∞}.

In the last five chapters I have gradually introduced set theory to art practice. Basically I have ‘swapped’ my modeling tools and materials for this mathematical instrument and looked into some of the consequences this produces in my art practice. In this last chapter I intend to highlight some of the key conclusions from the introduction of this mathematical instrument to art practice and suggest further research into an art practice I have termed: ‘sets art’.

i. {∞} and Ø exist. The Infinite Set God or Substance {∞}, the subset Empty Set Ø and all its elements exist semantically, linguistically and conceptually. {∞} and Ø are sublime immaterial objects, constructs of our intellect, the result of our ability to abstract and they need human conciousness to be presented and to exist.

ii. {∞} is totality. The Infinite Set {∞} God or Substance is in my opinion analogous of a total system, an infinite totality present in everything and everywhere, transcendent and absolute, independent and objective, immanent and inherent, fluid and elastic. This totality is not limited to time or space, it stretches beyond the limits of nature but not detached from it, since it can partly manifest in the physical world. In other words the Infinite Set {∞} God or Substance and the subset or Empty set Ø is an infinite whole, an entirety. As this video demonstrates24.

24 Go to appendix reference 8.

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iii. ‘Recovering artistic freedom’. I am a strong believer that for too long artistic freedom has been undermined by the laws of mimesis, bureaucracy, materiality, empiricism, and the phenomena of space and time. I believe this harms and undermines artistic freedom and in order to find the answers to the most fundamental metaphysical questions, achieve greater artistic freedom, reveal paradoxes, uncover unhealthy bureaucratic practices, promote learning and nurture flux in the arts, fine artist need to let go of these laws and find new ground. This task may be possible with the aid of the mathematical instrument of set theory; a practice that I have termed ‘sets art’. Sets art is a triumph in the creation of sublime immaterial expressions which are accompanied by an organization of thought and an economy of mediums, where the fine artist is not a consumer of materials but first and foremost a creator. I believe that ‘sets art’ heralds a recovery of artistic freedom and a departure from commodified theoretical views so predominant in the fine arts. Sets art creates a formulation which if followed can instigate diverse opportunities for the enhancement of the artists’ learning and growth.

iv. The aesthetics of {∞}. Where to position the aesthetics of the Infinite Set {∞} God or Substance {∞} is a task which needs doing. In my opinion the Infinite set {∞} can be understood and perceived as ‘anti-art’ as it describes a part of the soul through calculation and number rooted in pure thought. This part of the soul it describes is total and absolute, immanent and singular positioned in, by in I mean enclosed, within. The Greek word mimesis ‘representation’ is now a days used to describe artistic creation as a whole and interpret to mean a rather literal imitation. The production of the artist (painter or sculptor) are imitations of life which has itself a secondary reality, neither painter nor sculptor have any knowledge of what they imitate. So this art is secondhand unreal telling us nothing about life. (Plato, 1955: 359). As a result the Infinite Set {∞} is an artistic creation that denies ‘the reflection/object relation’, reacting against the idea of mimesis and the poetic reflection of ‘nature’, hence closer to truth and away from mimesis (Badiou, 2005:15). So this move away from the tradition of mimesis highlights in my opinion a new aesthetic era, which I call post-mimetic, where the creator draws from the inner and non geometrical rather than from ‘the reflection/object relation’ and the poetic reflection of ‘nature’.

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So where does this novel -post-mimetic- proposition come from? Historically it can be first located in Plato’s Republic. The Greek thinker, a refined connoisseur of all the arts of his time, shares a reactionary judgment directed against mimesis only where military music and patriotic song are spared. Such view contrasts with the classical and romantic schemas. The later one suggests that art alone is capable of truth. So art accomplishes what philosophy can only point toward. Art in this romantic schema is the real body of truth the ‘literary absolute’. This real body is a glorious body. Philosophy is the withdrawn an impenetrable father-art is the suffering son who saves and redeems. Genius is crucifixion and resurrection. In this respect is art itself that educates, because it teaches of the power of infinity held within the tormented cohesion of a form (Badiou, 2005:5). Art delivers us from the subjective barrenness and bleakness of the concept. Art is the absolute as subject-its incarnation. The figure of the poet-thinker is born. Now if we add singularity and immanence to our XX century mimetic, cassical and romantic schemas we generate a novel proposition, what Badiou regards as in-aesthetics (Badiou, 2005:5): ‘By “inaesthetics” I understand a relation of philosophy to art, maintaining that art itself is a producer of truths, makes no claim to turn art into an object for philosophy. Against aesthetic speculation, describes the strictly intra-philosophical effects produced by the independent existence of some works of art’. A novel schema that generates truths and these truths are given nowhere than in the art being generated. At this stage art becomes pedagogical because it produces truths and because education has never meant anything but learning truth. At this stage we find the problem of the relation of the infinite and the finite. A truth is an infinite multiplicity. This was the insight proper to the partisans of the romantic schema before they obliterated their discovery in the aesthetic diagram of finitude of the artists as the Christ of the idea. Or to be more conceptual: the infinity of a truth is the property whereby it substracts it self from its pure and simple identity with the establish forms of knowledge (Badiou, 2005:15). A work of art is essentially finite. It is trebly finite. First of all it exposes itself as finite objectivity in space and time. It is always regulated by a Greek principle of completion: it moves within the fulfillment of its own limit. It signals its display of all the perfection which it is capable. Finally

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it sets up as an inquiry into the question of its own finality. It is the persuasive procedure of its own finitude. The work of art is in fact the only finite thing that exists, art creates intrinsic finitude. (Badiou, 2005:11). Thus, if one whishes to argue that the work is a truth, one will have to maintain that it is the descent of the infinite-true, what I have termed the infinite set {∞}, into finitude. Precisely what the romantic schema defends. So it seems clear the use of set theory as my instrument allows me to realize of the finitude of art, but also makes me realize of the possibility of creating infinity in the form of the Infinite Set {∞} hence maintaining a novel aesthetic schema in my practice, a post-mimetic position which reacts against the idea of mimesis and the poetic reflection of ‘nature’ hence drawing from the inner soul.

v. Beyond {∞}. As this thesis draws to an end I begin to wonder about what might be beyond the Infinite Set {∞} and what also might be the next stage of my research. As a result I have decided to operate the infinite set and remove a few of its members: these are the integers, the natural numbers as well as the Empty Set Ø so that I can get to the Uncountable Set {U}, which I believe lies beyond the Infinite Set {∞}. My opinion is built on the mathematical fact that the Infinite set is countable. I can count its members, which equal 7, so the cardinality of the Infinite Set {∞} is 7. However the cardinality of the uncountable set {U} is uncountable. This fascinating property makes me realize that uncountability is what lies beyond infinity, an uncountability which is illogical, vast, huge, sublime and which can be understood to a greater degree through the study of Naïve set theory25. So I have arrived at the next stage of my research, a research which seems to be driven by a curiosity to unearth the very foundations of fine art practice with the aid of the mathematical instrument set theory. This uncountable set {U} is equitable to anything uncountable, like an uncountable noun, and is not art an uncountable noun in the linguistic sense, as are literature and education? So if art is linguistically an uncountable noun then the Uncountable Set {U} is art. By Miguel Oliveros.

25 Is one of several theories of sets used in the discussion of the foundations of mathematics.

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Appendix: Reference 1: Title: {} is the empty or pure potential, 2009 Media: Transparency Miguel Oliveros http://www.flickr.com/photos/36765241@N08/4348952199/ Reference 2: Title: The infinite set {∞} God or Substance, 2009 Media: Installation (Acetate transparency and seven blank Russian dolls) Miguel Oliveros http://www.flickr.com/photos/36765241@N08/4047771447/

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Reference 3: ‘The Sephiroth’ Media: Ink on paper. Author: Unkwown

Reference 4: Title: ‘Conception into material space num I.’ 2009. Media: White stoneware reinforced with metallic gold. Miguel Oliveros http://migoliveros.blogspot.com/2009/09/opus-num-i-form-empty.html Reference 5: Title: Oscillating progression, 2009 Media: mp3 Miguel Oliveros http://www.myspace.com/migueloliveros

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Reference 6: Title: ‘Saint Francis in Meditation’ 1635-39 Media: Oil on canvas Francisco de Zurbaran

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Title: ‘Saint Francis standing in Ecstasy’, 1663. Media: Polychrome wood. Pedro de la Mena:

Reference 7: Title: {∞} U Ø={∞}, 2010. Media: Digital video Miguel Oliveros http://www.youtube.com/watch?v=7NTL-eb8uGk

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Reference 8: Title: The desired signal, 2009. Media: Digital video Miguel Oliveros http://www.youtube.com/watch?v=KIX_9n7ZXKw Reference 9: Title: {∞} is God or Substance, 2009. Media: Acetate, manifesto and 7 blank Russian dolls. Miguel Oliveros

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Edward Kasner and James Newman 1940. Mathematics and the imagination. Penguin books Brian Massumi 2002. Parables for the virtual, movement, affect, sensation. Duke University Press. S. Pancoast M.D. 2005. Kabbala: or true sience of light. Kessinger Publishing. Spinoza 1910. Ethics and on the correction of the understanding. Everyman’s Library. John Locke and John W. Yolton 1985. Essay concerning human understanding (Volumes 1 and 2). Everyman Paperbacks.