Fearghus raftery by AA School

The True Time Image

Fearghus Raftery Fifth Year Diploma Unit Seven

The Architectural Association School of Architecture 36 Bedford Square Bloomsbury 2016

01 Introduction 09

PART ONE 02 Timelessness and Newtonianism 17 03 The Final State of Equilibrium 33

PART TWO 04 Time as Fundamental 43

PART THREE 05 Bergsoniam Cinema 51 06 The True-Time-Image 69

Introduction

What is time? This question is one that cuts to the heart of our human existence. We perceive a flow of moments that together constitute our life. From womb, to tomb, everything we think, do or feel, exists in time. It is the most universal of human feelings, and yet scientists and philosophers have repeatedly denied its objective existence beyond that of an illusion. Whether found in the writings of Julian Barbour (1999) for example, or indeed in the notes of Einstein, we find evidence of the solace found in the disappearance of time from our understanding of existence: â&#x20AC;&#x2DC;Now he has departed from this strange world a little ahead of me. That means nothing. People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion.â&#x20AC;&#x2122; Albert Einstein, in a letter of condolence to the Besso family1. Despite this I believe firmly that time is an intrinsic property in understanding our existence, and its reality is the subject of much of this text. The central quality of time to our existence is one of paramount importance to our day-to-day being, and has become the leading principle of investigation in my own work since a visit in 2005 to the permanent collection at the Tate Modern. I came across a dimly lit room situated in the centre of one of the primary galleries. With only one door and no windows I was curious as to what was hung in there and why it had this secluded, seemingly elevated presence over the other work on display. Surrounding two wooden pews were eight of Mark Rothkoâ&#x20AC;&#x2122;s Seagram Murals that pulsated with enigmatic

INTRODUCTION

beauty. It was a series that crept up on me like a shudder, until I sat down in front of No.6, and the shudder became like a rolling thunder. The depth present in the windows of intense, dark colour struck me as about as close to infinity as I would ever get, they were like nothing I had ever seen before, yet also, in some way, communicated everything I had ever known. I went on to spend over two hours in that room, periodically leaving, only to come back and marvel at the complexity of the work in such a crystalline form. It was a moment that since I have been able to ascribe as the beginning of my own fascination with basic human emotions2. I have come to know much more about Rothko’s work since then, particularly this series, and I am yet to find a more exquisite communication of the overpowering complexity of human thought. In this series I see a parallel with the misleading simplicity of our notion of time. A concept of paramount importance that may well be easy to miss, amongst all the Pollock’s and Warhol’s. By referring to the ‘simplicity’ of our notion of time I am of course referring to the modern daily references to time, time as a metric, time as a tool of commerce and modern living. As Aristotle and Einstein wrote extensively about time, in the least simplistic of ways, and their arguments will feature extensively in this investigation. Relics referring to our ingrained perception of time and the eternal can be found in the language, laws, science and culture of our everyday lives. Our entire existence takes place within time but the ‘truest’ aspects of it lie outside of this standard. The things we perceive as really true are those that are now, but always will be true, they are elevated to a position that transcends time. The acceptance of mortality is understood as an absolute because it remains true in every circumstance. Beauty and justice are spoken of as timeless. Whether we worship at a temple or a church, or practice complex experiments; the principle of a God, that is both immanent and transcendent (an idea that has permeated human reality for thousands of years), and the principles of mathematics are elevated to a timeless realm. This leads to a paradox in our existence which is that we are governed by a time bound reality, but the things we truly admire exist in a timeless world, it is a two tier existence that leads us to a state of disaffection from what is of most importance to us. We speak of ‘rising to the occasion’, which is traceable to the theory of the ancients that the Gods lie in a realm above us, and conversely we speak of ‘falling in love’ which is referring to the surrender to a loss of control. More specifically the opposition of rising and falling here references that hell is beneath us, we sink towards the earth, and that God and everything we ultimately desire exists above us. This goes some way to conveying the boldness of the claim that time is fundamental and what is not conveyed in this short introduction will

INTRODUCTION

be outlined in detail later. It is my aim with part one of this text to examine the foundations for a timeless picture of reality in theoretical physics. Then to put forward a case for the reality of time in in part two, before constructing my own principle of the true-time-image in part three, through discussions on Bergson’s theories of movement. These sections can loosely be understood as comments on time and movement from the perspective of; theoretical and practical physics, and philosophical writings on cinema. The reason for the strong sense of sequence in each of the sections and the three parts is to frame each argument with respect to the last. In order to discuss Bergson’s principles of movement and time, it is necessary to have discussed Einstein’s concept of spacetime, and in order to discuss spacetime it is necessary to have discussed Newton’s laws of motion etc… These three sections together will form my case for the use of film as a principle medium reflecting the essentialness of time and the emergent qualities of space. It is important to note at this point, that I am neither a physicist nor a philosopher, but I have always been fascinated with the questions that are asked at the intersection between these two fields. What is written here does not constitute an index or inventory of either of the fields, but a process of thought and understanding that I have formulated from the perspective of the architect. My own personal inspiration lies in equal parts; in the gaps of scientific understanding, and in the richness of the experience of films. It is in this domain, that this thesis is to be understood. Perhaps it is my own fascination with basic human emotions3, as Mark Rothko eloquently put it when describing his Seagram series, that has lead me to the fields of theoretical physics in search of explanations. Or it could be a reflection on the training of the architect; one that is defined by the practical implementation of principles to achieve and end that surpasses the means. I would also assert that there is no more relevant discussion than that, which is at the forefront of our understanding of what it means to exist as a human being.

PART ONE

Timelessness and Newtonianism

In this, the first section of this thesis I will discuss the foundations of our understanding that time is an illusion. I have mentioned how the ‘eternal’ or ‘timeless’ have entered our language and colloquialisms, but this of course is partly as a result of the fundamental theories of classical and modern physics, which at each step of their inception gently remove the importance of time. Or perhaps a fairer description would be that they fail to recognise the significance of what we call ‘now’ the present moment and its distinction from the past and future. The analogy is one of turning your back on inconvenient truths in favour of resolution and completeness. As you will see this part makes a formidable argument in favour of the case that time is not real. In the 17th century, using an inclined plane and a brass ball, Galileo Galilei made the important discovery that falling bodies trace parabolas1. It is a beautifully simple observation that came about from another; namely that falling bodies travel with a constant acceleration, whatever their size, or how hard they are thrown. This observation remains true however the experiment is conducted. You can propel a ball at varying speed, many times, from different heights and the path it takes will always be that of the parabola. The importance of this discovery cannot be underestimated because it is one of the first examples of mathematics being united in the everyday earthly realm,

TIMELESSNESS AND NEWTONIANISM

producing a ‘law’ of nature. Since then countless objects have fallen near the surface of the earth and this law has always remained true. Parabola’s as a mathematical concept existed well before this discovery2 but until then, no one had correctly asserted that this principle could be found in how objects move in reality. The perfect simplicity3 of the parabola is misleading in its description of reality. In actual fact, the ball that is thrown has a shape, colour and material, which the parabola fails to describe. It was probably affected by wind if it was thrown outside and most importantly of all it occurred in time. It left the hand of the person who threw it, rose slightly, then fell, and then it entered the past as an event. The parabola is and always will be a curve. It is in this regard that I speak of curves as timeless. It is an idea constituted of pure thought, parabolas do not exist in reality, we have invented them as a mechanism for measuring or at best understanding the world around us. An interesting way of illustrating the timelessness of such an assertion, and one method that I will revisit in parts two and three, is to imagine a film clip of the ball being thrown. If the background and mechanism for launching the ball were erased from each frame, to run the film backwards or forwards would be irrelevant to the observer, as no discernable difference can be identified in the path the ball took. This ‘symmetry in time’ is a re-occurring feature in the theories of 20th century physicists and perhaps the strongest argument that time, as we think of it, is an illusion. It is possible find approximations of the parabola outside of balls thrown, in a piece of string held loosely and allowed to sag under its own weight in the middle. Or similarly in the cables of a suspension bridge, but importantly they are always approximations of the parabola, with real life inconsistencies and imperfections. In this lies the foundation of the paradox of using mathematical principles to describe reality. What physicists study is unreal, and yet it somehow explains reality. What Galileo did was identify a particular concept, that until that point was reserved only for descriptions of the gods and the heavenly realm, and thread it into the experiences of everyday life on earth. There was no special qualification for objects falling and tracing parabolas but a single unified rule that everything follows. This cannot be underestimated as an influential discovery because until then there were two realms of existence. The heavens, containing timeless perfection and immortality, and the earthly sphere, containing us flawed humans, mortality and limitation. What was postulated when Galileo made this discovery was that, perhaps, there was

a deeper unified connection between these two worlds, between time-bound reality and timeless mathematics. Galileo was not the first to discover that motion can be coupled with curves, but he was the first to associate it with motion on earth. Long before him, the ancients had postulated that the planets moved in circles around the earth4. It was after all, consistent with their records and observations. Indeed Aristotle noted:

L CIRC

HYPE

RBOL

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‘in the whole range of time past, so far as our inherited records reach, no change appears to have taken place either in the whole scheme of the outermost heaven or in any of its proper parts’ (Simplicius and Mueller, 2014).

X P

A EL

LIP

A BOL PARA

HYPE RBOL

This principle is consistent with the theory that the natural state of anything is at rest. It was their thinking that if there was movement in the heavenly realms it would be nothing short of perfection, and thus the movement would trace the circumference of a circle5, the most perfect of mathematical shapes. It took Kepler’s discovery that the planets, specifically in his case that the orbit of Mars traces an ellipse6, for that dogma to be smashed and the questions leading to the discovery of the Sun’s place at the centre of our solar system to be asked. The following step was to be made by Isaac Newton in the connection between the heavenly ellipse and the earthly parabola. The legend of Newton goes that his epiphany came to him when he noticed apples falling in an orchard, whilst contemplating the motion of the moon. It was a discovery that lead to the unification of all motions whether propelled, dropped or orbiting, into a single set of laws of motion7. A clue to the mathematical unity of Galileo and Kepler’s discoveries can be seen in the geometry of conic sections. These are made when a plane intersects with a cone. On rotating the plane that intersects the cone, it is possible to illustrate that, in fact, circles, ellipses and parabolas belong to the same mathematical description. This is a notion that seems second nature to us but it took over half a century for this discovery to be made, namely that the falling we experience on earth and the orbiting of massive planetary bodies in space are propelled by the same force, gravity8. Newton’s first law captures the movement of a body if there is no force acting upon it, that of a straight line, and his second law of motion states that if there is a force acting on the body it will cause an acceleration of it9. So for the planets to

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CIRC

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be in orbit around the sun, the sun must be exerting a force on them, enough that they do not move in straight lines through space but trace ellipses, curves and hyperbolas depending on whether they are making one-off passes by the Sun, or travelling in a closed orbit. Newton’s laws of motion have a beautiful simplicity that is directly at odds with our sublime experience of nature. Therefore Newton was able to incorporate both Kelper’s observation of the planetary ellipse and Galileo’s observation that falling objects on the surface of the earth trace parabolas, into one theory of motion, the law of gravitation. Once it was identified that Kepler and Galileo had both made observations of the same phenomena, the world of science and particularly physics lived in a grand unified territory of mathematics. Our world, as far reaching as the outermost heavens, was fired by the perfection of divine curves and eternal mathematics. If Newton’s theory of gravity did not exorcise time from our understanding of nature then Einstein’s theory of general relativity certainly did. Literature, art, philosophy and just about every other field is littered with references to Einstein’s theories10. To properly address the notions of relativity theory there are a few definitions that I need to clarify, specifically that of motion, and more specifically that of position and time, as motion is almost always understood as change in position over time. Position can be given in two senses, that of the relational and the absolute. Object A is X distance from object B and Y distance from object C. This example is akin to giving an address, number 36, on Bedford Square, in Bloomsbury. These are relative positions that narrow down from some point of general interest into a specific place. The problem with giving relational positions is that there is no total frame of reference, where is London, in the UK, where is the UK, on Earth, where is the Earth, orbiting the Sun etc… one can imagine this scenario carrying on for ever, and indeed it has got very close. Space agencies across the world own maps of the universe giving relative positions for everything within it, billions of light years across11. However, crucially the measurement is never accurate enough and will always need some larger reference with which to place the rest of the information. The Newtonian paradigm was a success of the contrary, the absolute notion of position. For Newton, to define position you had to consider motion. Motion is the change in relative position (without considering time). One object moves relative to the other and therefore some sort of motion has taken place.

TIMELESSNESS AND NEWTONIANISM

But as anyone who has ever traveled by train knows, it is possible to observe motion when there is none, and of course it is also possible to observe no motion whatsoever when in fact there is plenty12. Newton found the relativity of motion problematic13 because it is as valid from observation that the sun moves around the earth, not the other way round, and this in turn makes it difficult to explain the causes of motion, like with the trains at Reading station there is a moment where I am not able to distinguish which train is moving. He therefore postulated that there was some sort of absolute space. He thought of absolute space as running through everything we know in the universe, an invisible aether, to which everything was referenced. This stops the infinite expansion of relative positions discussed earlier and gives meaning to motion and particularly position, but the problem remains that no one has ever detected it or measured it. No one has ever measured a position that was not a relative position14. So to refer to it within predictions ensues that the prediction cannot be tested through experiment. This of course is not a new idea and it was known to Newton to be a problem within the theory of absolute space, but it did not bother him. He was deeply religious and for him the notion of absolute space had philosophical meanings beyond that of science15. The fact that absolute space could not be detected only served to infer the existence of a Godly presence throughout the universe. The same argument was put forward in favour of absolute time. Time, like position is relative: ‘No one has ever measured a position that was not a relative position… All clock and calendar readings are relative times, just as addresses are relative positions.’ (Smolin, L. 2014). So relative space and time remains, and is the only method we have of studying phenomena. Einstein’s role in unifying them into what became known as spacetime is the final point in my case for time being unreal. Considering Muybridge’s work studying motion has greatly helped me understand the depth of the fusion between time and space. See in Figure three, Muybridge’s Animal and Human Locomotion 1887. A man is pictured centrally in a series of photographs jumping forward, we can imagine taking measurements of the man’s position at different points in the jump. His position relative to the ground, relative to the starting position and the point

TIMELESSNESS AND NEWTONIANISM

in time that measure is given. The measurement of time is produced by the photograph from which we are measuring (t1, t2, t3…); as with Muybridge’s studies of motion he used an electrically timed series of shutters to capture the motion16, famously for the first time, of a horse but in this case it is a man jumping forward. From this series of numbers we can produce a timeless table and study the data of the jump, inferring the motion that happened over and over again in the same way for eternity. Indeed here I am studying the motion of a man who created it in 1887. These numbers form a frozen record of the motion they are not the motion itself, and the confusion of motion and time continues when we take the numbers in the table and produce a graph of them. The man’s jump in reality traced a parabola as predicted by Galileo, and when the measurements of distance are plotted against the time it took for the jump to take place, what is produced is also a time reversible parabola. This is a false indication of movement and one that Bergson condemns in Creative Evolution ‘It [time] no more applies to becoming, so far as that is moving, than the bridges thrown here and there across the stream follow the water that flows under their arches’. To assume that the movement indicated in the graph is the same as, or is in fact actual movement is to make the error of spatialising time. A timeless curve cannot be a property of real motion, rather a representation of a record of arbitrary measurements of that motion. To call motion timeless is illogical, as actual motion is nothing but the expression of time. What Einstein did to space and time, with relativity theory, can loosely be understood within the equivalence principle17: ‘processes must unfold in a uniform gravitational field in exactly the same way as a frame of reference accelerated uniformly in a space free of gravity’ (Barbour, J. 2000) That is, that the natural state is one of falling. What we feel when we stand up is not gravity pulling us down, but the floor pushing up on our feet. Whilst Newton proposed that gravity acts to accelerate a body with a force inversely proportional to its mass, Einstein proposed that gravity acts on bodies with a force proportional to its mass18. In short these effects cancel each other out, so that any object falling, due to gravity, will accelerate at the same rate. What Einstein proposed was the symmetry of forces acting on a mass

TIMELESSNESS AND NEWTONIANISM

within space. It was not an absolute space, in which objects are subject to moving with no reciprocal action on space. The mass of the moving body also changes the nature of space. This has profound consequences for the nature of time that can be illustrated through geometry in the principles of geodesics. An object falling in Newton’s absolute space will trace a straight line, as we have seen, because it is the shortest distance between two points. In Einstein’s spacetime the line that is the shortest distance between two points can be curved, as if it were on the surface of a sphere, like a airplane flying from London to Tokyo, the shortest distance is an arc. The curvature of spacetime acts to transmit the forces of gravity on matter to cause it to move along geodesics, but additionally the mass of matter can curve the geometry of spacetime. This dynamical notion of space and time has all sorts of implications for the passage of what we call time on Earth. The famous quip of the ‘twin paradox’ is one, based on the idea that the passage of time is affected by acceleration, in addition to being affected by proximity to mass. Hypothetically if we were to take two twins born minutes apart on earth, and send one in a rocket on a return trip to the depths of space at the speed of light, time for that twin would stand still (not accounting for the time it takes to accelerate to that speed etc…). Many years later when this twin returned to earth, they would have aged only slightly, in comparison to the twin who remained on earth who would have aged exactly as much as the time it took for the first twin to make the journey. This is of course completely untested, however we do have actual real world implications of the manipulability of time even within our everyday experience. Satellites that orbit the earth enabling our GPS communications systems are fitted with atomic clocks, correct to the accuracy of 1 nanosecond (1x10−9 seconds or 0.0000000001 seconds), they take into account both the theories of special relativity and general relativity. The speed at which they move relative to us on earth means that time on board a satellite moves 7 microseconds in a day slower than on earth. In addition to this, their much further relative distance from the Earth’s mass speeds up time onboard a satellite, by 45 microseconds a day, relative to our clocks on earth. The overall affect is a -38 microsecond in every day correction onboard a satellite, to keep their clocks running accurate time compared to that on Earth. These margins sound small, but consider that a few flawed clocks across only some of the satellites in orbit around earth would be enough to throw off GPS systems on earth by up to 100’s of

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kilometers. GPS systems that run in everything from mobile phones to atomic weapons, the unreality of time is about as real as it can possibly be.

The Final State of Equilibrium

The problems with relativity being used to give a picture of the entire universe are well known. It is a useful method for describing the particulars of a given system; in this case our solar system, but it fails to give a picture of the universe as a whole, and more importantly for this text it fails to explain basic questions about the reality of time that we observe. Why do we remember the past and not the future? Why can I not manipulate time in the way I transverse space? As far as relativity is concerned you can transverse time as you do space1, all the equations constituting relativity theory are time reversible, like the film of the ball run backwards, they make sense whichever way time flows. This is its major argument for time being an illusion, but this is of course at odds with our existence; a warm cup of tea left on a desk will eventually cool, and no matter how long you leave it, it will never warm up again. In this chapter I will discuss how the foundations laid by classical physics have been built on to create an absurd picture of reality in 21st century physical theories. As I have stated before, the nature that surrounds us is incredibly complex, if we study the evolution of life on earth, we are confronted with the intricacy of the organisms that constitute it. This is a highly improbable state, and it is the same for the universe as a whole. The multitude of organized galaxies and planets orbiting stars has evolved out of not much more than

THE FINAL STATE OF EQULIBRIUM

clouds of gas and plasma. This improbable state requires explanation, as it is not simply accidental. Nothing can jump from simplicity to complexity instantaneously. Intrinsically eventual complexity requires the ramping up of a series of steps of exponentially increasing complexity over time. This implies a strong order, or line of time. Philosophers and physicists who argue in favour of time being an illusion support the unification of modern physics’ greatest triumph, quantum physics, with theories of cosmology producing the quantum theory of cosmology2. A school of thought characterized by the laws of thermodynamics. According to these laws, and indeed the laws of 19th century physics, the universe is destined to end in a state of equilibrium; a uniform state of matter and energy distributed throughout space in which nothing will happen, ignoring some random fluctuations. Time as we have understood thus far being the measure of change, will cease to exist without change in environment. This theory is interestingly analogous to the Aristolean theory of the natural state of everything being at rest. Science has progressed a great deal since his observations of no change in the outermost heavens3, and yet some of our most contemporary theories still reflect this tendency. The heat death of the universe as this final state of equilibrium is known, is based on the laws of increasing entropy4. Entropy simply put, corresponds to the number of different microstates a closed system can have to realise any particular macrostate. For example if we describe a glass of water in terms of its entropy, we can say that the system is contained by the limits of the glass, and to identify its macrostate one would suggest it has a temperature, in this case 21°C. This description has a very large entropy, because it is describing the average energy (temperature) of each of the molecules that make up the water. The energy of a molecule we know is a description of its movement, so in saying the glass is at 21°C we are giving billions of possible ways in which the microstate of the system can be configured to achieve this macrostate. The water molecules could be in any number of given positions throughout the glass. However if I was to state the precise location of each molecule and its direction of movement I would be giving a description with very low entropy, because there is only one way in which the system can be configured in order to result in the given macrostate (temperature of the water). Essentially those two descriptions describe the same thing, a glass of water at 21°C, but one is hugely more effective than the other, in terms of the level of data required to describe it. What the second

THE FINAL STATE OF EQULIBRIUM

law of thermodynamics states is that any closed system will tend towards a configuration of the most entropy. Say for example the glass of water now has a drop of dye in it. This too is an extremely low entropy configuration for the water with the dye in to have; as at the point where the dye enters the water, all the molecules of the dye are located in one place near the top of the glass, and all the water molecules are distributed evenly across the volume of the container. As we know the dye will eventually, over the course of 20 minutes or so, spread evenly across the glass of water producing an even distribution of both water and dye molecules, this is its’ state of equilibrium and is a high entropy state. This state is the most probable state for the glass of water to be in because each of the possible microstates it could be in are equally probable, however there are vastly more microstates where the water and the dye are evenly distributed than those where the dye stayed concentrated in the top of the glass. These logical descriptions are actualised by the fact that the molecules in the water are in chaotic motion and therefore randomize their movement. So concerning the quantum state of systems, the most likely result is an increase in entropy to the point of highest entropy which we call equilibrium. This, the second law of thermodynamics faced much criticism in its early inception because of its asymmetry, namely that entropy always increases. Because it concerns the laws of motion at the atomic level, it was postulated that it could not be a time asymmetric law. The laws of motion defined by Newton, as we have seen are symmetrical in time. Einstein’s theory of general relativity too is symmetrical with the nature of space acting on matter as matter too influences space, so how can it be that this law is not time reversible? Indeed these questions were later found out to be correct and it was discovered by Henri Pointcaré that the second law needed correcting. Entropy does indeed sometimes decrease, forming a more ordered state; it is just very improbable that it does. As long as the system is finite there will be periods where entropy decreases before increasing again, these fluctuations are very rare and take a long time to occur. The time it takes to observe this change in state is known as Pointcaré recurrence time, and forms the last argument in the expulsion of time from our understanding of the universe. Imagine a video clip of an expanse of water, into which a large amount of dye was introduced and we slowly watch as the dye creeps across the expanse to form a uniform state of distribution, it would be correct to observe that

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this is a strongly directional process and running it backwards would indeed indicate that time had been reversed, unlike the ball tracing a parabola in my earlier example. However if we observe the video over Pointcaré recurrence time there will be fluctuations in the entropy of the system, leading to periods where the dye is highly concentrated in various areas of the frame, before dissipating back into a state of equilibrium; and this would look much the same should the video clip be reversed, in fact it would be indiscernible from the original. When we view the time-symmetry of thermodynamics from the perspective of cosmology and the evolution of the universe the questions in which I started this chapter, and indeed this thesis, become even more interesting as almost every solution to the laws of physics with respect to quantum cosmology, ends with the state of the universe in placid equilibrium5. The analogy is that of the surface of a pond being restored to still surface tension, after a stone was skipped over the surface, but our observations tell us that the universe is nothing like a still pond, in fact it is more akin to rough seas, with dynamic waves and eddies thrashing around. We know that the universe we inhabit is very special, it is a highly ordered state6, so why is it that after almost 14 billion years since the big bang the universe is certainly not in equilibrium7? This problem lies in the relationship the laws of nature have with freely determinable initial conditions. Newton believed God positioned the planetary bodies into absolute space with specific motions, which have given rise to the laws of motion we observe. Einstein’s theory added to this principle the notion of the big bang, that is to say, a series of specific initial conditions, giving rise to the current state of the observable universe. Of these specifiable initial conditions the vast majority would have led to universes much less interesting than ours. So the burden of explaining why the universe is the way that it is falls to the specification of a vastly improbable initial state. This principle is directly at odds with the probabilistic nature of quantum cosmology, (the probability of an increase in the entropy of a system is vastly higher than a decrease) and is one that in part two, I will examine further in relation to the time symmetry we have discussed, found in Newton’s and subsequently Einstein’s laws.

PART TWO

Time as Fundamental

We have seen that across the gradual development of modern physics from Galileo and Kepler, through Newton, and onto Einstein and modern theories of quantum gravity and quantum cosmology, that the nature of time has been systematically ignored in favour of a picture of reality that is timeless. Indeed Bergon in Creative Evolution states: â&#x20AC;&#x2DC;Modern Science must be defined preeminently by its aspiration to take time as an independent variableâ&#x20AC;&#x2122;1. Nearly all physical theories constituting descriptions of the universe deny the existence of time, and postulate that what we experience as the present moment, is just an indication of change that will cease when eventually the universe ends in heat death and there is no more change to observe. The cosmos will truly be frozen in this timeless model. This is a formidable argument in favour of the timeless picture of reality, and whilst I revere the great thinkers I have discussed in this text, and their beautiful explanations of complex phenomena, the theories of the timeless picture of reality are, while exciting; containing black holes, mysterious dark energy, time travelling twins and half-dead-half-alive cats2, profoundly lacking in their descriptions of the experience of one of our most basic human feelings, time. This is an avenue that now forks in two directions; along one is the timeless picture of the world in which we accept the inconsistencies in the physical theories describing our reality, the other represents a persistent opinion that the methods we use to describe the reality

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around us, ought to do just that. To discuss effectively what I refer to as the reality of time, I would like to introduce the whole, as Deleuze speaks of it in Cinema One: ‘As soon as the whole is given to one in the order of forms or poses, or in the set of anyinstant-whatevers, then either time is no more than the image of eternity, or it is the consequence of the set; there is no longer room for real movement’ (Deleuze, G. 2005). I will expand on this statement in detail in the following chapter, but what is of importance here is that he has made a distinction between the false movements indicated through taking the Whole as given. This is the frame in which this chapter is to be understood, that is to say that what was discussed in part one takes the whole as given. The Newtonian paradigm, that we have found to extend into Einstein’s theory of relativity, as successful as it is, is inadequate when used to try to answer the bigger questions about the nature of time that we experience. When we analyse the movement of a ball through a parabola, we take the whole as given at the start of the process, this misses the true movement in reality, and is what is being referred to here, when Deleuze states; ‘there is no longer room for real movement3’. Perhaps the principle point in extending the Newtonian paradigm to questions of the whole universe is that, there is no way to define the whole universe. As we know it, the universe happens only once, and we are within it. We cannot take an external perspective with which to analyse it, as it is impossible not to be anywhere other than a moment of time within it. I have spoken briefly about the strong sense of the direction of time in the sequential events that lead to complexity from a simple state, and also in regard to our own feelings of the passage of time. It is in these ‘Arrows of Time’ that the strongest arguments in favour of time being fundamental are found4. Everyday we experience ‘arrows of time’ indicating the directionality of time; a cup of tea left out goes cold, the same cup knocked off the table will shatter, and not spontaneously re-assemble, we age from days to months, to years, eventually we die and there is no reversal of that process whatsoever. If the final state of equilibrium is taken as the reality of our position in the universe, there would be no directionality of time, like the video of the water with dye moving around in it, there are only temporary fluctuations in the state of the whole, because the physics describing that process are time symmetric, any solution

TIME AS FUNDAMENTAL

to the equation has a counter solution with all the charges of the atoms reversed and left and right swapped over etc. To use these laws to describe our physical reality would suggest that there were cups of tea that warmed up when left out, or shattered cups that re-formed and there were people that aged backwards. The reason these things do not happen is referred to as the problem of the arrow of time5. There are in fact many of them and they are loosely defined as follows: The Cosmological arrow of time, this points towards the fact that the universe is expanding and this expansion is accelerating. The Biological arrow of time, this points towards people, plants animals being born, aging and then dying. The Thermodynamic arrow of time, which states that the entropy of a system will always increase. The Experiential arrow of time, this is the fact that time flows from the future, through the present and into the past, and the Electromagnetic arrow of time, which points towards light moving from the past into the future, thus what we see is slightly in the past. Many physicists, who hypothesize the unreality of time, have in fact accounted for these inconsistencies within their theories. However crucially as I mentioned at the end of the previous section, it is necessary to select time-asymmetric initial conditions at the inception of the universe6, in order to preserve the current time-symmetric models of particle physics, in a theory that accounts for why we see strongly directional processes in time. The fact that time-symmetric laws, like that we have seen in the first part of this text have evolved out of asymmetrical initial conditions, greatly weakens this hypothesis. The inconvenience of the selection of the initial conditions is passed on, so we are left with no rational reason why it is, that it was that way. This is not to mention that vastly improbable initial conditions that have lead to a universe governed by time-symmetry is not consistent with the modes of the paradigm of quantum physics, which is a science of probabilities. The arguments offered in part one for the unreality of time form a strong case, but as we have seen, the very aspects of the theory that make it particularly successful for describing closed systems, are the same principles that diminish its credibility when applied to the universe as a whole.

PART THREE

Bergsonian Cinema

Theoretical physics has provided the framework for which I would like to examine the use of film within architecture. The argument for time being an illusion is impressive, however we have understood time to be of a more fundamental property, than any of the laws of the 20th century, and indeed the more modern theories suggest. It is impossible to deny the essential quality of time in our understanding of existence. So now we must begin to understand the way in which the use of film is essential as a medium that can deal with this particular quality of time, and subsequently the nature of what it is to exist. You may wonder why it is that I believe this, if the use of film has been a recurring example in my expression of the inadequacy of time-symmetric laws. Indeed this has been an obstacle in my formulating this thesis, over and over again. There seemed to me to be certain truths and untruths about both the theories of physical process I have discussed, and the theory of film I will discuss. On the one hand we have the undeniable truths that lie in the beautifully simple descriptions of physical phenomena, like propelled balls under the influence of gravity will always trace parabolas, but as discussed, to logically imply these laws to explain the nature of time, or indeed movement, is to find a dead end. As I will demonstrate through the examining of Bergsonâ&#x20AC;&#x2122;s theses on movement, we will find ourselves in much the same situation, namely that the filmic description of movement and

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therefore time, has its own truths and untruths. I hope however to move past these in a proposal for the technical use of film that surpasses the means. One in which it is possible to construct a true image of time, from nothing but the fundamental properties of film. It is not a hypothesis evolving the special adaptation of advanced equipment, or even specialist knowledge, the tools to create a true image of time are and have been available for many years; but more a theory of movement, space and time that reflects the existential questions that marked the beginning of this study. I will introduce Bergsonâ&#x20AC;&#x2122;s theses on movement in three parts, these theories examine movement very much from the perspective of cinema, but as I hope will be made clear, the principles with which each thesis is constructed will correspond to, and compliment, how we have understood the theories of classical and modern physics in part one. Bergsonâ&#x20AC;&#x2122;s first principle of movement is that movement is distinct from space covered1. This may at the outset be mistaken for a contradiction with how Newtonian physics was analysed in the preceding chapters. After all, was movement not suggested to be the change of relative position in time? It was, and is, but what Bergson is rejecting here is not the change in place or time that occurs, but the relationship, particularly modern, but actually both modern and classic notions of movement have to the distances covered during that movement. It is possible to talk about distance in so many different units, metric or imperial, ancient or modern, and indeed the same distinction can be made about each, but for this example I will discuss the kilometer. If we say that an object has moved from point A to point B which are a kilometer apart, we could easily describe the movement as a series of one meter lines, one thousand of them in varying directions and even planes if necessary. To carry on from the example in part one, each one-meter line would have a triplet of numbers; a starting coordinate, a finishing coordinate and a time taken between them both, to give a table of fairly high precision describing the path of the movement over 1 kilometer and the speed of the object including acceleration and deceleration. This would give us three-thousand numbers describing the movement of the object, and indeed we could account for the position of the object at each millimeter, producing threemillion numbers describing the objectâ&#x20AC;&#x2122;s movement. The point that Bergson is making here is that it does not matter how many measurements are taken, each measurement is an immobile section2 of movement, and the movement in

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question will always occur between the two points measured: ‘On the one hand, you can bring two instants or two positions together to infinity; but movement will always occur in the interval between the two (…) On the other hand, however much you divide and subdivide time, movement will always occur in a concrete duration [durée]3’ (Deleuze, G. 2005) The distinction made here, is one that movement is the present act of covering, and space covered is past. To divide movement is to change qualitatively what it is. This bears much resemblance to the Newtonian paradigm that introduced the timeless curve into our conception of movement. To produce the parabola of the man’s jump in Muybridge’s study, several measurements were taken or the movement was divided and subdivided in time and thus, the actual movement was missed. In both examples, a movement occurred in time, it was further divided and sub divided to identify what Deleuze refers to as, immobile sections4 of movement, (these are akin to the reel of stills on a strip of film that subject to being passed through a light projector, project the illusion of movement as we see it in cinema) these were then reconstituted to form an abstract representation of the movement in, abstract time. Abstract movement, plus, abstract time. Abstract time is a term used by Deleuze in his examination of Bergson’s theses on movement and a reference to the apparatus of the cinema. The cinematographic illusion takes place by the exact means with which I have just dismissed as the reconstitution of movement through immobile sections. The projection device of the cinema is bestowed with the same homogenous mechanical time with which the film was taken using a film camera, namely 24 fps. This is the same illusion we encountered in the first example I gave in part one of the ball and the parabola which, spatialised time using triplets of measurements containing coordinates and time taken, only this time the cinema is reconstituting movement with the use of still images that are mobilized by passing through the projection device with a mechanical abstract time. We therefore are to understand from Bergson’s first thesis on movement that it is two-fold. Movement is distinct from space covered, but this contains the presupposition that movement cannot be reconstructed by adding to immobile sections the idea of abstract time. In the case of our ball tracing the parabola, the movement is not defined by connecting the various

BERSONIAN CINEMA

measurements that were taken during its flight into a parabola curve, and in the case of cinema; by the adding of a mechanical, twenty-four frames per second homogenous time. Bergson’s second thesis on movement goes some way to expressing the particulars outlined in his first, and particularly the presupposition about the reconstitution of movement from immobile sections with the addition of abstract time. He identifies that there are two ways of reconstituting movement, the ancient and the modern: ‘For antiquity, movement refers to intelligible elements, Forms or Ideas which are themselves eternal and immobile5’ (Deleuze, G. 2005) The ancients reproduced movement from forms that themselves are eternal and immobile; in order for this to happen the form itself must be grasped as close as possible to the movement in a matter-flux6. I have found it helpful to think of this as a potentiality that is contained within the form. We need only to refer to Lacoön and His Sons for a fine example of this. This Hellenistic sculpture, recounting the tale of Lacoön, who after warning the Trojan citizens of trusting gifts from the Greeks was imminently killed along with his two sons by serpents sent by Poseidon, is perhaps the clearest embodiment of movement into a timeless and eternal form. It is this that Bergson is referring to in explaining the classical reconstitution of movement, from eternal poses7 that are themselves immobile. The sculpture does not move and has not, since the last piece of marble was chipped away to leave the form we now see, and yet it recounts the entire tale to this day. Each fold of marble delicately conveys the softness of the fabric slipping from the writhing body of Lacoön, or the flesh that is bitten into by the serpent. The sculpture therefore is a salient moment that forms the synthesis of the movement: ‘The forms or ideas […] are supposed, like the childhood or old age of a living being, to characterize a period of which they express the quintessence, all the rest of the period being filled by the passage, of no interest in itself, from one form to another form8’ (Bergson, H. 2015) Deleuze speaks of these eternal poses as privileged instants and they are in contrast to the any-instant-whatevers that describe modern movement.

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He elegantly states that instead of producing an intelligent synthesis of movement, a sensible analysis was derived from it9. It is this that I refer to when citing the example of the ball that traces a parabola, or even Muybridge’s studies of movement. The idea of transcendental formal poses that themselves embody movement; movement that between poses, is of no consequence because they themselves are the synthesis of it, has been replaced by the idea of a succession of equidistant instants. These instants are chosen arbitrarily, as we have discussed in the example of movement over the course of a kilometer, it is possible to describe it with one; ten, one-hundred, one-thousand, or millions of numbers. Film belongs to this modern conception of movement, the any-instant-whatever. However it is here that we encounter a similar argument that we found in part one, what is the significance of a system that produces false movement? From the point of view of science it has little or no significance, after all, the same illusion can be supposed by looking at a graph or perhaps even a table of numbers. Throughout this text I have cited the example of understanding physical phenomena through imagining films of balls flying or water moving, but it is this way round that these occurred. The physical process was isolated using mathematics (in most cases) and then the demonstration of it through the use of a video clip was suggested, as a method of approximate confirmation. Therefore to reduce the movement down to a series of any-instant-whatever’s is an approach of sensible analysis, to then build up the illusion of this movement through the addition of abstract time would seem inconsequential. If we reconsider the classical conception of movement, like in a ballet, built from the formal transition of eternal poses, or privileged instants. Can we not categorize cinema here with the high art of the ancients? It would seem not, as even whilst considering film’s dependency on the privileged instant; an example of which would be Muybridge’s study, The Horse in Motion, where there is a brief instant in the horse’s gallop in which all four limbs are off the ground that characterizes the motion, it is only one amongst any number of any-instant-whatevers. That is to say that the privileged instant of the classical conception of movement, whilst it may still appear as an any-instant-whatever in the modern conception of movement, is reduced to uniform importance among the number of any-instant-whatevers. It would seem film, whilst belonging to this modern notion of movement, does not fit exactly the specifications of a science or an art. Although the two theories of movement are distinct from

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one another, it is important to remember that the same effect is reached with both, that of false movement. In both cases a whole10 is being constructed, on the assumption that ‘all is given’: ‘As soon as the whole is given to one in the order of forms or poses, or in the set of any-instant-whatevers, then either time is no more than the image of eternity, or it is the consequence of the set; there is no longer room for real movement’ (Deleuze, G. 2005). So are we in the same position as we were with timeless curves, and the Newtonian paradigm? Deleuze suggests not: ‘For, if the ancient conception corresponds closely to the ancient philosophy, which aims to think the eternal, then the modern conception, modern science, calls upon another philosophy’ (Deleuze, G. 2005). ‘Bergson’s second thesis […] makes possible another way of looking at the cinema, a way in which it would no longer be just the perfected apparatus of the oldest illusion, but, on the contrary, the organ for perfecting the new reality’ (Deleuze, G. 2005). In this lies the crux of, not only the position of time within the framework of the modern theories of physics, but also time’s position with respect to film. We have seen in part one the timelessness of mathematical principles in their description of reality, cups of tea that get hotter and people ageing backwards. So is my dismissal of this quality the denial of its validity? Absolutely not. It would be quite audacious to suggest the inaccuracy of the theories of Newton and Einstein, apart from untrue, as I have said, they lead to testable, accurate predictions and have played intrinsic roles in the developments of science since. So we can confirm their validity. What I have presented in parts one and two is an argument for a new conception of timeless laws, into a singular theory that accounts for our experience of time. I do not have this theory, or indeed any idea what it may be, but it is in this way that we must address the apparent contradiction in using film as a mechanism for creating a true image of time. Whilst film reconstitutes movement, through the addition of an abstract time to mobile sections,

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which is analogous in this case to the laws of physics taking time as an independent variable, this is not a dismissal of the possibility of the same medium creating a true time image. In fact, it is far from it, as Deleuze writes it is the organ for perfecting the new reality11. Before embarking on what I have loosely referred to as the true time image I must finally put forward Bergson’s third thesis on movement. It will form the final point in a trio of principles that together form the basis with which to understand the true time image. On this we will return to the example of the glass of water that I used in part one, as Bergson uses this famous example in creative evolution, with respect to dissolving sugar: ‘if I want to mix a glass of sugar and water, I must, willy-nilly, wait until the sugar melts. […] For here the time I have to wait is not that mathematical time […] It coincides with my impatience, that is to say, with a certain portion of my own duration’ (Bergson, H. 2015) Apart from the omission that stirring the lump of sugar will lead to a quicker dissolving time in the water, what Bergson is referring to here is a qualitative change in the whole being an expression of duration, his own duration in fact. Deleuze identified concrete duration [dureé]12 in his analysis of Bergson’s first thesis on movement, and it demonstrates well the principle of his third. The time in which Bergson waited for the sugar lump to melt in the glass of water was unchangeable, unlike the time in which we encountered in part one where it is characterized by being relative. Any unit may be used to measure it, as it is taken as a quantifiable, and subsequently dividable whole. What Deleuze does, by effectively naming the time that Bergson is referring to as concrete duration, is distinguish the difference between the divisible time, that may be used to express the state of the molecules of water amongst which the molecules of sugar are eventually suspended, and the time in which the state of the water changed, from that of a glass of water containing some sugar to that of a glass of sugar water. The movements of the molecules have expressed a change in the Whole that encompasses the glass, the water and the sugar; this change is a manifestation of duration. But we have encountered the problems with taking the whole as given; indeed it is Bergson himself, who condemns this process as the error of modern science. The Bersonian whole is not givable because it is open, constantly changing,

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in new and novel ways or to put it another way, inherently unpredictable. Each time we can see an expression of duration, the time it takes for a cup of tea to cool to room temperature, we can assert that there is a whole that is changing: ‘The whole and the ‘wholes’ must not be confused with sets. Sets are closed, and everything which is closed is artificially closed […] a whole is not closed, it is open; and it has no parts’ (Deleuze, G. 2005) Deleuze clearly expresses the difference between the whole and the set. The whole being necessarily open must always be. It is a state of relentless change, of one qualitative state to another. Any expression of a closed set within this is an artificial break with the duration, and it does not affect the whole that continues. The sets are in space, and therefore the whole, but the whole exists in duration. The formula for Bergson’s first thesis on movement namely, immobile sections plus abstract time, is concerned with the movement within a set of finite parts. That is the false movement that we can see when we analyse a video clip of Muybridge’s man who jumps forward, or the ball that traces a parabola both forwards and backwards. The formula for this, his third thesis on movement is; real movement, plus, concrete duration13. This formula is the expression of the whole that changes, one that is open. The consequence of this third thesis is that with respect to movement we have identified three levels of analysis. Firstly the sets or systems, which have divisible parts; a man, a series of shutters and a floor, secondly the translation of this movement from point A to point B changing the relative positions of the parts, and thirdly the expression of change in the whole that is made by the movement, point A, B, the Man, and all that encompasses them has now changed as a result of the jump. From this we can see that the movement itself has two features, that of a change between parts of a system, and that of an expression of change in the whole. Consider the dividing up of parts of a set, as the identifying of immobile sections or any-instant-whatevers to which abstract time is added, and the movement that is established between the mobile sections, (immobile sections that are mobilized through the addition of abstract time) relates these parts or set to the duration of a whole. This third theses which is contained in the first chapter of Matter and Memory, insightfully expresses a sort of matryoshka

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of scales in the act of movement, whilst an instant (or still) is an immobile section of movement, movement is a mobile section of duration, or the Whole. The Whole we speak of here is akin to the experience of duration. It can be likened to the arrows of time I outlined in discussing the theories of the heat death of the universe, which were irreversible and express a qualitative change. This insight enables a further layer of understanding with respect to the incomplete theories stipulating a final state of equilibrium. Any closed system will follow the laws of thermodynamics, but it is exactly this that is the problem, we are not closed systems, our universe is certainly not a closed system, and if it is not closed, it must be open, at least in the Deleuzian sense that the whole is not given or givable, it is subject to constant change and evolution, a duration, or, to endure.

The True-Time-Image

It would seem movement can be thought of in three scales. I first outlined the mobilization of immobile sections; these are analogous in the case of film to the stills (instants) of a reel of film that is passed before a light projector as a cinematic device. Secondly; this cinematograph1, subsequent to the reel of film being passed at the correct speed past it, displays the movement that is the subject of the video, and thirdly there is the change in the whole, which is expressed by the movements of its parts. The immobile section is mobilized in the cinematograph producing movement; this movement then forms a mobile section of duration when, comprehended indirectly as the result of a change in the parts of a set. Would this then suppose, that we have managed to specify the whole? As we saw with respect to theoretical physics in part one, asserting the whole as anything other than a quality whose nature is to change constantly leads to a dead end. Galileo, Newton and Einsteinâ&#x20AC;&#x2122;s theories examine physical phenomena under the pretense that the whole is a given quantity, and thus, whilst producing sublime formulae and accurately testable predictions for closed subsystems of the universe, they miss the truest qualities of our existence like the palpable nature of concrete duration. If we are to envisage a true image of time, through film, we must apply the three levels of the Bersonian analysis of movement to the film as a whole. Stills, movement and duration become, framing, cutting and

THE TRUE TIME IMAGE

montage. The apprehension of a whole, that is, some portion of duration, is an indirect result of the montage of video. The first level, and therefore stage in constructing a true-time-image, is that of the shot. The shot can be constructed in many different ways, including a mobile viewpoint, and changes in spatial sequence. If we consider the fixed shots that characterize the work of Roy Andersson, where all events take place within a fixed viewing point, and contrast this with, for example, Carax’s Holy Motors, the sequence where Mr. Oscar leads a band through the cathedral, playing the accordion. There is what could be described as a fixed shot in both cases. One where the angle, height or position of the camera never changes, the only movement in the shot takes place between the parts it is comprised of like a sort of animated painting, and the other where Mr. Oscar is kept in the centre of the frame always facing forward and the same distance from the lens. In a sense the subject of the shot is fixed, at least within the frame, but in the second, Mr. Oscar and the band, gradually growing in numbers as the shot evolves, trace a trajectory through the cathedral whose spatial configuration is only revealed as it has already passed. In other words the camera moves backwards. The sequence is in actual fact one shot, uncut and 3 minutes long, it is not fixed in the Andersson sense, but with one subject and one pictorial composition it is difficult to place it into another category. In both cases there is a make-up of the shot that could be described as fixed, that is certainly at odds with the cinematography in Malick’s The Tree of Life, where it would be difficult to describe any shot, of which there are an extremely vast number, where the viewpoint is fixed. All this is to say that it is not simple to talk in general terms about ‘fixed’ or ‘mobile’ shots. Nevertheless I will try, as it is on defining this first level of the true-time-image that we will build the second and third levels of this thesis. We have encountered the fixed frame, the antithesis of which must be the mobile frame, consider here the running shot in Steve McQueen’s Shame. The camera opens on the central character Brandon who is leaving his high rise flat to go for a run. Without cutting we follow Brandon through the streets of New York at exactly the same speed as his running pace, briefly exchanging the horizontal movement of the camera with the vertical movement of his body as he jogs on the spot waiting for a pedestrian signal at a traffic interchange. Here I am reminded of Bergson’s example of the glass of sugared water, and the time that it takes for the transformation (not translation) to occur. This is not a mathematical time equally

THE TRUE TIME IMAGE

applicable to any point in history but a time that is lived, as Bergson says, it coincides ‘with a certain portion of my own duration’2. ‘The wholly superficial displacements of masses and molecules studied in physics and chemistry would become (…) what the position of a moving object is to the movement of that object in space.’ Bergson (2015) Fixed and mobile frames cannot be the only two categories for defining this first level of the true-time-image, for the frame has many more tendencies that just that of its own movement, or lack there of. We must also consider the spatial composition of the frame. In this it is useful to understand the techniques of composition used by painters, after all, similarly to the impressionist painters of the late 19th century Eisenstein was also influenced by Japanese print composition techniques. We can therefore understand the composition of the frame as at least as varied as the construction of the pictorial plane in painting. A composition can be comprised of verticals and diagonals, horizontals and leading perspective lines, as in the work of Andersson, or tend toward the elimination of Euclidian space, consider here the reoccurring sequences in Jonathan Glazer’s Under the Skin, where the central character Laura lures victims back to a house in Glasgow, the interior of which has indiscernible three-dimensional space. This is just to speak of the strictly composed frame, if the shots of Andersson exist as examples of highly composed frames, then where is the un-composed frame? Perhaps we could consider in this case Welles’s The Lady from Shanghai, as in the climatic scene set in a house of mirrors, gunshots distort the reflections we see constantly shifting and reconfiguring our perception of the composition. Glazer’s shots in Under the Skin of the interior of the Glaswegian house whilst being an example of the total elimination of spatial reference within the frame, must also serve to exemplify the rarefacted shot. The counterpart to the saturated shot, rarefaction in the filmic sense occurs when the frame is reduced in visual density to a few fundamental components, or further to a lack of any discernable parts whatsoever. It can be a powerful tool in the construction of a filmic sequence as we see in Under the Skin, where it is contrasted with the saturated detail of the woodland shots towards the end of the film and the beach scene, wherein the simple density of pebbles on the shore provides a frame thick with absorbing depth and detail. Often of

THE TRUE TIME IMAGE

equal importance to that that is in shot, there is of course the consideration of the out-of-shot. That is to say, the consideration of what is left out of the set comprising the frame can be as important as what is included and is in fact nearly always determined by what is in shot. Framing the shot whether; fixed, mobile, composed, disordered, saturated or rarefacted is a process of identifying the parts that make up the set. This is a determinable quantity of things that can be cataloged under the unity of that particular frame. We know however of the importance of reoccurring objects or characters across shots and conversely the sudden absence of such things. So it is important not to think of the catalogue of the shot as a fixed entity. It is a quantifiable as I have mentioned, but flexibly so, not so as to be imprecise or worse unsure as to where the components of a frame are catalogued, but to allow for the multiplications of a parts position in various sets. Importantly this allows for the connections of these sets even if by the finest thread to each other as part of the whole. This is the power that the reoccurring object brings when it re-appears in film, like the fragment of rope in Hitchcockâ&#x20AC;&#x2122;s Rope. These individual parts of sets have the power to transverse barriers of time, space, immateriality and materiality, as we see with Kubrickâ&#x20AC;&#x2122;s monolith in 2001: A Space Odyssey. We can say that the set is that of a precise quantity, whether numerical or not, definable to exact boarders and indeed subsequently divisible infinitely. But this is not to say that the logical addition of the quantities of each set is to specify the whole. We have seen the inadequacies of systems that specify the whole as a givable quantity. Rather the whole, in the case of the true-time-image, is that which prevents the simple addition of any given number of sets, being identical to it. To synthesize the results of this investigation into the constituents of the frame, we are able to say that framing the shot is the process of defining its parts. It is given quantity that can be considered as the sum of its parts, as in the case of the examples discussed in Under the Skin, or it can be read as a spatial configuration as in the films of Andersson. It can be considered as a perspectival point of view as in Holy Motors or an exercise in specifying the unspecified, defining the out-of-shot. Sometimes indicating a set which is larger that that of the frame, or suggesting a cross relation to another set in which both form a part of the whole. It is this final quality that alludes to the method of extending the shot to the act of the second level of the true-time-image, cutting. We have seen movement concerned with the changing of relative positions

THE TRUE TIME IMAGE

between parts of the set, this is what we have understood as the shot or frame, the result of the determination of movement between its parts. Therefore the second level of the true-time-image must address the determination of the shot within the context of the whole. In so far as the movement that was analyzed in the previous chapter had a second part, namely, the expression of the whole, or some part of it. ‘Thus movement has two facets, as inseparable as the inside and the outside, as the two sides of a coin: it is the relationship between parts and it is the state [affection] of the whole’ Deleuze (2005) Firstly the movement alters the respective positions of the constituents of the frame, but secondly the movement itself is a mobile section of the whole. To return to the example of the glass of sugared water, the movement on the molecular level expresses the changing of the relative positions of the constituents of the glass, in this case the water molecules and the particles of sugar. This is analogous the level of the frame in the true-time-image, however this change, with respect to the film, would be inconsequential if it did not further suggest the transformation of some qualitative state in the water, and this is the cutting of the shot. The state of the glass changing from containing water, with some sugar in, to a glass of sugared water, is expressed by the cut of the shot. That is to say the ‘in’ point and ‘out’ point. This can be manipulated to express any section of the whole desired however small or large, it is a question of determining the shot, in time. Consider a camera rushing into the toilet of a Japanese bar. It falls to the ground to rest for a minute before slowly rising up towards the kaleidoscopic light in the ceiling, as it draws closer to the light the frame is rarefacted to the point of a total elimination of density. This movement of the camera expresses the change in position of the various sets, but it is only necessary as a method of communicating a portion of the whole that has changed, inferred through this movement. In this example, in Gaspar Noé’s 2009 film Enter The Void, the young man enters the toilet cubicle alive, is shot and subsequently dragged out dead. The relative movement of the parts of the set, the frame, or the first level of the true-time-image is what infers the absolute change in the whole that occurs. The cutting of the shot is what produces these two facets3 from the movement. Cutting is concerned with both the movement of parts of the

THE TRUE TIME IMAGE

set or a few sets, and in the expression of an absolute change in the whole or a whole. In this example the shot is expressing this change in the whole, but it also happens to be the moment of a paradigm shift in the total duration of the film. The frame as delineated into the shot, is therefore tending towards two ends of a spectrum, that of communicating the movement between parts of the set and that of inferring an absolute change in the whole. The result is that movement at the second level of the true-time-image, can be thought of as intermediary between the establishing of the frame, and the montage of the whole film. This brings us to the third level of the true-time-image, and the consideration of the montage in film. More specifically montage is the composition of moving images together to form an inferred image of time. Throughout this text I have referred to film in its most basic sense, so as to avoid connotations with ‘a film’ or ‘a motion picture’, which has implications of carefully edited sequences and considered cuts. In parts one, two and up to this point in part three, the term film as a noun has referred to the idea of the raw constituents of a film. That is, the footage used to construct a filmic sequence, and not the edited results of large entertainment companies, or what are referred to as ‘motion pictures’. However at this final step in the delineation of the true-time-image this boundary becomes more blurred, as I begin to refer to the film in the sense of an edited sequence of footage. This is not to say that it is a film or a motion picture, although it might be, but quite simply the addition of two or more considered shots, into a sequence that has a directionality in the sense that it is viewable in time. I have referred to montage briefly throughout part three of this study as the method of constructing the true-time-image, but without justification of this principle by either fact or example. We know that between the beginning and end of a piece of film something has changed. We saw this in consideration of Bergson’s theses on movement and in respect of the example of Muybridge’s Human and Animal Locomotion that the whole has changed once the film has run. However what it is that has changed, some sort of duration or whole, is only communicated indirectly as a result of the movement images that construct it. The process of montage is what extracts the inferred image of time from the movement, or lack thereof, that is the subject of the film. Therefore it is quite necessarily an inferred image of time. That is to say the representation of a whole or some portion of duration is not direct in

THE TRUE TIME IMAGE

the sense of observing a man jump forward, from point A, to point B, but that this process, whatever it may be, infers some change in the state of the whole that encompasses points B, A, the man and everything in between. This duration that is expressed is not the homogenous, mathematical time implied in the theories of Newton and Einstein, but what Deleuze refers to as concrete duration4. It is the strongly palpable sense of a directional time, missing in the principles of theoretical physics, that is inferred through montage. This notion of inferred time is not to say that the whole is communicated only once the filmic sequence has finished, far from it. Concrete duration, as inferred by the montage of film, has a primacy beyond that of the comparison between the juxtaposed. For example the succession of fixed shots can be used to presuppose the idea of a montage over the use of a mobile camera, leading to a different composition of duration. Whilst it is a strongly directional duration, it is important to make the distinction here between this and that of a linear time. It is directional only in the sense that it is constantly moving, whether forwards, backwards, sideways, or inside out, it is unstoppably changing as is encountered only when the whole is open, or, unspecified. Finally to consider the three Bergsonian levels of movement, the movement of immobile sections, the movement of the parts relative to one another, and the change in the whole expressed in the movement, we can observe a reciprocity between them that enables each level to preconfigure the other. This is reflected in the construction of the true-time-image as we can see that the result of the montage of the film is mirrored by the illusion of movement that has marked the outset of my investigation. That is, an inferred property. However as we saw when constructing movement from arbitrary instances in time, a sensible analysis of a movement is created forming a false representation, whilst critically with the true-time-image what amounts is something else. An effective image of duration occurs from the formulation of a series of filmic instances.

Epilogue

An inferred image of time as we have encountered in part three of this investigation, is something not so different from the physical theories examined in part one. The beginning of this investigation was marked by a search for a description of the existential quality of time. Our experience of being has an intrinsic link to time, but it is this property that is at odds with not only the way our language has adopted principles of timelessness, but also the way science has constructed explanations of this reality. The rationality of this field of study forms a logic that only relates to a given point of reference. It is the result of an artificially siloed investigation, without the consideration of a coherence with other forms of knowledge. Most physical scientists are not aware of the discussions between the significant artists of today, let alone examine their theories in the context of these discussions. Are architects aware of what social scientists pushing the boundaries of their research are trying to achieve? Let us consider that for those who understand the world in terms of economics, the ground beneath our feet is a resource to be exploited, an economic problem to be solved with a cost-benefit analysis. For the environmentalist it is a pristine territory to be preserved from any human encroachment whatsoever, but both have missed the point because they compartmentalize their realm of expertise from the surrounding reality. That is to say in context of this study, that the physical scientist alone cannot

EPILOGUE

account for the basic human emotions we encounter in our time on this earth. The Ptolemaic model of the universe positioned divine celestial bodies into a timeless realm beyond that of the messy mortality of earth, which contained decay and change. What I hope to have begun to unpick in this study is the parallels that can be drawn with the removal of what I have come to describe as time from the physical scientistâ&#x20AC;&#x2122;s understanding of reality, and this Ptolemaic model. As an architect I relate space to millimeters, I can measure a room to be six by four meters, but I have missed in every sense the space of that room, in the same way Galileoâ&#x20AC;&#x2122;s parabola misses the movement of the ball. It is a numeric delineation of the space but to directly understand the space I must walk into it, and through it. This in itself changes the nature of the room because as I do this, the events that unfold there influence my perception of it. As time continues to move, I may have walked through the space many times and begun to form memories that too effect my perception of it. Without light I may take longer to transverse this room increasing the perceived size of it, or its temperature may cause me to experience the emptiness as more intense. So is the architect not desperately grabbing to find new expressions of space than the millimeter? What I have set out through parts one, two, and three of this investigation is a proposal for a different logic of space, one that is governed by, but not limited to, our experience of time. The true-time-image is not an individualized area of filmic study, it is built on the principles of theoretical physics, in consideration of philosophyâ&#x20AC;&#x2122;s understanding of movement, and our own directly profound sense of time, to form the actualization of a new relational philosophy. One of a duration, to replace the faith in transcendence to a timeless uniform state of reality, with one of an ever-expanding territory of intrinsic complexities, constantly shifting and re-shifting spatial sequences. One that any architecture must be.

NOTES AND REFERENCES

Introduction

PART ONE

Timelessness and Newtonianism 1 Found in a letter to the Besso family on hearing about the death of his friend Michele Besso. Einstein himself died one month and three days after Besso, on the 18 April 1955. 2 Rothko, M. (2006) Writings on art. Edited by Miguel LopezRemiro. New Haven: Yale University Press

1 Drake, S. (1973) Galileo Gleanings XXII: Galileo’s Experimental Confirmation of Horizontal Inertia: Unpublished Manuscripts, Isis, Vol 64. pp 291305 2

Ibid.

Ibid., pp 291

3 The definition of a parabola; like that of the line; the shortest distance between two points, or the circle any number of points located equidistant from another point, it is defined as any number of points equidistant from both a line and a point. 4 The Geocentric Model, or Geocentrism is a description of the cosmos where Earth is at the orbital centre of all the celestial bodies. It was the dominant model among many ancient civilizations including Ancient Greece. 5 Simplicius and Mueller, I. (2014) Simplicius: On Aristotle on the heavens 1.2-3. Bloomsbury London. 6 Smolin, L. (2014) Time Reborn : from the Crisis in Physics to the Future of the Universe. UK Penguin Books. 7

Crowell, B. (2000) Newtonian Physics. Later Printing edition

8 This idea preceded the other questions Newton was able to answer, one of which was, ‘how does this force decrease over distance’. It was known that it must decrease, because earth is orbiting the sun and yet we do not accelerate towards it, we are stuck down here on this planet’s surface. The

answer is that the force decreases proportional to the square of the distance, the actual mathematics of this is fairly simple and grasped by most students of physics early in their studies, but what is of importance for this text is that the answer is mathematical, and what was of great significance at the time was that the mathematics is simple 9

Crowell, B. (2000) Newtonian Physics. Later Printing edition

10 The theory of general relativity is widely regarded as difficult to understand or at the very least, complex. I however, would make the point that it is like most of the discoveries we have discussed thus far, at its core quite simple, almost crystalline, a feature I think is necessary for its infiltration of popular culture. It requires like most theories a very simple change in perception. 11 See paper: Courtois, H. M (2013) ‘Cosmography of the Local Universe’ DOI: 10.1088/0004-6256/146/3/69 12 I regularly use the trains on the Great Western line from London to Oxford, and almost every time during the wait for my train to leave Reading station, I am reminded of the relativity of motion. Looking out across to the adjacent platform from a stationary train there is quite frequently another train pulling away that will give me the impression that we are moving. Only until of course it leaves my field of view, to race off and I am given the rest of the station as a reference that I am in fact still waiting for my own train to get going. 13 Smolin, L. (2014) Time Reborn : from the Crisis in Physics to the Future of the Universe. United Kingdon: Penguin Books. pp 28 14

Ibid., pp 27

15 Barbour, J. B. (2000) The End of Time. 4th edn. London: Phoenix (an Imprint of The Orion Publishing Group Ltd) pp 22 16

Shimamura, Arthur P. (2002). “Muybridge in Motion: Travels in

Art, Psychology, and Neurology” (PDF). History of Photography 26 (4): 341– 350. 17 Barbour, J. B. (2000) The End of Time. 4th edn. London: Phoenix (an Imprint of The Orion Publishing Group Ltd) pp 154 18 Smolin, L. (2014) Time Reborn : from the Crisis in Physics to the Future of the Universe. United Kingdon: Penguin Books. pp 28

The Final State of Equilibrium

PART TWO

1 Barbour, J. B. (2000) The End of Time. 4th edn. London: Phoenix (an Imprint of The Orion Publishing Group Ltd) pp 139-142

Time As Fundamental

2 Barbour, J. B. (2000) The End of Time. 4th edn. London: Phoenix (an Imprint of The Orion Publishing Group Ltd)

3 Simplicius and Mueller, I. (2014) Simplicius: On Aristotle on the heavens 1.2-3. United Kingdom: Bloomsbury Academic.

Bergson, H. (2015) Creative Evolution. London: Continuum. pp 355

2 Reference to ‘Schrödinger’s Cat Paradox’ a thought experiment conducted using the principles of quantum mechanics, much popularized and written about. See Schrödinger, E. and Erwin (2012) What is life?: the physical aspect of the living cell ; with, Mind and matter ; & Autobiographical sketches. Cambridge University Press.

4 Schrödinger, E. and Erwin (2012) What is life?: Cambridge: Cambridge University Press. pp 67-75

3 Deleuze, G. (2005) Cinema I: The Movement-Image. London: Continuum. pp 7.

5 Smolin, L. (2014) Time Reborn : from the Crisis in Physics to the Future of the Universe. United Kingdon: Penguin Books. pp 193-203

4 ‘Time’s Arrow’, is a concept developed in 1927 by the British astronomer Arthur Eddington, chapters in reference to this theory are found in (Barbour, J. 2000), (Smolin, L. 2014) and (Gribbon, J, R. 1985) among others.

6 Barbour, J. B. (2000) The End of Time. 4th edn. London: Phoenix (an Imprint of The Orion Publishing Group Ltd) pp 23

5 Smolin, L. (2014) Time Reborn : from the Crisis in Physics to the Future of the Universe. United Kingdon: Penguin Books. pp 204

6 Smolin, L. (2014) Time Reborn : from the Crisis in Physics to the Future of the Universe. United Kingdon: Penguin Books. pp 206

Ibid., pp 193-203

The True-Time Image

PART THREE

Bergsonian Cinema

1 Deleuze, G. (2005) Cinema I: The Movement-Image. London: Continuum. pp 1.

1 Bergson identified the ‘cinematograph’ as a term in Creative Evolution referring to the mechanism of the reconstitution of a movement. Not necessarily a film projector he goes on to liken the cinematograph to the process of natural perception, stating; ‘we hardly do anything other than set going a kind of cinematograph inside ourselves’. Bergson, H. (2015) Creative Evolution (Classic Reprint). United States: Forgotten Books. pp 322-3

Ibid., pp 1

3 Deleuze, G. (2005) Cinema I: The Movement-Image. London: Continuum. pp 20.

Ibid., pp 4

Bergson, H. (2015) Creative Evolution. London: Continuum. pp 349

9 Deleuze, G. (2005) Cinema I: The Movement-Image. London: Continuum. pp 4. 10

Ibid., pp 7

Ibid., pp 8

Ibid., pp 1

Ibid., pp 11

Bergson, H. (2015) Creative Evolution: pp 10

Ibid., pp 1.

TEXTS

Barbour, J. B. (2000) The End of Time. 4th edn. London: Phoenix (an Imprint of The Orion Publishing Group Ltd ).

Ponto, A. and Ponte, A. (2012) The House of Light and Entropy. London: Architectural Association Publications.

Bergson, H. (2015) Creative Evolution (Classic Reprint). United States: Forgotten Books.

Rothko, M. (2006) Writings on art. Edited by Miguel Lopez-Remiro. New Haven: Yale University Press.

Bergson, H., Jacobson, L., Lewis, M. and Henri, B. (1999) Duration and simultaneity: Bergson and the Einsteinian universe. Edited by Robin Durie. 2nd edn. Manchester: Clinamen Press.

Simplicius & Mueller, I. (2014) Simplicius: On Aristotle on the heavens 1.2-3. United Kingdom: Bloomsbury Academic.

Bergson, H., Palmer, W. S. and Paul, N. M. (2004) Matter and Memory. United States: Dover Publications. Bergson, H. and Henri, B. (2000) Time and Free Will. Adamant Media.

Schrödinger, E. and Erwin (2012) What is life?: the physical aspect of the living cell ; with, Mind and matter ; & Autobiographical sketches. Cambridge: Cambridge University Press. Smolin, L. (2014) Time Reborn : from the Crisis in Physics to the Future of the Universe. United Kingdom: Penguin Books.

Crowell, B, (2000) Newtonian Physics. Later Printing edition Drake, S. (1973) Galileo Gleanings XXII: Galileo’s Experimental Confirmation of Horizontal Inertia: Unpublished Manuscripts, Isis, Vol 64 Deleuze, G. (2005) Cinema I: The Movement-Image. Edited by Hugh Tomlinson and Barbara Habberjam. 7th edn. London: Continuum International Publishing Group. Deleuze, G. (2013) Cinema II: The Time-Image. Edited by Hugh Tomlinson and Robert Galeta. London: Bloomsbury. Deutsch, D. (1998) The Fabric of Reality: Towards a Theory of Everything. London: Penguin Books. Gribbin, J. R. (1985) In search of Schrödinger’s cat. London: Black Swan. Kennedy, J. B. (2003) Space, Time and Einstein: An Introduction. United Kingdom: Acumen Publishing.

Sommerfeld, A., Perrett, W., Jeffery, G. B., Einstein, A., Minkowski, H. and Davis, F. A. (1952) The principle of relativity: A collection of original memoirs on the special and general theory of relativity. New York: Dover Publications.

ESSAYS

Eisenstein, S. M. (1989) ‘Montage and Architecture’, Assemblage, (10), pp. 111–131. doi: 10.2307/3171145. Courtois, H. M (2013) ‘Cosmography of the Local Universe’ DOI: 10.1088/00046256/146/3/69 Shimamura, Arthur P. (2002). “Muybridge in Motion: Travels in Art, Psychology, and Neurology” (PDF). History of Photography

FILMS

There Will Be Blood (2008) Directed by Paul Thomas Anderson [Film]. USA: Paramount Vantage, Miramax.

Mystery train (1989) Directed by Jim Jarmusch [Film]. USA: JVC Entertainment Networks.

The Master (2012) Directed by Paul Thomas Anderson [Film]. USA: The Weinstein Company.

Coffee and cigarettes (2004) Directed by Jim Jarmusch [Film]. USA: Asmik Ace Entertainment.

En duva satt pﾃ･ en gren och funderade pﾃ･ tillvaron (2015) Directed by Roy Andersson [Film]. Sweeden: Roy Andersson Filmproduktion AB.

The Limits of Control (2009) Directed by Jim Jarmusch [Film]. USA: Focus Features.

El ﾃ］gel Exterminador (1966) Directed by Luis Buﾃｱuel [Film]. Mexico: Producciones Gustavo Alatriste.

No Country For Old Men (2008) Directed by Ethan Coen Joel Coen [Film]. USA: Paramount Vantage, Miramax.

Holy Motors (2012) Directed by Leos Carax [Film]. France: Pandora Filmproduktion.

Donnie Darko (2002) Directed by Richard Kelly [Film]. USA: Pandora Cinema.

The Curious Case of Benjamin Button (2009) Directed by David Fincher [Film]. USA: Warner Bros.

2001: A Space Odyssey (1968) Directed by Stanley Kubrick [Film]. USA/UK: Shepperton Studios.

Soylent Green (1973) Directed by Richard Fleischer [Film]. USA: MetroGoldwyn-Mayer (MGM).

The Shining (1980) Directed by Stanley Kubrick [Film]. USA/UK: Warner Bros.

Under the Skin (2014) Directed by Jonathan Glazer [Film]. UK/USA: Film4, British Film Institute (BFI).

Underground (1995) Directed by Emir Kusturica [Film]. Pandora Filmproduktion.

Rope (1948) Directed by Alfred Hitchcock [Film]. USA: Warner Bros.

Twin Peaks: Fire Walk With Me (1992) Directed by David Lynch [Film]. USA: New Line Cinema.

Rear window (1954) Directed by Alfred Hitchcock [Film]. USA: Paramount Pictures. Vertigo (1958) Directed by Alfred Hitchcock [Film]. USA: Alfred J. Hitchcock Productions. Down by law (1986) Directed by Jim Jarmusch [Film]. USA: Black Snake, Grokenberger Film Produktion.

Lost Highway (1997) Directed by David Lynch [Film]. USA: Asymmetrical Productions. Mulholland Dr. (2002) Directed by David Lynch [Film]. USA: Les Films Alain Sarde. Rabbits (2005) Directed by David Lynch [Film Short]. USA. Inland empire (2007) Directed by David Lynch [Film]. USA: StudioCanal.

Badlands (1974) Directed by Terrence Malick [Film]. USA: Warner Bros. The Tree of Life (2011) Directed by Terrence Malick [Film]. USA: Fox Searchlight [United States]. La jetée (1962) Directed by Chris Marker [Film]. France: Argos Films. Shame (2012) Directed by Steve McQueen [Film]. UK: See-Saw Films. Take Shelter (2011) Directed by Jeff Nichols [Film]. USA: Grove Hill Productions. Enter the void (2010) Directed by Gaspar Noé [Film]. France: Fidélité Films. Dark city (1998) Directed by Alex Proyas [Film]. USA: Mystery Clock Cinema. Je t’aime je t’aime (1968) Directed by Alain Resnais [Film]. France: Les Productions Fox Europa Altered States (1980) Directed by Ken Russell [Film]. USA: Warner Bros. Taxi Driver (1976) Directed by Martin Scorsese [Film]. USA: Columbia Pictures Corporation. Relatos salvajes (2015) Directed by Damián Szifrón [Film]. Argentina: Corner Producciones. Stalker (1980) Directed by Andrei Tarkovsky [Film]. Soviet Union: Kinostudiya Mosfilm. The Lady from Shanghai (1948) Directed by Orson Welles [Film]. USA: Columbia Pictures Corporation.

IMAGES

Page 08 - Image 01: Rothko, M. (1958) Black on Maroon: The Seagram Murals.

Page 44 - Image 17: 2001: A Space Odyssey (1968) Directed by Stanley Kubrick. DoP: Geoffrey Unsworth.

Page 10 - Image 02: Mulholland Dr. (2002) Directed by David Lynch. DoP: Peter Deming.

Page 46 - Image 18: The Lady from Shanghai (1948) Directed by Orson Welles. DoP: Charles Lawton.

Page 12 - Image 03: Holy Motors (2012) Directed by Leos Carax. DoP: Yves Cape, Caroline Champetier.

Page 50 - Image 19: Taxi Driver (1976) Directed by Martin Scorsese. DoP: Michael Chapman.

Page 16 - Image 04: Page 18 - Image 05:

Parabola Diagram (2015) Fearghus Raftery.

Page 52 - Image 20: Rabbits (2005) Directed by David Lynch.

Figure of the heavenly bodies, An illustration of the Ptolemaic geocentric system by Portuguese cosmographer and cartographer Bartolomeu Velho, 1568 (Bibliothèque Nationale, Paris).

Page 54 - Image 21: Laocoön and His Sons - Detail (cc. 200BC-70AD) Agesander, Athenodoros and Polydorus.

Page 20 - Image 06: Conic Sections Diagram (2015) Fearghus Raftery. Page 22 - Image 07: Courtois, H. M (2013) Cosmography of the Local Universe. Video still from the film showing the relative positions of observable galaxies surrounding our own. Page 24 - Image 08: Shame (2012) Directed by Steve McQueen. DoP: Sean Bobbitt. Page 26 - Image 09: Muybridge, E (1887) Human and Animal Locomotion. Page 28 - Image 10: Page 30 - Image 11:

Rear window (1954) Directed by Alfred Hitchcock. DoP: Robert Burks. Dark city (1998) Directed by Alex Proyas. DoP: Dariusz Wolski.

Page 32 - Image 12: En duva satt på en gren och funderade på tillvaron (2015) Directed by Roy Andersson. DoP: István Borbás, Gergely Pálos.

Page 56 - Image 22: Laocoön and His Sons (cc. 200BC-70AD) Agesander, Athenodoros and Polydorus. Page 58 - Image 23: Muybridge, E (1878) The Horse in Motion. Page 60 - Image 24: Page 62 - Image 25:

The Tree of Life (2011) Directed by Terrence Malick. DoP: Emmanuel Lubezki. Under the Skin (2014) Directed by Jonathan Glazer. DoP: Daniel Landin.

Page 64 - Image 26: Holy Motors (2012) Directed by Leos Carax. DoP: Yves Cape, Caroline Champetier. Page 66 - Image 27: Resnais, A. (1968) Je t’aime je t’aime. DoP: Maxime Alexandre. Page 68 - Image 28: The Master (2012) Directed by Paul Thomas Anderson. DoP: Mihai Mălaimare. Page 70 - Image 29: No Country For Old Men (2008) Directed by Ethan Coen, Joel Coen DoP: Roger Deakins.

Page 34 - Image 13: Rope (1948) Directed by Alfred Hitchcock. DoP: William V. Skall.

Page 72 - Image 30: The Shining (1980) Directed by Stanley Kubrick. DoP: John Alcott.

Page 36 - Image 14: Enter the void (2010) Directed by Gaspar Noé. DoP: Benoît Debie.

Page 74 - Image 31: The Master (2012) Directed by Paul Thomas Anderson. DoP: Mihai Mălaimare.

Page 38 - Image 15: El Ángel Exterminador (1966) Directed by Luis Buñuel. DoP: Gabriel Figueroa.

Page 76 - Image 32: The Tree of Life (2011) Directed by Terrence Malick. DoP: Emmanuel Lubezki.

Page 42 - Image 16: The Tree of Life (2011) Directed by Terrence Malick. DoP: Emmanuel Lubezki.

Page 78 - Image 33: The Tree of Life (2011) Directed by Terrence Malick. DoP: Emmanuel Lubezki. Page 80 - Image 34: La jetée (1962) Directed by Chris Marker.

Page 82 - Image 35: Badlands (1974) Directed by Terrence Malick [Film]. USA: Warner Bros. DoP: Tak Fujimoto. Page 84 - Image 36: Donnie Darko (2002) Directed by Richard Kelly [Film]. USA: Pandora Cinema. DoP: Steven Poster.