Mark Ward

Virtual Organisms

The Startling World of Artificial Life

Pan Books

pg 72


Keywords : Conway's Game of Life - unpredictability - a complex world that derives from simple premises - Von Neumann's cellular automaton - emulate any self-replicating machine - act like a universal Turing machine - By picking the right rules Conway believed that he was, in some less complicated way, rerunning a process that takes place in our own universe. At some point (perhaps Planck time) everything was set up, the rules were established and the whole thing was left to run. The same rules determined what happened to new generations of organisms in our universe. - CA - living organisms are physical systems made up of elements operating to a set of rules -some cells in the body act like computers and process information - Ed Fredkin - Stephen Wolfram - Wolfram declares himself frustrated by the slow progress of biology to reveal how living processes are organized and the way they work. He has strong opinions and is contemptuous of most of biology, seeing it as mere naturalism rather than an investigation into fundamentals. 'What we call life is something that is defined more by its history and heritage than its properties,' he says. The problem with life is that it is hard to know what is important and what is not. Wolfram says that while models of living systems can be built, typically they have not been very successful, usually because they are over-complicated. Wolfram thinks that CAs may be a way to investigate those properties and gain a much better understanding of how life is organized. Wolfram says that by analysing CAs 'one may, on the one hand, develop specific models for particular systems, and, on the other hand, hope to abstract general principles applicable to a wide variety of complex systems. - one-dimensional CA - CAs can be divided into four different classes. The first sort of rule sets prodoced patterns that quickly died out. The second class found a stable form and reproduced it for ever. A third type produced chaotic patterns that keep growing. The patterns produced are fractals. Patterns that look the same at different scales. The fourth sort produced patterns that never settle down and grow and contract irregularly. - Fractal patterns - Chris Langton - the order goes I, II, IV, III - The most interesting systems on Earth, the living ones, are a tricky mixture of both complexity and chaos - lambda value - critical phase transition - universality - life uses information to maintain itself in the critical phase transition region - recursive systems - phase transition

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CA - a complex world that derives from simple premises

GAME OF LIFE - establish a profound connection between living things and the logical world.
...a link between the complexity of the world we find ourselves in and an artificial world that is easier to study but reveals much about both. The central point is this:
living organisms are physical systems made up of elements operating to a set of rules.

The connection between CAs and life is not purely computational. There is evidence that some cells in the body act like computers and process information

The connection is phenomenological, which essentially means that living things and CAs do the same things. The complex dynamic activity you find in fruit flies, societies and cells is also found in CAs

Ed Fredkin set up the Information Mechanics Group as a way of exploring his contention that all physical phenomena are rooted in information

Stephen Wolfram: The problem with life is that it is hard to know what is important and what is not. Wolfram says that while models of living systems can be built, typically they have not been very successful, usually because they are over-complicated. Wolfram thinks that CAs may be a way to investigate those properties and gain a much better understanding of how life is organized.

If it is the case that recursive systems are widely used in nature, then starting to classify them could also help us to understand them. At the very least they could be used to model them. It is unlikely, though, that living systems use only one sort of dynamic system. Wolfram is convinced that Class III and IV CAs are most lifelike.

Chris Langton: At lambda values around 0.5 the behaviour of the CA is either complex or chaotic. But Langton realized that the most interesting parts of all are at the regions between these recognizable states. As the CA passed from one region to another descriptions of what was happening got longer, once within the new region fewer words were needed to describe what was happening. Only in this transition region are the stable and propagating structures like gliders seen. It is the place where universal computation can take place. It is the crucible of life.

Langton called this sweet spot a 'critical phase transition' and it is not jost a phenomenon of the CA universe, similar events are found in the natural world too.


It is not only ALife researchers that are interested in phase transitions. Work on phase transitions has revealed that at critical junctures in the development of a system organization spontaneously emerges. This behaviour has been found in a huge variety of systems. Everything from heart attacks to earthquakes, brains and businesses have been found to be on or passing through phase transitions at some point in their development. Some systems, usually living organisms, seem to be stuck in this state. Because of the ubiquity of this phenomenon the field of research it is part of is called 'universality'. It implies that at certain times different systems act in exactly the same way. The individual elements within them cease to matter as information dynamics takes over.


...there is a lot of evidence that life uses information to maintain itself in the critical phase transition region


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Games, Trains and Pentominos - Conway's Game of Life

What makes the Game of Life so compelling is its unpredictability. The simplest patterns of cells can give rise to the most complex forms. At times a computer screen running Life seems to resemble a primordial pond as stable organisms grow out of the dark, thrash briefly around the screen and disappear again into the murk. As Game of Life chronicler William Poundstone has observed: 'The Life universe is one of the most vivid examples anyone has found of a complex world that derives from simple premises."

The Game of Life is not really a game. Most games played on boards are won or lost because of the lack or skill of the players, but with the Game of Life there are no players, no winners or losers, everyone is a spectator to the strangest of sports. It is a window on to another mathematical universe with you in the creator's seat, perhaps this is another secret of its appeal. The universe of the Game of Life still remains largely unexplored. It is a world still awaiting its Magellans, Drakes and Darwins. ALife researchers are happy to be the ones charting these seas and cataloguing the flora and fauna they find.

A natural history of the Game of Life universe already exists. Lifeline, the journal compiled by fans of the game, became a record of the lifeforms that were found by those exploring the Life universe. All the objects and organisms found so far have been given names and, just as in the natural world, they are divided into species, genera and phyla. Some lifeforms never change and as a result are known as 'still lifes'. They get names like 'block', 'loaf' or 'beehive'. Others are known as blinkers or oscillators because, though stable, persistent forms, they switch between a variety of states. Some of these go by the name of 'traffic lights' because they pass through several stages and on a fast computer appear to blink like twinkling lights.

Still other shapes are mobile and slowly move around the Life grid. One five-cell shape called a 'glider' passes through a four-stage process that moves the whole shape one square diagonally. Also discovered in the Life universe are forms that go by the name of 'starships', 'glider guns' and 'puffer trains'. Some of these objects are 'natural' because they often arise naturally in the Life universe. Others are 'engineered' because they have never been seen to occur naturally and have to be constructed for their properties to be investigated.

One astonishingly fecund shape is the 'r' pentomino. It goes by this name because it is a five cell edgeconnected form that looks a little like a lower case r (see above). Despite its unassuming appearance the 'r' pentomino is capable of producing an astonishing number of patterns. It takes 1300 generations for the 'r' pentomino to settle into a stable state during which time it will have produced: 8 blocks - 6 gliders 4 -beehives 4 blinkers -1 boat - 1 loaf - 1 ship

So far, so whimsical, but this does not seem to have much to do with establishing a link between an artificial universe and the real world, or between living things and squares on a computer screen.

Von Neumann's cellular automaton was so complex partly because he was patterning it after the computers he had just finished working on and partly because he wanted it to adhere to specific mathematical proofs. These established that it could emulate any self-replicating machine and that it could act like a universal Turing machine. This theoretical machine was developed by the British mathematician Alan Turing and was capable of emulating the processing capabilities of any other machine.

Conway thought that the most important aspect of von Neumann's automaton was the fact that it could act as a universal computing machine. This is part of the reason that it took a long time to find the ideal set of roles for Life. Conway had to tinker in order to ensure his version did the same job. In doing this he was trying to establish a profound connection between living things and the logical world.

By picking the right rules Conway believed that he was, in some less complicated way, rerunning a process that takes place in our own universe. At some point (perhaps Planck time) everything was set up, the rules were established and the whole thing was left to run. The same rules determined what happened to new generations of organisms in our universe.

The use of the same rules over and over again, recursively, has once again produced ships, loafs and beehives. This time though they are not made up of squares on a computer screen; instead they are tea clippers, French sticks and homes for honeymaking insects. Cellular automata are at the heart of ALife. The ideas underpinning them are what makes ALife worth doing.

They forge a link between the complexity of the world we find ourselves in and an artificial world that is easier to study but reveals much about both. The central point is this: living organisms are physical systems made up of elements operating to a set of rules. There is no need, or room, for non-physical forces such as souls to get involved. Some of the rules operating in living things we know about, others are proving harder to grasp and uncover. The number of rules operating, the number of elements involved and the ways they can interact make it difficult to understand what is happening in actual organisms. The blooming, buzzing confusion makes it hard to pick out what is relevant and what is superfluous.

What we need is a way to remove all the extraneous elements to reveal the essence, what it is about living things that keeps them going. CAs are that way. They remove the muscle, flesh and bone and leave the essential rules exposed. Although in the case of CAs the number of rules operating are fewer than in living organisms, nothing, apart from the superfluous, should be lost. Despite the fact that there are only a few rules the complex forms that result and the fact that they emerge out of a system that is computationally universal lends weight to the claim that by studying a CA you are studying life: life in the raw and life that is much more tractable than doing experiments with fruit flies, cats or rats.

The connection between CAs and life is not purely computational. There is evidence that some cells in the body act like computers and process information. A convincing case can be made for a link in this sense but it is not one that CA researchers pursue. They leave that to the robot makers (see Chapter Three). The connection is phenomenological, which essentially means that living things and CAs do the same things. The complex dynamic activity you find in fruit flies, societies and cells is also found in CAs. Using CAs to model these moving targets makes them easier to study. Boston University physics professor Tom Toffoli thinks that the only reason CAs are worth studying is because of this connection with real life. Toffoli says that mathematically CAs are not that interesting. Although it must be said that the mathematics of CAs are easier to work with than those of other dynamic systems like water flowing round a propeller or air over a wing. Toffoli is another alumnus of Arthur Burks' Logic of Computer group at Michigan. It was there that he did his PhD thesis on what CAs were worth saving for. The conclusion of his thesis was that the saving grace of CAs was their close affinity with reality. Before Toffoli did his research many thought that CAs had little connection with the real world because the basic physics of the two worlds differed widely. But Toffoli was able to show that in fact there were strong affinities between the two. The connection showed that both worked in the same way. As such they could legitimately be used to model and study problems in this field. Once he had got his PhD Toffoli became the first staff member of the newly formed Information Mechanics Group at MIT. The research group was set up by Ed Fredkin one of computer science's oldest hackers who has made enough money out of the field to buy his own Caribbean island. Fredkin also has an abiding interest in CAs. He set up the Information Mechanics Group as a way of exploring his contention that all physical phenomena are rooted in information.

At MIT Toffoli hooked up with Norman Margolus and got to work on developing a dedicated CA computer. They needed a faster way to crank through the time steps of a CA. Even a powerful general-cell universe every minute or so, far too slow to do anything useful. This was especially true for the researchers because one of the problems they were interested in tackling was turbulence in fluids, which has long been mathematically intractable. Fluids are made up of many trillions of interacting particles so to be able to model these in real time demands a computer that can work on the same scale. A decade of work has produced CAM-8, an eighth generation cellular automata machine that can update a CA quicker than a supercomputer could. CAM-8 deals with a million million cells at a time and is being used to simulate crystallization, reaction-diffusion systems and fluid flows. Modelling these types of physical systems on conventional computers or even supercomputers is usually an exercise in frustration. The numbers of particles in a liquid and the number of ways they can interact are staggering and eat up computer time. CAM machines mean anyone can study such things easily.

The particles in fluids can be represented in such detail that Toffoli now considers that he is not working with a computational system but instead he says he is manipulating 'programmable matter" In his opinion he has demonstrated that CAs possess sorhe of the same properties of the stuff found in the real world but with the advantage of being easy to manipulate and set up to tackle a particular problem.

The link with the real world may not stop with fluid flows and studies of turbulence. There are those who think that many biological phenomena, such as the markings on some shells, the growth of snowflakes and even the onset of cancer may be evidence of CAs at work.

Stephen Wolfram is the man looking for the influence of CAs in biology. British-born Wolfram is an intellectual wunderkind who went up to Oxford University aged 16 and got his doctorate from Cal Tech aged 20. At Cal Tech he kept very exclusive company, working with Nobel laureate Richard Feynman and theoretical physicist Murray Gellmann. After leaving Cal Tech Wolfram took up a post at the Institute of Advanced Study,' where von Neumann worked when he first thought up the idea of CAs and a fitting place to continue the investigation into their properties.


Wolfram declares himself frustrated by the slow progress of biology to reveal how living processes are organized and the way they work. He has strong opinions and is contemptuous of most of biology, seeing it as mere naturalism rather than an investigation into fundamentals. 'What we call life is something that is defined more by its history and heritage than its properties,' he says. The problem with life is that it is hard to know what is important and what is not. Wolfram says that while models of living systems can be built, typically they have not been very successful, usually because they are over-complicated. Wolfram thinks that CAs may be a way to investigate those properties and gain a much better understanding of how life is organized. Wolfram says that by analysing CAs 'one may, on the one hand, develop specific models for particular systems, and, on the other hand, hope to abstract general principles applicable to a wide variety of complex systems.

Before moving on to fundamentals though Wolfram had to do a little naturalism of his own. He had to classify the different sorts of patterns CAs can produce.

CAs can differ in several ways. They can be two dimensional like the Game of Life and have their rules operate both horizontally and vertically. In such a CA the eight squares surrounding each cell determine the fate of the central cell in the next time step. A one dimensional CA works only horizontally, with each generation plotted on a new line. Only the cells to the right and left of an individual cell affect its fate in each generation. The history of a one dimensional CA can be grasped in a glance because every generation is preserved on its own line.

CAs can also differ in their rule sets. John Conway experimented with a lot of different rules before he found the perfect balance between expansion and order. What changes is the fate of the central cell given the state that its neighbours are in. In some rule sets two live neighbours means a living cell dies, in others it will mean that it stays living. Subtle changes in the rules can have profound effects on the patterns produced by the CA.

The one-dimensional CA on which Wolfram did his initial work had 256 different rule sets. Wolfram seeded the first line of his CA with a random number of live cells, then tried out the different rule sets to discover the kinds of patterns they produced.

He found that CAs can be divided into four different classes. The first sort of rule sets prodoced patterns that quickly died out. The second class found a stable form and reproduced it for ever. A third type produced chaotic patterns that keep growing. The patterns produced are fractals. Patterns that look the same at different scales. The fourth sort produced patterns that never settle down and grow and contract irregularly. The classes that Wolfram identified do not just apply to CAs, they also seem to have parallels with the behaviours seen in dynamic systems.

Class I CAs swiftly reach what are known as limit points, effectively dead ends. Class II CAs produce patterns that are very similar to the small, discrete cycles like gyres, eddies and waterspouts that sometimes appear in liquids and gases. Class III CAs tend to produce patterns that are chaotic and never settle down; global weather patterns are the classic example of this kind of dynamic system.

Class IV CAs are hard to define. They are easy to identify when set against the other classes of CAs but as Chris Langton, another longtime CA fan, says: 'no direct analog for them has been identified among continuous dynamic systems'. They produce complex structures that persist over long periods of time, like life.

Wolfram's survey was empirical rather than analytical but it seems to have revealed some qualitative differences between CAs. His results have been independently corroborated and extended by others in the ALife field. The survey has important implications for anyone who believes that CAs can be used to study complexity or analyse some biological phenomena. Wolfram believes that organisms often unknowingly employ CA type systems to create some of their characteristics. One of the most striking examples of this can be found on the shell of the mollusc Natica enzona. Anyone comparing the patterns on the shells of these molluscs and some of the patterns that form in a CA would be hard pressed to deny some sort of connection. If it is the case that recursive systems are widely used in nature, then starting to classify them could also help us to understand them. At the very least they could be used to model them. It is unlikely, though, that living systems use only one sort of dynamic system. Wolfram is convinced that Class III and IV CAs are most lifelike.

Fractal patterns are found throughout the natural world. In 1997 physicist Geoffrey West and ecologists James Brown and Brian Enquist published a paper in Science that explained, as they put it, the 'template of life'. One of the great puzzles of living organisms is why all animals obey the l same simple law for metabolic rate.

Whales may be millions of times larger than mice but they do not consume millions of times more energy. The energy demands of an animal follow a consistent and predictable formula called Kleiber's law, but until 1997 no one knew why. West, Brown and Enquist found that fractals were involved. The trio built a model that songht to explain why this was so. They reasoned that many multicellular living things are sustained by the transport of food and/or energy through a branching transport mechanism such as the circulatory system. It turns out that the most efficient way to move these materials around is through a fractal system that splits and grows exactly like the blood vessels in the bodies of animals. Some animals may have larger versions but all the examples of lungs or blood vessels or other transport systems are different only in terms of scale. Some plants use a similar system to move nutrients around. This explains why the branch patterns of some trees bear a remarkable similarity to the pattern of airways within the lungs.

There is a limit to how small the finest gradations of this system can go that is dictated by the size of the particles passing through them. With blood vessels the size of red blood cells is the limiting factor but even then these cells can be squashed slightly to enable them to slip through narrow capillaries. Even so, as the system grows and is used in larger animals it remains the same at different scales. Given this it is no surprise that the energy needs of animals grow predictably as the size of the beast increases.

Distinctive fractal patterns have also been found in breast cancer cells that should make it easier to spot malignancies. When a cell becomes cancerous the DNA in its nucleus forms into irregular clumps. Oncologists familiar with cancer cells can often spot this clumpiness but sometimes they miss the tell

Wolfram for one is convinced that the central paint about CAs will prove its worth even if the truth of it has so far failed to penetrate the scientific community to any great degree. 'It is an intuition that has not been fully absorbed,' he says. 'The main point is that you can have a very simple rule and initial conditions and from that can effortlessly build behaviour of great complexity.'

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Where Life Thrives

CAs may also be able to help us appreciate some other facts of life such as the conditions under which it flourishes, what drives evolution and the best places to look for it.

The man who blazed this trail is Chris Langton, a pivotal figure in the ALife movement. It was Langton who coined the term Artificial Life, organized the first ALife conference in 1987 and in doing so single handedly bronght together a group of people who did not know they had common research interests until Langton showed them they did. Without him there would be no ALife movement. Langton carried out a survey of CAs very similar to Wolfram's although he based his conclusions on thousands of runs rather than just hundreds. He did this because: 'Classification is not enough. What is needed is a deeper understanding of the structure of the observed classes and of their relationships to one another. Developing this deeper understanding led Langton to discover a key metric, which he dubbed lambda, that is correlated to the ease with which information can flow in the artificial world of the CA. If, as many people think, life depends for its survival on processing information, then lambda could be a very important measure. At the same time he has revealed how life manages to stay alive and beat off the attempts of the Universe at large to dismantle it.

Consider a 2D CA, such as Conway's Game of Life. In that CA the fate of every cell in the next time step is determined by two factors: the state that cell is currently in, i.e. on or off, alive or dead; the state of the eight neighbouring cells around it. Each of the nine cells we are considering can be in any one of two states, so at any time the neighbourhood will be in any one of 29 possible configurations. We can completely define everything that can happen in this corner of our pocket universe by constructing a table with 512 entries. Each entry in the table represents one configuration. This effectively defines the physics of this neighbourhood.

The configuration of the neighbourhood determines the fate of the cell at its heart. In some situations it could give rise to a living cell and in others a dead cell. In our example CA there are S12 ways of filling in this table. Lambda is the ratio of how many living cells or '1s' there are in a given CA divided by the total possible number of results, in this example 512.

Langton's exploration yielded several interesting results. Firstly he found that Wolfram's four classes were in the wrong order. As the value of lambda increases CAs pass thrungh several distinct states, just as Wolfram observed. But the order goes I, II, IV, III. The CAs that produce the complex patterns come before rather than after ones that give rise to chaotic patterns. The difference between the two is subtle.

'Complex' is a difficult concept to define. Intuitively we can grasp that people are more complex than flies but it is hard to formally define how. Flies and humans have a lot in common, DNA for a start, but their behaviours are very different. We can do some thingsthat flies cannot, like algebra, but there are many things, such as flying through bushes, that humans cannot match. It's hard to say which one is more complex. 'Chaotic' though is easier to pin down. There are measurable characteristics that reveal how chaotic a system is. Some of these measures are mathematical, one is called a Lyapunov exponent and can reveal a system's sensitivity to initial conditions. Exquisite sensitivity is one of the signal states of chaos. Other characteristics reveal themselves when chaotic systems are modelled on computer. When modelled in this way patterns can be found that are invisible in the real world system. Anyone simply observing something like the weather might be forgiven for thinking that it was largely random and it was only possible to predict what would happen next on a very short time scale. In fact, order is hidden within the weather and it is anything but random. The most interesting systems on Earth, the living ones, are a tricky mixture of both complexity and chaos.

Wolfram's classification was purely empirical so this reordering was not overturning any great insight or long held belief belief. Shuffling the coins in your pocket does not change their value, merely the order in which you pick them out. Langton thought that the fact that the classification system should be ordered differently after a more systematic search was highly significant.

The changing lambda value gave rise to patterns that fit very well with Wolfram's classification system. CAs that have a low lambda value are not very interesting. If any patterns emerge at all they quickly die out. As lambda increases the universe of the CA becomes busier and patterns begin to propagate. The most interesting CAs, those that correspond to Wolfram's classes III and IV, have lambda values that centre on 0.5, when a balance between 0s and 1s, living and dead, is emerging. In these CAs patterns, rhythms and stable structures emerge. Then as lambda approaches 1 the CA becomes increasingly unstable and any structures that do emerge are quickly consumed by the frenetic pace of life and death.

At lambda values around 0.5 the behaviour of the CA is either complex or chaotic. But Langton realized that the most interesting parts of all are at the regions between these recognizable states. As the CA passed from one region to another descriptions of what was happening got longer, once within the new region fewer words were needed to describe what was happening. Only in this transition region are the stable and propagating structures like gliders seen. It is the place where universal computation can take place. It is the crucible of life.

Langton called this sweet spot a 'critical phase transition' and it is not jost a phenomenon of the CA universe, similar events are found in the natural world too. When substances are changing from solid to gas they pass through just such a region, their liquid state. Liquids are very difficult to study because they exhiLit such complicated behaviours. What is important about liquids is not what they are made of but the way that the elements within them start to organize themselves. At the point of a 'phase transition' the chemical properties of the particles start becoming largely irrelevant. Instead the information each one carries becomes more important, local interactions no longer determine how the fluid acts. Interactions take place across the fluid, the movements of the whole mass become coordinated and organized. How exactly this happens is still being investigated but evidence for it is overwhelming.


Exactly the same change is taking place in a CA at the point of a 'phase transition'. The actions of the elements are starting to become coordinated across the whole structure. This has led ALife researchers to speculate that CAs are probably very good models of living organisms. This affinity is bolstered by the fact that CAs deal only with information. There are no chemicals present in a CA and no thermodynamics but these experiments show that this does not matter. If the essence of an organism is the information within it then something that deals with nothing but information is probably a good model. All that is important at this phase transition point is organization, CAs. are abstracted away from chemistry, but they lose nothing in the process.

It is not only ALife researchers that are interested in phase transitions. Work on phase transitions has revealed that at critical junctures in the development of a system organization spontaneously emerges. This behaviour has been found in a huge variety of systems. Everything from heart attacks to earthquakes, brains and businesses have been found to be on or passing through phase transitions at some point in their development. Some systems, usually living organisms, seem to be stuck in this state. Because of the ubiquity of this phenomenon the field of research it is part of is called 'universality'. It implies that at certain times different systems act in exactly the same way. The individual elements within them cease to matter as information dynamics takes over. It means that studying life with CAs, as long as they are of the same universality class, is a valid enterprise because in some situations exactly the same thing is happening in living systems as is happening in a CA.

Research into the dynamics of hydrogen-bond networks found in water has revealed very complicated structures and interactions. Langton speculates that these might have acted as a template for the organic compounds swilling around in the Hadean seas and given life something of a jump start.

The implications of this insight are far reaching. It removes the distinctions between living organisms and how they organize themselves and computer hardware and software and how that is organized. As Langton says: 'However, if it is properly understood that hardness, wetness, or gaseousness are properties of the organization of matter, rather than properties of the matter itself, then it is only a matter of organization to turn "hardware" into "wetware" and, ultimately, for "hardware" to achieve everything that has been achieved by wetware, and more'. A two-way street has been established. There is no barrier to computers starting to take on the properties of living things and living things often have the properties of computers. What this also gives clues to is how exactly life got going in the first place. Vitalism was the philosophy that there was some lifeforce that kept living things alive. While no one believes this any more it has proved hard to say just exactly what should take its place. Information is looking like a good bet.

Langton says that there is a lot of evidence that life uses information to maintain itself in the critical phase transition region.

Cell membranes hover in a quasi liquid/solid state and DNA is constantly being zipped and unzipped. The brain too has to be kept within a very narrow temperature band to function normally. There is a narrow region in which life thrives. Life avoids lambda values at the extremes because at these places there is either too much or not enough information around. Equally a chaotic universe is one that life finds inhospitable. As he puts it life has 'learned to steer a delicate course between too much order and too much chaos. It is the threat that keeps us going, the threat of a plummet into chaos or being frozen in stasis that keeps us so very much alive.



Mark Ward

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