## A Humbling Reminder To Our ‘Selves’… Kurt Gödel’s Incompleteness Theorems

### March 31, 2011

So here it comes… We’re about to look at why the idea/concept of a ‘self’ could be one of the greatest human delusions of all time. I know… It’s a pretty tall order. But still, it’s one that has been slowly changing the way I view things here on this wondrous home of a planet over the last few months. But before I share with you my journey – one that demonstrated to me how the seemingly obvious certitude of an ‘I’, or my ‘self’, might really be only a flawed assumption, which in turn became an illusion bourn from grammatical syntax – I would like to introduce another story… One that lays out the ground work between the two extremes of certainty and uncertainty, making evident that any definite human knowledge is, at its core, not a definite as we’d sometimes like to think… And, thus, all certitudes that we might presume or cling to become subject to uncertainty.

The story here is about an Austrian logician, who, despite his untimely death, still remains to this very day a great hero and inspiration to me. His name is Kurt Friedrich Gödel (b. 1906, d. 1978)… His ideas were revolutionary in the field of logic and shook the foundations of mathematics, providing insights into the limitations of what can be known. In fact, I believe some of his insights might also demonstrate – in a parallel sort of way – how what we think we know about our ‘selves’ might actually not be what is the actually case… In fact, it might go one step further and demonstrate something rather unexpected. But I digress…

For the moment, I would simply like to leave you with this great BBC radio documentary, narrated by Melvyn Bragg, that clearly and elegantly describes the life and work of Kurt Gödel, a great friend and college to the late Nobel prize physicist, Albert Einstein.

Gödel’s Incompleteness Theorems

Melvyn Bragg and guests discuss an iconic piece of 20th century maths – Gödel’s Incompleteness Theorems. In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope and fear. The edifice of maths was grand and ornate but its foundations, called axioms, had been shaken. They were deemed to be inconsistent and possibly paradoxical. At the conference, a young man called David Hilbert set out a plan to rebuild the foundations of maths – to make them consistent, all encompassing and without any hint of a paradox.

Hilbert was one of the greatest mathematicians that ever lived, but his plan failed spectacularly because of Kurt Gödel. Gödel proved that there were some problems in maths that were impossible to solve, that the bright clear plain of mathematics was in fact a labyrinth filled with potential paradox. In doing so Gödel changed the way we understand what mathematics is and the implications of his work in physics and philosophy take us to the very edge of what we can know.

With Marcus du Sautoy, Professor of Mathematics at Wadham College, University of Oxford; John Barrow, Professor of Mathematical Sciences at the University of Cambridge and Gresham Professor of Geometry and Philip Welch, Professor of Mathematical Logic at the University of Bristol.

## Uncoiling The Spiral Of Being: Math, Escher And Hallucinations

### September 8, 2010

Last night I had a dream… A spiralling coil of color unfolded its serpentine and slithering body before my mind’s inner eye. Patterns danced in such an orchestrated synchronicity, so as to complect into a delicate and balanced interplay of form and function, all actions and reactions – though it was hard to tell which were which anymore, because of the temporal passage that had clouded all the previous causes to things – feeding back into the source, creating new snaking forms of colorful displays… Never ending, never repeating exactly, so interdependent on everything else around them, looking for nourishment and inspiration in themselves and those around them, every part of it guided by a wild and beating leviathan heart, a heart that was run by the only certainty I could ever find… That of uncertainty… That of chaosAn open ended function that was the only pure motivation for all universal being and which itself, alone, could only describe and create such a miraculous and highly dynamical order… “I” was a part of it… And in reflecting all of what “I” saw unraveling around me, this rhythm of chaotic movement began to shine through my very Being, allowing me to try to define myself in self-similar patterns… Patterns similar to those that “I” witnessed going on around me, allowing me a vain hope to understand what “I” is… While providing me with all I needed to partake in this dance of joyous wonderment before me; understandings were nothing more that rippling imaginations that carelessly skittered over and through the patterns of consciousness… Shape that had been fluxing within my brain’s complex and structured form… And still, I could only try to understand why, like almost everyone else, “I” tried to find similar reasons for Being in the ocean of delusion that swelled and sank around me… It was the only way “I” had known how to be throughout my entire life… And this was how the wonder twisted through my living, convoluting flow… A pattern that embraced every aspect of our Being, clutching “my” particle-like body into the blossom of its infinite totality….

Perhaps this was what many people before me had decided to call “God…” Mainly because they hadn’t properly understood its essence and nature… After, the wise mystics of the East followed the way of this unspeakable, indescribable beast. The Tao, they called it. “The Way.” And still it remains the only way to be, to dream and to live in harmony with all under heaven. Riddled with self-similarity, it writhed and pulsed to various rhythms running through its Being, all running inside and outside of each other, layering into and out of itself, fluxing with such precision that it might have been a silken fabric so finely woven, that the very threads we but atomic braids of molecular chains, of which any movement could upset the natural order and cause a mighty ripple to undulate throughout itself.

In all honesty I can’t remember how long this phantasm of interconnected geometry lasted… All I know is that I woke with a sudden jolt to find myself in bed with the covers strewn half on me and half on the floor. In someways I was relieved to find myself back home… But also I had a distinct sense of underlying melancholy that seemed to underpin my sleepy head… Sort of like when one departs the company of good friends. Slowly as my mind came back into focus, I found myself thinking of M. C. Escher‘s work. The seeming parallels that ran through my mind joined my dream up with Escher’s precise visions of nature’s “natural” symmetry. These in turn linked up with my own personal first hand experiences with mescaline, psilocybin, DMT and LSD… I haven’t tripped in a long, long time now. And I doubt I will need to ever again. What I had to learn from these powerful allies of the plant world, I did. They have kindly shown me all that I need to see. Within their own tapestries of mind, from the altered states of consciousness that they seem to so gracefully and naturally induce, I found myself faced with patterns as complex as those that I had seen on the Alhambra.

Yes… That’s it. That’s what all this reminds me of… The Moorish architecture of the Alhambra… There is so much of divine Moorish masonry to be found in Granada… And funnily enough it’s almost a year ago to the day that I arrived back from there… Perhaps, this is where my dream came from… Parallels in our orbit around our star, echoing through the structure of my brain. Perhaps I should provide a brief setting for this slight tangent… Between 710 and 713 A.D., Spain had been overrun by the Moors (populations of Berber, Black African and Arab peoples from Northern Africa), and these Islamic conquerors naturally introduced the ornate Moorish, or Moresque or Hispano-Moresque, style of design to the Iberian Peninsula, and is especially noted in the architecture of Southern Spain, which is centred and personified in the Alhambra, located in the city of Granada.

The Moors were not entirely driven out of the Southern provinces until 1610, but in the nine hundred years intervening, the Moresque style flourished sporadically throughout many portions of Spain. And one can see why… The splendour of this mode of design brought nearly everyone who saw it closer to a true sense of wonder regarding the creation of all things than anything else at the time. During the Romanesque period a large part of the country was still under Moorish rule… Here the balanced European form mingled with Islamic sensibilities, producing wondrous Romanesque structures laced with Moresque imagery and pattern. This marriage of form inspired the late M. C. Escher so much during his first visit in 1922, that he is reportedly to have said, “I have never before seen such concentrated inspiration in all the world!” After this his works of art began to take a very different turn. From the Italian country side sketches and etchings, he slowly incorporated this Moorish symmetry into his designs. While the Moors we forbidden to use any human or animal forms in their art – mainly because humans and animals were considered to be the divine and perfect work of Allah, and any human representation could only ever be an imperfect representation of the creator’s master work, and thus a blaspheme – Escher began to break this mould and used images of animals and plants in tessellations of wondrous cunning. These tessellations began to feature predominantly throughout most of the work of his later life. And rather than limiting them to just the snug, tightly fitting geometries of mathematical sensibilities… He opened them up with his imagination into metamorphosing consternations. It was almost as if Escher had seen the key to the universe, and had unlocked the door, through which it began to speak through him.

I know… I know… Sounds like a sort of far fetched fantasy derived from a dream I had… However, I’m going to present an idea in the form of an article that I found on the Twitter vine not too long ago. It is entitled “Uncoiling The Spiral: Math And Hallucinations” and was written by Marianne Freiberger.

Uncoiling The Spiral: Math And Hallucinations

Think drug-induced hallucinations, and the whirly, spirally, tunnel-vision-like patterns of psychedelic imagery immediately spring to mind. But it’s not just hallucinogenic drugs like LSD, cannabis or mescaline that conjure up these geometric structures. People have reported seeing them in near-death experiences, as a result of disorders like epilepsy and schizophrenia, following sensory deprivation, or even just after applying pressure to the eyeballs. So common are these geometric hallucinations, that in the last century scientists began asking themselves if they couldn’t tell us something fundamental about how our brains are wired up. And it seems that they can.

Computer generated representations of form constants. The top two images represent a funnel and a spiral as seen after taking LSD, the bottom left image is a honeycomb generated by marijuana, and the bottom right image is a cobweb.

Geometric hallucinations were first studied systematically in the 1920s by the German-American psychologist Heinrich Klüver. Klüver’s interest in visual perception had led him to experiment with peyote, that cactus made famous by Carlos Castaneda, whose psychoactive ingredient mescaline played an important role in the shamanistic rituals of many central American tribes. Mescaline was well-known for inducing striking visual hallucinations. Popping peyote buttons with his assistant in the laboratory, Klüver noticed the repeating geometric shapes in mescaline-induced hallucinations and classified them into four types, which he called form constants: tunnels and funnels, spirals, lattices including honeycombs and triangles, and cobwebs.

In the 1970s the mathematicians Jack D. Cowan and G. Bard Ermentrout used Klüver’s classification to build a theory describing what is going on in our brain when it tricks us into believing that we are seeing geometric patterns. Their theory has since been elaborated by other scientists, including Paul Bressloff, Professor of Mathematical and Computational Neuroscience at the newly established Oxford Centre for Collaborative Applied Mathematics.

How The Cortex Got Its Stripes…

In humans and mammals the first area of the visual cortex to process visual information is known as V1. Experimental evidence, for example from fMRI scans, suggests that Klüver’s patterns, too, originate largely in V1, rather than later on in the visual system. Like the rest of the brain, V1 has a complex, crinkly, folded-up structure, but there’s a surprisingly straight-forward way of translating what we see in our visual field to neural activity in V1. “If you imagine unfolding [V1],” says Bressloff, “You can think of it as neural tissue a few millimetres thick with various layers of neurons. To a first approximation, the neurons through the depth of the cortex behave in a similar way, so if you compress those neurons together, you can think of V1 as a two-dimensional sheet.”

The visual cortex: the area V1 is shown in red.

An object or scene in the visual world is projected as a two-dimensional image on the retina of each eye, so what we see can also be treated as flat sheet: the visual field. Every point on this sheet can be pin-pointed by two coordinates, just like a point on a map, or a point on the flat model of V1. The alternating regions of light and dark that make up a geometric hallucination are caused by alternating regions of high and low neural activity in V1 — regions where the neurons are firing very rapidly and regions where they are not firing rapidly. To translate visual patterns to neural activity, what is needed is a coordinate map, a rule which links each point in the visual field to a point on the flat model of V1. In the 1970s scientists including Cowan came up with just such a map, based on anatomical knowledge of how neurons in the retina communicate with neurons in V1 (see the box on the right for more detail). For each light or dark region in the visual field, the map identifies a region of high or low neural activity in V1.

So how does this retino-cortical map transform Klüver’s geometric patterns? It turns out that hallucinations comprising spirals, circles, and rays that emanate from the centre correspond to stripes of neural activity in V1 that are inclined at given angles. Lattices like honeycombs or chequer-boards correspond to hexagonal activity patterns in V1. This in itself might not have appeared particularly exciting, but there was a precedent: stripes and hexagons are exactly what scientists had seen when modelling other instances of pattern formation, for example convection in fluids, or, more strikingly, the emergence of spots and stripes in animal coats. The mathematics that drives this pattern formation was well known, and it now suggested a mechanism for modelling the workings of the visual cortex too.

…And How The Leopard Got Its Spots

The first model of pattern formation in animal coats goes back to Alan Turing, better known as the father of modern computer science and Bletchley Park code breaker. Turing was interested in how a spatially homogeneous system, such as a uniform ball of cells making up an animal embryo, can generate a spatially inhomogeneous but static pattern, such as the stripes of a zebra.

Turing hypothesised that these animal patterns are a result of a reaction-diffusion process. Imagine an animal embryo which has two chemicals living in its skin. One of the two chemicals is an inhibitor, which suppresses the production of both itself and the other chemical. The other, an activator, promotes the production of both.

Initially, at time zero in Turing’s model, the two chemicals exactly balance each other — they are in equilibrium, and their concentrations at the various points on the embryo do not change over time. But now imagine that, for some reason or other, the concentration of activator increases slightly at one point. This small perturbation sets the system into action. The higher local concentration of activator means that more activator and inhibitor are produced there — this is a reaction. But both chemicals also diffuse through the embryo skin, inhibiting or activating production elsewhere.

For example, if the inhibitor diffuses faster than the activator, then it quickly spreads around the point of perturbation and decreases the concentration of activator there. So you end up with a region of high activator concentration bordered by high inhibitor concentration — in other words, you have a spot of activator on a background of inhibitor. Depending on the rates at which the two chemicals diffuse, it is possible that such a spotty pattern arises all over the skin of the embryo, and eventually stabilises. If the activator also promotes the generation of a pigment in the skin of the animal, then this pattern can be made visible. (See the Plus article How the leopard got its spots for more detail.)

Turing wrote down a set of differential equations which describe the competition between the two chemicals (see the box on the right), and which you can let evolve over time, to see if any patterns emerge. The equations depend on parameters capturing the rate at which the two chemicals diffuse: if you choose them correctly, the system will eventually stabilise on a particular pattern, and you can vary the pattern by varying the parameters. Here is an applet (kindly provided by Chris Jennings) which allows you to play with different parameters and see the patterns form.

Patterns In The Brain

Neural activity in the brain isn’t a reaction-diffusion process, but there are analogies to Turing’s model. “Neurons send signals to each other via their output lines called axons,” says Bressloff. Neurons respond to each other’s signals, so we have a reaction. “[The signals] propagate so quickly relative to the process of pattern formation, that you can think of them as instantaneous interactions.” So rather than diffusion, which is a local process, we have instantaneous interaction at a distance in this case. The roles of activator and inhibitor are played by two different classes of neurons. “There are neurons which are excitatory — they make other neurons more likely to become active — and there are inhibitory neurons, which make other neurons less likely to become active,” says Bressloff. “The competition between the two classes of neurons is the analogue of the activator-inhibitor mechanism in Turing’s model.”

Stripy, hexagonal and square patterns of neural activity in V1 generated by a mathematical model.

Inspired by the analogies to Turing’s process, Cowan and Ermentrout constructed a model of neural activity in V1, using a set of equations that had been formulated by Cowan and Hugh Wilson. Although the equations are more complicated than Turing’s, you can still play the same game, letting the system evolve over time and see if patterns in neural activity evolve. “You find that, under certain circumstances, if you turn up a parameter which represents, for example, the effect of a drug on the cortex, then this leads to a growth of periodic patterns,” says Bressloff.

Cowan and Ermentrout’s model suggests that geometric hallucinations are a result of an instability in V1: something, for example the presence of a drug, throws the neural network off its equilibrium, kicking into action a snowballing interaction between excitatory and inhibitory neurons, which then stabilises in a stripy or hexagonal pattern of neural activity in V1. In the visual field we then “see” this pattern in the shape of the geometric structures described by Klüver.

Symmetries In The Brain

In reality, things aren’t quite as simple as in Cowan and Ermentrout’s model, because neurons don’t only respond to light and dark images. Through the thickness of V1, neurons are arranged in collections of columns, known as hypercolumns, with each hypercolumn roughly responding to a small region of the visual field. But the neurons in a hypercolumn aren’t all the same: apart from detecting light and dark regions, each neuron specialises in detecting local edges — the separation lines between light and dark regions in a part of an image — of a particular orientation. Some detect horizontal edges, others detect vertical edges, others edges that are inclined at a 45° angle, and so on. Each hypercolumn contains columns of neurons of all orientation preferences, so that a hypercolumn can respond to edges of all orientations from a particular region of the visual field. It is the lay-out of hypercolumns and orientation preferences that enables us to detect contours, surfaces and textures in the visual world.

Connections in V1: Neurons interact with most other neurons within a hypercolumn. But they only interact with neurons in other hypercolumns, if the columns lie in the direction of their orientation, and if the neurons have the same preference.

Over recent years, much anatomical evidence has accumulated showing just how neurons with various orientation preferences interact. Within their own hypercolumn, neurons tend to interact with most other neurons, regardless of their orientation preference. But when it comes to neurons in other hypercolumns they are more selective, only interacting with those of similar orientations and in a way which ensures that we can detect continuous contours in the visual world.

Bressloff, in collaboration with Cowan, the mathematician Martin Golubitsky and others, has generalised Cowan and Ermentrout’s original model to take account of this new anatomical evidence. They again used the plane as the basis for a model of V1: each hypercolumn is represented by a point (x, y) on the plane, while each point (x, y) in turn corresponds to a hypercolumn. Neurons with a given orientation preference Θ (where Θ is an angle between 0 and π) are represented by the location (x, y) of the hypercolumn they’re in, together with the angle Θ, that is, they are represented by three bits of information, (x, y, Θ). So in this model V1 is not just a plane, but a plane together with a full set of orientations for each point.

If two elements (x,y,θ) and (s,t,θ) interact, then so do the elements of the same orientation at (x+a,y+b) and (s+a,t+b), and the elements of orientation -θ at (x,-y) and (s,-t).

In keeping with anatomical evidence, Bressloff and his colleagues assumed that a neuron represented by (x0, y0, Θ0) interacts with all other neurons in the same hypercolumn (x0, y0). But it only interacts with neurons in other hypercolumns, if these hypercolumns lie in their preferred direction Θ0: on the plane, draw a line through (x0, y0) of inclination Θ0. Then the neurons represented by (x0, y0, Θ0) interact only with neurons in hypercolumns that lie on this line, and which have the same preferred orientation Θ0.

This interaction pattern is highly symmetric. For example, the pattern doesn’t appear any different if you shift the plane along in a given direction by a given distance: if two elements (x0, y0, Θ0) and (s0, t0, ϕ0) interact, then the elements you get to by shifting along, that is (x0 + a, y0 + b, Θ0) and (s0 + t, y0 + b, ϕ0) for some and , interact in the same way. In a similar way, the pattern is also invariant under rotations and reflections of the plane.

A lattice tunnel hallucination generated by the mathematical model. It strongly resembles hallucinations seen after taking marijuana.

Bressloff and his colleagues used a generalised version of the equations from the original model to let the system evolve. The result was a model that is not only more accurate in terms of the anatomy of V1, but can also generate geometric patterns in the visual field that the original model was unable to produce. These include lattice tunnels, honeycombs and cobwebs that are better characterised in terms of the orientation of contours within them, than in terms of contrasting regions of light and dark.

What’s more, the model is sensitive to the symmetries in the interaction patterns between neurons: the mathematics shows that it is these symmetries that drive the formation of periodic patterns of neural activity. So the model suggests that it is the lay-out of hypercolumns and orientation preferences, in other words the mechanisms that enable us to detect edges, contours, surfaces and textures in the visual world, that generate the hallucinations. It is when these mechanism become unstable, for example due to the influence of a drug, that patterns of neural activity arise, which in turn translate to the visual hallucinations.

Beyond Hallucinations

Bressloff’s model does not only provide insight into the mechanisms that drive visual hallucinations, but also gives clues about brain architecture in a wider sense. In collaboration with his wife, an experimental neuroscientist, Bressloff has looked at the connection circuits between hypercolumns in normal vision, to see how visual images are processed. “People used to think that neurons in V1 just detect local edges, and that you have to go to higher levels in the brain to put these edges together to detect more complicated features like contours and surfaces. But the work I have done with my wife shows that these structures in V1 actually allow the earlier visual cortex to detect contours and do more global processing. It used to be thought that you process more and more complex aspects of an image as you go higher up in the brain. But now it’s realised that there is a huge amount of feedback between higher and lower cortical areas. It’s not a simple hierarchical process, but an incredibly complicated and active system it will take many years to understand.”

Practical applications of this work include computer vision — computer scientists are already building the inter-connectivity structures that Bressloff and his colleagues played around with into their models, with the aim of teaching computers to detect contours and textures. On a more speculative note, Bressloff’s research may also one day help to restore vision to visually impaired people. “The question here is if you can somehow stimulate part of the visual cortex, [bypassing the eye], and use that to guide a blind person,” says Bressloff. “If one can understand how the cortex is wired up and responds to stimulation, perhaps one would then have a better way of stimulating it in the right way.”

There are even applications that have nothing at all to do with the brain. Bressloff applied the insights from this work to other situations in which objects are located in space and also have an orientation, for example fibroblast cells found in human and animal tissue. He showed that under certain circumstances these interacting cells and molecules can line up and form patterns analogous to those that arise in V1.

People have reported seeing visual hallucinations since the dawn of time and in almost all human cultures — hallucinatory images have even been found in petroglyphs and cave paintings. In shamanistic traditions around the world they have been regarded as messages from the spirit world. Few neuroscientists today would agree that spirits have anything to do with it, but as messengers from a hidden world — this time the hidden world of our brain — these hallucinations seem to have lost none of their potency.

by Marianne Freiberger

For me that article just magically linked up some seemingly random dots that had been lingering in my mind… Ones that were loosely drifting around on a plane of understanding that seemed to – only at the best of times – be based on flights of fancy and mathematical musings of divine symmetry… Could the reason why I, and others, are so drawn to these tapestries of geometrical wonder be because this pattern is naturally residing in the brain’s architecture? Could the key to our modes of perception regarding the surrounding universe be found – amazingly enough – in the roots of our minds? Is the mysticism lying behind the Alhambra’s amazing architecture linked to the patterns locked deep within the brains structure? Is that where our notions of God and the divine come from i.e. the imagery of divine knowing and interrelatedness that came to haunt my dream last night?

For me there is no doubt that there is a strong link between the spiritual ecstasy that I have experienced in altered states of consciousness and while viewing Escher’s works of art… Perhaps those followers of Allah, who invaded the Iberian Peninsula and left their indelible mark on the Spanish people’s cities and towns, saw a similar connection too. Certainly it is mentioned that the prophet Muhammad experienced visions while meditating within a cave for several weeks every year. It is here in this cave on Mount Hira, near Mecca, that he apparently experienced a direct countenance with the angel Gabriel who revealed many things to him. Certainly adherents and prophets of other religions also recount similar marvels and revelatory experiences (see Aldous Huxley‘s “The Perennial Philosophy”).

While I am not religious… I am aware of a pattern of mind that links these spiritual experiences into a similar and all encompassing perennial philosophy. Perhaps the key to this insight lies within ourselves through direct experience, rather than in notions and metaphors of an omniscient and omnipotent god/group of gods. Perhaps it’s time we forgot our differences and looked for the key to understanding our experiences through consciousness itself… Where we relate to one another through our patterns of mind and body… A view that would be free from delusion and ‘self’ impossed egocentric understandings… ? Perhaps psychedelics are a type of direct key to seeing this pattern of the divine… ? And perhaps our notions of an eternal creator is nothing more than the same patterns we see springing forth in the mind in altered states of consciousness… Perhaps this direct experience of the divine is so powerful that it leaves us reeling with a deep feeling of connect… Mainly because it is what we really are at base… And thus we dedicate such intricate, beautiful and inspiring architecture – a testament to the divine nature of our being – to those ideals of God that many of us hold so high. Perhaps this is why some many of us find the Mandelbrot set so mesmerising… Perhaps Escher knew this deep down… ?

If you would like to see where I sourced the article, entitled “Uncoiling The Spiral: Maths And Hallucinations,” from, please click here.

## Comic… !?

### July 5, 2010

What can I say… Too much XAOS and a funny five minutes gave rise to these two little oddities.

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AND/OR

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OR if you’d like to learn more about nonlinear dynamical systems, please read James Gleick’s “Chaos: The Making Of A New Science.” The first three people to E-mail me by clicking here will receive a free copy of the book! Just remember to enter the address you’d like the book to be delivered to…

## The Chaos Within: Positive Affect And The Complex Dynamics Of Human Flourishing

### June 15, 2010

I’ve spoken about it before… Patterns reside at all levels of life, whether we see them or not. Patterning is everywhere within and without of ourselves. We like to think we can grasp it and change its functionality, desiring to know what it’ll do next… But to control something so sensitive and so fickle is pure delusion upon our part. Rather we are set adrift on a sea of chance, which is so sensitive, that to even think about it seems to change the essence of what it actually is and how it behaves.

Lao Tzu once wrote about “the mysterious quality of the Tao…” For he must have glimpsed at man’s never ending and intrinsic need to understand nature’s flow and design… Why would man want to do this? So as to control and utilise – perhaps even exploit – the essence of all things under heaven… And possibly even within heaven itself. Certainly nothing is held sacred anymore… For understanding seems to explain away any mystical edge that the unknown might have held. Even chaos, while the principles behind its essence certainly are being developed and refined in clearer modes of understanding, still can never be predicted exactly with so many sensitive variables housed within its delicate and susceptible mechanism. Still, from this vague understanding of “God, or Nature’s” ways, our morality seems to disregard this untouchable divinity and aims to solely tighten mankind’s own egocentric and self-imposed purpose here on Earth. If only we could connect with the Tao… How soft and yielding we would all learn to be.

“The Tao produces all things and nourishes them; it produces them and does not claim them as its own; it does all, and yet does not boast of it; it presides over all, and yet does not control them. This is what is called ‘the mysterious Quality’ of the Tao.”

Here I feel Lao Tzu essentially tapped into the essence of what modern science came to know as “chaos…” And where chaos begins, classical science seems to have trouble with its own steadfast footing. To understand concepts behind something which is practically impossible to predict, let alone control, is fair play… But to desire to control something which is unpredictable is dim-witted idiocy. Lao Tzu knew that the unpredictable nature of all things was the essence of that which created and gave life to all things. It does not obviously present itself to any investigator, as Edward Lorenz discovered while using differential equations to create a virtual weather system. And thus, with its hidden and subtle being, it does not boast of its own wonder… As we now know, nonlinear dynamical systems are found literally everywhere in nature and the universe. The chaos within these dynamical systems “presides over all…” Yet the flexibility of these modes of interaction between all discrete units can never yield to, nor allow, any predictable control. Why? For all the subtle, minuscule, almost indiscernible changes made within the system, give rise to eddies that writhe and bubble over the edge of certainty and thus can never be forecast with any indubitable conviction. Here in lies the essence of the Tao… Of chaos itself.

No doubt some of you have realised by now that the main theme running through this website is centred around aspects of chaos and nonlinear dynamics – what one perceptive philosopher, namely Baruch Spinoza, termed to be “God, or Nature.” The end aim of this is to demonstrate how the complexity of our universal experience and of universal being, which look at notions of who and what we really we are, all interlink into one vastly complex, and almost unknowable picture of order woven out of a fabric of disorder. As if this essence was what man’s notions of God were developing into. Or if if we were to look at it all more rationally, then to somewhat summarise this long chain of interlinking events, the Buddhists chose to call this majestic tapestry “Interdependent Origination.”

Chaos admittedly has notions of disorder and irregularity running through out its rough and irregular flow… But it is this disorder that acts as an amazingly complex function of universal discourse, providing order and consistency at congruent levels of flexibility, thus generating immense diversity… In my humble opinion it is this juxtaposition of order and disroder that allows a stability within a mode of suppleness which feeds-back into itself, allowing us to learn within standards of conformity, and yet evolve, over time, into ever modifying manners of new understanding and functionality. For example, our perception of the passing of time is directly associated with the dynamical discharge of our neural net. We are limited to states of temporal regularity through the mechanisms of our own bodily designs. We only have to try to swat a fly to see this.

Evolution is occurring within – and upon – all levels of dynamical interaction, whether these are social discourses within society or mental arrangements of schemas within our minds… OR even if they are atomic and molecular interactions within chemical systems, such as goes on within our brains and bodies… These processes even stretch to encompass vast expanses of gaseous shapes that are being tugged and pulled by gravitational forces of moving/shifting suns, solar systems and black holes within nebulous areas of space… Change, no matter how sharp or quick, ever so softly folds back onto itself into new renditions of behavioural patterning. No doubt we will be hard pressed to see all these levels if we know nothing about chaos theory OR the Tao.

Some might well ask why we should even bother to try to see these elusive processes… And yet all of these processes deeply penetrate our society’s totality, affecting us in ways that are far too subtle to mention with our rudimentary understand of things… Only a Buddha could possibly ‘see’ them clearly enough to understand them truly, without corrupting the purity of their nature with society’s own crass and cumbersome perception of things. We, as human beings – who are made from this algorithm of Life: a vast interacting net of chaotic flow – rely upon the “mystery” of the Tao’s essence to function. So profound and all pervading is it, that it operates on – and across – so many levels of energetic continuity, all of which are intertwined in a complexity that only “God, or Nature” could ever truly become self-aware of… And yet I feel we need to see this, even if it is only in part. Especially because of our present extremely self-centred and heavy modes of living and being i.e. pollution of the environment, destruction of forests, etc… When we see the interconnectedness of everything we will notice that these levels of universal interplay are so ethereal and disarming that, when understood with the patterns within ourselves, we will find it easier to truly open ourselves up to the universe in a way that will shed light on understanding why so many human beings choose to do such seemingly silly things with their lives i.e. believe in a deity of some kind, etc… Once we become familiar with these chaotic ebbs and flows, we may see anew through cleansed insight, so as to understand why altruistic behaviour has naturally been selected for (religions, whether you like it or not, do possess the marks of altruistic behaviour)… And why, as Susan Blackmore discusses in her book entitled “The Meme Machine,” altruism spreads more altruism.

So, before we get to the point of this blog, let’s look at what Susan Blackmore wrote about Altruism in her book, “The Meme Machine.”

The Altruism Trick

In today’s world I am going to assume that we can ignore meme-gene coevolution. This might be an oversimplification, because as long as there are two replicators they will interact with one each other. However, the pace of memetic evolution is now so fast, relative to that of genetic evolution, that we can safely ignore the latter for most purposes. The genes cannot keep up. What we cannot ignore is the legacy left by the long process of coevolution. The brains we have are the big and clever brains created by meme-gene coevolution. The way we think and feel is a product of that evolutionary process, and now determines which memes do well and which do not. We like sex, so sex memes get a head start: different ones for men and for women. We like food and we like power and excitement. We find maths hard, and so mathematical memes need a lot of encouragement. The structure of our language affects which memes are more easily passed on. The theories and myths we have created affect the way we deal with new memes. And so on.

Note that sociobiology has made a different simplifying assumption and has ignored the role of memes. For many purposes this has been an adequate approach, and we can use many of the findings of sociobiology to provide insight into the brains we have and the ideas and behaviours that come easily, but it cannot provide the whole picture. Our concern now will be what happens when vast numbers of memes compete to get into, and stay in, limited numbers of increasingly educated and overworked brains.

We must resume the meme’s eye view; remembering that all that counts in the life of a meme is whether or not it survives and replicates. I shall find myself saying that memes ‘want,’ ‘need,’ or ‘try to do’ something. But we must remember that this is only shorthand for saying that the ‘something’ will improve the chances of the meme’s being copied. Memes do not have conscious intentions; nor do they actually strive to do anything at all. They are simply (by definition) capable of being copied, and all their apparent striving and intentionality comes from this. When anything can be copied it can end up having few or many copies made. Memes may be successfully copied because they are good, true, useful or beautiful – but they may be successful for other reasons too. It is those reasons I now wish to explore.

A meme that gets into a meme-fountain will do better than one that only gets into meme-sinks. We can guess who the meme-fountains are. Indeed, many experiments in social psychology show who is most often emulated. Powerful people (and people who dress in the trappings of power), people perceived as experts, and people in authority are all examples of ‘imitate-the-successful.’ All these people are more likely to get others to do what they say or to accept their ideas; as salesmen, advertisers and politicians have long known. In discussing the ‘power button’ Brodie (1996) suggests that TV shows use large cars, guns and flashy clothes to gain more air time and so promote their kinds of memes. Fames spreads memes, as when television and film stars are watched by millions of viewers, so changing the fashions in clothes, speech, smoking or drinking, cars, food and lifestyle. But not everyone is powerful, and there are other kinds of meme-fountain. For example, we are more likely to be persuaded by someone we perceive as similar to ourselves, and a clever sales trick is to mirror the actions of the potential buyer or to pretend to having similar beliefs or hobbies (Cialdini 1994).

I have already suggested that one way to spread memes is to behave altruistically, and I now want to consider some of the consequences of this less obvious way of becoming a meme-fountain. First, altruistic behaviour spreads copies of itself – so making us more altruistic. Second altruism helps to spread other memes – so providing a trick that memes can use to get themselves copied.

Let us consider first the copying of altruistic behaviour itself. Imagine two different memes (or sets of memes). One is a set of memes for helping your friend when she is in trouble – whether it is giving her a lift when her car breaks down or listening to her troubles when her boyfriend leaves her. The other is a set of memes for ignoring what your friend needs. These are behaviours that can be copied from one person to another and so they must be memes. Note that I uese the phrase ‘a meme for something.’ This is potentially dangerous because it might be taken to imply that there is a particular instruction explicitly stored somewhere in a brain which tells the person to help their friend – and this can easily be made to look ridiculous. This interpretation is not necessary, however. All that is necessary is to assume that people imitate aspects of each other’s behaviour and that when they do so something is passed on from one to the other. We do not need to agonise about what that something is. The simple fact is that if imitation happens (as it surely does) then something has been passed on and that something is what we call the meme. So when I say a ‘meme for helping your friend’ I only mean that some aspect of helping behaviour has been passed on by one person copying the other.

Now we can ask the important question: which of these two memes will do better? The first meme will – it will make your friend like you more and want to spend more time with you. She will therefore become more helpful to her other friends, and so the meme will gradually spread. The same simple logic applies to any meme which helps its carrier to become more popular. The people who pick up these memes are not aware of what they are doing, they just find themselves wanting to be more like the nice people, not the nasty ones. They find they want to help and be kind and feel bad if they do not. Just as many of our human emotions serve the genes, so these ones serve the memes – and they are no less noble for that.

Does this mean that everyone will become nicer and nicer and nicer without limit? Of course not. The main reason why not is that being kind and generous and altruistic is expensive in terms of time and money. There are always pressures acting against altruism, and there are always other strategies for memes to use. However, in general it means that people will be more altruistic than they would be if they were incapable of imitation.

This is an example of meme-driven altruism in a modern context (and note that this is different from the memetic driving of genes for altruism which I considered at the end of the previous chapter). In this kind of meme-driven altruism, actions that are costly and done for someone else come about through memetic competition. Because these actions are driven by memes and not genes they need not necessarily be in the person’s genetic interest. These cases, in which the genes do not benefit and the memes do, provide test cases for a memetic explanation. People who devote their entire lives to charitable work or to the caring professions while having no children of their own are examples. Their sacrifice cannot easily be explained in terms of genetic advantage, but can be simply explained in terms of memetics.

In principle, meme-driven altruism ought to be able to produce the most pure and selfless generosity. Indeed, it may occasionally do so. However, altruism not only works to spread itself but also acts to spread other memes as well. This provides a mechanism open to exploitation by other memes. This, I suggest, is exactly what happens. I shall describe several ways in which memes can exploit the process of meme-driven altruism. These are all versions of what I shall call the ‘altruism trick.’

The altruism trick depends on the simple idea that a meme that gets into an altruistic or likeable person (like Kevin) is more likely to be copied than one that gets into a meany (like Gavin). So what kinds of meme (other than memes for altruism) can get into the altruist?

First, some memes look like altruism even if they are not, and so they can fit easily in an already altruistic person, and second, memes can group together into memeplexes that use various tricks to get into altruists.

Looking like altruism

The first is an obvious trick, to look like altruism. A meme that makes a person appear to be kinder and more generous will increase the chances of that person being imitated and so of that meme being spread, without incurring great costs. There are many examples of this kind of behaviour. We smile at people a lot, and we smile back at people who smile at us first. We say kind and polite things to them – ‘How are you?’ ‘I do hope your parents are well’ ‘Have a nice time at the party’ ‘How may I help you?’ ‘Have a good day’ ‘Happy New Year.’ With all these common memes we give the impression of caring about the other person, even if we do not. That is why they are successful memes. Our ordinary everyday conversation is full of such memes.

Closely related to this is the sort of meme that sneaks easily into an altruist. Memes do not exist in isolation. All memes, at least at some phases of their lives, are stored in human brains, and humans are complicated creatures who strive to maintain some kind of consistency to their ideas. This ‘consistency principle’ is crucial in understanding a lot of human thought and action. If a given person tends to be altruistic, whether because of a genetic tendency to act that way, or because he has picked up lots of altruistic memes during his/her lifetime (or most likely because of both), then other altruism memes are more likely to gain a foothold there.

Let us suppose a new meme comes along in the lives of Kevin and Gavin; suppose they both hear a plea to save their used stamps and send them to some charity. This new meme is far more likely to be accepted and acted on by Kevin than Gavin. It fits well with his other behaviour. He thinks of himself as a caring person and so on. If he refused to take part he would suffer ‘cognitive dissonance,’ the unpleasant consequence of holding two incompatible views – in this case, his idea of himself as a caring person and refusal to help with the stamps. Many psychological studies have shown that people will work to reduce dissonance between incompatible ideas, and also that consistency itself is generally admired and emulated (Cialdini 1994; Festinger 1957). This idea is less likely to take hold of Gavin. He would suffer no cognitive dissonance by refusing to help in this or any other way.

The need for consistency and the avoidance of dissonance provide the context in which memes club together in different people. Once someone is committed to a particular set of memes, other memes are more or less likely to find a safe home in that person’s repertoire of arguments, beliefs, and behaviours. We find this kind of generalisation of memes in all sorts of contexts. You might think it is just common sense that nice people do nice things and nasty people do nasty things but memetics puts this common-sense fact in a slightly different light. Memes can succeed or fail because of the genetic propensity of the people they come across, also because of the memes already present in those people.

The situation is all the more complex because of changing fashions. The memes which are acceptable will shift as the whole meme pool changes. At one time, certain types of charitable giving will seem appropriate, but a few years later, completely different kinds will take over. But this complexity should not cloud the basic principle. Once meme-driven altruism has got going it will generalise. Memes for all sorts of kind and generous acts can take hold more easily in people who are already infected with altruistic memes and who have invested in a particular view of themselves. These people are copied more than other people and so these memes spread more widely.

This process can be used to understand all sorts of otherwise rather baffling actions. Let us take kindness to animals, Many people go out of their way to help animals in distress. There are homes for dogs and cats, and refuges for sick donkeys and injured wildlife. There are game parks and great international attempts to save species from extinction. There are ‘Save the Animals’ charity shops, and greetings cards that support wildlife organisations.

I say this is baffling because there is no easy explanation of all this inter-species kindness in terms of rational self-interest, genetic advantage, or evolutionary psychology. Rescuing an injured tiger would not benefit a hunter-gatherer. Animals were not domesticated until about ten thousand years ago in the ‘Fertile Crescent’ to the east of the Mediterranean, as recently as one thousand years ago in America, and not at all in some parts of the world (Diamond 1997). Therefore during most of our evolutionary past, the animal around us have mostly been either been potential prey for eating or predators trying to eat us. Saving them from death makes no genetic sense; nor does working to relieve their suffering. I have never come across a sociobiological explanation of kindness to animals, although I can think of several possibilities. Animals cannot, on the whole, pay back the favours; so direct reciprocal altruism is no explanation. However, a possible argument is that reciprocal altruism has given us the emotions that drive this behaviour. We feel empathy with suffering animals and want to relieve it; we feel guilt if we do not, and so on. Another possibility is that we raise our status in the reciprocal altruism stakes by appearing kind. I am not convinced that this makes sense, because of the high potential costs of such behaviour. Surely, natural selection would have weeded out any tendencies to be too kind to animals, especially wild and dangerous. These theories are also hard to test.

Why do we do it then? I suggest that kindness to animals can easily take hold because it fits well in people who are already infected with altruism memes. They see themselves as kind people and have an investment in continuing to be so. The way they behave makes them more likely to be imitated, and so kindness to animals spreads.

Exactly the same argument applies to the increasingly widespread practise of refusing to eat meat. Humans were clearly designed to eat a certain amount of meat. Meat is high in protein and fat, and was probably necessary to feed the increasingly large brain of our far ancestors. Yet now many people, myself included, do not eat meat. Some argue that they feel better on a vegetarian diet and a few do not like meat, but most say they are affected by the suffering of the animals bred and killed for food. I suggest that vegetarianism succeeds as a meme because we all want to be like the nice people who care about animals, and so we copy them. Not everyone will get infected by this meme; some like meat too much and others have sets of memes that are not very compatible with this one. Nevertheless, it does quite well. Vegetarianism is a mimetically spread altruistic fashion.

If this is right we should expect to be able to trace the historical origins of such memes as they gradually appear and take hold of whole populations. We should not expect to find such actions in societies with little communication and few ways for memes to spread. We would expect them to be most common in societies in which people have plenty of resources to spare and plenty of opportunities for picking up new memes. We should not necessarily expect people to brag about being kind to animals, but simply to find themselves wanting to be so.

Note that it is not necessary that the superficially kind actions should actually help the animals in question. An injured animal that is rescued is helped in the short term, and a potential battery hen that is never hatched is almost certainly better off for never having existed. But the long-term prospects are dubious, especially when it comes to schemes for saving whole habitats or species. The memetic approach makes it easy to understand why particular behaviours spread even when they do not achieve what they are supposed to achieve. It is not just that people make mistakes in their reasoning, which we know all too well, but that they are especially likely to make certain sorts of mistakes – in this case copying behaviours that look altruistic.

A final example of this kind is recycling waste. Recycling is certainly a meme – that is, a behaviour that people pick up by copying other people, whether they read about it, see it on television or discover that all their neighbours are doing it. Many people put a great deal of effort into separating different kinds of waste, storing them in their house or garage, taking them to recycling points, and buying recyclable goods. The recycling meme has been an enormously successful one, spreading far and wide in the developed world an driving a massive amount of human activity. Some experts argue that the energy thus used is far more than would be needed if the materials were simply dumped and new ones made. I have no idea whether this is true, but from the memetic point of view it does not matter. We would expect these kinds of behaviour to spread because they are easily picked up by people who already do all kinds of generous, caring ‘green’ activities, who are therefore seen as altruistic and are therefore copied. The whole ‘green-movement,’ and the effort put into it, is just what you would expect of meme-driven altruism in action.

Memeplexes and the altruism trick

Memes which have nothing to do with altruism can benefit from ‘copy-the-altruist’ by just tagging along for free. Like Kev the caveman’s flashy blue-feathered arrows, some memes may just by luck happen to be carried by more altruistic people, but this luck is not a memetic process that can be relied on. Instead, we can expect memes to have devised strategies for getting into altruistic people without actually being altruism memes themselves (or more accurately – memes that happened to have such strategies should have survived better than those without, and we should be able to observe them around us). Are there such examples?

Yes. They range from little groups of co-memes to very complicated memeplexes. Remember that the essence of any memeplex is that the memes inside it can replicate better as part of the group than they can on their own. Some simple ones will show the principle. For the first type we need to assume that people want to be liked. This part of the principle I have been following that people imitate people they like more than people they do not. Imitating people you like should be a good way to become liked yourself and being liked should ensure that people are nicer to you.

Now, let us take some actions a parent might try to persuade a child to do, such as clean, say please and thank you to Auntie Dawn, or stay a virgin until after marriage. Why should children obey the instructions? They might obey out of fear or coercion, but a common trick is to turn the instruction into ‘Good children keep their clothes clean,’ ‘Nice people say people and thank you,’ or ‘Good girls don’t have sex before marriage.’ These simple memeplexes consist of just two parts; the instruction and the idea of being good. ‘People won’t like you if do that’ is another, as are hints that nice people vote conservative, people like us eat dinner at eight, or kind people go to church.

More complicated memeplexes can build up around the kinds of altruism I considered before, such as kindness to animals and recycling, and lots of other memes can jump on board. The recycling symbol is a little scrap of information that has been successfully copied around the world. The names and logos of all the charities are other examples, as are collecting boxes that are rattled in the street, the practises of having charity shops, of distributing special bags to collect goods in, and many other activities that thrive in the world of charitable giving. As memeplexes evolve and become more complicated, new niches are created in which new kinds of meme can thrive. In the examples I have given here, the spread of charitable giving opens up niches for all sorts of other memes to thrive.

You can even sell music and fashion using altruism. Bob Geldof really did give money to the starving in Africa but he sold millions of record at the same time. Princess Diana’s memorial fund really is funding her charities but it is spreading millions of Diana memes in the process – pictures, stories, personal reminiscences, speculations and scandals, videos of her life and times, not to mention the words and tune of Candle in the Wind.

These are simple examples, but they are sufficient to show that meme-driven altruism is an obvious meme-trick read for exploitation. It should not, therefore, surprise us to find that many of the most powerful and widespread memeplexes use it in various forms. Pre-eminent are the religions. One of the mechanisms is simple, once you think about it memetically. a religion which persuades its follows to be more altruistic will spread because of the altruism trick.

I once was cycling in the park in Bristol when my bicycle chain fell off. Before I could jump off to put it back two young men raced up to me, politely offered help, expertly put the chain back on, and stood smiling kindly at me. ‘Thank you very much,’ I said, feeling a little bewildered. For I had never seen them before and I was not a ravishing sight in my Felix-the-cat bike helmet. God was soon on their lips, quickly followed by Joseph Smith and Salt Lake City. The Mormon faith is ably and deliberately spread by the altruism trick. It doesn’t work on everyone, but it works well enough to keep the memes alive.

The altruism trick works like this. Take a political party, a religious sect, a cult, a local benevolent society, or any complex belief system. Incorporate within it the idea that its follower should do good works. These good works will then make the followers more likeable and so people will copy them – copying in the process all the other memesin the belief system. Of course, this mechanism does involve actual ‘good works,’ as did Geldof and Diana. Others only give the appearance of doing good, or just persuade their followers to think they are doing good. Others exploit the sense of obligation induced by giving gifts – the proselyte does you a good turn, now feel obligated to him/her, and the obvious way to repay this obligation is to do what he wants, that is, to take on his memes (or at least give the appearance of doing so). There are many variations on this basic ‘altruism trick.’ I will consider how some of them work, as well as further implications of Allison’s (1992) beneficent norms, when dealing in more detail with religions.

Note that this trick effectively makes people work for the memes they carry. People who join the cults or adopt the ideologies give away their possessions, do good works, or help others, because this helps copy the memes that have infected them. Other people then copy them and they also begin to work for the memes. This is one reason why memeplexes that use this trick have survived in the past and why there are so many of them around now. This is the second time we have met the idea of people working for their memes (the first was in relation to sex and spreading memes rather than genes) and we will meet it again. In this sense we can say that the memes are driving human behaviour.

If this seems frightening then we need to ask ourselves why. What does drive human behaviour? Much of the antagonism towards Darwinism, sociobiology, and indeed any science of human behaviour, stems from an apparent desire to see ourselves as magical autonomous agents in charge of our own destinies. I shall tackle the basis of this view later, but for now just say that yes, memetics does undermine this view. We can describe any behaviour in numerous different ways for different purposes, but underneath them all lies the competition between replicators. Memes provide the driving force behind what we do, and the tools with which we do it. Just as the design of our bodies can be understood only in terms of natural selection, so the design of our minds can be understood only in terms of memetic selection.

Debts, obligations and bartering

Can the theory of memetic altruism be tested? One approach would be to test the basic assumptions on which it rests. the main assumption is that people preferentially copy people they like. I have assumed this because there are substantial hints in the literature that this is so. In his widely cited book on the psychology of persuasion, the American psychologist, Robert Cialdini (1994) reviews the evidence that people are more easily influenced by, and more likely to agree to a request or buy a product from people they like. Tupperware parties work because the host/hostess invited friends who like them and therefore more likely to buy products they do not want. Successful car dealers charm their intended purchasers by complimenting them, appearing to be similar to them, giving away small concessions or appearing to take their part against the boss, all of which increases their client’s liking for the dealers and hence the ease with which the victims can be separated from their money. The major factors that increase liking include physical attractiveness, similarity, cooperativeness, and the belief that the other person likes you. One record-breaking salesman even used to send out thirteen thousand cards a month to his clients saying ‘I like you’ – and presumably he was not wasting his money.

What is not so clear is whether liking leads directly to imitation. This has not been much studied by social psychologists, perhaps, because the importance of imitation per se has not been emphasised. If it does, the other consequences should follow; that people buy more products from, are persuaded to change their minds by, and often agree with people they like. In other words, the social psychological findings described above may be a consequence of a deeper underlying tendency to want to copy people we like. The experiments that need to be done, therefore, should look more closely at the imitation of actions carried out by likeable and unlikeable people. For example, we might ask people to watch ‘liked’ and ‘disliked’ models of carrying out a task in different ways, and then do the task themselves. Experiments could then go on to find out just how best to manipulate liking so as to produce the most effective imitation. If the same manipulations affect simple imitation of actions as well as persuasion and agreement with beliefs, this would be suggestive that a similar process is going on in both. I have also assumed altruistic behaviour makes people more likeable. This may seem too obvious to need testing, but we could use similar experiments to test the main consequence of this – that is, that acting altruistically will induce people to imitate you. If these predictions were not born out of the entire basis of this kind of meme-drive altruism would be undermined.

The outcome of such experiments might be complicated by the effects of the ‘reciprocal rule.’ It is well known in social psychology that people obliged to repay any kindness shown to them, and feel obligated if they do not (Cialdini 1995). This tendency is culturally widespread and probably related to the fact that aid from rich to poor countries is not always well received (Moghaddam et al. 1993). Presumably, reciprocity stems from our evolved use of reciprocal altruism. Now, if an observer in one of our experiments has a kindness done to them they may feel obligated to the model – an unpleasant feeling which might disincline them to like the model and so complicate the issue. The most interesting outcome from the memetic point of view would be if imitating the altruist (i.e. taking on their memes) acted as a kind of reciprocation. By this I mean that one person could ‘pay back’ a kindness by taking on the other person’s ideas.

This effect can be seen to follow from a combination of the ‘reciprocation rule’ which derives from reciprocal altruism, and Allison’s beneficent norm ‘Be good to those who imitate you.’ According to this rule, if A imitates B, B should now feel obliged to A. So, for example, not only does the professor want to be nice to her students but all of us should be kinder to people who agree with us, or take on our ideas, or imitate us in other ways. If the process works both ways then if C gives D a gift, D will feel obliged to C and may pay back the obligation by agreeing with C (or taking on her memes in some other way). In ordinary life we may be seeing this in the tendency of guests to agree with their host’s ideas, or of people in subordinate positions to agree with those who have power over them, or in the tricks used by religions that I discussed above. Finally, this could lead to people trading off their obligations by bartering goods against imitation in all possible combinations. So, for example, the guest who brings a fine present should feel under less obligation to agree with the host than the one who does not.

If the idea of exchanging goods for taking on memes seems unfamiliar, we might think of the bartering of memes that goes on all around us. We are used to the idea of paying for the information we want, by buying books or newspapers, paying our TV licence, or buying tickets to the cinema, but if people want to impose their ideas on us then they should have to pay to get our attention, like advertisers and politicians do. I shall return to this in considering the way information is put onto the Internet at the cost of the provider, not the user.

All these exchanges could be investigated. Imagine an experiment in which James expresses some unpopular idea, or solicits people to join his organisation, or whatever. Among a group of people present, Greg gets up and publicly agrees with James. Now James should feel obliged to Greg and so be more likely to act generously towards him than to the others. Such experiments could find out whether exchanging memes could become a kind of currency like exchanging goods.

Other experiments might bring together people of opposed view points, or people who disagree about the right way to do something, and find out what methods they actually use to change one another’s minds. Studies of attitude change have often been done where material gain is at stake, such as in advertising and political persuasion, but this theory predicts that people will, if given the chance, be more generous to people who already agree with you, nor to those whom you judge as being beyond conversion. The greatest altruism should be shown to those who are capable of being convinced (Rose 1997).

The effects of reciprocation are a little more complex, however. Imagine the following experiment. Just two people are involved (though in practice we would need to repeat it with many pairs). Janet is asked to express her opinion on some controversial topic while Meg listens in silence. Janet now acts generously in some way towards Meg (perhaps by buying her a coffee or offering to help with something). Meg is then asked to say how much she like Janet. We should obviously expect that Meg will express greater liking for Janet when she has been generous towards her than when she was not. Now we give Meg the chance to say what she thinks about the controversial topic and again measure her liking for Janet. The theory makes two predictions. The first is more obvious, that Meg is more likely to express agreement when Janet has given her something. The second is less so, that expressing agreement acts as a kind of repayment of the kindness. so we should predict that if Meg now publicly agrees with Janet (whether that is really her opinion or not) she will now like Janet more than if she does not. In other words, Meg likes Janet not only because she was kind to Meg, but because Meg has paid off her debt by agreeing and so need no longer feel under any obligation to Janet.

This is an extremely artificial situation but I have tried to keep it simple. More realistic ways of taking on someone’s memes might be to copy their actions in some more concrete way, to agree to pass on information to someone else, to write down what they say, to join a group they belong to, and so on, but I hope the principle is clear – that liking for a generous model would be increased if the subject were given the chance to imitate her, because the sense of obligation was reduced. This is, I suggest, a counter-intuitive outcome that could not readily be predicted or explained on any other theory.

If these predictions are correct they suggest that memes and resources can be bartered against each other in all sorts of ways. We should be able to pay people to accept or ideas, agree with people to pay of debts, and force people into agreement by what appears to be generous actions. There are interesting implications here for the power of money to coerce people into agreement. Some of the predictions are fundamental to the processes underlying meme-driven altruism and therefore, if they do not work out, my theory is wrong.

by Susan Blackmore

Also… I’d like to present Blackmore’s take on religions as memeplexes, as I feel – combined with an understanding that religions originate in the ways that either Elizabeth Culotta describes in “On The Origin Of Religion” and/or Matthew Taylor discusses in “God On My Mind” – it uses memetics as a truly revolutionary tool for understanding why we are so prone to producing delusions of reality and then forget not to take them with “a pinch of salt,” showing us why and how these beliefs are prone natural selection for their altruistic properties, which ensure a better survival mechanism of our species.

Religions As Memeplexes

Like it or not, we are surrounded by religions. The ‘Great Faiths’ of the world have lasted thousands of years and affect our calendars and holidays, our education and upbringing, our beliefs and our morality. All over the world people spend vast amounts of time and money worshipping their gods and building glorious monuments in which to do it. We cannot get away from religions, but using memetics we can understand how and why they have such power.

All the great religions of the world began as small-scale cults, usually with a charismatic leader, and over the years a few of them spread to take in billions of people all across the planet. Imagine just how many small cults there must have been in the history of the world. The question is why did these few survive to become great faiths, while the vast majority simply died out with the death of their leader or the dispersal of their few adherents?

Dawkins was the first to give memetic answers (Dawkins 1986, 1993, 1996b), although his ideas on religion have frequently been criticised (Bowker 1995; Gatherer 1998). He took Roman Catholicism as an example. The memes of Catholicism include the idea of an omnipotent and omniscient God, the belief that Jesus Christ was the son of God, born of the virgin Mary, risen from the dead after his crucifixion and now (and for ever) able to hear our prayers. In addition, Catholics believe that their priests can absolve them from their sins after confession, the Pope literally speaks the word of God, and when priests administer the mass, the bread and wine literally change into the flesh and blood of Christ.

To anyone uninfected with any Christian memes these ideas must seem bizarre in the extreme. How can an invisible God be both omnipotent and omniscient? Why should we believe a two-thousand-year-old story that a virgin gave birth? What could it possibly mean to say that the wine ‘literally’ becomes the blood of Christ? How could someone have died for our sins when we were not even born? How could he rise from the dead, and where is he now? How could a prayer, said silently to yourself, really work?

There are many claims for the efficacy of prayer in healing the sick, and even little experimental evidence (Benor 1994; Dossey 1993), but few of the experiments have controlled adequately for placebo effects, expectation, and spontaneous recovery, and some have shown that people with the strongest religious faith were less likely to recover from acute illness (Kind et al. 1994). Against the claims are hundreds of years of people praying for the health of their royal families or heads of state with no apparent effect, and the inability of modern-day religious healers to make any obvious difference in hospitals. Then there are all those countless wars in which both sides routinely pray for God to help their side and kill the enemy. Yet millions of people all over the world profess themselves Catholics and pray to Jesus, his mother Mary, and God the Father. They spend vast amounts of their valuable time and money supporting and spreading the faith to others, and the Catholic Church is among the richest institutions in the world. Dawkins (1993) explains how religious memes, even if they are not true, can be successful.

The Catholic God is watching at all times and will punish people who disobey His commandments with most terrible punishments. – burning forever in hell, for example. These threats cannot easily be tested because God and hell are invisible, and the fear is inculcated from early childhood. A friend of mine showed me a book he once treasured as a child. It had pictures of a little good boy and a little bad boy. You could open up the flaps of their blazers and inside the good boy find a white and shinning heart, while the bad boy had a black spot for every sin he had committed. Imagine the the power of that image when you cannot see inside your own body and must only imagine the little black spots piling up and piling up – when you talk in class or cheat in a test, when you take your sister’s toy or steal a chocolate biscuit, when you think a bad thought, or doubt God’s truth and goodness… every one a black spot.

Having raised the fear, Catholicism reduces it again. If you turn to Christ you will be forgiven. If you honestly repent of your sins, bring up your children as Catholics, and go regularly to mass, then, even though you are unworthy and sinful, God will forgive you. God’s love is always available but at a price, and that price is often overlooked completely because it is paid so willingly. It is the price of investing massive amounts of time, energy and money in your religion – in other words, working for their memes. As Dawkins pointed out, Catholics work hard to spread their Catholicism.

I previously described several meme tricks that New Age memeplexes use. All these can be found in religions too. First, like alien abduction and near-death experience memes, religions serve a real function. They supply answers to all sorts of age-old human questions such as: Where do we come from? Why are we here? Where do we go when we die? Why is the world full of suffering? The religious answers may be false but at least they are answers. Religious commitment may give people a sense of belonging, and has been shown to improve social integration in the elderly (Johnson 1995). Religions may also incorporate useful rules for living, such as the dietary laws of Judaism or rules about cleanliness and hygiene which may once have protected people from disease. These useful functions help carry other memes along.

The truth trick is liberally used. In many religions, God and Truth are virtually synonymous. Rejecting faith means turning away from Truth; converting others mean giving them the gift of the true faith. This may seem odd when so many religious claims are clearly false, but there are many reasons why it works. For example, people who have a profound experience in a religious context are inclined to take on the memes of that religion; people who like or admire someone may believe their truth claims without question. At the extreme, people will even tell lies for God and manage to convince themselves and others that they do so in the name of truth – as when when ‘Creation Scientists’ proclaim ‘The Truth’ that the early earth is only six thousand years old, and back it up with denials of the fossil record, or claims that the speed of light has slowed since the creation so as to give the illusion of a vast universe and an ancient planet (Plimer 1994).

I’d like to add a foot note here regarding an aspect of Buddhism. Within Buddhist doctrine there is the comprehension of rebirth i.e. reincarnation of ourselves OR our ‘souls’/’selves’ into new future lives. Having read several books and watched several films concerning the this phenomena of reincarnation, my instinct is still dubious about whether this aspect of Buddhist belief is really an actual fact… Or whether it is really a convenient ‘myth,’ designed with the ultimate intention of spreading as much good will and compassion between as many human beings as possible, as soon as possible, while we are here on Earth. I mean… If I became an enlightened being, with great compassion and love guiding my every action toward all fellow sentient beings, then I would ultimately realise that not all human beings would be ready to give up their existence in Saṃsāra. I would also clearly see that not all beings would be willing to develop and become compassionate to their fellow men and women, let alone other sentient beings… The main reason being is that the “delusion of consciousness” would be way too deeply ingrained in our very essence for the majority to give up in an instant. And, while I would be aware that ‘change’ will take time, especially in a world where people try to instil consistency and homogeneity into their lives, blanking any distressing chances that may occur… My ultimate goal – to prevent/minimise the suffering of all living beings here in Saṃsāra – should be achieved as quickly as possible to minimise the amount of suffering endure in this moment. Thus, due to the inertia of delusion within the fabric of society, along with all of our self-centred tendencies created at the dawn of time – and Life – here on Earth, as the ultimate survival mechanism powered by the process of natural selection… I would need some serious leverage to get people to believe and understand that selflessness, sacrifice, material asceticism, along with unbiased generosity and diverse altruistic behaviour towards all sentient beings, were the only way to minimise OR prevent the totality of all suffering. And, as I would be well aware of how easily the unenlightened mind might grasp to false understandings and delusions about its present reality, I would be very well inclined to develop a meme that would get all of humanity to contemplate their own social impact upon all others within this and future times. In preparing this meme, I would certainly devise a strategy that would exploit every aspect of our human traits of selfishness and self-centred tendencies, thus provoking people to consider their future lives and their future suffering in terms of how well they perform here, in the present. Because of the inertia of these tendencies, the majority of human beings who listened to this meme would primarily act out of selfish, evolutionary driven concern their own happiness. However, somewhere along the way they might well develop a genuine compassionate stance towards all Life here on Earth, and thus awake from self-centred tendencies and delusions to see the interconnectedness of all reality and being.

Beauty inspires the faithful and brings them closer to God. Some of the most beautiful buildings in the world have been constructed in the name of Buddha, Jesus Christ, or Mohammed. Then there are the beautiful statues and alluring stories in Hinduism; stained glass, inspiring paintings, and illustrated manuscripts; uplifting music sung by tremulous choir boys and vast choirs, or played on great organs. Deep emotions are inspired to the point of religious ecstasy or rapture which then cries out for – and receives – an explanation. The ecstasy is real enough, but from the memes’ point of view, beauty is another trick to help the reproduce.

The altruism trick permeates religious teachings. Many believers are truly good people. In the name of their faith they help their neighbours, give money to the poor, and try to live honest and moral lives. If they are successful then generally people come to lie and admire them and so are more inclined to imitate them. In this way not only does good and honest behaviour spread, but the religious memes that were linked to that behaviour spread too. Alongside this comes merely the semblance of good behaviour. Hypocrisy can flourish when goodness is defined not only as kind and altruistic behaviour, but as sticking to the rules and obligations of the faith. Much of the money donated to churches, temples, or synagogues is not used for the poor or needy, but to perpetuate the religion’s memes by erecting beautiful buildings or paying for clergy. Activities that spread memes are also defined as ‘good’ even though their benefit is questionable, such as saying prayers at specified times, saying grace at every meal, and keeping one day of the week as a day of worship. In this way huge chunks of every believer’s time are willingly devoted to maintaining and spreading the faith.

Many people think of Mother Teresa as a saint. Indeed, she may soon be officially canonised by the Catholic Church. She is many people’s idea of the truly selfless and altruistic heroine. But what did she actually do? Some of the inhabitants of Calcutta accuse her of diverting attention from the real needs of the city’s poor, giving Calcutta a bad name and of helping only those who were prepared to take on Catholic teachings. Certainly, she was fiercely anti-abortion and anti-birth control. Many of the people she helped were young women with no access to contraceptives, little ability to avoid being raped, and almost no access to health care if they became pregnant. Yet she steadfastly maintained her Catholic opposition to the one thing that would have helped them most of all – control over their reproductive lives. Whatever we may think about how much she really helped the starving people of Calcutta there is no doubt that her behaviour effectively spread Catholic memes by using the altruism tick.

Even evil and cruelty can be redefined as good. The Koran states that it is good to give hundreds of lashes to an adulteress and to have no pity on her. You might well think that Muslim women can avoid this by not committing adultery, but Warraq (1995) explains in unpleasant detail what life can be like in countries that adhere strictly to Islamic law. Women may be powerless to resist sexual abuse, and afterwards must take the punishment while the men who abused them them get off free. Since women are objects of disgust, a man is supposed to not to touch a women he does not have rights over. Women are routinely locked away and, if they are allowed out, must walk behind the man and suitably covered – which in many countries means being covered head to toes in a smothering garment with just a tiny little grille to look out of. Obeying such rules to the letter makes a Muslim ‘good,’ regardless of the misery it creates.

Returning to more honest uses of goodness and altruism, Allison’s (1992) theory of ‘beneficent norms’ applies especially well to religions One of his general rules is ‘Be good to your close cultural relatives’; the memetic equivalent of kin selection. But how do you know who they are? This rule tracks biological kinship in cultures with predominantly vertical transmission, since in these cultures you acquire most of your memes from biological relatives, but with horizontal transmission other means of recognition are needed. One is ‘Be good to those who act like you.’ It works like this. If you see someone else who acts the same way as you do, it is likely that you both have cultural ancestors in common. If you now help him you make it more likely that he will be successful, and hence that he will pass on his memes, including the rule ‘Be good to those who act like you.’ Allison calls this a ‘marker scheme.’ He gives the examples of wearing a turban or abstaining from certain foods, but we might add supporting Manchester United or listening to hip-hop, as well as genuflecting or wearing a little portrait of your guru round your neck. He adds that markers that are costly or difficult to learn can deter exploitation by outsiders. Apart from languages, a good example is religious rituals. Many of these require years to learn and others, such as ritual circumcision, are certainly costly for an adult.

The result of this kind of altruism is that people are kind and generous to the in-group and not to outsiders. This boosts the well-being of the group’s members and hence makes them more likely to be imitated, and so pass on the faith. This is exactly what we see in many of the world’s greatest religions. Although the instruction to ‘love thy neighbour as thyself’ is commonly taken to mean ‘love everyone,’ in a tribal context in which it was first written it may have been meant more literally – in other words love your own tribe, and your own family, but not everybody else (Hartung 1995). Even the admonition not to kill may originally have applied only to the in-group. Hartung points out that the rabbis of the Talmud used to hold an Israelite guilty of murder if he intentionally killed another Israelite, but killing other people did not count.

Some religions positively encourage murder and war against people of other faiths. Islam has fatwas and jihads to justify killing unbelievers, and especially those who harm or renounce the faith. In February 1989, the Ayatollah Khomeini delivered his famous fatwa on the author Salman Rushdie. This is a direct call to all Muslims to murder Rushdie for daring to blaspheme against the holy Koran in his book Satanic Verses. When the punishment for renouncing or criticising a religion is so severe, the memes are very ably protected.

Hindus, Muslims, and Christians alike have gone to war again and again in the name of God. When a few hundred Spaniards murdered thousands of Incas, leading to the destruction of an entire civilisation, they did it for the glory of God and the holy Catholic Faith. In a subtler way religious missionaries are still destroying ancient cultures even today. People have been tortured, burned alive, and shot because they believed the wrong thing. Religions teach that God wants you to spread his True understanding to all the world and it is therefore good maim, rape, pillage, steal and murder.

We see how the conspiracy theory protects UFO memes; similar mechanisms protect religious memes. As Dawkins (1993) points out, good Catholics have faith; they do not need proof. Indeed, it is a measure of how spiritual and religious you are that you have faith enough to believe in completely impossible things without asking questions, such as that the wine is really turned into blood. This assertion cannot be tested because the liquid in the cup still tastes, looks and smells like wine – you must just have faith that it is really Christ’s blood. If you are tempted by doubt, you must resist. Not only is God invisible but he ‘moves in mysterious ways.’ The mystery is part of the whole package and to be admired in its own right. This untestability protects the memes from rejection.

Religious memes are stored, and thus given improved longevity, in the great religious texts. The theologian Hugh Pyper (1998) describes the Bible as one of the most successful texts ever produced. ‘If “survival of the fittest” has any validity as a slogan, then the bible seems a fair candidate for the accolade of the fittest of texts.’ (p.70) It has been translated into over two thousand languages, exists in many different versions within some of those languages, and even in a country like Japan, where only one or two per cent of the population are Christians, more than a quarter of all households possess a copy. Pyper argues that Western culture is the Bible’s way of making more Bibles. And why is it so successful? Because it alters its environment in a way that increases the chances of its being copied. It does this, for example, by including within itself many instructions to pass it on, and by describing itself as indispensable to the people who read it. It is extremely adaptable, and since much of its content is self-contradictory it can be used to justify more or less any action or moral stance.

When we look at religions from a meme’s eye view we can understand why they have been so successful. These religious memes did not set out with an intention to succeed. They were just behaviours, ideas and stories that were copied from one person to another in a long history of human attempts to understand the world. They were successful because they happened to come together into mutually supportive gangs that included all the right tricks to keep them safely stored in millions of brains, books and buildings, and repeatedly passed on to more. They evoked strong emotions and strange experiences (see William Sargant’s “Battle For The Mind”). They provided myths to answer real questions and the myths were protected by untestability, threats, and promises. They created and then reduced fear to create compliance, and they used the beauty, truth and altruism tricks to help their spread. That is why they are still with us, and why millions of people’s behaviour is routinely controlled by ideas that are either false or completely untestable.

. . . . . . . .

No one designed these great faiths with all their clever tricks. Rather, they evolved gradually by memetic selection. But nowadays people deliberately use memetic tricks to spread religions and make money. Their techniques of memetic engineering are derived from long experience and research, and are similar to those used in propaganda and marketing; with radio, television and the Internet, their memes can spread far further and faster than ever before.

by Susan Blackmore

Here I am going to make a bit of an assumption. One that, for me, has proven to be – on the whole – a fact. When it comes to ultimate truths and emotional happiness, these two aspects of choice in modern day human life are very interchangeable with one another. Over the last few years I have noticed that people tend to prefer, and thus, gravitate towards, agreeable circumstances in which they can flourish socially and personally, rather than seek out ultimate and/or painful truths/realisations/understandings. No doubt, believing is certainly easier than thinking. Especially when some incentives are thrown in to prevent thinking, as Blackmore discusses above in “Religions As Memeplexes” i.e. death, social outcasting, etc… We all crave some form of social contact, and to be outcast from a social tribe that we belong to can be almost as destructive as death. As Adolf Hitler once said, “What luck for rulers, that men do not think.” And from this warped basis of being the second World War came about. Either way, many choose agreeable circumstances in which to flourish, over disagreeable circumstances. As Barbara L. Fredrickson and Marcial F. Losada discuss in their paper entitled “Positive Affect and the Complex Dynamics of Human Flourishing,” positive affect plays a major role in people’s lives, bringing contentment, good health – and thus longevity and greater chances to spread their genes – as well as increased creativity and output… All of which I think we can call ‘good’ things for natural selection.

What predicts whether people will flourish or languish? Are the predictors similar for individuals, relation- ships, and larger groups? Drawing together existing theory and research on affect and nonlinear dynamic systems, we propose that a key predictor of flourishing is the ratio of positive to negative affect.

Over time, and in both private and social contexts, people experience a range of pleasant and unpleasant emo- tions and moods, and they express a variety of positive and negative evaluative sentiments or attitudes. We use affect to represent this spectrum of valenced feeling states and attitudes, with positive affect and positivity interchangeably representing the pleasant end (e.g., feeling grateful, upbeat; expressing appreciation, liking) and negative affect and negativity representing the unpleasant end (e.g., feeling contemptuous, irritable; expressing disdain, disliking). The affective texture of a person’s life—or of a given relation- ship or group—can be represented by its positivity ratio, the ratio of pleasant feelings and sentiments to unpleasant ones over time. Past research has shown that for individu- als, this ratio predicts subjective well-being (Diener, 2000; Kahneman, 1999). Pushing further, we hypothesize that— for individuals, relationships, and teams—positivity ratios that meet or exceed a certain threshold characterize human flourishing. Although both negative and positive affect can produce adaptive and maladaptive outcomes, a review of the benefits of positive affect provides a particularly useful backdrop for our theorizing.

. . . . . . . .

Benefits of Positive Affect: Empirical Evidence

A wide spectrum of empirical evidence documents the adaptive value of positive affect (for a review, see Lyubomirsky, King, & Diener, in press). Beyond their pleasant subjective feel, positive emotions, positive moods, and positive sentiments carry multiple, interrelated benefits. First, these good feelings alter people’s mindsets: Experiments have shown that induced positive affect widens the scope of attention (Fredrickson & Branigan, 2005; Rowe, Hirsch, & Anderson, 2005), broadens behavioral repertoires (Fredrickson & Branigan, 2005), and increases intuition (Bolte, Goschkey, & Kuhl, 2003) and creativity (Isen, Daubman, & Nowicki, 1987). Second, good feelings alter people’s bodily systems: Experiments have shown that induced positive affect speeds recovery from the cardiovascular aftereffects of negative affect (Fredrickson, Mancuso, Branigan, & Tugade, 2000), alters frontal brain asymmetry (Davidson et al., 2003), and increases immune function (Davidson et al., 2003). Third, good feelings predict salubrious mental and physical health outcomes: Prospective studies have shown that frequent positive affect predicts (a) resilience to adversity (Fredrickson, Tugade, Waugh, & Larkin, 2003), (b) increased happiness (Fredrickson & Joiner, 2002), (c) psychological growth (Fredrickson et al., 2003), (d) lower levels of cortisol (Steptoe, Wardle, & Marmot, 2005), (e) reduced inflammatory responses to stress (Steptoe et al., 2005), (f) reductions in subsequent-day physical pain (Gil et al., 2004), (g) resistance to rhinoviruses (Cohen, Doyle, Turner, Alper, & Skoner, 2003), and (h) reductions in stroke (Ostir, Markides, Peek, & Goodwin, 2001). And fourth, perhaps reflecting these effects in combination, good feelings predict how long people live: Several well-controlled longitudinal studies document a clear link between frequent positive affect and longevity (Danner, Snowdon, & Friesen, 2001; Levy, Slade, Kunkel, & Kasl, 2002; Moskowitz, 2003; Ostir, Markides, Black, & Goodwin, 2000).

. . . . . . . .

The varied good outcomes empirically linked with positive affect support the broaden-and-build theory, which asserts that positive emotions are evolved psychological adaptations that increased human ancestors’ odds of survival and reproduction (Fredrickson, 1998). The theory holds that unlike negative emotions, which narrow people’s behavioral urges toward specific actions that were life-preserving for human ancestors (e.g., fight, flight), positive emotions widen the array of thoughts and actions called forth (e.g., play, explore), facilitating generativity and behavioral flexibility. Laboratory experiments support these claims, showing that relative to neutral states, induced negative emotions narrow people’s momentary thought–action repertoires, whereas induced positive emotions broaden these same repertoires (Fredrickson & Branigan, 2005).

The theory holds that in contrast with the benefits of negative emotions—which are direct and immediately adaptive in life-threatening situations—the benefits of broadened thought–action repertoires emerge over time. Specifically, broadened mindsets carry indirect and longterm adaptive value because broadening builds enduring personal resources, like social connections, coping strate- gies, and environmental knowledge. As an illustration, consider the link between interest and exploration. Re- search shows that initially positive attitudes—like interest and curiosity—produce more accurate subsequent knowl- edge than do initially negative attitudes—like boredom and cynicism. Positivity, by prompting approach and exploration, creates experiential learning opportunities that con- firm or correct initial expectations. By contrast, because negativity promotes avoidance, opportunities to correct false impressions are passed by (Fazio, Eiser, & Shook, 2004). These findings suggest that positive affect—by broadening exploratory behavior in the moment—over time builds more accurate cognitive maps of what is good and bad in the environment. This greater knowledge be- comes a lasting personal resource.

Although positive affect is transient, the personal re- sources accrued across moments of positivity are durable. As these resources accumulate, they function as reserves that can be drawn on to manage future threats and increase odds of survival. So experiences of positive affect, al- though fleeting, can spark dynamic processes with down- stream repercussions for growth and resilience.

Whereas traditional perspectives hold that positive affect marks or signals current health and well-being (Die- ner, 2000; Kahneman, 1999), the broaden-and-build theory goes further to suggest that positive affect also produces future health and well-being (Fredrickson, 2001). Put dif- ferently, because the broaden-and-build effects of positive affect accumulate and compound over time, positivity can transform individuals for the better, making them healthier, more socially integrated, knowledgeable, effective, and resilient. Supporting this view, prospective studies by Fredrickson and colleagues have shown that positive affect at initial assessment predicts increases in well-being sev- eral weeks later, in part by broadening people’s mindsets (Fredrickson & Joiner, 2002) and building their psycholog- ical resources (Fredrickson, Brown, Cohn, Conway, & Mikels, 2005). This evidence motivates our prediction that positive affect is a critical ingredient within flourishing mental health.

by Barbara L. Fredrickson & Marcial F. Losada

I doubt we really have to go into why “negative emotions tend to bring about a malaise in health”. Any one who has suffered from depression will know how negative states of mind can radically alter one’s life in its unfolding. Bearing in mind the crippling nature of negative emotions, on the whole, natural selection will tend to favour those of us who are experiencing more positive emotional states. Certainly we can all notice within ourselves that we will tend to gravitate towards favourable conditions which fit with our schemas and memetic dispositions… We seek out good will and fun times… Nearly all of us love a laugh and joke every now and then… And the majority of us prefer them more often than not.

Somewhere in this understanding, it is my belief that religions provided – and probably still does provide – a sort of “broaden-and-build” aspect for positive emotions that broaden’s one’s awareness and encourage novel, varied, and exploratory thoughts or actions. While religions on the whole are a tough meme to deviate from nowadays, they no doubt provided our earlier ancestors – who were more prone to barbaric idiosyncrasies, which could easily cause negative repercussions within any social dynamic i.e. war, death, loss, starvation, etc… – with a means of social bonding with other men and women by way of similar belief systems, regardless of personality type, tribal stature, and/or ethnic origin. Thus, in my humble opinion, religion probably propagated one of the first type of truly universal social dynamics between multicultural races and creeds, thereby opening up cultural barriers and clearing obstacles of language and social fear.

While we know some zealots use religion to prevent this dissolution of cultural barriers – whatever their reasons are i.e. memetic pride, ego-centric righteousness, etc… – we shouldn’t think of religions as negative. These obsessives hijack the essence of the constructive memeplex and destroy any modicum of goodwill left in their sanctuary. We should be aware that religions were probably the evolutionary mechanism that brought about our present global society to the state of functionality that it presently resides in. Thus it was an important factor within our history’s social fabric. Everywhere we look, religion was the reason why trade and social harmony blossomed… And why wars devastated nations. Within social circles of religious pragmatism, human beings were able to flourish and transcend petty disputes and fears. Who cares that they were not based on real veritable and empirical facts… They, on the whole, provided a basis for good health and positive affect within everyone’s social dynamic. This in turn provided our ancestors – and us indirectly – with a basis for better adaptive evolutionary forms and modes of being and behaving towards one another.

Despite the advantages that religious follower were endowed with… We might well have forgotten in our hearts how deeply interconnected to mother Earth we all are. No doubt capitalism and religious decree in this “Battle For The Mind” has loosened our understanding of how we link to the Tao… To chaos itself. But we will be reminded of them when we fall from grace by taking any capitalist or religious motive too literally and/or seriously. If we do not awake from this literal delusion of self-supporting corporate enterprise that can apparently exist and create solutions that go beyond mother nature’s natural ways to provide us with all we need independently within Earth’s limited biosphere, wars might well destroy many of us, or changes in the Earth’s delicate balance will ensure that climatic repercussions will dwarf anything seen before, as well as occurring more quickly than anything that our ancestors might have known, breaking the habits of our developed nations. We will need to understand these aspects that lie behind religious and group memetics before any catastrophic events occur… Mainly because our survival will depend upon them once again.

Certainly Blackmore’s ideas regarding the ‘Altruism Trick’ are most interesting and somewhat familiar, and I have, without a doubt, noticed many similar pressures for memetic agreements within social exchanges, most of which have been posited from altruistic donations between people within my ‘circle’ of friends. All of these memetic agreements seem to yield to a similar dynamical flow that allows us all to interact and relate to one another across varying levels of social collaboration. Only one person that I know seems to hold back from any such yielding to others… While I find this trait endearing on many levels within her character, I have noticed that her seemingly unshakable preserve toward her own memetic ideals/schemata sometimes becomes inverted, mainly when she deliberately chooses to agree to disagree with everyone else, especially when placed under any pressure to conform, even if it is to conform to her already professed memetic make-up!? Saying that, I am very aware of the reasons behind her remaining independent of the ‘pack,’ and cannot fault her for doing so.

If one remains mindful to one’s own mental processing while undergoing social exchanges between their friends, family, colleagues and even complete strangers – noting in particular the reasons as to why we might sometimes agree with presented ideals that might otherwise countermand one’s own basic principles and intuition, I feel Blackmore’s theory on altruism – presented above – will satisfy some of the criteria for these ‘slips-of-mind’ rather succinctly.

But regardless of whether Blackmore’s theory is really correct or not, there lies an even deeper process that allows us to understanding how we make these decisions… As we all know, we are “attracted” to acts of kindness shown towards ourselves and others, and might even be disposed to allow our own views to temporarily disseminate while we repay of a debt of kindness acceding to a donor’s meme (see William Sargant’s “Battle For The Mind”).

A Nonlinear Dynamic Systems Perspective

We favor a nonlinear dynamic systems approach to positive affect for several reasons. First, theory and research on affective phenomena have already established that emotions are multicomponent systems that simultaneously alter patterns of thinking, behavior, subjective experience, verbal and nonverbal communication, and physiological activity. Second, such multicomponent affect systems are dynamic: They change over time as the various components within the affect system mutually influence one another. For instance, just as positive thinking and positive actions can trigger pleasant feeling states, so too can pleasant feeling states trigger positive thinking and positive actions (Fredrickson & Joiner, 2002).

by Barbara L. Fredrickson & Marcial F. Losada

This process of choosing to perform an altruistic act – this behaviour of selecting – utilises the disorder of ordering chaos. Thus I feel that Barbara L. Fredrickson and Marcial F. Losada’s suggestion that a nonlinear dynamical systems perspective best fits a psychological model for understanding the complex dynamics of human flourishing is right on the money. Surely it is obvious that the behavioural net of our brain/mind continuum has a naturally selective and highly dynamic method for choosing and selecting appropriate methods for optimal habitual survival mechanisms. And this chaotic mental continuum of ours is one which has been naturally selected for as the best collective survival mechanism that posits a ‘healthy’ type social flourishing for our species within any given environment here on Earth. No doubt I have already written about observations that suggest that this chaotic mechanism of neuronal behaviour exists – see “Self-Similarity ~ Fractals, fractals everywhere…” But having been given the chance to read this amazing paper (thanks to a ‘happyseaurchin’), entitled “Positive Affect And The Complex Dynamics Of Human Flourishing,” which discussed the notions and processes surrounding how we choose “up-beat” behaviour over “down-cast, just plodding through life” behaviour made deep intuitive sense in a way that I hadn’t felt before. Seems that the same basins of attraction found within Earth’s weather systems also present their familiar ‘lemniscate’ shapes within our patterns of selective mind.

So I ask… Is there a tendency for chaos to be built into naturally successful dynamical systems? If so… Why would this be the case? Could it be because this nonlinear complexity yields truly amazing adaptive qualities within the systems that utilise its open-ended modus operandi, and thus, because of its robust and varied behavioural patterning, overcomes nearly all obstacles/threats to its survival and so becomes naturally selected for? Thus… Could we reason that altruistic behaviour spawned from the sea of chaos inherent within our own being… Allowing us to develop in a multi-cultural and – on the whole – peaceful society??? After all, a ratio of 2.9 from ‘positive affect’ over ‘negative affect’ is apparently the key to human flourishing.

I ask these questions because – while on an intuitive level I am certain these notions will point us in the right direction to understanding the essence of our Being – I do not want to be presumptuous about whether they are in actual fact correct. That I will leave up to the scientists who might happen upon this this page and feel inspired enough to test this hypothesis.

## Self-Replicating Chemicals Evolve Into Lifelike Ecosystem

### May 6, 2010

I have already written several blogs about Life… You know, the scientific aspects of Life… Trying to understand it all a bit better… Asking really ‘silly’ questions about things like “When Does Life Really Become Life?” Or “What Is Life?” All the way through to “Just How Did Life Seed Here On Earth?” Thrown in with clangers like “Might We Be Able To Create Life In The Laboratory To Recreate Those Initial Conditions That Gave Rise To Life As We Know It Here On Earth?” And, would you believe, I even thought I could attempt to discuss “What This Experience Of Being Alive Really Is And How It Came About!” Wow… What delusions of grandure, eh? Lock me up and throw away the key…

Anyway… Would you believe, after all that, I’m back at this door again??? Trying to understand whether it’s as obvious as it seems… As obvious as it feels, even… That Life naturally happens, whether you want to believe it or not, independently and regardless of any divine creator or omnipotent god that we care to imagine. This time someone else has opened the doorway to another side – and another aspect – of this reality that we think we understand so well… They’ve prised it open just that little bit further than before… Just ever-so-slightly more… And with that, what we can now see shinning back through that widening crack, would you believe… Is that it seems self-replicating chemicals can evolve into lifelike ecosystems!?!? Similar to those found here on Earth!?!?

So… Along with the fractal geometry that lies hidden within the heart of our cellular make upAnd what with all the other properties of the universal star stuff of atoms… Which are like Lego building blocks… Isn’t that almost enough to allow us to begin to see past the delusions of the yester-year? Can’t we just accept that life is a natural aspect of universal unfolding? That we all come from natural cosmic phenomena? And one day we will all go back there…

Well… I certainly can’t tell you what to think. So I’ll just have to let you decide for yourselves on that one…

But first, before you make up your mind, just have a “butchers-hook” at this…

Self-Replicating Chemicals Evolve Into Lifelike Ecosystem

Life makes more of itself.

And now so can a set of custom-designed chemicals. Chemists have shown that a group of synthetic enzymes replicated, competed and evolved much like a natural ecosystem, but without life or cells.

“So long as you provide the building blocks and the starter seed, it goes forever,” said Gerald Joyce, a chemist at the Scripps Research Institute and co-author of the paper published Thursday in Science. “It is immortalized molecular information.”

Joyce’s chemicals are technically hacked RNA enzymes, much like the ones we have in our bodies, but they don’t behave anything like those in living creatures. But, these synthetic RNA replicators do provide a model for evolution — and shed light on one step in the development of early living systems from on a lifeless globe.

Scientists believe that early life on Earth was much more primitive than what we see around us today. It probably didn’t use DNA like our cells do. This theory of the origin of life is called the RNA World hypothesis, and it posits that life began using RNA both to store information, like DNA does now, and as a catalyst allowing the molecules to reproduce. To try to understand what this life might have looked like, researchers are trying to build models for early life forms and in the process, they are discovering entirely new lifelike behavior that nonetheless isn’t life, at least as we know it.

As Joyce put it, “This is more of a Life 2.0 thing.”

The researchers began with pairs of enzymes they’ve been tweaking and designing for the past eight years. Each member of the pairs can only reproduce with the help of the other member.

“We have two enzymes, a plus and a minus,” Joyce explains. “The plus assembles the pieces to make the minus enzyme, and the minus enzyme assembles the pieces to draw the plus. It’s kind of like biology, where there is a DNA strand with plus and minus strands.”

From there, Joyce and his graduate student Tracey Lincoln, added the enzymes into a soup of building blocks, strings of nucleic bases that can be assembled into RNA, DNA or larger strings, and tweaked them to find pairs of enzymes that would reproduce. One day, some of the enzymes “went critical” and produced more RNA enzymes than the researchers had put in.

It was an important day, but Joyce and Lincoln wanted more. They wanted to create an entire population of enzymes that could replicate, compete and evolve, which is exactly what they did.

“To put it in info speak, we have a channel of 30 bit capacity for transferring information,” Joyce said. “We can configure those bits in different ways and make a variety of different replicators. And then have them compete with each other.”

But it wasn’t just a bunch of scientist-designed enzymes competing, like a miniature molecular BattleBots sequence. As soon as the replicators got into the broth, they began to change.

“Most of the time they breed true, but sometimes there is a bit flip — a mutation — and it’s a different replicator,” explained Joyce.

Most of these mutations went away quickly, but — sound familiar? — some of the changes ended up being advantageous to the chemicals in replicating better. After 77 doublings of the chemicals, astounding changes had occurred in the molecular broth.

“All the original replicators went extinct and it was the new recombinants that took over,” said Joyce. “There wasn’t one winner. There was a whole cloud of winners, but there were three mutants that arose that pretty much dominated the population.”

It turned out that while the scientist-designed enzymes were great at reproducing without competition, when you put them in the big soup mix, a new set of mutants emerged that were better at replicating within the system. It almost worked like an ecosystem, but with just straight chemistry.

“This is indeed interesting work,” said Jeffrey Bada, a chemist at the Scripps Institution of Oceanography, who was not involved with the work. It shows that RNA molecules “could have carried out their replication in the total absence” of the more sophisticated biological machinery that life now possesses.

“This is a nice example of the robustness of the RNA world hypothesis,” he said. However, “it still leaves the problem of how RNA first came about. Some type of self-replicating molecule likely proceeded RNA and what this was is the big unknown at this point.”

I mean… Seriously… Throw in a bit of self-similarity, along with many, many, many lashings – so many that it might well ‘seem’ to boarder with infinity – of complexity, and can we surely not begin to see obvious parallels between how human life arose on Earth from the “primordial soup” and those three “clouds of winners” that arose from the broth of enzymes? Aren’t these really just similar phenomena unfolding across vastly different scales of both size and time? A vast ocean of atomic interactions that occur upon the closed ecosystem that we call Earth vs. another closed ecosystem of much smaller proportions i.e. the very humble sterile laboratory flask? Are these not self-similar patterns… Patterns that elude toward a subtle and intrinsic ideal of temporal universal unfolding?

Dare I say it… Could we even begin to call this phenomenon “GOD“!? Well… If you want to equate the Mandelbrot set, via modes of analogy, to the thumb print of God, primarily because we observe these fractal like patterns almost everywhere within nature… And, thus, we begin to use them to describe God as Spinoza did i.e. “God, or Nature” as an ‘unknowable’ and ‘unfathomable’ reality of the whole of existence/creation, then I just might possibly begin to agree with you.

## Life, As We Know It, Is Written Into The Laws Of Reality

### May 5, 2010

This is a neat and brief post. It gets to the point… And just leaves enough to think about. So none of my usual ranting or raving here. “Phew!” I hear you say. And all I’m gonna say is that… A recent mathematical analysis says that Life, as we know it, is written into the laws of reality.

Will Humans and Extraterrestrial Life Share DNA Roots?

A recent mathematical analysis says that life as we know it is written into the laws of reality. DNA is built from a set of twenty amino acids – the first ten of those can create simple prebiotic life, and now it seems that those ten are thermodynamically destined to occur wherever they can.

For those unfamiliar with thermodynamics, it’s the Big Brother of all energy equations and science itself. You can apply quantum mechanics at certain scales, and Newtonian mechanics work at the right speeds, but if Thermodynamics says something then everyone listens. An energy analysis by Ralph Pudritz, a theoretical astrophysicist and director of the Origins Institute at McMaster University shows that the first ten amino acids are likely to form at relatively low temperatures and pressures, and the calculated odds of formation match the concentrations of these life-chemicals found in meteorite samples.

They also match those in simulations of early Earth, and most critically, those simulations were performed by other people. The implications are staggering: good news for anyone worried about how we’re alone, and bad news for anyone who demands some kind of “Designer” to put life together – it seems that physics can assemble the organic jigsaw all by itself, thank you very much, and has probably done so throughout space since the beginning of everything.

The study indicates that you don’t need a miracle to arrive at the chemical cocktail for early life, just a decently large asteroid with the right components. That’s all. The entire universe could be stuffed with life, from the earliest prebiotic protein-a-likes to fully DNAed descendants. The path from one to the other is long, but we’ve had thirteen and a half billion years so far and it’s happened at least once.

The other ten amino acids aren’t as easy to form, but they’ll still turn up – and the process of “stepwise evolution” means that once the simpler systems work, they can grab the rarer “epic drops” of more sophisticated chemicals as they occur – kind of a World of Lifecraft except you literally get a life when you play. And once even the most sophisticated structure is part of a replicating organism, there’s plenty to go round.

Early Earth was covered with carbonaceous material from meteorites and comets that provided the raw materials from which first life emerged. In his new book, The Eerie Silence, astrophysicist Paul Davies of Arizona State University suggests that the original cells would have been able to pick and choose from the early Earth’s organic cocktail. To the best of our knowledge, he writes, “the twenty-one chosen by known life do not constitute a unique set; other choices could have been made, and maybe were made if life started elsewhere many times.”

Posted by Luke McKinney with Casey Kazan

Or to find out more about the scientific paper which both these articles were inspire by i.e. ‘“A thermodynamic basis for prebiotic amino acid synthesis and the nature of the first genetic code.” By Paul G. Higgs, Ralph E. Pudritz. arXiv, April 6, 2009.,’ then please click here.

## What Time Is It?

### March 2, 2010

I like it when people leave comments and offer their own perceptive stance on their world view. It usually results in my learning something really important about the world… Something that I’m sure I knew on some level (having learnt most of statistics at university) but just never really had the foresight to translate it into real world analogies. Well… I’m glad to say it’s happened again!

Relating to current escalating global population levels and, thus, the resulting increase in consumption of resources, we’d be all well advised to watch this lecture entitled “Arithmetic, Population And Energy,” given by Albert A. Bartlett, Professor Emeritus in Nuclear Physics at Colorado University at Boulder. Here Professor Bartlett felicitously explains what it means to see an annual 7% increase in growth, asking questions like “What’s the doubling time for 7% growth?” and “Should we be promoting disease?” so as to bring these ideas into a crystal clear perspective… With a touch of humour here and there.

So where do we start? Well, let’s start in Boulder, Colorado. Here’s my home town. There’s the 1950 census figure, 1960, 1970—in that period of twenty years, the average growth rate of Boulder’s population was 6% per year. With big efforts, we’ve been able to slow the growth somewhat. There’s the 2000 census figure. I’d like to ask people: let’s start with that 2000 figure, go another 70 years—one human life time—and ask: what rate of growth would we need in Boulder’s population in the next 70 years so that at the end of 70 years, the population of Boulder would equal today’s population of your choice of major American cities?

Boulder in 70 years could be as big as Boston is today if we just grew 2.58% per year. Now, if we thought Detroit was a better model, we’ll have to shoot for 31?4% per year. Remember the historic figure on the preceding slide, 6% per year? If that could continue for one lifetime, the population of Boulder would be larger than the population of Los Angeles. Well, I’ll just tell you, you couldn’t put the population of Los Angles in the Boulder valley. Therefore it’s obvious, Boulder’s population growth is going to stop and the only question is, will we be able to stop it while there is still some open space, or will we wait until it’s wall-to-wall people and we’re all choking to death?

Now, every once in a while somebody says to me, “But you know, a bigger city might be a better city,” and I have to say, “Wait a minute, we’ve done that experiment!” We don’t need to wonder what will be the effect of growth on Boulder because Boulder tomorrow can be seen in Los Angeles today. And for the price of an airplane ticket, we can step 70 years into the future and see exactly what it’s like. What is it like? There’s an interesting headline from Los Angeles. (“…carcinogens in air…”) Maybe that has something to do with this headline from Los Angeles. (“Smog kills 1,600 annually…”)

So how are we doing in Colorado? Well, we’re the growth capital of the USA and proud of it. The Rocky Mountain News tells us to expect another million people in the Front Range in the next 20 years, and what are the consequences of all this? (“Denver’s traffic…3rd worst in US…”) These are totally predictable, there are no surprises here, we know exactly what happens when you crowd more people into an area.

Well, as you can imagine, growth control is very controversial, and I treasure the letter from which these quotations are taken. Now, this letter was written to me by a leading citizen of our community. He’s a leading proponent of “controlled growth.” “Controlled growth” just means “growth.” This man writes, “I take no exception to your arguments regarding exponential growth.” “I don’t believe the exponential argument is valid at the local level.”

So you see, arithmetic doesn’t hold in Boulder. I have to admit, that man has a degree from the University of Colorado. It’s not a degree in mathematics, in science, or in engineering. All right, let’s look now at what happens when we have this kind of steady growth in a finite environment…

Thus I ask if this could be a new slogan for the “Optimum Population Trust“? And perhaps when we tie this idea up with consumption, it might be a reason to change our habits, like finding the goods we need off “FreeCycle” rather than ‘buying’ them brand new in the shops OR throwing away what we think we don’t need or can’t use?

A BIG thank you to Andrew Soon for bringing this to my attention!

## The ‘Idea’ Of Infinity…

### March 17, 2009

“If any philosopher had been asked for a definition of infinity, he might have produced some unintelligible rigmarole, but he would certainly not have been able to give a definition that had any meaning at all.” Bertrand Russell

In this brief essay on the ‘infinite,’ I do not want to ramble on about uncertainties or truths. My aim here is not to lecture. Rather it is to encourage… So instead of joining the dots together in an obvious proclamation of basis, I am happy to quote certain others’ works that have more pertinently and eloquently touched aspects of the ‘infinite’ over the years, with a hope that the reader’s mind will naturally settle on the splendor lying behind the complex and distracting facades of catechism.

1. William Blake

William Blake (28 November 1757 – 12 August 1827) was an English poet, painter, and printmaker. Largely unrecognized during his lifetime, Blake is now considered a seminal figure in the history of both poetry and the visual arts of the Romantic Age. His prophetic poetry has been said to form “what is in proportion to its merits the least read body of poetry in the English language”. His visual artistry has led one modern critic to proclaim him “far and away the greatest artist Britain has ever produced”. Although he only once journeyed farther than a day’s walk outside London during his lifetime, he produced a diverse and symbolically rich corpus, which embraced ‘imagination’ as “the body of God”, or “Human existence itself”.

William Blake in an 1807 portrait by Thomas Phillips.

In one of his most insightful poems “The Auguries of Innocence”, he states:

“To see a world in a grain of sand,
And a heaven in a wild flower,
Hold infinity in the palm of your hand,
And eternity in an hour.”

For the full poem, please visit: http://www.artofeurope.com/blake/bla3.htm

What could such majestic tapestry mean? Well… Perhaps to the bovine logician, or the unenlightened literary reader, this idea might fall short of the lofty missive prescribed by Blake’s godly eye. But thankfully, with today’s scientific awareness of all things great and small, this notion may be better ‘understood’ with only a lax dedication towards ‘knowing’ the world around oneself better.

2. Niels Fabian Helge von Koch

Niels Fabian Helge von Koch (January 25, 1870 – March 11, 1924) was a Swedish mathematician who gave his name to the famous fractal known as the Koch snowflake, one of the earliest fractal curves to be described.

He was born into a family of Swedish nobility. His grandfather, Nils Samuel von Koch (1801–1881), was the Attorney-General of Sweden. His father, Richert Vogt von Koch (1838–1913) was a Lietenant-Colonel in the Royal Horse Guards of Sweden.

Von Koch wrote several papers on number theory . One of his results was a 1901 theorem proving that the Riemann hypothesis is equivalent to a strengthened form of the prime number theorem.

He described the Koch curve in a 1904 paper entitled “On a continuous curve without tangents constructible from elementary geometry” (original French title: “Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire”).

The Koch snowflake (or Koch star) is a mathematical curve and one of the earliest fractal curves to have been described. (Actually Koch described what is now known as the Koch curve, which is the same as the now popular snowflake, except it starts with a line segment instead of an equilateral triangle. Three Koch curves form the snowflake.)

The Koch curve is a special case of the Cesaro curve where:

$a=\frac{1}{2}+\frac{i}{\sqrt{12}}$,

which is in turn a special case of the de Rham curve.

One can imagine that it was created by starting with a line segment, then recursively altering each line segment as follows:

1. divide the line segment into three segments of equal length.
2. draw an equilateral triangle that has the middle segment from step 1 as its base and points outward.
3. remove the line segment that is the base of the triangle from step 2.

The Koch snowflake/star is generated using the same recursive process but starting with an equilateral triangle rather than a line segment. After doing this once for the Koch snowflake, the result is a shape similar to the Star of David.

The Koch curve is the limit approached as the above steps are followed over and over again.

The Koch curve has an infinite length because each time the steps above are performed on each line segment of the figure there are four times as many line segments, the length of each being one-third the length of the segments in the previous stage. Hence the total length increases by one third and thus the length at step n will be (4/3)n: the fractal dimension is log 4/log 3 ≈ 1.26, greater than the dimension of a line (dimension 1) but less than Peano’s space-filling curve.

Iterations of the von Koch curve...

Ever smaller and smaller… As one zooms into the Koch curve, steady self-similarity is exuded infinitly:

3. Karl Menger

In mathematics, the Menger sponge is a fractal curve. It is the universal curve, in that it has topological dimension one, and any other curve (more precisely: any compact metric space of topological dimension 1) is homeomorphic to some subset of it. It is sometimes called the Menger-Sierpinski sponge or the Sierpinski sponge. It is a three-dimensional extension of the Cantor Set and Sierpinski Carpet. It was first described by Austrian mathematician Karl Menger in 1926 while exploring the concept of topological dimension.

A Menger sponge, iterated four times...

Each face of the Menger sponge is a Sierpinski cerpet; furthermore, any intersection of the Menger sponge with a diagonal or medium of the initial cube M0 is a Cantor set.

The Menger sponge is a closed set i.e. it contains its own boundary (unlike the Mandelbrot set); since it is also bounded, the Heine-Borel theorem implies that it is compact. Furthermore, the Menger sponge is uncountable and has Lebesque measure 0.

The topological dimension of the Menger sponge is one, the same as any curve. Menger showed, in the 1926 construction, that the sponge is a universal curve, in that any possible one-dimensional curve is homeomorphic to a subset of the Menger sponge, where here a curve means any compact metric shape of Lebesgue covering dimension one; this includes trees and graphs with an arbitrary countable number of edges, vertices and closed loops, connected in arbitrary ways.

In a similar way, the Sierpinski cerpet is a universal curve for all curves that can be drawn on the two-dimensional plane. The Menger sponge constructed in three dimensions extends this idea to graphs that are not planar, and might be embedded in any number of dimensions. Thus any geometry of quantum loop gravity can be embedded in a Menger sponge.

Interestingly, the Menger sponge simultaneously exhibits an infinite surface area and encloses zero volume. This idea of the infinite held within the finite is perhaps not such a revelation as it might initially seem…

A ‘simpler’ more visual way to understand the complexity of Menger’s idea can be seen in the follow animation:

http://www.pure-mirage.com/html/MillersMengerSpongeFastPlay.htm

4. Benoît B. Mandelbrot

Benoît B. Mandelbrot (born 20 November 1924) is a French mathematician, best known as the father of fractal geometry. He is Sterling Professor of Mathematical Sciences, Emeritus at Yale University; IBM Fellow Emeritus at the Thomas J. Watson Research Cente; and Battelle Fellow at the Pacific Northwest National Laboratory. He was born in Poland. His family moved to France when he was a child, and he was educated in France.

In mathematics, the Mandelbrot set, named after Mandelbrot himself, is a set of points in the complex plane, the boundary of which forms a fractal. Mathematically, the Mandelbrot set can be defined as the set of complex values of c for which the orbit of 0 under iteration of the complex quadratic polynomial zn+1zn2c remains bounded. That is, a complex number, c, is in the Mandelbrot set if, when starting with z0=0 and applying the iteration repeatedly, the absolute value of zn never exceeds a certain number (that number depends on c) however large n gets.

In other words… Part of the charm of the set is that it springs from such a simple equation: z2 + c. The terms z and c are complex numbers, which consist of an imaginary number (a multiple of the square root of –1) combined with a real number. One begins by assigning a fixed value to c, letting z = 0 and calculating the output. One then repeatedly recalculates, or iterates, the equation, substituting each new output for z. Some values of c, when plugged into this iterative function, produce outputs that swiftly soar toward infinity. Other values of c produce outputs that eternally skitter about within a certain boundary. This latter group of c‘s, or complex numbers, constitutes the Mandelbrot set.

When plotted on a graph consisting of all complex numbers, the members of the set cluster into a distinctive shape. From afar, it is not much to look at: it has been likened to a tumor-ridden heart, a beetle, a badly burned chicken and a warty figure eight on its side.

A closer look reveals that the borders of the set do not form crisp lines but seem to shimmer like flames. Repeated magnification of the borders plunges one into a bottomless phantasmagoria of baroque imagery. Some forms, such as the basic heartlike shape, keep recurring but always with subtle differences.

The Mandelbrot set shows more intricate detail the closer one looks or magnifies the image, usually called “zooming in”. The following example of an image sequence zooming to a selected c value gives an impression of the infinite richness of different geometrical structures, and explains some of their typical rules.

The magnification of the last image relative to the first one is about 10,000,000,000 to 1. Relating to an ordinary computer monitor, it represents a section of a Mandelbrot set with a diameter of 4 million kilometres. Its border would show an inconceivable number of different fractal structures…

And here I will leave you with a quotation…

“Pure mathematics is, in its way, the poetry of logical ideas.”  Albert Einstein