From Mandelbrot working in the IBM laboratories to Feigenbaum working on the universal nature of chaos to the Germans, Peitgen and Richter trying to make sense of nature the answer was the same: Fractals are universal in the morphology of nature. Their existence means that no phenomenon can ever be satisfactorily explained on the basis of specific local events. It also means that in a sense the Newtonians, intuitively, were right and everything is predetermined: man’s fate is written in the stars; affected by the time of birth. Determinism however operates by the application of limits and within those limits reigns chaos!
Presaging the modern scientific developments at a slightly earlier date Alistair Crowley had said that “man is capable of being, and using, anything which he perceives, for everything that he perceives is in a certain sense part of his being...”.
That much is certainly true for fractals are active even within us: Though the anthropomorphic theory of semen has long since been discarded, DNA cannot specify the vast number of detail that goes in the particular spatial structure of man, animal or plant, but it can specify a repeating process of bifurcation and development that is in nature the same for all!
Mandelbrot in his study of the shapes of nature discovered that whether studying vuscular, pulmonary or botanical trees or the formation of snowflakes there was, waiting to be perceived, an underlying unity. Not a similarity of appearance or characteristics but (as magic has long specified) a similarity of process.
To the eyes of chaos scientists’ discovery a rising column of smoke breaking into wild swirls, a flag flapping in the wind, a dripping faucet, the weather, the flight of a plane, oil flowing in a pipe, cars on the motorway, the spread of galaxies in the solar system, the rise and fall of prices on the stock exchange and the emotions of a populace are all governed by the same invisible but all pervading principle.
The world view that is emerging from the discoveries of Chaos is one of infinite processes contained within finite limits. The mind of man containing the entire process of the Universe. The falling of rain from the sky attributed as much to the prayers of the shaman as to global weather conditions. The death of a king, the birth of a child; as connected to the spatial configuration of the planets as that configuration is linked to the presence of man on Earth.
It is singularly ironic that nearly 200 years after Franz Anton Mesmer’s death and the discrediting of his theory of animal magnetism his fellow countrymen, mathematician Heinz-Otto Peitgen and physicist Peter H. Richter would spend sleepless nights in their laboratory studying the magnetization and demagnetization of materials in order to fathom the workings of nature.
As the computer-generated pictures of the physical processes involved grew and grew in complexity they increased their computer magnification until at last one picture loomed particularly clear: the Mandelbrot set!With a nod to Mesmer and the enlightened thinkers that preceded him they wrote in their laboratory notes “Perhaps we should believe in magic”.
Wednesday, July 25, 2007
Tuesday, June 5, 2007
The Magic of Nature
The science of Chaos was born out of the persistent attempts of a determined group of people from a dozen different scientific disciplines who, often working alone and in direct opposition to orthodox scientific beliefs, strove to make sense of what appeared essentially senseless and chaotic.
Working in a holistic manner that sought to look at the effect they were studying as a whole rather than isolate a single one of its parts, they came to grips with nothing less than the boiling broth of the magician: creating order out of anarchy...on a cosmic scale!
Their holistic approach paid off.
They found that there is a correspondence of scaling that is constant in everything, from the way leaves on a tree are shaped to the shape assumed by the dancing flame of a candle.
They realised what magicians have known all along: To make things work you do not require a minute knowledge of the working of every possible part of the connection you are studying, but a visual approximation of the generality governing it. Much like visualising the effect rather than the entire complex sequence of events that must lead to it.
Nature does the rest.
The man credited with laying down the foundations of the new science is physicist Mitchell J. Feigenbaum. His playground of speculation was a by now familiar numerical territory known as a complex plane that is composed of ‘real’ and ‘imaginary’ numbers, now recognised as arbitrary as both sorts can be as real or imaginary as any other sort.
What is remarkable is that the modern day definition of the complex plane sounds like an updated reiteration of the astral plane concept propagated by Eliphas Levi in 19th century Paris as a way of recovering the microcosm and macrocosm which science had rejected. As we’ve already seen the complex plane consists of two axis where numbers co-exist with their opposites. Levi said that the astral plane gives a picture of the “ultimate reality comprised by a unity compounded of opposites”!
Working within the context provided by the complex plane, Feigenbaum discovered that he could visualise shapes that corresponded not only to static things but also to motion.
Eliphas Levi in The Key to the Mysteries, wrote that the astral plane is filled with astral light “which is the fluidic and living gold of alchemy” and to control it is to master all things, “To direct the magnetic forces is then to destroy or create forms; to produce to all appearance or to destroy bodies; it is to exercise the almighty powers of Nature”!
The procedures and trappings of ritual magic then became -like the studying of the scientist- a means of directing and shaping the Will, making it part of the network of correspondences. Links between the universe and the human mind, which obtained in miniature all factors existing in the world outside it.
Even more to the point, the astral plane is the realm in which thoughts, imaginings and desires have an independent reality. In modern magical theory it is there that the traditional ascent of the spheres mentioned in The Sefer Yetsirah or Book of Creation takes place, enabling man to ascend to the point where he can see the nature of God.
Studying the pictures of the fractal shapes provided by mathematical manipulations in the complex plane, scientists can at last see a simple, beautiful, unifying order underlying the fabric of chaotic processes. An order that is encountered from the microscopic to the macrocosmic. An order that may reveal, according to Australian physicist Paul Davies, not just the nature of God but how God thinks!
Working in a holistic manner that sought to look at the effect they were studying as a whole rather than isolate a single one of its parts, they came to grips with nothing less than the boiling broth of the magician: creating order out of anarchy...on a cosmic scale!
Their holistic approach paid off.
They found that there is a correspondence of scaling that is constant in everything, from the way leaves on a tree are shaped to the shape assumed by the dancing flame of a candle.
They realised what magicians have known all along: To make things work you do not require a minute knowledge of the working of every possible part of the connection you are studying, but a visual approximation of the generality governing it. Much like visualising the effect rather than the entire complex sequence of events that must lead to it.
Nature does the rest.
The man credited with laying down the foundations of the new science is physicist Mitchell J. Feigenbaum. His playground of speculation was a by now familiar numerical territory known as a complex plane that is composed of ‘real’ and ‘imaginary’ numbers, now recognised as arbitrary as both sorts can be as real or imaginary as any other sort.
What is remarkable is that the modern day definition of the complex plane sounds like an updated reiteration of the astral plane concept propagated by Eliphas Levi in 19th century Paris as a way of recovering the microcosm and macrocosm which science had rejected. As we’ve already seen the complex plane consists of two axis where numbers co-exist with their opposites. Levi said that the astral plane gives a picture of the “ultimate reality comprised by a unity compounded of opposites”!
Working within the context provided by the complex plane, Feigenbaum discovered that he could visualise shapes that corresponded not only to static things but also to motion.
Eliphas Levi in The Key to the Mysteries, wrote that the astral plane is filled with astral light “which is the fluidic and living gold of alchemy” and to control it is to master all things, “To direct the magnetic forces is then to destroy or create forms; to produce to all appearance or to destroy bodies; it is to exercise the almighty powers of Nature”!
The procedures and trappings of ritual magic then became -like the studying of the scientist- a means of directing and shaping the Will, making it part of the network of correspondences. Links between the universe and the human mind, which obtained in miniature all factors existing in the world outside it.
Even more to the point, the astral plane is the realm in which thoughts, imaginings and desires have an independent reality. In modern magical theory it is there that the traditional ascent of the spheres mentioned in The Sefer Yetsirah or Book of Creation takes place, enabling man to ascend to the point where he can see the nature of God.
Studying the pictures of the fractal shapes provided by mathematical manipulations in the complex plane, scientists can at last see a simple, beautiful, unifying order underlying the fabric of chaotic processes. An order that is encountered from the microscopic to the macrocosmic. An order that may reveal, according to Australian physicist Paul Davies, not just the nature of God but how God thinks!
Chaos in all directions
It wasn’t like that always however. Mathematics was one of the less glamorous of the sciences and mathematicians, in the public eye, were no more exciting than accountants.
This all changed one wintry afternoon in 1975 when an IBM mathematician by the name of Benoit Mandelbrot, preparing his first major book-length work for publication, thumbed through a Latin dictionary looking for a word that would describe some peculiar-looking shapes his calculations had come up with.
He came across the adjective fractus from the verb frangere - to break. And, with a little playing around, the word fractals, was born.
Fractals, as the name suggests, are a family of jugged, tangled, twisted, splintered and fractured shapes which seem to underlie the very fabric of nature. They are present not only in static shapes like serrated edges and coastlines but also in the shapes formed by charting the scaling of motion (in the way a butterfly beats its wings or a pendulum swings, for example) or the rise and fall of cotton prices in the Stock Exchange and the way molecular cells transmit data.
Many of us will have probably seen the twisted, colourful designs which fractals today make, but what is truly beautiful about them is that their forms, as complicated as the mind of God according to those who study them, require but the most basic of instructions to recreate.
Using powerful IBM computers to analyse the formation of these structures, Mandelbrot discovered that they are but a variation of a single fractal shape which has since become known as the Mandelbrot set.
The essense of the discovery illustrates the sensitivity of any event to initial conditions and became the foundation of the inter-disciplinary science of Chaos.
Like new magicians, the Chaoticians that sprang up in the wake of Mandelbrot’s discovery, did not look upon the world in the reductionist, analytical manner of their predecessors but sought to gain an understanding of the underlying simplicity governing the behaviour of complex systems.
What Chaos teaches is that nothing can ever be predicted with accuracy because even the tiniest change in initial conditions can be responsible for tremendously large effects.In a statement of almost metaphysical quality chaoticians say that “the gentle beating of the wings of a butterfly in China is responsible for the tornadoes in Texas”!
If you think that’s overstating matters a little, or even edging away from the cold, precise logic of science, more shocks are in store, for the language used by today’s Chaoticians to describe the nature of fractals and the physical events they affect parallels that used by the historian and theoritician of magic, Eliphas Levi, and subsequently the controversial, self-styled ‘Great Beast’ Alistair Crowley.
This all changed one wintry afternoon in 1975 when an IBM mathematician by the name of Benoit Mandelbrot, preparing his first major book-length work for publication, thumbed through a Latin dictionary looking for a word that would describe some peculiar-looking shapes his calculations had come up with.
He came across the adjective fractus from the verb frangere - to break. And, with a little playing around, the word fractals, was born.
Fractals, as the name suggests, are a family of jugged, tangled, twisted, splintered and fractured shapes which seem to underlie the very fabric of nature. They are present not only in static shapes like serrated edges and coastlines but also in the shapes formed by charting the scaling of motion (in the way a butterfly beats its wings or a pendulum swings, for example) or the rise and fall of cotton prices in the Stock Exchange and the way molecular cells transmit data.
Many of us will have probably seen the twisted, colourful designs which fractals today make, but what is truly beautiful about them is that their forms, as complicated as the mind of God according to those who study them, require but the most basic of instructions to recreate.
Using powerful IBM computers to analyse the formation of these structures, Mandelbrot discovered that they are but a variation of a single fractal shape which has since become known as the Mandelbrot set.
The essense of the discovery illustrates the sensitivity of any event to initial conditions and became the foundation of the inter-disciplinary science of Chaos.
Like new magicians, the Chaoticians that sprang up in the wake of Mandelbrot’s discovery, did not look upon the world in the reductionist, analytical manner of their predecessors but sought to gain an understanding of the underlying simplicity governing the behaviour of complex systems.
What Chaos teaches is that nothing can ever be predicted with accuracy because even the tiniest change in initial conditions can be responsible for tremendously large effects.In a statement of almost metaphysical quality chaoticians say that “the gentle beating of the wings of a butterfly in China is responsible for the tornadoes in Texas”!
If you think that’s overstating matters a little, or even edging away from the cold, precise logic of science, more shocks are in store, for the language used by today’s Chaoticians to describe the nature of fractals and the physical events they affect parallels that used by the historian and theoritician of magic, Eliphas Levi, and subsequently the controversial, self-styled ‘Great Beast’ Alistair Crowley.
The Complex Plane
It would be all too easy, at this stage, to make a great deal about the traditional, age-long connection of mathematics with magic.
I won’t because it will neither lead anywhere nor provide any insights beyond the fact that at every stage of human history, there is a body of knowledge that is fiercely guarded from outsiders and may acquire semi-mystical status. And if you think that we’re beyond this stage now, just spend some time in the company of any self-styled computer ‘expert’ and you’ll see what I mean.
What I will make a point of mentioning however is that from the very first moment we looked at our world, mathematics has provided a key to both representing it and understanding its evolution.
Galileo Galilei rightly said, way ahead of his time, that “Mathematics is the language in which God wrote the Universe.” Today complex algorithms enable us, if we wish, to numerically codify everything we see around us, including our own selves and represent it in mathematical terms.
The capacity to do that has proved a double-edged knife. On the one hand it gave us greater understanding and it has given us the almost magical power to make predictions. From forecasting the weather to predicting the potential power of an explosion.
On the other hand, it armed Newtonians with the emasculating belief that everything was predictable in a clockwork universe in which we functioned as simple cogs in a machine of truly universal proportions. This single belief, more than anything else, stunted scientific thought for a great many years and proved almost the death of every magical concept.
Whatever the drawbacks however, the advantages of representing everything in terms of numbers formed the basis of ‘formalism’ in mathematics. This allowed mathematics to become more and more the formal manipulation of symbols and it gave rise to the place where mathematicians can dream while awake and the manipulation of both real and imaginary numbers can affect the world. Today, this is known as the Complex Plane of numbers. In very simple terms the complex plane is comprised of two axis at right angles to each other.
One axis goes from east to west and goes onto infinity, and on it is every positive and negative number we know (which are called ‘real’ numbers). The other axis, goes from north to south. It too is also infinite and on it, like familiar shadows, are the so called imaginary numbers. Each one representing the imaginary doppleganger of a real number.
The reason for this arrangement is that instead of looking at numbers on a single line which would give a one, dimensional and thus rather limiting, view of the world, we can now look at them in two dimensions.
Every number we want now can be expressed as a combination of its real and imaginary coordinates. This means that it does not exist on its individual line but rather somewhere in one of the four quadrants of the complex plane.
This simple technique allows mathematicians to examine not only the solidity of objects (say like a cube or a square) but also to study normally invisible quantities, like the shapes of motion, and the formations of temperature differences!
Their sojourns through the Complex Plane have made confirmed Neoplatonists out of some of the best mathematicians, who in turn have found themselves, unwittingly reiterating some of Plato’s most profound statements regarding the state of reality.
The Princeton mathematician Kurt Gödel, who formulated the dictum (known as Gödel’s theorum) which states that no matter how precise mathematical computations become there will always be truths whose existence cannot be mathematically proved, envisaged these truths as already existing in a Platonic domain somewhere “out there”, beyond our limited, mortal ken. More recently, the Oxford mathematician Roger Penrose said that “Mathematical truth is something that goes beyond formalism,” and went on to write that “There often does appear to be some profound reality about these mathematical concepts, going quite beyond the deliberations of any particular mathematician. It is as though human thought is, instead being guided towards some external truth - a truth which has a reality of its own, and which is revealed only partially to anyone of us.”And discussing the implications of the system of complex numbers to be found in the complex plane Penrose rather apocryphically said that he felt it had “a profound and timeless reality”!
As if the examples of the overt similarities between the complex plane of mathematics and the Astral plane of High magic were not enough, the apparent ability to enter the complex plane (limited naturally only to those who’re adept at mathematics,) and toy around in it has given rise to discoveries and assertions which in turn have drastically altered the way we look at, and relate to the world around us (any of it sounds familiar so far?).
I won’t because it will neither lead anywhere nor provide any insights beyond the fact that at every stage of human history, there is a body of knowledge that is fiercely guarded from outsiders and may acquire semi-mystical status. And if you think that we’re beyond this stage now, just spend some time in the company of any self-styled computer ‘expert’ and you’ll see what I mean.
What I will make a point of mentioning however is that from the very first moment we looked at our world, mathematics has provided a key to both representing it and understanding its evolution.
Galileo Galilei rightly said, way ahead of his time, that “Mathematics is the language in which God wrote the Universe.” Today complex algorithms enable us, if we wish, to numerically codify everything we see around us, including our own selves and represent it in mathematical terms.
The capacity to do that has proved a double-edged knife. On the one hand it gave us greater understanding and it has given us the almost magical power to make predictions. From forecasting the weather to predicting the potential power of an explosion.
On the other hand, it armed Newtonians with the emasculating belief that everything was predictable in a clockwork universe in which we functioned as simple cogs in a machine of truly universal proportions. This single belief, more than anything else, stunted scientific thought for a great many years and proved almost the death of every magical concept.
Whatever the drawbacks however, the advantages of representing everything in terms of numbers formed the basis of ‘formalism’ in mathematics. This allowed mathematics to become more and more the formal manipulation of symbols and it gave rise to the place where mathematicians can dream while awake and the manipulation of both real and imaginary numbers can affect the world. Today, this is known as the Complex Plane of numbers. In very simple terms the complex plane is comprised of two axis at right angles to each other.
One axis goes from east to west and goes onto infinity, and on it is every positive and negative number we know (which are called ‘real’ numbers). The other axis, goes from north to south. It too is also infinite and on it, like familiar shadows, are the so called imaginary numbers. Each one representing the imaginary doppleganger of a real number.
The reason for this arrangement is that instead of looking at numbers on a single line which would give a one, dimensional and thus rather limiting, view of the world, we can now look at them in two dimensions.
Every number we want now can be expressed as a combination of its real and imaginary coordinates. This means that it does not exist on its individual line but rather somewhere in one of the four quadrants of the complex plane.
This simple technique allows mathematicians to examine not only the solidity of objects (say like a cube or a square) but also to study normally invisible quantities, like the shapes of motion, and the formations of temperature differences!
Their sojourns through the Complex Plane have made confirmed Neoplatonists out of some of the best mathematicians, who in turn have found themselves, unwittingly reiterating some of Plato’s most profound statements regarding the state of reality.
The Princeton mathematician Kurt Gödel, who formulated the dictum (known as Gödel’s theorum) which states that no matter how precise mathematical computations become there will always be truths whose existence cannot be mathematically proved, envisaged these truths as already existing in a Platonic domain somewhere “out there”, beyond our limited, mortal ken. More recently, the Oxford mathematician Roger Penrose said that “Mathematical truth is something that goes beyond formalism,” and went on to write that “There often does appear to be some profound reality about these mathematical concepts, going quite beyond the deliberations of any particular mathematician. It is as though human thought is, instead being guided towards some external truth - a truth which has a reality of its own, and which is revealed only partially to anyone of us.”And discussing the implications of the system of complex numbers to be found in the complex plane Penrose rather apocryphically said that he felt it had “a profound and timeless reality”!
As if the examples of the overt similarities between the complex plane of mathematics and the Astral plane of High magic were not enough, the apparent ability to enter the complex plane (limited naturally only to those who’re adept at mathematics,) and toy around in it has given rise to discoveries and assertions which in turn have drastically altered the way we look at, and relate to the world around us (any of it sounds familiar so far?).
Tuesday, May 29, 2007
Images of the sleeping brain
In order to understand one of the founding tenets of High Magic think of a place where nothing concrete exists. Think of it perhaps as a different world or another dimension, removed from, but still very definitely a part of our world.
In this place of relative nothingness, reality is supplemented by representing it in a stylistic form comprised largely of symbols. The magician can enter here, interact with the ethereal inhabitants of this strange world in a meaningful manner, and effect actions that will eventually impact on the ‘real’ world.
He may, for example, as a result of his actions gain fresh, new knowledge and insights that will help him in his work, or, in a more literal sense, he may set in motion forces that will eventually alter some aspect of what constitutes reality. Psychotic as all this may sound, before we dismiss it out of hand it’d do good to take a look at how exactly it came about in the first place. The earliest mention of some sort of etheric representation of man were made by the Neoplatonists of ancient Greece, who believed that the soul descended through heavenly spheres to enter a physical body on earth and during this voyage was in turn affected by the influence of each planet and therefore formed what was regarded as “the soul’s spiritual envelope”.
They in turn relied on the Platonic concept of a separate, independent reality that simply exists somewhere “out there” and which we can only attempt -not entirely successfully- to discover.Far fetched as this concept may seem today, in its heyday it was as good an explanation as any for the brain’s ability to imagine things it could not possibly experience.In those early days of strictly linnear logic it was held that if one did not directly or indirectly know of something, then his ignorance of it was equally unknown to him and hence it was not ignorance at all. Thus knowledge was more a journey of rediscovery than a sojourn into the unknown. To be able to imagine worlds and planetary arrangements where no physical man had ever been, for example, meant that the etheric mind (with its inherently greater capabilities) had somehow been there before it had entered the body.
This was a concept that gained tremendous popularity when it was rediscovered and restated in 1471 by the Florentine philosopher and Medici prodigeé, Marsilio Ficino.
Working from a pilfered Greek manuscript of the Hermetica, delivered directly from Macedonia to Florence by a Medici agent, Ficino propagated the concept, of an etheric or ‘astral’ body that supplied a set of consonances between man and the heavens.
At the time no explicit mention was ever made of the body having an astral, conscious ‘double’ able to enter this etheric plane but, nevertheless, as the idea became more and more popular the seeds of astral travel were, unknowingly, being sown.
Now, astral travel, the ability of a magic adept to somehow project his mind into another plane, is a tenet that’s found at the very heart of High Magic. It requires us to believe that not only does the astral plane exist but that it can and does influence our lives in a very direct manner. Modern Freudian psychology has already cut its teeth in explaining how the associations thrown up by a ‘free-floating’ brain can dredge up esoteric symbolism in the mind and can present us with both solutions to current problems (hence Kekulé, amongst others) and also frighten us with the spectre of past ones recurring.
Jungians, in turn, have explained about the posited existence of archetypes in the brain so, that it would appear that what magicians have been swearing by for thousands of years are little more than self-created delusions. Mere ‘representations’ thrown up by the brain attempting to make sense of logical concepts when the analytical part of it has been switched off.
If things were left at that we could just say that, hey! Know what? All that recitation of mantras in smoky atmospheres is enough to addle anybody’s brains and psychologists have got it right. This astral travel stuff is just “all in the mind”. But we’ve already seen that the mind and everything in it are an inescapable part of what constitutes our Reality. We have seen that our perception of that reality can influence our subsequent actions to a positive or a negative effect. And we have furthermore seen that the way we perceive the world, the assumptions we are likely to make about it, may in fact play a large part in creating what we actually do perceive.
Confusing, no?
To avoid the logic trap of saying that what we perceive is true otherwise we cannot possibly perceive it, let us strip the concept of the astral plane of its historical baggage and examine it for what it really is.
Devoid of magical connotations, the astral plane then becomes an imaginary plane, a representational mode of our more concrete reality which contains none of the constraints (and hence all of the possibilities) of the concrete world. This, naturally means that somehow, it represents a ‘truer’ picture of our reality. One which we, bound by the physical limitations of our concrete senses, are unable to directly experience.
The magician etherically (read mentally) then, shedding these mortal limitations, enters this plane and by manipulating the symbolic representations that he encounters within it, achieves a greater understanding of the concrete world he normally inhabits. It’s as simple as that. And if it beggars belief, well it shouldn’t, for as concepts go, this one is logically sound.
And even hard-nosed mathematicians have been, quietly, entering this very same plane for many years.
In this place of relative nothingness, reality is supplemented by representing it in a stylistic form comprised largely of symbols. The magician can enter here, interact with the ethereal inhabitants of this strange world in a meaningful manner, and effect actions that will eventually impact on the ‘real’ world.
He may, for example, as a result of his actions gain fresh, new knowledge and insights that will help him in his work, or, in a more literal sense, he may set in motion forces that will eventually alter some aspect of what constitutes reality. Psychotic as all this may sound, before we dismiss it out of hand it’d do good to take a look at how exactly it came about in the first place. The earliest mention of some sort of etheric representation of man were made by the Neoplatonists of ancient Greece, who believed that the soul descended through heavenly spheres to enter a physical body on earth and during this voyage was in turn affected by the influence of each planet and therefore formed what was regarded as “the soul’s spiritual envelope”.
They in turn relied on the Platonic concept of a separate, independent reality that simply exists somewhere “out there” and which we can only attempt -not entirely successfully- to discover.Far fetched as this concept may seem today, in its heyday it was as good an explanation as any for the brain’s ability to imagine things it could not possibly experience.In those early days of strictly linnear logic it was held that if one did not directly or indirectly know of something, then his ignorance of it was equally unknown to him and hence it was not ignorance at all. Thus knowledge was more a journey of rediscovery than a sojourn into the unknown. To be able to imagine worlds and planetary arrangements where no physical man had ever been, for example, meant that the etheric mind (with its inherently greater capabilities) had somehow been there before it had entered the body.
This was a concept that gained tremendous popularity when it was rediscovered and restated in 1471 by the Florentine philosopher and Medici prodigeé, Marsilio Ficino.
Working from a pilfered Greek manuscript of the Hermetica, delivered directly from Macedonia to Florence by a Medici agent, Ficino propagated the concept, of an etheric or ‘astral’ body that supplied a set of consonances between man and the heavens.
At the time no explicit mention was ever made of the body having an astral, conscious ‘double’ able to enter this etheric plane but, nevertheless, as the idea became more and more popular the seeds of astral travel were, unknowingly, being sown.
Now, astral travel, the ability of a magic adept to somehow project his mind into another plane, is a tenet that’s found at the very heart of High Magic. It requires us to believe that not only does the astral plane exist but that it can and does influence our lives in a very direct manner. Modern Freudian psychology has already cut its teeth in explaining how the associations thrown up by a ‘free-floating’ brain can dredge up esoteric symbolism in the mind and can present us with both solutions to current problems (hence Kekulé, amongst others) and also frighten us with the spectre of past ones recurring.
Jungians, in turn, have explained about the posited existence of archetypes in the brain so, that it would appear that what magicians have been swearing by for thousands of years are little more than self-created delusions. Mere ‘representations’ thrown up by the brain attempting to make sense of logical concepts when the analytical part of it has been switched off.
If things were left at that we could just say that, hey! Know what? All that recitation of mantras in smoky atmospheres is enough to addle anybody’s brains and psychologists have got it right. This astral travel stuff is just “all in the mind”. But we’ve already seen that the mind and everything in it are an inescapable part of what constitutes our Reality. We have seen that our perception of that reality can influence our subsequent actions to a positive or a negative effect. And we have furthermore seen that the way we perceive the world, the assumptions we are likely to make about it, may in fact play a large part in creating what we actually do perceive.
Confusing, no?
To avoid the logic trap of saying that what we perceive is true otherwise we cannot possibly perceive it, let us strip the concept of the astral plane of its historical baggage and examine it for what it really is.
Devoid of magical connotations, the astral plane then becomes an imaginary plane, a representational mode of our more concrete reality which contains none of the constraints (and hence all of the possibilities) of the concrete world. This, naturally means that somehow, it represents a ‘truer’ picture of our reality. One which we, bound by the physical limitations of our concrete senses, are unable to directly experience.
The magician etherically (read mentally) then, shedding these mortal limitations, enters this plane and by manipulating the symbolic representations that he encounters within it, achieves a greater understanding of the concrete world he normally inhabits. It’s as simple as that. And if it beggars belief, well it shouldn’t, for as concepts go, this one is logically sound.
And even hard-nosed mathematicians have been, quietly, entering this very same plane for many years.
Wednesday, May 23, 2007
In the plane of the impossible
Now, it is no mean feat to dream without falling asleep. At the best of times it takes a little hard work and the right attitude. It’s what prayer and meditation have always been about and the fact that both forms of focussing the mind have survived to our day, and indeed are currently enjoying a revival, testifies to their efficacy.
Scientists, in general however, and mathematicians in particular, have always prided themselves on the fact that they don’t need to resort to such ‘unscientific’ methods in order to transport their minds into other worlds. Over the years they’ve evolved their own means of taking physically impossible jaunts through etheric worlds and, to the chagrin of yogis and mystics, have also managed to get paid for it. But before we look at their techniques it’s good to acknowledge that even the staunchest advocates of the scientific method have to sleep sometimes, and when they do, what they dream about makes for some very interesting assumptions.
One wintry day in 1865, in the clogged with horse-drawn buggies streets of Vienna, a notable German chemist by the name of Friedrich Kekulé, while waiting for his driver to take the buggy out of a traffic-jam, fell into a tired snooze.
He was tired because for the past few months he’d been working on a most vexing problem: that of discovering how exactly the chain of carbon atoms are linked in the benzene molecule.As he snoozed, he dreamt of carbon atoms in the form of dancing snakes, and as he watched (in his dream) their taunting dance, they all joined hands and formed a circle.
The discovery of the cyclical structure of the benzene molecule laid the basis for the foundation of organic chemistry and Kekulé, naturally, received all the credit for it. After all it had been his dream.
His closing words at the convention where he presented his findings were: “Let us learn how to dream gentlemen, and then perhaps we’ll learn to discover the truth!”Shamelessly I’ll use this classic example to hark back to my earlier analogy of the brain as a computer and the mind as the software that’s ran on it. The apparent ability of the mind to provide surprising answers and unexpected insights when to all intents and purposes, the brain has been ‘switched off’, is echoed by the half-joking comments of today’s computer programmers about their software misbehaving when the hardware is switched off.
While these concerns are fairly recent and date only as far back as the construction of fourth-generation computers, it is a fair assumption to make that given slightly different tools with similar functions, people with similar ambitions will largely replicate both each other’s successes and problems.
The brain has been mankind’s oldest tool, bent to the same problem-solving tasks as modern day computers and their attendant programmers. So it should not be surprising when the brain’s ‘software’ is capable of problem-solving even when the ‘wetware’ has been apparently switched off.
Company employees of the software giant Microsoft, humourously refer to inexplicable glitches caused by apparently inert software as ‘gremlins in the machine’. But the ‘gremlins’ as a quick jaunt through the history of magic, which has always had the brain and its function on centerstage, will show, have been there for a very, very long time.
Scientists, in general however, and mathematicians in particular, have always prided themselves on the fact that they don’t need to resort to such ‘unscientific’ methods in order to transport their minds into other worlds. Over the years they’ve evolved their own means of taking physically impossible jaunts through etheric worlds and, to the chagrin of yogis and mystics, have also managed to get paid for it. But before we look at their techniques it’s good to acknowledge that even the staunchest advocates of the scientific method have to sleep sometimes, and when they do, what they dream about makes for some very interesting assumptions.
One wintry day in 1865, in the clogged with horse-drawn buggies streets of Vienna, a notable German chemist by the name of Friedrich Kekulé, while waiting for his driver to take the buggy out of a traffic-jam, fell into a tired snooze.
He was tired because for the past few months he’d been working on a most vexing problem: that of discovering how exactly the chain of carbon atoms are linked in the benzene molecule.As he snoozed, he dreamt of carbon atoms in the form of dancing snakes, and as he watched (in his dream) their taunting dance, they all joined hands and formed a circle.
The discovery of the cyclical structure of the benzene molecule laid the basis for the foundation of organic chemistry and Kekulé, naturally, received all the credit for it. After all it had been his dream.
His closing words at the convention where he presented his findings were: “Let us learn how to dream gentlemen, and then perhaps we’ll learn to discover the truth!”Shamelessly I’ll use this classic example to hark back to my earlier analogy of the brain as a computer and the mind as the software that’s ran on it. The apparent ability of the mind to provide surprising answers and unexpected insights when to all intents and purposes, the brain has been ‘switched off’, is echoed by the half-joking comments of today’s computer programmers about their software misbehaving when the hardware is switched off.
While these concerns are fairly recent and date only as far back as the construction of fourth-generation computers, it is a fair assumption to make that given slightly different tools with similar functions, people with similar ambitions will largely replicate both each other’s successes and problems.
The brain has been mankind’s oldest tool, bent to the same problem-solving tasks as modern day computers and their attendant programmers. So it should not be surprising when the brain’s ‘software’ is capable of problem-solving even when the ‘wetware’ has been apparently switched off.
Company employees of the software giant Microsoft, humourously refer to inexplicable glitches caused by apparently inert software as ‘gremlins in the machine’. But the ‘gremlins’ as a quick jaunt through the history of magic, which has always had the brain and its function on centerstage, will show, have been there for a very, very long time.
Sunday, May 20, 2007
It's all a dream
The very fact that we can dream events which are lifelike, and on occasion, can be precognitive, begs the question: Where do dreams come from?
Trying to answer the very question physicist and science-fiction writer John Gribbin, seized upon the possibilities offered by two related theories: The quantum theory for describing the behaviour of matter at a sub-molecular level, and the many-worlds theory of John Wheeler.
The former theory implies that at a sub-molecular level, everything that is possible, also happens, while the latter, states something very similar, but on the scale of the entire universe.
So, according to Wheeler (and the quantum theory for micro-molecules) there is not just a single world, but an infinite array of all possible worlds, including some in which we do not exist at all. Everything that can possibly happen at every instant of the day and night does happen and statistical possibility is only dictated by the inability of our awareness to cross the divide between all these worlds and see that indeed this is so.
This divide, whatever it may be made of, is what restricts our awareness to a single world. The car, that nearly ran into the back of you on the motorway this morning, for example, did in fact ran into you, in one of those other worlds, only your awareness (and this is a thorny issue in its own right) was focussed on a world where that possibility did not materialise, which brings us full circle to the argument that the mind is capable of ‘shaping’ reality.
Gribbin says, that if the many worlds do exist ,in such an infinite array, then, occasionally our minds may be able to come in contact with our ‘doubles’ in these other worlds.To use a rather naive example, the three course meal you dreamt you were having, rather than being the result of your feeling a little peckish as you went to bed, may have been the result of your double’s activities in another world.
By the same token however, this double (or infinite number of doubles) must occasionally dream of our activities and puzzle where their dreams come from.
Wonderfully mind-bending staff as all this may be, its implications are clear enough. Either there is no such thing as fantasy and everything we can possibly imagine actually does happen (which puts paid to the concept of the creativity of fiction writers) or else we are all equally insubstantial.We, in our concrete, tangible, world enjoy no less a statistical probability to exist than the world of our dreams. To us, certainly, this world is solid enough, or at least it appears to be so. But to those inhabitants of those other myriads of parallel worlds we are just a dream, and the further away we move from the worlds on either side of us, the smaller becomes the possibility of our existence and the less substantial we become to those trying to envision us.
So, next time your head hits the pillow you may be heading not for the oblivion you think you deserve for having put up with the daily rote of traffic jams; cash-flow problems; and the constant wear and tear of work, but for a magical jaunt through space, time and the universe. Mathematicians of course, have been doing this for some time now. The beauty of it though is that they have been doing it without the benefit of sleep.
Trying to answer the very question physicist and science-fiction writer John Gribbin, seized upon the possibilities offered by two related theories: The quantum theory for describing the behaviour of matter at a sub-molecular level, and the many-worlds theory of John Wheeler.
The former theory implies that at a sub-molecular level, everything that is possible, also happens, while the latter, states something very similar, but on the scale of the entire universe.
So, according to Wheeler (and the quantum theory for micro-molecules) there is not just a single world, but an infinite array of all possible worlds, including some in which we do not exist at all. Everything that can possibly happen at every instant of the day and night does happen and statistical possibility is only dictated by the inability of our awareness to cross the divide between all these worlds and see that indeed this is so.
This divide, whatever it may be made of, is what restricts our awareness to a single world. The car, that nearly ran into the back of you on the motorway this morning, for example, did in fact ran into you, in one of those other worlds, only your awareness (and this is a thorny issue in its own right) was focussed on a world where that possibility did not materialise, which brings us full circle to the argument that the mind is capable of ‘shaping’ reality.
Gribbin says, that if the many worlds do exist ,in such an infinite array, then, occasionally our minds may be able to come in contact with our ‘doubles’ in these other worlds.To use a rather naive example, the three course meal you dreamt you were having, rather than being the result of your feeling a little peckish as you went to bed, may have been the result of your double’s activities in another world.
By the same token however, this double (or infinite number of doubles) must occasionally dream of our activities and puzzle where their dreams come from.
Wonderfully mind-bending staff as all this may be, its implications are clear enough. Either there is no such thing as fantasy and everything we can possibly imagine actually does happen (which puts paid to the concept of the creativity of fiction writers) or else we are all equally insubstantial.We, in our concrete, tangible, world enjoy no less a statistical probability to exist than the world of our dreams. To us, certainly, this world is solid enough, or at least it appears to be so. But to those inhabitants of those other myriads of parallel worlds we are just a dream, and the further away we move from the worlds on either side of us, the smaller becomes the possibility of our existence and the less substantial we become to those trying to envision us.
So, next time your head hits the pillow you may be heading not for the oblivion you think you deserve for having put up with the daily rote of traffic jams; cash-flow problems; and the constant wear and tear of work, but for a magical jaunt through space, time and the universe. Mathematicians of course, have been doing this for some time now. The beauty of it though is that they have been doing it without the benefit of sleep.
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