December 30, 2009
Basically I’ve just read this neat little blog… And I wanted to highlight it within another blog here, as I feel it beautifully illustrates the confusion that can arise when trying to understand the complex idea of the “whole” through terms of simple units of basic processes. One should never take literally the romantic notions of simplicity that mankind likes to use to describe nature’s tortuous flow. We should be continually on our guard against embracing these ideals without remembering what they really are… In this case, Daisyworld is nothing more than a tool which helped crystallise the notion that feedback to the environment can alter the forces of natural selection, something that has been described as ‘selective feedback’ (Lenton, 1998) and as ‘system-dependent selection’ (Lansing et al., 1998).
As I have written once before… From time immemorial, man has desired to comprehend the complexity of nature in as few elementary concepts as possible. And having forged the new scientific disciplines of Chaos and Fractal geometry, We have been able to transmute some of the complexity that We witness around us into simple yet ominpotent ideas that give us the chance to glimpse at the underlying order which lies behind an ancient and seemingly impenetrable process, one which seems to guide almost every flow of nature here on Earth… Chaos, which was once perceived to bear only total disorder and pandemonium, actually allows one to see similar patterns repeating themselves across various and sundry dynamical systems… Systems, that upon a first glance, might seem unattached/unconnected/unalike. But to a trained eye, and with brute force of computational calculation, one can yield patterns from within their flow that elude to the presence of attractor like basins. Thus, in today’s modes of understanding, the computer has truly become mightier than the pen… For it allows man to study the central ‘ideal’ underlying our Chaotic design in a ‘manageable’, if somewhat over-simplified, way – just as Euclid’s perfectly flat plane once allowed scholars to study the basic system of ‘ideals’ lying behind all geometric shapes and forms.
But, as mankind all too readily discovers time and again, ‘reality’ is obviously much, much, much more complex than these ‘ideals’ could ever truly demonstrate… So these ‘romantic’ tools are simply the toys with which we ‘infants’ play, allowing us to kindle the flames of a Knowing that will ultimately arouse and illuminate new and previously unseen concepts; concepts which lie hidden deep within the Universal Whole. For just as a child plays with models of cars and dolls, simulating adult behavior, until one day they realize and become what they have imitated for so long… So too Life will begin to sufficiently understand the fathomless flow of the Tao, so that we may ultimately release ourselves into the ever evolving currents of creation, and drift along its majesty, free from the infantile callowness that our cradle, planet Earth, has let us hang on to for so long…
Thus I present Bill’s blog, which I feel raises some very interesting and pertinent questions concerning James Lovelock and Andrew Watson’s classic computer simulation, “Daisyworld…” A simulation that was brought into being simply as a toy that might allow one to develop an understanding about how the weather here on Earth might regulate itself.
Musings On Daisyworld
James Lovelock and Andrew Watson’s classic computer simulation Dasiyworld is a major proof for the Gaia (“Earth as one organism”) hypothesis. In the simulation, a planet has only two species, white daisies and black daisies. The black daisies warm themselves; the white ones cool themselves. According to the simulation, when the planet’s temperature is cooler there is a predominance of black daisies, and when it warms the white daisies increase in number as the black ones decrease. The idea is that the combination of the white and black flowers serves to regulate the planet’s temperature to a certain extent. The Daisyworld planet’s temperature is more moderate than that of an empty planet because of this balancing effect. This has been used to “prove” the Gaia hypothesis because it highlights that fact that organisms can unwittingly work together to function as one large organism.
However, I feel I must deprecate this idea. Though I cannot refute the fact that organisms often work together as a single organism, there are too many random factors involved for this hypothesis to be true. Evolution itself is a random factor, brought about by the mutation of genes. A random mutation could easily create a new species that does not fit into “Gaia.” I suspect humans are the perfect example of this—how is it that Gaia would welcome a species that is psychologically unstable but can build nuclear weapons? Also, environmental or other external factors can clearly unbalance this cycle.
Because of all this, it is absurd to think that this kind of a relationship between species exist for more than a short period of time. Though this kind of symbiosis can occasionally occur, the idea that the whole planet follows this pattern seems a bit of a stretch.
And I posted the following response:
An Antidote To “Musings On Daisyworld”
Just read your article “Musings on Daisyworld.” And I couldn’t help but notice this particular part of your musings:
“A random mutation could easily create a new species that does not fit into ‘Gaia.’ I suspect humans are the perfect example of this—how is it that Gaia would welcome a species that is psychologically unstable but can build nuclear weapons? Also, environmental or other external factors can clearly unbalance this cycle.”
Bearing this in mind… I wanted to ask you a question.
If everything is natural i.e. mankind was produced by natural laws of physics, chemistry, nature, evolution and natural selection, to name but a very small few of the billions and billions and billions of processes that precluded our creation… AND which precluded all other life forms on earth too… Then… By who’s “meter” are you assuming a species “does not fit into ‘Gaia’”?
The reason why I ask this is… I fail totally to see the point of the question that you have asked here… Why should this be an issue? Why should we even ponder this? Im essence there is no true answer for this. It is a matter of perception. In many ways it is much like an ant, with all its miniscule capabilities and its own perceptive drives, asking “how is it that man would welcome “iced-cream” into a world where the average ambient temperature is 10 degrees C above the freezing point of water? For ice is unstable at such high temperatures, and tends towards melting!”
For an ant to wonder at this (if indeed an ant does wonder at such things), using its own perceptive stances of the miniscule is nothing more than the ant exercising its own egocentric views via a rhetorical question. For when the ant asks, “Why does man produce ‘iced-cream’ in temperatures that hamper the ‘iced-cream’s’ nature i.e. turns it from solid, ‘joyous’ iced scoops of colorful, creamy flavor, into a gooey, runny, warm mess… Thus why would man welcome it into his world?”, it is failing to understand the true nature of man. So what could the ant be missing?
Well… Despite the fact that this world, on the whole, does not provide “iced-cream” with a suitable ambient temperature at which to exist… I suppose there are many, many reasons why man would welcome “iced-cream” into his world. Most of these reason we, as human beings, may never know, OR even glimpse at, ourselves. But some of the reasons we do know, for sure, are things like: man enjoys cream. It’s soft, creamy texture is pleasing to our pallet. Plus it’s tasty. And when it’s “iced” it is a cooling thing to eat on hot days, as when ingested, it lowers our body temperature sufficiently to keep us cool. There are other deeper reasons behind man’s “likes” and “dislikes” too… Reasons which many of us do not even consider to question ever in our short lifetimes i.e. cream is fatty, which has high energy potential for our bodies, and fat can easily be stored for future energy needs… Man likes to remain cool, because the Glycolysis metabolic pathway and other bodily functions and related chemical reactions, all run better at cooler ambient temperatures than a hot stuffy day affords. AND then there are others, like… Man likes sweet things because sweet things denote the presence of sugars, which the brain (using 80% of the energy needs of the body) needs to remain active with i.e. think, ponder with and regulate the rest of the body…
So just imagine how an ant’s little six legged body, which has feelers, eyes and jaws with which to roam, perceive and chew its way around it’s environment… How could an ant understand what it is like to be a human? By a similar decorum… For a human to understand why Gaia would create an organism that can blow itself up with nuclear weapons (and possible destroy a lot of life on earth doing so)… Well… We would need to let go of our human understanding, and think like a “Gaian” would. However, this is a hard thing to do when one is only a humble, egocentric human being.
Buddha noted this when he reached enlightenment (or emptiness), and posited the Buddhist theory of Interdependent Origination.
I’m a mathematician/philosopher/musician, who is looking into chaos theory and the interdependency of variables within dynamical systems. And while I once used to avidly try to understand why things happen as they do… I’ve got to say… After 10 years of studying complex systems, the more I look at trying to understand the seemingly random nature of non-linear dynamical equations, the more I realize that it’s impossible to do so thinking like a human does… Rather than using reason, it’s better to look at abstract patterns within the dynamical system’s flow, and look for similarities between data sets… Why? Because randomness ultimately has no meaning… Random is random. Chaos is random, and thus seemingly unpredictable at best… When we try to marry up abstract ideas with infallible human logic, we sometimes ascribe meaning to something where no meaning really lies. Kurt Gödel and other philosophers demonstrated this beautifully.
However… Once I let go of the need to understand, I realized that there was some kind of underlying order interlinking most non-linear dynamical systems together. These patterns, while undiscernible through simple observation, primarily due to their unpredictable chaotic flows, gave rise to analogous shapes when analyzed under computer iteration i.e. Lorenz attractor like patterns plotted in 3D phase spaces… And these molds of chaotic flow, while precisely unpredictable, actually allowed me to gain a good general idea of the over all outcome of a system. Many of these patterns crop up time and again across a broad range of nonlinear dynamical systems, many of which don’t actually seem to be related to each other in anyway whatsoever… That is, they look unrelated only IF you think like a human being does.
Chaos does not preclude human logic or understanding… Chaos, while understood in very simplified terms, is still precisely unpredictable. When we ultimately understand it… IF we ever ultimately understand it… Then it would become predictable.
Thus… While we understand what chaos means in a very simplified manner i.e. we still use very simple data sets to model immensely complex, real-world, chaotic systems like the weather, or turbulence patterns within fluid flow… To get our models to even work in a ‘slightly’ refined way of real world happening is still at best a fiction.
I think what Lovelock and Watson’s classic computer simulation showed, more than anything, was a very over simplified version of a dynamical system i.e. a planetary system who’s overwhelming complexity (a complexity that resides within the simple non-linear dynamics of an isolated world) simply resides on nothing more than how two species of daisy interact, regulating temperature change, and affecting one another’s growth patterns. No doubt it’s very simple… Malignly so… But that’s the beauty of it. Complexity comes from simplicity. Lovelock and Watson’s simulation is the simple, little part of the whole, which gives the biggest clue as to how complex the real world system is.
Just like in the Zen story “God,” these individual parts are not an accurate representation of the whole. NOT IN THE LEAST! But when this simple idea is iterated out into other seemingly unrelated areas i.e. how the pH of the soil might also affect daisy growth, and how pH of the soil is regulated from the black and white coloration chemicals within the petals of the flowers (black produces a high, alkaline pH, while the white produces a low, acid pH, for example), OR how partial pressures of carbon dioxide, nitrogen and other atmospheric gases also affect their growth and spread patterns, etc… Then we can begin to marvel at the complete picture of the “elephant.”
When all of our “simple” points of view come together… And we see all of those little systems interlinking i.e. soil types, cloud cover, sun spots, etc… All of which, when iterated over and over again, show the shear enormous complexity of nature’s universal flow across the macroscopic and microscopic… Then we can see the whole. This is what Spinoza spoke of… “God, or Nature!”
Take this simplified idea of Daisyworld, and add another 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 variables into it… The majority of which are interrelated to one another indirectly, while only some might be directly related, and we “begin” to touch on the infinitely complex interrelationship of all systems here on earth, and in the universe. No doubt some species are interlinked in ways that are simply dipolar in effect i.e. perhaps in closed-off ecosystems, like in underground caverns… But, as you so rightly pointed out, this is not the case on the whole. Rather than simple duplexes, like the Daisyworld described in Lovelock and Watson’s simulation, things in our world are interlinked in intricate, cascading chains of complexity, forming vast multiplexes of dynamical systems… Multiplexes that are near on infinite in measure, and which would probably take the whole of mankind, and many, many, many Deep-Thoughts the lifetime and breadth of eternity to unravel.
Spinoza once said, that with a system so complex i.e. “God, or Nature,” the only “thing” that would ever be capable of grasping/knowing all its wonder and understanding its ultimate flow… Would be the system itself! For the system itself IS the totality of itself. Thus it can BE everything it is at all times. And as it unravels, it does what its design intended it to do. Thus it becomes omnipotent and omnipresent. We are parts of the whole, nothing more and nothing less. If we open try to understand the world/universe through man-made terms/notions, we can become as blind as the ant trying to understand “iced-cream.” We need to forget all we have learnt, having learnt it, and empty ourselves to begin to glimpse the Tao… To see past the dogmas of misunderstanding. We need to empty ourselves, and remain humble before “God, or Nature…”
So what Lovelock and Watson’s computer simulation essentially shows, is only just a fractured little bit of simplicity, within a manageable type of complexity. This gives us a taste for the system’s dynamic mode of interaction. It’s only one man-made romantic notion to demonstrate the essence of complexity within a multitude of self-similar multiplexing cascades. And, thus, with this simplicity grasped, one can then begin to reiterate this idea, over many different modes of interaction, to see how the totality of the whole’s unimaginable complexity interlinks into the divinely multifarious flow of creation… While mere men see only walls, floors and ceilings to a room i.e. we use our intellect to separate the whole into manageable bites sized parts (just the men feeling the elephant), Buddha saw the “ceiling, wall, floor, carpet, chair, table continuum,” where everything merged and was interdependent with everything else. Why I do my best to view the simple complexities from a “Buddha-like” point of view, I find the math that I do easier to simply DO… Doing without the need to understand.
Here, away from understanding, Buddha sat for the rest of his existence, free from the delusion of man’s own self-made suffering… And thus he was able to clearly see the super-fine weave on the complex tapestry of Life’s dynamical, interlinked threads, which were made up of fibers, made up of individual strands, made up of polymer like molecules, that were really strings of atomic structures, which were made up of electron and proton arrangements… Into the infinity, and out again, of existence.
This is ultimate wisdom (jñana in Sanskrit). This ultimate wisdom refers to a direct realisation which is non-dualistic, and contradicts the way in which we ordinarily perceive the world. The experience of ultimate truth or emptiness is beyond duality.
It is important to remember that emptiness here does not refer to nothingness or some kind of nihilistic view. Emptiness refers to the fact that ultimately, our day-to-day experience of reality is wrong, and is ‘empty’ of many qualities that we normally assign to it. Thus asking the question, “How is it that Gaia would welcome a species that is psychologically unstable but can build nuclear weapons?” is forged from nothing but mankind’s own self-imposed delusion.
Describing this non-dual experience in words is not really possible, as language is based on duality and contrasts. Trying to explain this experience – which contradicts our normal perception – is a bit like explaining colours to someone who is born blind; difficult to say the least.
Thus it is a similar story with Daisyworld and weather dynamics. Trying to understand chaos/unpredictability is like trying to describe why randomness is random. If we understood why randomness was random, it would become predictable… And as we have seen chaos theory has allowed mankind a certain amount of predictability for the totality of a system over long periods of time. However, within a higher resolution time-frame the system is still unknowable. Much in the same way, when we call nothing “nothing,” we make it something. But by calling nothing “nothing” we can grasp the idea of nothing as something.
Such is the dichotomy of true understanding… And here, dare I say, lies the way of Zen and the Tao.
No doubt… Before we can walk that path, a simplicity within understanding must be grasped to see the complexity of the Way. For once we grasp these basic “ideals,” then we can hope to begin to engage ourselves with the Way in which the Tao flows. But to impose our own dualist views onto the universe i.e. “A random mutation could easily create a new species that does not fit into ‘Gaia.’” is to misunderstand the nature of the universe. To glimpse the Tao, we must be like the drop of rain that gives itself to the ocean. When let go of what we think, and find emptiness in the totality of the whole (as Spinoza called it, “Nature, or God”), then we can truly begin to Know… Otherwise we will only muse upon man-made grooves.
Which reminds me… Whenever my uncle used to see me jumping ahead of the game while trying to build a wooden model tug boat, because I wanted to avoid doing the boring complex bits… Bits that seemingly had no purpose in their individuality… But non-the-less added up to the whole… “Small steps, boy. Small steps. For it’s all in those small steps taken each day that we will add up to the distance of our lifetimes.”
I hope that made sense… And I hope it sort of addresses the questions you’ve so pertinently raised… At least in some manner?
To find out where I sourced Bill’s article from, please click here.
OR to learn more about Daisyworld, please click here.
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Nature forms many patterns. Some are orderly in space but disorderly in time, others orderly in time but disorderly in space. Some patterns are fractal, exhibiting structures self-similar in scale. Others give rise to steady states or oscillating ones. Pattern formation has become a branch of physics and material science, allowing scientists to model the aggregation of particles into clusters, the fractured spread of electric discharges, and the growth of crystals in ice and metal alloys. The dynamics seem so basic – shapes changing in space and time – yet only now are the tools (i.e. computers and programs to run lengthy iterative ideas with) available to better understand them.
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It is a fair question now to ask a physicist, ‘Why are all snowflakes different?‘
Ice crystals form in the turbulent air with a famous blending of symmetry and chance, tapping into the special beauty of six-fold indeterminacy (due to di-hydrogen monoxide’s physical properties). As water freezes, crystals send out tips, the tips grow, their boundaries become unstable, and so new tips shoot out from the sides. Snowflakes obey mathematical laws of surprising subtlety, and it was impossible to predict precisely how fast a tip would grow, how narrow it would be, or how often it would branch. Generations of scientists sketched and catalogued the variegated patterns: plates and columns, crystals and polycrystals, needles and dendrites. The treatises treated crystal formation as a classification matter, for lack of a better approach.
Growth of such tips, dendrites, is now known as a highly nonlinear unstable free boundary problem, meaning that models need to track a complex, wiggly boundary as it changes dynamically. When solidification proceeds from outside to inside, as in an ice tray, the boundary generally remains stable and smooth, its speed controlled by the ability of walls to draw away the heat. But when a crystal solidifies outwards from an initial seed – as a snowflake does, grabbing water molecules while it falls through the moisture-laden air – the process becomes unstable. Any bit of boundary that gets out ahead of its neighbors gains an advantage in picking up new water molecules and therefore grows that much faster – the “lightening-rod effect”. New branches form, and then subbranches.
One difficulty was in deciding which of the many physical forces involved are important and which can be safely ignored. Most important, as scientists have long known, is the diffusion of the heat released when water freezes. But the physics of heat diffusion cannot completely explain the patterns researchers observe when they look at snowflakes under microscopes while growing them in the laboratory. The heart of the new snowflake model is the essence of chaos: a delicate balance between forces of stability and forces of instability; a powerful interplay of forces on atomic scales and forces on everyday scales.
Where heat diffusion tends to create instability, surface tension creates stability. The pull of surface tension makes a substance prefer smooth boundaries like the wall of a soap bubble. It costs energy to make surfaces that are rough. The balancing of these tendencies depends on the size of the crystal. While diffusion is mainly a large-scale, macrosopic process, surface tension is strongest at the microscopic scales.
Traditionally, because the surface tension effects are so small, researchers assumed that for practical purposes they could disregard them. Not so. The tiniest scales proved crucial; there the surface effects proved infinitely sensitive to the molecular structure of a solidifying substance. In the case of ice, a natural molecular symmetry gives a built-in preference for six directions of growth. To their surprise, scientists found that the mixture of stability and instability manages to amplify this microscopic preference, creating the near-fractal lacework that make each snowflake different and original. The mathematics came not from atmospheric scientists but from theoretical physicists, along with metallurgists, who had their own interest. In metals the molecular symmetry is different, and so are the characteristic crystals, which help determine an alloy’s strength. But the mathematics are the same: the laws of pattern formation are universal.
Sensitive dependence on initial conditions serves not to destroy but to create. As a growing snowflake falls to earth, typically floating in the wind for an hour or more, the choices made by the branching tips at any instant depend sensitively on such things as temperature, the humidity, and the presence of impurities in the atmosphere. The six tips of a single snowflake, spreading within a millimeter space, feel the same temperatures, and because the laws of growth are purely deterministic, they maintain near perfect symmetry. But the nature of turbulent air is such that any pair of snowflakes will experience very different paths. The final flake records the history of all the changing weather conditions it has experienced, and the combinations may well be infinite.
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For if we start to look at infinities, as Gregor Cantor did (see a BBC documentary called “Dangerous Knowledge“) i.e. the flea, on the back of the flea, on the back of the flea, ever smaller and smaller and smaller… Then we could start dividing up a single degree’s change in temperature into infinities… And if one then combines this ‘exacting’ variable with all the possible other infinite variables of humidity, impurity density, wind speeds, etc… Then perhaps we can begin to see the endless possibilities that allow each flake to be truly unique.
It is here that I feel a powerful metaphor exists for the way our conscious/unconscious minds and attitudes are shaped along our journey through everyday life. When we are born into this world, we enter with a small body and a (nearly) blank and highly sensitive mind. As we move through the currents of care and love that we receive from those who tend to our daily needs, so our minds too begin to accumulate these patterns of love, caring and joy, as well as the hurt and even neglect, that we will use to express ourselves later on in life. Just as the tiniest scales of moisture, temperature, wind speed, etc… affect the infinitely sensitive molecular structure of the solidifying water that proves crucial to the geometrical shape that each snowflake will become; so too we respond just as sensitively to our early experiences… Experiences which prove crucial to our future choices and directions that we will take in life. Love bolsters the stability we seek to grow from, that we learn and create with; while neglect forges an instability and needy yearning. Both the stability and instability within our mind sets are gradually amplified from their microscopic beginnings, creating a near-fractal lacework of memories and emotions, that oscillate like a ‘strange attractor’ does, making each person so individual and so unique.
I cannot stress enough how sensitive we all are as human beings to our initial conditions. We absorb all the subconscious expressions of those around us. Expressions that emanate from body language, subtle intonations in the way we speak to one another, as well as what we think. These expressions stretch back the course of one’s life. Just as the final “flake” records the history of all the changing “weather” conditions it has experienced in its brief voyage here on Earth, so too the character of a person relays the history of experiences that has “weathered” upon their consciousness and physical form. Like a growing flake that falls to earth, floating in the winds for an hour or more, the choices made by the branching tips (that surround the seeding crystal) at any instant, depend deeply on such things as temperature, the humidity, and the presence of impurities in the atmosphere… So the six senses of any human being, living, feeling and growing within the social and environmental spaces it inhabits, are shaped by the same emotions and energies as those that are being projected into the world around them. Just as the laws of growth for a snow flake are purely deterministic i.e. every event is causally determined by an unbroken chain of prior occurrences, so we too will maintain a near perfect symmetry to ideas and attitudes projected into our surrounding environment. The nature of life’s turbulent flow is such that any pair of humans will experience very different attitudes to one another within life’s flow.
According to the Buddhist theory of interdependent origination, body and mind are dependent upon each other. In order to keep the body pure and normal, one must abstain from killing and harming others, stealing another’s property, committing adultery, drinking and using addictive drugs. Speech must also be kept pure by abstaining from lying, verbal abuse, deceit, and the avoidance of idle talk. The suitability of words can be assessed by examining five pairs of antonyms: words that are suitable to their occasions and those not so suitable; words that fit the facts and those that don’t; words that sound pleasant and those that sound rude; words that are beneficial and those that are harmful; and words that are sympathetic and that those are hateful.
So something we should all remember is, these experiences that we provide to others always serve to create… They can create both positive and negative aspects of mind. So be mindful of your current situations and your attitudes towards life. Whatever words we utter should be chosen with care, for people will hear them and be influenced by them for good or ill. When our minds are filled with sympathy and compassion, they will be resistant to the negative cycles we experience. We should not really let callus, unruly, indulgent words pass from our lips, especially when these words grow out of feelings of anger and hatred. The words we speak should always be words of sympathy and wisdom.
Let us all be mindful of the initial sensitivity of our life’s force and direction. And let us respect the chaos within and use it wisely to inspire the ever changing and wondrous patterns of life to abound. Because, while all the patterns of nature and mind are equally as beautiful as the rest, we must understand that negative actions can just as easily propagate as positive ones. We don’t want to shorten life, as wars and misunderstanding seem to so often do. All life really is so special and unique here on Earth. We have all surely won the lottery of existence! And so it should be treasured and adorned with encouragement to grow and encourage growth.
I’ll leave you with a quote from Wilson “Snowflake” Bentley:
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“Under the microscope, I found that snowflakes were miracles of beauty; and it seemed a shame that this beauty should not be seen and appreciated by others. Every crystal was a masterpiece of design and no one design was ever repeated. When a snowflake melted, that design was forever lost. And just to think, that that much beauty was gone, without leaving any record behind…”
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P.S. Many thanks to Ms. C. J. Kingsley for pointing out the lack of acknowledgement to James Gleick’s work, which has now been rectified.