Polynomial

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).

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”

Hi Bill…

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?

Warmest regards,

Karl

To find out where I sourced Bill’s article from, please click here.

OR to learn more about Daisyworld, please click here.