Order vs. Randomness

[Sword of Christ]

You have precisely balanced order to produce life but nature has some room to do it's own thing as well, evolution could have produced intelligent beings a little different to humans for instance.

[Rayaan]

I get that idea, I don't think it is so. We know many examples where we control the rules of a "game", and choose them to be extremely simple, and can observe emergent complexity. Think of the game of life with a certain size field. There is complete control over the rules, and they are just two instructions. Would you say that all possible resulting life-like complexity you get out of it if you start with all possible initial conditions (*) is encoded in those two simple algorithmic rules to the extent that these two rules are identical with these complex "worlds" which can result from them? I just don't think it is sensible to equate the two.

(*) I consider the union of all these games, thus eliminating the information content in any specific initial condition from the argument, reminiscent of many worlds QM

As you just demonstrated, atheists occasionally like to bring up John Conway's Game of Life to prove that biological complexity doesn't require an intelligent designer.

But there are two points to this argument that (ironically) turn the tables on themselves:

1. An important question that you should ask yourself is, how were the initial rules for the Game of Life created? Did its creator Conway just blindly make up those rules in a couple of seconds (almost without even thinking), or did he exert a lot of mental effort and experimentation behind the process?

The answer to the above, apparently, is that the creator chose a few simple but very carefully selected rules - after a long period of experimentation - by trying to simplify and incorporate von Neumann's mathematical models of self-replicating systems into a virtual simulation. This shows us that the four simple rules in the Game of Life required intelligent engineering, that the rules behind the simulation (initially at least) required a level of foresight, a plan, or a goal that one had to work under in order to be able to create them. Therefore, it would be counter-intuitive to think that the underlying laws of the universe generating complexity didn't require any foresight or planning behind them, unlike the Game of Life.

2. Even though the Game of Life is a conceivable analogy of a basic aspect in nature (i.e. complexity arising from simpler, fundamental laws), it is hardly useful in explaining the amount of depth and the layers of complexity that exist in the real world, considering that the physical universe is enormously larger and that the laws of physics are considerably more complex than just the four rules implemented in the Game of Life. Therefore, the similarities drawn between the Game of Life and the physical universe are extremely superficial.

Even something like this ...

http://www.newscientist.com/article/mg20...vaRxc7v7O9

is almost nothing compared to living cells.

Ok, I don't know whether they are real (on some days I'm a mathematical Platonist, on other days I'm not) but let's say it is so for the sake of argument.
Why then intelligence? Even with scare quotes, what justifies it?

Because even though there may simpler, fundamental rules that gave rise to complexity in the universe, it still implies an intelligent engineering behind them for reasons that I explained in my comments above. To put it in another way, the rules themselves are like "programs" in a computer that eventually produce complexity, and the rules or programs have to be selected very carefully and not randomly (especially in an extremely fine-tuned universe such as ours) which by abductive reasoning necessitates them to be the rules of an imperceptible foresight and intelligence as opposed to just being something totally arbitrary.

Secondly, according to the patternist philosophy of mind, patterns are foundational to mental information processing: "A mind is thus a collection of patterns that is associated with a persistent dynamical process that achieves highly-patterned goals in highly-patterned environments." The whole universe itself is a complex environment of patterns, i.e. patterns within patterns and so on, which is the characteristic of a mind according to patternist philosophy. Refer to the following post where I posted some sources that explain this idea:

http://atheistforums.org/thread-23665-po...#pid600425

[Alex K]

Cheers,

I get that idea, I don't think it is so. We know many examples where we control the rules of a "game", and choose them to be extremely simple, and can observe emergent complexity. Think of the game of life with a certain size field. There is complete control over the rules, and they are just two instructions. Would you say that all possible resulting life-like complexity you get out of it if you start with all possible initial conditions (*) is encoded in those two simple algorithmic rules to the extent that these two rules are identical with these complex "worlds" which can result from them? I just don't think it is sensible to equate the two.

(*) I consider the union of all these games, thus eliminating the information content in any specific initial condition from the argument, reminiscent of many worlds QM

As you just demonstrated, atheists occasionally like to bring up John Conway's Game of Life to prove that biological complexity doesn't require an intelligent designer.

But there are two points to this argument that (ironically) turn the tables on themselves:

1. An important question that you should ask yourself is, how were the initial rules for the Game of Life created?

Ok, so do I read you correctly that you concede that all we need to assume at some point to obtain the complexity of physics, life in the universe is a suitable set of simple rules? And you now shift your argument to: we need an intelligent designer to get these simple rules in the first place.

Did its creator Conway just blindly make up those rules in a couple of seconds (almost without even thinking), or did he exert a lot of mental effort and experimentation behind the process?

The answer to the above, apparently, is that the creator chose a few simple but very carefully selected rules - after a long period of experimentation - by trying to simplify and incorporate von Neumann's mathematical models of self-replicating systems into a virtual simulation. This shows us that the four simple rules in the Game of Life required intelligent engineering, that the rules behind the simulation (initially at least) required a level of foresight, a plan, or a goal that one had to work under in order to be able to create them. Therefore, it would be counter-intuitive to think that the underlying laws of the universe generating complexity didn't require any foresight or planning behind them, unlike the Game of Life.

Now that we have partly agreed that the necessary prerequisites to have complexity and life are reducible to a set of very simple rules, you seriously argue that this is a problem because they need an explanation, and yet, postulating a preexisting intelligent creator, which is a like bazillion times more complicated thing, is totally plausible and doesn't require a proportionally more elaborate justificiation? Come on.

2. Even though the Game of Life is a conceivable analogy of a basic aspect in nature (i.e. complexity arising from simpler, fundamental laws), it is hardly useful in explaining the amount of depth and the layers of complexity that exist in the real world, considering that the physical universe is enormously larger and that the laws of physics are considerably more complex than just the four rules implemented in the Game of Life. Therefore, the similarities drawn between the Game of Life and the physical universe are extremely superficial.

The "playing field" in nature is incredibly more fine grained than any simulation. The necessary rules which describe everything relevant for the purposes of this discussion, are all captured in the Standard Model of Particle Physics - a bit more elaborate than Conway's, but still fit on a coaster. It is a matter of quantity, not quality, that makes the difference here. Like the difference between the neural network in my text recognition software, and my brain.

Even something like this ...

http://www.newscientist.com/article/mg20...vaRxc7v7O9

is almost nothing compared to living cells.

Sure, it's almost nothing compared to living cells, because as I said above the playing field is much much more high resolution, and the rules a bit more elaborate. But think early replicators, even before RNA. Not as far away from this simulation as you'd think. The rest is darwinian evolution.

[Rayaan]

Ok, so do I read you correctly that you concede that all we need to assume at some point to obtain the complexity of physics, life in the universe is a suitable set of simple rules? And you now shift your argument to: we need an intelligent designer to get these simple rules in the first place.

...

Now that we have partly agreed that the necessary prerequisites to have complexity and life are reducible to a set of very simple rules, you seriously argue that this is a problem because they need an explanation, and yet, postulating a preexisting intelligent creator, which is a like bazillion times more complicated thing, is totally plausible and doesn't require a proportionally more elaborate justificiation? Come on.

I get why you are so puzzled by this, and I think the reason is mainly because you don't understand the complex relationship between simplicity and complexity, and how these two concepts themselves are what we fundamentally interpret as forms of mental information processing (as I shall explain below). All of this, once again, complements the notion that intelligence and order are not incidental but rather fundamental aspects of reality.


1. What is simplicity? Is simplicity something physical?

Obviously, no, simplicity is not something tangible, but rather it is a concept that is evoked in our minds because of the background knowledge that we have of more complex/complicated objects in reality. In other words, the idea of "simplicity" exists only because our thought processes simultaneously relate it with the idea of "complexity." They are both concepts that are mutually intertwined because they are relative to each other.

Something "complex" requires more information to describe and something "simple" requires less information to describe, but again, the "less information" and the "more information" are not identifiable except in terms of the relationship that the two concepts have in our minds.

2. The ultimate simplicity that describe the universe has to be the most sophisticatedly simple.

As strange as this may sound to you, my perception is that the "simple" rules already have all the complexity encoded within them. It's just that the complexity is more hidden from us because the complexity is in a "compressed" state (i.e. inside the simplicity). Therefore, no matter how much scientists believe that it's possible for them discover the simplest and the "ultimate" law behind the universe, it's never going to happen because that fundamental law contains an even greater amount of surprise and mystery behind it - which conceals more and more information about itself - and thus it will always remain beyond our full comprehension.

The point is, there is a simplicity lurking behind all the complexity, and at the same time there is complexity lurking behind the simplicity, otherwise they wouldn't be what they are. So if there is a deep simplicity underlying everything in the universe (which I believe there is), then that would be the ultimate sophistication, the ultimate creativity. As Leonardo da Vinci very wisely noted in the same respect, "Simplicity is the ultimate sophistication."

3. Humans are intrinsically biased towards simplicity.

Our brains are inclined to search for simpler explanations over complex ones. And this process of finding the shortest and simplest description possible is a basic element of the cognitive ability that we refer to as "understanding" or "comprehension." Finding simpler descriptions of reality increases the depth of our understanding. As Einstein once stated, "If you can't explain it simply, you don't understand it well enough" ... but again, paradoxically, "understanding" itself is a complicated process.

But, let us see one way to understand what it means to "understand," as simply as possible. From an information-theoretic point of view, all forms of understanding are technically different forms of "data compression," which means that we transform a larger set of data or inputs that exist in our minds into a simpler and shorter set of data (i.e. to get an understanding). As the mathematician Gregory Chaitin said (quoted in Marcus Chown's The Never-Ending Days of Being Dead), "Understanding is compression," and then he says, "Ockham's razor is simply saying that the best scientific theory is the most compressible."

This approach to epistemology fits perfectly with the patternist philosophy of mind as well because data compression (or understanding) is the same thing as the act of linking things together by identifying patterns around us. I read in a paper recently which argues that even our consciousness and our mental states are but elements of data compression that we experience subjectively.

4. The universe being the product of a "simple but sophisticated" law would be indistinguishable from a designed universe.

To explain that, here's a thought experiment:

Suppose that a scientist, by a feat of astounding genius (and some luck), discovered the simplest and the "ultimate" law behind life, the universe, and everything. But what was the mechanism that was necessary for him to be able to do all of this? Essentially, it was the orderly data compression carried out by his brain, which we interpret as understanding. Technically, however, understanding and the entire essence of understanding (or data compression) are one and the same. So, understanding = simplification = data compression.

But if you think about it, that fundamental law (or entity, force, or whatever) that he learned about must have data compression - the essence of understanding - as a feature encoded within itself in order for him to be able to understand anything in the first place. If the essence of understanding was not already already built into the simplest instruction (or law), then there would be no way for him to even conceive anything. So, even if you don't call it "God," "Yahweh," or "Allah," that fundamental law would possess self-awareness and understanding on a scale that would make it just as complex as an intelligent designer. Thus it would equally reasonable to think that the universe is a product of intelligent design.

5. Even the whole picture of physics is ultimately a mental consequent. As the physicist David Bohm said, "Physics is a form of insight and as such it's a form of art."

Therefore, if anyone tries to simplify the nature of the physical world to the simplest thing possible through the study of physics, then he will never succeed in proving it to be simpler than the mind because mind and physics are inextricably connected; mind and physics are bound together. So such a goal would be like using his mind to escape his own mind - which is impossible.

[Rayaan]

From an information-theoretic point of view, all forms of understanding are technically different forms of "data compression," which means that we transform a larger set of data or inputs that exist in our minds into a simpler and shorter set of data (i.e. to get an understanding). As the mathematician Gregory Chaitin said (quoted in Marcus Chown's The Never-Ending Days of Being Dead), "Understanding is compression," and then he says, "Ockham's razor is simply saying that the best scientific theory is the most compressible."

I came across another insightful paper today that elaborates on this model of epistemology, i.e. that all cognitive processes are essentially forms of data compression.

And then the physicist extends this compression-based model of the mind and says that, in some sense, 'simplicity' is equivalent to 'reality.'

What does this have to do with the elusive concept we call 'reality'? If 'reality' belongs to the realm of cognitive systems, then it must be firmly anchored on the concept of information, which is all cognitive systems, natural or artificial, have access to. In other words, reality is an information-based construct of our brains - a model - and one we could certainly call an illusion, too. And since, as we will argue, models are to represent information in simple terms, the notion of reality arises, ultimately, from the search for simplicity. In some sense 'simplicity' is equivalent to 'reality'.

Also, here are two great books which explain how a "deep" and "elegant" simplicity underlies all the myriad of complex interactions and seeming randomness that pervade the universe.

Deep Simplicity: Bringing Order to Chaos and Complexity (by John Gribbin)

Elegance in Science: The Beauty of Simplicity (by Ian Glynn)

[Angrboda]

2. Even though the Game of Life is a conceivable analogy of a basic aspect in nature (i.e. complexity arising from simpler, fundamental laws), it is hardly useful in explaining the amount of depth and the layers of complexity that exist in the real world, considering that the physical universe is enormously larger and that the laws of physics are considerably more complex than just the four rules implemented in the Game of Life. Therefore, the similarities drawn between the Game of Life and the physical universe are extremely superficial.

This is simply an argument from incredulity, and thus its conclusion is fallacious.

2. The ultimate simplicity that describe the universe has to be the most sophisticatedly simple.

As strange as this may sound to you, my perception is that the "simple" rules already have all the complexity encoded within them. It's just that the complexity is more hidden from us because the complexity is in a "compressed" state (i.e. inside the simplicity). Therefore, no matter how much scientists believe that it's possible for them discover the simplest and the "ultimate" law behind the universe, it's never going to happen because that fundamental law contains an even greater amount of surprise and mystery behind it - which conceals more and more information about itself - and thus it will always remain beyond our full comprehension.

The point is, there is a simplicity lurking behind all the complexity, and at the same time there is complexity lurking behind the simplicity, otherwise they wouldn't be what they are. So if there is a deep simplicity underlying everything in the universe (which I believe there is), then that would be the ultimate sophistication, the ultimate creativity. As Leonardo da Vinci very wisely noted in the same respect, "Simplicity is the ultimate sophistication."

In terms of the Kolmogorov-Chaitin concept of information, the measure of information is how tightly you can make the simplest expression which, when uncompressed, yields the original data set. "Sophistication" is not a concept in information that I am familiar with, but since you keep appealing to Chaitin and compressibility, this would seem to be the appropriate guess as to which framework you're using. (If you prefer Shannon and informational entropy, correct my misapprehension.) I think that while the rules are certainly an important component of the information in the universe, the number of potential states is also a factor in determining how much total information is present; thus you can't just ignore the size of the universe as a part of what allows for such immense complexity because in doing so, you are simply discarding information content because it is inconvenient to your argument. As best I can tell, what you're suggesting is that certain simplicities are themselves possessed of inherent complexity. Beyond the meaning inherent in the Kolmogorov-Chaitin definition of information, this idea seems incoherent.

[Rayaan]

This is simply an argument from incredulity, and thus its conclusion is fallacious.

Then what exactly does the Game of Life explain about the physical universe, aside from being a demonstration of complexity emerging from simple rules?

Just some cellular automatons moving around on a screen with no knowledge, feelings, awareness, nothing ...

In terms of the Kolmogorov-Chaitin concept of information, the measure of information is how tightly you can make the simplest expression which, when uncompressed, yields the original data set.

That sounds correct.

To put it in another way, the Kolmogorov-Chaitin complexity (also called algorithmic information or algorithmic entropy) is the size in bits for the shortest program that would yield the original uncompressed data set (or object) in question. A greater compressibility means that it has a greater simplicity behind it, while a lesser compressibility would mean that it is more complex than simple.

"Sophistication" is not a concept in information that I am familiar with, but since you keep appealing to Chaitin and compressibility, this would seem to be the appropriate guess as to which framework you're using. (If you prefer Shannon and informational entropy, correct my misapprehension.)

"Sophistication," "elegance," "beauty," "subtleness," whatever you call it ... these are all more or less subjective qualities that are often used by mathematicians when they refer to something that maximizes some measure of utility while minimizing the information content. In the same view, computer scientist Jürgen Schmidhuber in the following paper explains how compressibility is a key aspect of beauty and of things like art, music, science, creativity, novelty, jokes, etc., which are all complex.

Driven by Compression Progress: A Simple Principle Explains Essential Aspects of Subjective Beauty, Novelty, Surprise, Interestingness, Attention, Curiosity, Creativity, Art, Science, Music, Jokes

I argue that data becomes temporarily interesting by itself to some self-improving, but computationally limited, subjective observer once he learns to predict or compress the data in a better way, thus making it subjectively simpler and more beautiful. Curiosity is the desire to create or discover more non-random, non-arbitrary, regular data that is novel and surprising not in the traditional sense of Boltzmann and Shannon but in the sense that it allows for compression progress because its regularity was not yet known. This drive maximizes interestingness, the first derivative of subjective beauty or compressibility, that is, the steepness of the learning curve. It motivates exploring infants, pure mathematicians, composers, artists, dancers, comedians, yourself, and (since 1990) artificial systems.

http://arxiv.org/abs/0812.4360

I think that while the rules are certainly an important component of the information in the universe, the number of potential states is also a factor in determining how much total information is present; thus you can't just ignore the size of the universe as a part of what allows for such immense complexity because in doing so, you are simply discarding information content because it is inconvenient to your argument.

I haven't discarded information content nor the size of the universe, but essentially my point was that information - or even an infinite amount of information - without the existence of underlying rules (or programs) to control their future interactions would never be able to produce localized complexity all by themselves. Therefore, the rules are not just an important component of information but they are an indispensable component with regards to how information behaves (or to what is generally known as "computation" or "information processing").

As best I can tell, what you're suggesting is that certain simplicities are themselves possessed of inherent complexity. Beyond the meaning inherent in the Kolmogorov-Chaitin definition of information, this idea seems incoherent.

The Kolmogorov-Chaitin definition of information doesn't actually have an operational definition of what "simplicity" is. It is just a mathematical method of measuring the amount of complexity of a given data set or output which relies on how much it can be compressed (or simplified) in terms of the algorithmic information content. It has more to do with quantity than quality, so the idea that simplicities themselves possess an inherent complexity (in a qualitative/utility sense) is not necessarily in contradiction with such a definition.

Chaitin himself acknowledges that the practical incalculability of a data does not necessarily mean that it is truly random. So the "randomness" of any particular case is actually impossible to prove or disprove. There still may be an underlying order behind such seeming randomness, which would make them sophistacatedly simple.

There are a few other objections to the Kolmogorov-Chaitin concept of information when it comes to defining and measuring simplicity, one of them being that the process of data compression itself is a highly complex process since there are many different ways to do it (see Simplicity in the Philosophy of Science).

Data compression brings about analytic simplicity but only at the expense of being a complex phenomenon itself since it is inherently a manifestation of sophisticated "patterns" in spacetime that make up what we subjectively experience as "thoughts" and "comprehension." And that, once again, shows the paradoxical nature of simplicity.

[Angrboda]

I wasn't implying that your idea was in conflict with Kolmogorov-Chaitin. Your idea doesn't fit within the bounds of Kolmogorov-Chaitin's concept, thus it is original. Thus you need to support it with something, and saying that it's based on a subjective criterion doesn't make it any more coherent as an empirical concept, and likely less so. If your whole point is that, subjectively, the elegance of order arising from simplicity is great enough to warrant an inference to design, then that's not an empirical argument, but another argument from incredulity. My background is in mathematics, so while I appreciate the notion of elegance, I view that as more a property existing in a strange and disordered pattern throughout mathematical space. You're concentrating on one small area of that mathematical space and saying that the beauty you find in that space tells you something remarkable about that space; I look at all of mathematics, and, subjectively, tell you that it isn't remarkable that you can find pockets in all of math space with that combination of qualities. It's like arguments about numerology and the Koran, you're using finding a pattern after the fact as evidence of something special occurring during or before composition. That's just the Texas Sharpshooter fallacy: you've found a cluster of traits that look "special" and you've drawn a bullseye around them. It's simply not evidence of anything.

[Rayaan]

Thus you need to support it with something, and saying that it's based on a subjective criterion doesn't make it any more coherent as an empirical concept, and likely less so.

Ideas on simplicity and complexity (and the qualities that are attached to them) cannot be proven empirically because they are analytic concepts; they are in the realm of induction.

The idea that elegance is an aspect of simplicity/compressibility is indeed subjective but not irrational, even from mathematicians' point of view. I said that something is considered to be "elegant" in mathematics if it maximizes some measure of utility while minimizing the information content. If you think that this is something absurd, then go ahead and explain why you think so instead of telling me that I need to "support it with something" ... not to mention that I already posted two links that support the aforementioned view of simplicity (which you ignored), but here they are once again:

http://en.wikipedia.org/wiki/Mathematica...ion_theory

http://arxiv.org/abs/0812.4360

If your whole point is that, subjectively, the elegance of order arising from simplicity is great enough to warrant an inference to design, then that's not an empirical argument, but another argument from incredulity.

That was an inference. And just because an inference is "not an empirical argument" does not mean that it's an argument from incredulity. Non-empirical argument =/= argument from incredulity.

Oh, and since you're a theist (assuming you're not lying), what do you think would count as a "empirical argument" for design? Do you even know of any?

My background is in mathematics, so while I appreciate the notion of elegance, I view that as more a property existing in a strange and disordered pattern throughout mathematical space.

But to my knowledge, that particular view is clearly in conflict with Taoist philosophy as you claim to believe in. Taoism teaches quite the opposite (see below).

Trust in Nature as an Organic Pattern

The Chinese yin-yang conception of nature is an organic reproduction pattern of nature and the cosmos. Nature exists outside of and beyond human control. Taoists regard this human embedding in larger universal processes with wonder, awe, and deep appreciation.

In nature, there is an ordering - dizzying and exquisite in its variety - that exists endlessly. (Think of the infinitely proportioned, kaleidoscopic images of fractal geometry, and you'll begin to get a sense of the intricacy, beauty, and endless "scalability" of natural patterns in the Taoist view.)

This order, this series of resonances, is both indescribably vast and intricately interdependent. It is an order that includes other "makers' of order - like bees and humans. The associated notion from the poem "Desiderata" - that we are all children of the universe, on a par with the planets and the stars, and that the universe unfolds in the proper way whether or not we recognize it as doing so - comes close to providing a parallel with the Taoist reverence of nature and its patterns.

- The Complete Idiot's Guide to Taoism (p. 33)

And this:

Dao can be roughly thought of as the flow of the universe, or as some essence or pattern behind the natural world that keeps the universe balanced and ordered.

http://en.wikipedia.org/wiki/Tao#Descrip...he_concept


... and yet here you are (a Taoist) ironically telling me that you view elegance in the universe as more a property existing in a "disordered pattern" throughout mathematical space.

Or maybe I didn't understand something?

[Angrboda]

Thus you need to support it with something, and saying that it's based on a subjective criterion doesn't make it any more coherent as an empirical concept, and likely less so.

Ideas on simplicity and complexity (and the qualities that are attached to them) cannot be proven empirically because they are analytic concepts; they are in the realm of induction.

The idea that elegance is an aspect of simplicity/compressibility is indeed subjective but not irrational, even from mathematicians' point of view. I said that something is considered to be "elegant" in mathematics if it maximizes some measure of utility while minimizing the information content. If you think that this is something absurd, then go ahead and explain why you think so instead of telling me that I need to "support it with something" ...

Sorry for not following your links. I'm not interested in an in-depth debate on the subject. You suggest that you can increase utility while minimizing the information content. While there is a seeming elasticity between information content and compressed representations, according to Kolmogorov-Chaitin, that is an illusion. The minimum size of the smallest representation of a given amount of information is a fixed, though incomputable quantity. If you're accepting Kolmogorov-Chaitin, arguing that specific types of information content have better compressibility than others, you're simply confusing computability with actual quantification. In that case, you are in conflict with Kolmogorov-Chaitin. I really don't care all that much other than to suggest that you're appealing to information theoretic concepts in a way that is unsound. Design arguments have a much more substantial Waterloo when you get to the key inference. (I'd also suggest you don't understand the meaning of the term 'induction', as the way you've used it doesn't appear to conform to either the mathematical or philosophical meaning.)

If your whole point is that, subjectively, the elegance of order arising from simplicity is great enough to warrant an inference to design, then that's not an empirical argument, but another argument from incredulity.

Oh, and since you're a theist (assuming you're not lying), what do you think would count as a "empirical argument" for design? Do you even know of any?

By empirical I mean one in which you can provide robustly quantifiable probabilities under some form of Bayesian or other probability framework. Obviously, subjectively based arguments are hard to describe with any metric.

My background is in mathematics, so while I appreciate the notion of elegance, I view that as more a property existing in a strange and disordered pattern throughout mathematical space.

But to my knowledge, that particular view is clearly in conflict with Taoist philosophy as you claim to believe in. Taoism teaches quite the opposite (see below).

---

Trust in Nature as an Organic Pattern

The Chinese yin-yang conception of nature is an organic reproduction pattern of nature and the cosmos. Nature exists outside of and beyond human control. Taoists regard this human embedding in larger universal processes with wonder, awe, and deep appreciation.

In nature, there is an ordering - dizzying and exquisite in its variety - that exists endlessly. (Think of the infinitely proportioned, kaleidoscopic images of fractal geometry, and you'll begin to get a sense of the intricacy, beauty, and endless "scalability" of natural patterns in the Taoist view.)

This order, this series of resonances, is both indescribably vast and intricately interdependent. It is an order that includes other "makers' of order - like bees and humans. The associated notion from the poem "Desiderata" - that we are all children of the universe, on a par with the planets and the stars, and that the universe unfolds in the proper way whether or not we recognize it as doing so - comes close to providing a parallel with the Taoist reverence of nature and its patterns.

- The Complete Idiot's Guide to Taoism (p. 33)

And this:

Dao can be roughly thought of as the flow of the universe, or as some essence or pattern behind the natural world that keeps the universe balanced and ordered.

http://en.wikipedia.org/wiki/Tao#Descrip...he_concept

---

... and yet here you are (a Taoist) ironically telling me that you view elegance in the universe as more a property existing in a "disordered pattern" throughout mathematical space.

Or maybe I didn't understand something?

I'd say you don't understand either Taoism or mathematics sufficiently well.