A personal interlude. Back when I was in college, like a lot of science and math students, I read Chaos, by James Gleick. I was fascinated by the subject. And, being a physics major with a minor in computer science, did more than my share of experimentation.

At the time, I was taking my second semester of Physical Anthropology. Why is a long story and not really relevant. But I'd already impressed the teacher. Anyway, we'd gotten to the section on population dynamics and growth models, complete with some of sample models. This was Tuesday. By Thursday, I'd already coded them up, slapped them on a supercomputer (being a part time sysadmin has its benefits) and run through the entire phase space of the models. That Thursday, I showed my professor exactly where the models went chaotic. I showed how certain levels of stress on populations could lead to nonlinear population sizes and pointed out this would naturally lead to bottlenecking and could be used to fuel punctuated equilibrium.

She offered me a slot in grad school on the spot.

I really think this argument is invalid. First, it is a gross misrepresentation of fractal geometry to state that they are artifacts of complex design. They are the results of iterative applications of simple rules. Second, it is a gross misunderstanding of Evolution to think this is somehow an unrelated phenomenom. Evolution itself is an iterative application of relatively simple rules. Granted, the rules are more complex than the z <- z^2 + c of the Julia set, they are far simpler than quantum chromodynamics. Third, to assume that evolutionary mechanisms are not subject to chaos or do not employ the odd bit of fractal geometry is a *huge* unsupported assumption, and one I personally contradicted in my first year of anthro.

AND once again, even if there is this alternate source of complexity, that merely supports Dawkins' ultimate argument from a direction he didn't even consider, rather than undermining it.

The thing about math is, we build it. We build it every time we choose axioms or consider special cases. There's no god out there even in a counterfactual space of conceivable gods that could make arithmetic or geometry, defined as we normally define it, work any other way. Now, it would be possible for a god to make the universe such that the axioms of geometry do not represent anything; that's not the same. And a sufficiently perverse god could interfere with our cognition to prevent us from defining it, or prevent us from properly realizing the consequences of the definitions, etc..

So, once you've picked a fractal generator, you've already defined the infinitely detailed result - the rest is just doing the arithmetic. Asking why that works is not a question of theology, nor of science.

And it doesn't have much to do with the fractals you find in nature, of which the asparagus fern you posted is more typical. And I really don't know why you see so much in it. If a stalks grows up more than out you get a cylinder; and if it branches, and those branches branch, and it keeps going for a while, you get something that looks like a fractal tree. Both are basic geometry in their own way.

Obviously since you've shown that image on more than one occasion, you think there is something profound about the latter shape. But to me it seems really obvious that self-replicating cells would give rise to configurations with self-repeating parts, things as simple as flowing water do the same, and it only looks complex through the lens of traditional circles-and-squares geometry. Probably the least impressive thing about a real tree is that it keeps branching; the real complexity is where it stops, and turns to forming its own customized leaves, ornate flowers, pollen, seeds, stoma, cellular, and chemical components - anything beyond the basic growth pattern.

Likewise for the snail, the pattern on its shell is neat and interesting, but at the end of the day it's window dressing on a much more impressive piece of architecture. In talking about fractals as a source of complexity in living things, you are focusing on one aspect of the mathematics and physics that apply to the world, and to me it seems nothing compared to the fact that they are nothing like the random results of mathematics and physics you see outside life.

It's really starting to bother me when you restate what I just said and act as though it disproved my statements. Please stop reading me through your pre-established mental lens of what you expect a person of faith to believe and to argue. I can't respond to you in any meaningful manner when your responses have so little to do with what I actually said.

And please also stop assuming you know more than me about a given subject because you read up on it back in college. I may not be a scientist, but I've been studying chaos theory for twenty-five years now. I think I understand it a little bit better than you seem to give me credit for.



I think you mean it supports his ultimate conclusion, not his ultimate argument. As such, I don't think this is a legitimate move. You can build a new and different argument towards the same conclusion if you so choose, but that doesn't mean you've rescued Dawkins' original argument. Furthermore, you haven't actually supplied the new argument, you're just assumed it. It's impossible to respond to, because the particulars of it aren't explicit.



This, again, is a new and separate philosophical argument --several, really --about mathematics and about God, and not ones that have intuitively obvious, universally agreed-upon resolutions.



This is a bit of a dodge. It works, more or less, for self-similar fractals, those can be constructed more or less at will in predictable ways. But fractals like the Mandelbrot have structures with no clear connection with the simplicity of the processes that illuminate them. We did not "build" the Mandelbrot, we discovered it --or at least, that would be my claim.



This is a very legitimate criticism of my position. It is true that the types of fractals we have so far found in nature are of the simpler, self-similar variety, and not the more interesting type discussed above.

With that said, I'm not sure you are giving those fractal structures enough credit. Fractal shapes have astonishing efficiencies both in terms of information storage and in terms of (for example) packing a large surface area into a small volume. In addition, one of the key features of fractals is that small change in the generating code can change one highly complex final structure into another, equally complex, completely different structure --I'm sure the potential utility to evolution is obvious.

I also think your distinction between what is found in life and what is found in the universe outside life --which is crucial to Dawkins, by the way --is overstated. Patterns like the Great Spot on Jupiter, or earthly weather patterns display some of the same kinds of interesting features that we associate most closely with life, despite being non-biological in origin.

There are people who have done the actual work to draw these connections and establish their importance. I don't have the citations in front of me at this second, but I can try to pull them together if desired --I'll need them for my final paper anyway.

Absolutely. By the same token, a sphere is really effective at packing a large volume into a small surface area, and hexagons at tiling a plane without gaps. Each is a really simple geometric object in its own way - spheres are easily defined by the locus of a point, binary trees by iteration, and hexagons as convex hulls - and evolution has made use of its particular characteristics.

What I don't understand is why I'm supposed to treat the iterative one as different from the others. The one reason you mention is that it's easy to tweak one structure into another, but from what I can think of in nature mostly starts and ends with branching, and it simply doesn't impress me. We live in a universe with roughly Euclidean geometry; expanding evenly makes sphere with high volume, and repeatedly dividing makes trees with high surface area, and both show up accordingly.

And let me take it a step further: what fractals introduce is all apparent or emergent complexity, patterns which can be very hard to analyze with traditional math, but are still the result of simple rules. This is very different from the kind of complex design biologists talk about, where complex patterns come about through complex rules.


This kind of distinction applies here too. Patterns like weather might display the odd life-like feature, but you are blind if you think they are the same kind, because these are all spontaneous structures, with ornate patterns but little information content. They are the result of conditions and to a large extent their nature is dictated by them. We can marvel at simple math allowing such things, but from a naturalist perspective, they are already explained by it.

The complexity in biology is very different. Once you look past the superficial geometric outline of a tree or snail, you find an enormous number of moving parts, tailored by countless chemical reactions, shaped by countless different proteins, coded for by an irregular polymer of unbelievably exacting sequence. External conditions destroy them or leave their stamp, but they are hardly artifacts of those conditions. Instead they are shaped by a huge amount of particular information, and we would be at a loss to find one suddenly appear without another tree or snail as a blueprint.

And that's before mentioning the key point from before, that these parts have apparent teleology. This is what complex design refers to, not simply the odd intricate geometry from simple rules, but these bundles of tremendously detailed information that shape bodies to do particular things well beyond what math or physics could imply in the absence of such information. That some special shapes like fractals and hexagons can appear without so much information may be interesting, but it is an obviously different point.

You can find a hexagon that spontaneously generated on Saturn, a tree-shape at the mouth of the Nile, and yet never a snail except where another snail has been. The former are obviously the sort of things you expect to explain with physics, the latter can only be from the history of the species. The latter is the gap in material explanations that evolution fills, what the argument you quote is about. By treating both as simply a question of "complexity" without distinction, you are conflating two entirely separate matters.

I think I can generate a basic structure of an alternative argument, that avoids the flaw you are describing in Dawkins' argument, from your and drachefly's posts, as follows. First, your description of Dawkins' argument:



Then I only need to modify step 3 to avoid the criticism you describe:

1. Explaining complex design (which for Dawkins is 100% of the time biological in direct or indirect origin) is the most important question.
2. The only legitimate reason for belief in God is being unable to solve that question.
3. There exists an actual, complete, wholly sufficient and scientifically supported answer to the question.
THEREFORE
4. There is no legitimate reason for belief in God.

Of course, there are still some pretty severe problems with step 2; but your criticism applies only to the original step 3, and is thus sidestepped by this modified step 3.

CCC nailed it. Kitoba, it's not sufficient to point out something relevant that's missing from an argument to disprove the argument. You need to find something that actually makes the argument invalid - that breaks the dependency tree. Nothing in his argument relies on Evolution being unique as an explanation for life, simply that it does suffice to explain life.

I was also using irreducible complexity to refer to the concept used by creation scientists, because that's the only concept I've ever heard of called irreducible complexity. That's why I was pointing out that it is not just the same thing as being complicated; nor the same thing as looking designed. If you think a genuinely irreducibly complex biological structure wouldn't make a mess of Darwinian evolution, then you've misunderstood something - I'm not sure what. Irreducible complexity is pretty much defined as something which could not gradually evolve.



Again - it's not merely complexity Dawkins is talking about, but apparent complex design. All sorts of things are complicated, but not all of them look designed. Not all of them are easy to talk about in terms of purpose. When discussing living organisms, however, it is. Biologists use teleological language all the time. When discussing mysterious organs or structures in living things, they say that we don't yet know what this is for. Dawkins is talking about things like the complex countercurrent system in the bloodflow the flippers of dolphins or the legs of storks, which limit heat exchange with the body, thus allowing them to hang out in cold water without cooling their internal organs much. You say this sort of complexity doesn't necessarily need an explanation, but it does if you want to understand anything about organisms. If you don't care about biology, or where species came from, then no explanation is required. But if you do, then of course it is.

I'm not trying to cut the conversation off, but I do want to take a moment out from the discussion itself to thank people for sticking with me through this. These last few posts in particular have really helped me illuminate for myself what I'm trying to establish, and the places where I'll need to put more work in to do so adequately.

I'm not prepped yet to do formal responses, but I'll line out the avenues I plan to pursue:

@drachefly - I do think Dawkins is committed to evolution in particular being unique as an explanation for life. In fact I'm starting to realize that is in fact the key thing I want to establish: Dawkins has philosophical commitments to the unique and universal explanatory power of evolution that exceed, and in some cases even contradict what can be scientifically established.

I definitely need to do some more work in order to make the argument stick, but this conversation has helped me understand what the missing pieces are in order to get there.

@Leo - I think there are strong reasons to see biological complexity ultimately as a subset of a larger universe of complexity that doesn't have a hard boundary at the edge of life. But again, I'm not currently prepared to demonstrate that. I'll try to get together some of the cites I do have later.

@waffle - Sorry for being so testy in my last post --posting on too little sleep again. I do think if you reread my previous posts, you'll find that the argument is much more in line with your stated point of view than you had realized.

Ok, but if that's your take I'd like to be clarify that I'm not saying there is any inherent hard boundary; the same physics govern both and if you go far enough back one developed from the other. I'm saying there is a wide gulf between what we see today, simply because living things have spent billions of years elaborating billions of bits of information stored in DNA, and non-living things don't have any comparable store to explain.

My quote misattributed to waffle in the opening post, and now I don't get an '@'. I'm starting to feel unloved.

Sorry caffeine. I noticed the misquote as well, but didn't want to point it out because this thread is way beyond me. And I have a tendency to destabilize these POOP threads as well.

@Caffeine Oops, sorry

I do think you're making legitimate points, it's just that I don't have much to say one way or another to them. I'm much more interested in the complexity aspect of evolution than the design aspect. Maybe that's something I need to spend some time and energy contemplating --I would say that my intuitions on the subject are very different than either Dawkins' or Paley's. Maybe that should be a more central and explicit part of my argument.

@SillyGreenMonkey

Wallace is certainly a central figure in evolution, but I've never heard him referred to in theological circles. I also am not aware of any evidence that he promoted an intelligent design theology. I'm not sure why you cited him, or assumed that there's any reason I wouldn't want to call him a "True Christian." If it isn't abundantly clear by this time, I'm largely in agreement with the Darwin/Wallace theory, just not with the Dawkinsian variant of it.

Re the mandelbrot was discovered:

Sure we created math, and then afterwards discovered, that it had potential, that we never even guessed.

But we also created saws, and discovered uses for them http://www.youtube.com/watch?v=SQ9C5XrWYlM.

If we ever create something that is good for only the task, we have designed it for, and has no other uses to discover, that would have novelity value.

I totally agree that he is, but his argument against the existence of God doesn't rely on that commitment.