As with all such documents, a revision history is included at the bottom.
There is an often-heard complaint against scientific naturalism that reductionism is insufficient to explain high-order complexity. One way I have heard this complaint expressed is, “If all we are is molecules in motion, then where do ethics come from? Which molecule tells us that murder is wrong?”
This jumps between different levels of description. Which gas molecule caused a hurricane? None is individually responsible. Weather is the emergent complex behavior of large numbers of molecules. Simple systems, when recursion is applied, naturally produce stunning complexity. Google “Wada basins” and the “Mandelbrot set” for examples.
Cell biology is an emergent phenomenon of chemistry. Multicellular organisms are emergent cell biology. Neural networks are part of multicellular organisms. Consciousness is emergent neural networks. Psychology describes consciousness. Sociology is emergent psychology. Sociology includes ethics. Asking for the molecule that determines an ethical question is ignoring at least four levels of complexity.
Reductionism… the hobgoblin of little scientific minds. This is the notion that all of sociology is psychology, that all of psychology is biology, that all of biology is chemistry, and that all of chemistry is physics. Further, reductionism is the notion that if we simply understand the underlying science then we will have a full grasp of everything that is important at the higher levels of complexity.
Clearly the laws of physics are all that we need to understand the way the world works, right? “Little” scientists fall into this trap. Or more precisely, young scientists do, after they discover the amazing explanatory power of science and before they grasp the ridiculous complexity of the real world.
More visibly, religious nonscientists often think that all nonreligious scientists fall into this trap. Clearly there is no way that everything all the way up to sociology can be explained away as “just physics,” so there must be a God who put it together, right? I can’t count how many debates I have listened to or read wherein a charge is leveled at a scientist or an atheist that “molecules in motion” can’t explain the mind, or ethics, or some other high-order concept. “Which molecule is the one that determines that murder is wrong?” The reductionist can’t point to that molecule, therefore God did it.
The argument that we must choose reductionism or God ignores a vital concept. Emergent phenomena, the idea that high-order complexity can, and does, result from lower-order simplicity, gives us that third option. Let’s first look at some examples of the origins of complexity from simplicity, and then we’ll examine what this implies for the reductionism vs. God debate.
Geometric optics, or the ways that light behaves when interacting with mirrors, lenses, prisms, and so on, has been well understood for a very long time. The simplest phenomenon in geometric optics is simple reflection, where a ray of light bounces off a mirror at an angle that is equal to the angle with which it hit the mirror. There is a very simple experiment that you can do yourself that combines this one rule with four of the simplest three-dimensional objects around, the sphere, to produce staggeringly complex images. Take four mirrored spheres, such as Christmas tree ornaments, and stack them like cannon balls. Shine a light, like a flashlight, onto the spheres, and look in the holes between the spheres. Maybe put colored paper across the holes you aren’t looking through. You’ll see images like figure 3.
Here, the reflections-of-reflections-of-reflections form incredibly complex, truly beautiful patterns that are hard to believe result from simply four spheres, three sheets of paper, and a flashlight. Further, there is significant order in this complex pattern. To quote from an article where this was reported, “The image captured by a camera exhibits many boundaries between different colors, like those between states on a map, Dr. Ott said. But in the fractal pattern created by the four balls, he said, a tiny circle placed astride any boundary between colors will always contain all four colors, however small the circle is drawn.”
One might almost say that such a pattern must have been designed, to have such inherent perfection. But while the arrangement of the balls and colored walls was in a sense designed, the pattern was not. This remarkable pattern, rather, is a direct consequence of the mathematics of recursion. We’ll get to the importance of recursion in a bit.
For our second example, we’ll look at something from pure mathematics, known as the Mandelbrot set. Take any complex number of the form x + yi (where i is the square root of negative 1). The goal is to determine whether that point, which can be plotted on an x/y graph, is part of the set or not. We’ll take a very simple function, but apply it recursively, to each point. If the recursive application of that function tends toward infinity, then that point is not part of the set; if it doesn’t (i.e., if it is “bounded”), then it is. Here’s the function:
zn+1 = zn2 + c
We start with z0 = 0, and c is the complex number we are trying to evaluate. So, z1 = c. Square it and add c to get z2. Square that and add c to get z3. And so on. So, if we plot each point with black if it doesn’t go off to infinity, and with a different color based on how long it takes to determine that the point goes off to infinity, we get a picture that looks like figure 4.
This image is probably the most famous fractal. Zooming in gives some startlingly complex images, despite how simple the equation specifying the set is. For example, look at figure 5.
Why is the result of this simple calculation so amazingly complicated? Recursion.
For the third detailed example, let’s look at a truly large-scale, complicated phenomenon: weather. The physical forces that underlie weather are simple and well-understood. The kinetic-molecular theory of gases hasn’t changed much since 1905. Similarly, the thermodynamics of the phase changes of water are quite well understood. The solar heat input to, retained by, transformed within, and emitted from the various components of the geosphere are conceptually straightforward. But despite how simple and well-understood these underlying physical phenomena are, complex, ordered weather patterns such as frontal systems, hurricanes, and so on are not readily apparent as outcomes of these basic-level phenomena. The interactions among the components of the geosphere are manifold, and, as you might guess, recursive. There is a reason that weather is only forecast out to about ten days; the effects of these recursive interactions make the problem intractable past that point.
In all three of these examples, there is extreme complexity resulting from simple rules. In none of those cases does it make sense to attribute the resulting complexity to God. In all of these cases, recursive application of simple rules leads naturally to complexity.
So, let’s go back now to that hobgoblin known as reductionism. Chemistry is not just physics. No, it’s a lot of physics. More importantly, it’s a lot of interrelated, recursive physics. Even if every one of the basic processes underlying chemistry is simply basic physics, the aggregate explanation of the higher level behavior involves more than just physics. It includes things like statistical mechanics, chain reactions, and the competition between kinetic rates determining reaction outcomes. Every one of these ideas, and many more besides, is predicable from the laws of physics, but to do so you need to include a theoretical level-jump. Information theory, statistics, and even in some cases chaos theory. No, chemistry is not just physics. It is physics writ large.
We can do a similar analysis with biology. Take cell membranes. These little structures are just, in the reductionist view, lipids. Simple chemicals. But because of the statistics of large sets of these chemicals in an aqueous environment, their lowest-energy configuration is a lipid-bilayer. Shake up the lipids at the appropriate concentrations in water and you will get cell membranes. Spontaneously. Why? It’s more than just chemistry. It’s chemistry plus information theory plus chaos theory plus statistics. Biology is chemistry writ large.
These level-jumps are hard to describe theoretically, but we have a few examples of doing it successfully. Getting chemistry from physics is a fantastically successful example of this, and we are getting much closer to being able to get biology from chemistry. Further, we are beginning to develop the outlines of how to get psychology from biology. Recursively interconnected neurons forming a network and coupled to the outside world is more than just biology. It’s biology plus information theory plus chaos theory plus statistics. Psychology is biology writ large.
Let’s connect these ideas in an analogy to the Mandelbrot set above. If physics is the functional formulation of the Mandelbrot set… the simple equations… then chemistry is the resulting set. What about biology? Well, imagine now taking the Mandelbrot set (chemistry) and doing something recursive on that. In mathematical terms, that is a prospect that is very simple to express, but so complicated that to my knowledge the expected result hasn’t even been addressed as a possibility yet by mathematicians. Is it any wonder that biology is so rich and complicated?
How many times do we need to do meta-recursion before we get consciousness? At least one more, from biology to psychology, although you might want to include evolutionary ecology before that last step.
Reductionism, at least the forms that don’t account for emergent phenomena, doesn’t work. It ignores the fact that complicated systems have properties that are dependent on both the underlying properties of the building materials and the structure determined by how they are put together. To take an artificial example, you cannot predict the properties of a building by looking only at the properties of the steel, glass, and rock that were used to make it. To take a natural example, you cannot predict the electrical conductivity properties of a copper wire by looking only at the properties of individual, isolated copper atoms. The hierarchical increases in complexity make all the difference.
So which molecule is the one that says murder is wrong? I hope you can see now how this is asking a question at the wrong level. A question about ethical behavior is at least four levels of emergent phenomena away from molecules. Asking that question makes less sense than asking which molecule of water caused a hurricane.
It is easy for ordered complexity to arise from simplicity. And very often that ordered complexity is stunningly beautiful, as is exemplified by the figures earlier in this essay. How can beauty arise in such cold, synthetic systems?
The more telling question is, “Why are we surprised that it does?”
- June 12, 2014: Added short summary of argument thanks to a suggestion by Tweedledum. Added cartoons to illustrate the arguments (figures 1, 2, and 6). Corrected some grammar.