Complexity of Nature
Ideas thus made up of several simple ones put together, I call complex; such as beauty,
gratitude, a man, an army, the universe - John Locke, English Philosopher (1632-1704)
IntroductionThroughout human history the complex patterns that appear everywhere in nature have been cause for wonder and fascination. We are puzzled, for example, about how intricate snowflakes can form in plain air, and our minds boggle at the complexity of even the simplest living systems. Scientists have learned a great deal about natural pattern formation in recent years. Mostly, however, we have discovered how very much remains to be understood.
Think about ice ferns on a window a frosty winter day. We know that the molecules that water is made from are quite simple. They behave like small bricks that attract each-other.Nevertheless, they form ice ferns, like those on the picture, when they are deposited on a cold substrate. The ice ferns are a direct result of the molecules' tendency to be deposited next to each other, that is to say their relative attraction. What appears to be simple step by step is still the origin of complicated shapes.almost like living plants.The point is that we could not have guessed these forms only by looking at a single molecule. A vast number of molecules are needed to form an ice fern, typically on the order of billions. This is an example showing that a simple rule, repeated many times over, gives a complicated but identifiable result, where the whole is more than the sum of its constituents.
The ice ferns on the picture are from a car window and look
The ice ferns on the picture are from a car window and look
The ice ferns build themselves up step by step as the water molecules deposit on the cold glass surface. This is complexity. There is no architect behind the ice ferns. The secret behind the ice ferns' complicated form must be hidden in the interplay between the individual water molecules.
The question is how. Nature is loaded with similar examples that simple rules on a small scale give complex results on a level visible to the human eye. These include cumulus clouds on a summer day, an oak tree's thousand branches, waves on an agitated sea, or the stripes of the tiger.
Where to Start the Description?
Our understanding of a complex system depends on at which level we start to describe it. We may look at our ice ferns in an electron microscope, which shows single molecules, and on this scale they appear regular and simple. Looked at by eye from a close range, complexity emerges, but at a longer distance, say 20 meters, only a white spot is seen, which again is rather simple.Complex systems may also be considered as units, which can be pieced together to larger systems. Many trees make a forest; many clouds make a cloud cover, and so on. In the case of the forest, a tree plays the role of a component -- a green dot or a green particle in a forest that is complicated at some level. Maybe it grows along the coastline shaped by straights and bays, or maybe there is room for rivers winding through the landscape. From a far distance the forest itself can play the role as "particle", which together with all the other forests on the earth constitutes a substantial part of the earth's biosphere.
Description of Complex Systems
A main challenge in the study of complex systems is to find a description by numbers
(preferably not too many numbers). Only when measurements can be compared with
theoretical calculations, and vice versa, are we able to judge whether an idea is right or wrong.
In order to do that, we need numbers. A famous class of observations, which let themselves describe by a single number, are fractals. When something is fractal it consists of parts of many different lengths, and we can put a number on how many of the smaller pieces there are in comparison to how many there
are of the larger pieces. This number is called the fractal dimension. For instance, in a cup of coffee, see
Figure , there exist large, medium and small bubbles. If the relative amounts of these bubbles may be described by a number, then the bubbles may have a fractal dimension.
Do you see what the image to the right in Figure shows? It
cut through red cabbage. The pattern is complex yet identifiable to the observer, but it is not clear that one
may put a number on it.
Wiring diagrams for complex networks
a, Food web of Little Rock Lake, Wisconsin, currently the largest food web in the primary literature5. Nodes are functionally distinct 'trophic species' containing all taxa that share the same set of predators and prey. Height indicates trophic level with mostly phytoplankton at the bottom and fishes at the top. Cannibalism is shown with self-loops, and omnivory (feeding on more than one trophic level) is shown by different coloured links to consumers. (Figure provided by N. D. Martinez). b, New York State electric power grid. Generators and substations are shown as small blue bars. The lines connecting them are transmission lines and transformers. Line thickness and colour indicate the voltage level: red, 765 kV and 500 kV; brown, 345 kV; green, 230 kV; grey, 138 kV and below. Pink dashed lines are transformers. (Figure provided by J. Thorp and H. Wang). c, A portion of the molecular interaction map for the regulatory network that controls the mammalian cell cycle6. Colours indicate different types of interactions: black, binding interactions and stoichiometric conversions; red, covalent modifications and gene expression; green, enzyme actions; blue, stimulations and inhibitions. (Reproduced from Fig. 6a in ref. 6, with permission. Figure provided by K. Kohn.)
Wings, Horns, and Butterfly Eyespots: How Do Complex Traits Evolve?
Throughout their evolutionary history, organisms have evolved numerous complex morphological, physiological, and behavioral adaptations to increase their chances of survival and reproduction. Insects have evolved wings and flight, which allowed them to better disperse , beetles have grown horns to fight over females , and moths and butterflies have decorated their wings with bright circles of colored scales to scare off predators . The way that most of these and other adaptations first evolved, however, is still largely unknown. In the last two decades we have learned that novel traits appear to be built using old genes wired in novel ways , but it is still a mystery whether these novel traits evolve when genes are rewired de novo, one at a time, into new developmental networks, or whether clusters of pre-wired genes are co-opted into the development of the new trait. The speed of evolution of novel complex traits is likely to depend greatly on which of these two mechanisms underlies their origin. It is important, thus, to understand how novel complex traits evolve.
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