Of Mice and Cities
15 September 2006
Type/Items(s): I New Discoveries defining Complexity, Scientific Sessions
Submitted by: Jim Rudolf (ICVolunteers)
Contributors: Gavin McClure (ICVolunteers), Suraj Ravindran (ICVolunteers), Randy Schmieder (MCART)
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Nature is a complex system that defies definition by mathematical formulas... or is it? Can certain biological processes be defined quantitatively revealing a certain simplicity? Similarly, can social organizations be modelled using a similar method, resulting in general formulas that define societal behaviour? Theoretical physicist Geoffrey West, president of the Santa Fe Institute (SFI), posed these questions in his presentation entitled "Searching for Simplicity in Complexity; Growth, Innovation, Economies of Scale, and the Pace of Life from Cells to Cities."
Dr. Geoffrey West, Santa Fe Institute, New Mexico, USA, began by asking the following question: Can we construct a quantitative general theory of biological phenomena applicable at all scales based on fundamental principles that capture the essential features of life? The essential features he refers to include growth, reproduction, mortality and aging, evolution, etc. In other words, does a set of biological laws exist, similar to Newton's laws of physics? His own answer to the question is "no." Life is the most complex system in the universe, beyond description via "simple" formulas. Having said that, modelling can be used to find similarities between diverse biological systems. |
B-movies may be fun, but the open circulatory systems of arthropods and real, physical limits on their scaling means they are mostly bad science. Image: Kobal Collection |
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Despite the complexity of life, simplicity can manifest itself in nature as a scaling phenomenon, what Dr. West calls the "universal scaling laws in biology." Given biological attributes in the small-scale, these laws can be used to predict those attributes in the large-scale. This was demonstrated by taking data on the metabolic rate and body mass of animals, and then plotting that data on a logarithmic scale. The result of the plot is a relatively straight line with a slope of 3/4. Repeating this mapping exercise with various mammals and birds results in a similar line, which demonstrates Kleiber's Law of metabolic rate being equal to body mass raised to the 3/4th power. This general formula can be used to determine an animal's metabolic rate based on its body mass, and vice-versa. This equation allows scaling in an extraordinarily simple way, and also demonstrates economies of scale in biology: One gram of mouse muscle is 1/3 as powerful as 1g of dog muscle, and is 1/9 as powerful as 1g of elephant muscle. In biology at least, small may be beautiful but large is more efficient.
Simplicity can also be found in complexity when the growth curves of different animals are plotted. Charting animal weight versus age shows roughly the same curve across different species, with a burst of growth during infancy and then reaching a plateau when the animal becomes full-grown. This general curve demonstrates a "unity of organisms," or a simplicity hidden in complexity. Other examples are not hard to find. The relationship between the radius of an animal's aorta and its body weight can similarly be plotted on a logarithmic scale, but in this case with an exponent of 3/8 for the animal's mass instead of 3/4. Perhaps not coincidentally, the 3/8 exponent also defines the relationship between the radius of a tree trunk and the tree's weight.
Another example of unity of organisms can be found in the realization that the total number of heartbeats in a lifetime is independent of body size, and is approximately 1 billion beats. That is, a small animal with high metabolic rate (and therefore high heartbeat rate) will, in its short lifetime, have on average the same number of heartbeats as a much larger animal with slower metabolic rate (and slower heartbeat rate) in its long lifetime. This is true for species as diverse as mice, humans and elephants. Due to the fundamental principles of biology, organisms have evolved to minimize energy dissipation and maximize the scaling of their area in their environment. This is especially remarkable because each animal species evolved in its own environmental niche, independent of other animals, but nonetheless arrived at certain similar characteristics that apply across species.
We see that at least some biological systems obey laws that can be generally described quantitatively. What about social organizations? Are there similar scaling laws? To what extent can social organizations be seen as "simply" an extension of biological systems? Can the same technique used to describe growth and metabolism also be applied to cities or armies?
Dr. West believes that it can. By plotting data comparing different attributes (number of gasoline stations, amount of road surface, the speed at which citizen's walk etc.) to a city's population, similar straight lines appear when the data is plotted on a logarithmic scale. When we compare biological and social systems, a "beta" coefficient accounts for a radical difference between their behaviours. Biological systems always have a coefficient less than one; for social systems, beta is always greater than one.
A coefficient less than one, found in biological systems, promotes economies of scale. It is driven by efficiency optimization, and results in a sigmoidal growth curve when mass is charted over time. In contrast, social organizations, having a coefficient greater than one, are driven by creation of information, wealth and resources. Its growth curve is exponential and tends towards infinity over time. Having a coefficient greater than one drives growth in a city, but what are the consequences for social organizations? When population growth is mapped against natural resource use, the growth curve tends towards infinity, as natural resource use increases exponentially over time. In the worst case, reaching resource limits would result in the collapse of a city.
Resource depletion can be delayed via technological innovation, which in effect shifts the curve in time and delays depletion to a later point in time. But avoiding collapse while at the same time demanding continuous growth requires continuous innovation, with ever-shorter "reprieves" as the innovation cycle must speed up as resource use increases. To generalize the resulting behaviour based on the beta coefficient, we see that a coefficient less than one results in a slowdown in the pace of (biological) life as size increases. For a coefficient greater than one, the pace of (social) life increases with increasing size.
Dr. West has demonstrated that simplicity can be found in complexity, by deriving mathematical formulas to describe some biological systems. Further, he has shown that the same approach can be used for some social systems. While these results are fascinating, some might find that trying to quantify social processes might end up by removing emotion. Geoff West answers that it's even more poetic to look at stars when you know what's behind their shine. To go one step further in the dialogue, could this work help social scientists to better understand our world and/or could social scientists help Geoff West in pursuing the simplicity in the complexity of social interactions ? |
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