Complexity_ A Guided Tour - Melanie Mitchell [123]
Indeed, a general understanding of cascading failures and strategies for their prevention are some of the most active current research areas in network science. Two current approaches are theories called Self-Organized Criticality (SOC) and Highly Optimized Tolerance (HOT). SOC and HOT are examples of the many theories that propose mechanisms different from preferential attachment for how scale-free networks arise. SOC and HOT each propose a general set of mechanisms for cascading failures in both evolved and engineered systems.
The simplified models of small-world networks and scale-free networks described in the previous chapter have been extraordinarily useful, as they have opened up the idea of network thinking to many different disciplines and established network science as a field in its own right. The next step is understanding the dynamics of information and other quantities in networks. To understand the dynamics of information in networks such as the immune system, ant colonies, and cellular metabolism (cf. chapter 12), network science will have to characterize networks in which the nodes and links continually change in both time and space. This will be a major challenge, to say the least. As Duncan Watts eloquently writes: “Next to the mysteries of dynamics on a network—whether it be epidemics of disease, cascading failures in power systems, or the outbreak of revolutions—the problems of networks that we have encountered up to now are just pebbles on the seashore.”
CHAPTER 17
The Mystery of Scaling
THE PREVIOUS TWO CHAPTERS SHOWED how network thinking is having profound effects on many areas of science, particularly biology. Quite recently, a kind of network thinking has led to a proposed solution for one of biology’s most puzzling mysteries: the way in which properties of living organisms scale with size.
Scaling in Biology
Scaling describes how one property of a system will change if a related property changes. The scaling mystery in biology concerns the question of how the average energy used by an organism while resting—the basal metabolic rate—scales with the organism’s body mass. Since metabolism, the conversion by cells of food, water, air, and light to usable energy, is the key process underlying all living systems, this relation is enormously important for understanding how life works.
It has long been known that the metabolism of smaller animals runs faster relative to their body size than that of larger animals. In 1883, German physiologist Max Rubner tried to determine the precise scaling relationship by using arguments from thermodynamics and geometry. Recall from chapter 3 that processes such as metabolism, that convert energy from one form to another, always give off heat. An organism’s metabolic rate can be defined as the rate at which its cells convert nutrients to energy, which is used for all the cell’s functions and for building new cells. The organism gives off heat at this same rate as a by-product. An organism’s metabolic rate can thus be inferred by measuring this heat production.
If you hadn’t already known that smaller animals have faster metabolisms relative to body size than large ones, a naïve guess might be that metabolic rate scales linearly with body mass—for example, that a hamster with eight times the body mass of a mouse would have eight times that mouse’s metabolic rate, or even more extreme, that a hippopotamus with 125,000 times the body mass of a mouse would have a metabolic rate 125,000 times higher.
The problem is that the hamster, say, would generate eight times the amount of heat as the mouse. However, the total surface area of the hamster’s body—from which the heat must radiate—would be only about four times the total