Deep Simplicity
From Patterns
Contents |
Deep Simplicity by John Gribbin
Closed vs. Open Systems
Gribbin argues that much of science concerns itself with systems at a state of equilibrium, since these systems are linear (effect proportional to the cause), allowing them to be studied and modeled with relatively simple tools. The second law of thermodynamics ("Energy spontaneously tends to flow only from being concentrated in one place to becoming diffused or dispersed and spread out.") applies to closed systems that are continually moving towards a state of equilibrium. Entropy (degree of disorder or lack of structure) increases, while the amount of useful (localized) energy is always decreasing.
Gribbin argues that interesting systems are not in a state of equilibrium - they are open systems through which energy continuously flows and is dissipated. Open systems can locally reverse entropy by creating structure or order. A living organism is an example. It survives through energy flows that ultimately derive from the sun. An organism that is at perfect equilibrium is a dead organism, which makes it much less interesting. At various points in the lifespan of the organism, it may maintain itself in a state near to equilibrium (a relative degree of stability, moderate energy flows, modeled using linear equations) or may be far from equilibrium (high growth rate of embryo, large energy flows, modeled using non-linear equations).
Self-Organizing Systems
Gribbin covers many aspects of complexity theory:
- systems of simple components can result in complex behavior that we cannot accurately predict (e.g. 3-body problem in Newtonian physics, fractals)
- simple laws can re-appear in large systems as chaotic behavior over many components is smoothed out
- non-linear systems can be very sensitive to initial conditions (even minor rounding in computer simulations can result in dramatically different outcomes)
- non-linear systems (vortices behind a rock in a stream, dripping tap) display 'period-doubling' as energy flows increase (stable/equilibrium, 2-state, 4-state, rapid transition to chaotic or turbulent behavior)
Gribbin argues that interesting things happen just before an open system enters a chaotic state. These systems can organize themselves, spontaneously creating structure. Examples include Benard convection cells that form a honeycomb pattern on a thin layer of oil which is slowly heated, or Belousov-Zhabotinsky reactions where a chemical mixture oscillates between two states (often indicated by color changes or regularly shifting patterns). These systems also demonstrate period-doubling as the rate of energy or reactant flow reactants increases
Gribbin suggests that self-organizing systems are characterized by:
- multiple, simple components that interact in simple ways
- interacting positive and negative feedback loops (checks and balances, maintaining system near to one of several possible state)
- iterative processes (which can introduce non-linearity)
- flows of energy passing through the system and being dissipated
Power Laws
When the magnitude of earthquakes is plotted against the log of the frequency, a straight line results. Earthquakes appear to obey a 'power law' where the frequency decreases as the magnitude increases. The relationship is non-linear - there are 10 times more magnitude 6 earthquakes than magnitude 5. In addition, a magnitude 6 earthquake releases 10 times more power than a magnitude 5 earthquake. The existence of a power law across a wide range of scales suggests the existence of an underlying mechanism that is 'scale invariant'.
For reasons that unclear, 'power law' relationships appear in many systems. Music and the spoken word exhibit power law behavior when the frequency and of different loudness levels is compared. These signals contain information, different from either 'white noise' or a pure tone. The percent of extinction measured in 4 million year intervals, the number of genera compared to the life space, or the frequency of cities compared to their sizes are all related by a power law. Studies and models of traffic jams similarly suggest a power law relationship between frequency and size (number of vehicles involved). This implies a small trigger can cause a large traffic jam. Paradoxically, it also suggests that traffic flow will flow more smoothly at high volumes if the top speed is reduced. <Gribbin does not provide an explanation, although it might be related to period-doubling and the fast transition to turbulence at high levels of energy flow.>
Criticality
Traditionally, it was believed that earthquakes where caused by stress building up between tectonic plates. When the stress became too high, all of the pent-up energy was released through the earthquake. Large stresses led to large earthquakes, and these would be followed by periods of relative calm. Per Bak and Chao Tang have proposed a theory based on a common mechanism, where stress between tectonic plates builds to a critical point, followed by release of energy through a series of quakes at multiple scales. However, the system remains near the critical state. This implies that a small trigger can cause a large earthquake, and large earthquakes could happen at any time (although at a lower frequency than small earthquakes).
Observations and modeling of sand (or rice) piles show a similar behavior as earthquakes in the Bak and Tang theory. As grains are gradually added to the pile, areas where the angle of the pile is critical start to appear. A grain falling in this area can trigger a local avalanche. As more grains are added, these areas of criticality start to form networks, and their density increases. A single grain may now cause cascading avalanches of varying sizes. However, these avalanches tend to be self-limiting as the density of areas at a critical angle diminishes. The pile therefore remains close to criticality, even though energy is constantly being dissipated by avalanches. As in the revised earthquake model, the system never 'resets to zero'.
Further analysis led to the discovery that an individual grain falling on the pile is not necessarily swept away in the avalanche. The grain may burrow into the pile. Any grain can stay within the pile for any length of time, and conversely, no grain remains in the pile forever. According the Gribbin, the mechanism underlying the cycling of grains through the pile is not well understood. It does suggest that the system has an influence on the behavior of component parts, while every component part influences the system. "There are no components that sit around and, essentially, do nothing."
Stuart Kauffman of the Santa Fe Institute and author of At Home in the Universe did a 'thought experiment' involving a large number of buttons randomly arranged on a surface. Randomly chosen buttons are connected by threads. If a button is already connected by a thread, a new connection is added. The size of the largest cluster depends on the number of connections between or buttons, but initially grows slowly. When the number of threads reaches roughly 50% of the number of buttons, the size of the largest cluster rises rapidly, representing a 'phase transition' between a simple/disordered state to a complex/ordered state. Additional connections do not have as large an impact, resulting in an 'S-curve'. Similar to the sand pile, there is a relatively narrow range where interesting things happen. What is less clear is why the system might remain within this transition state. In the threads/buttons model, adding additional threads has a cost that is not associated with comparable benefits. <The analogy may be flawed, since the threads/button exercise does not have a way to dissipate energy>.
Simulations by Kauffman suggest that the number of connections between nodes is critical. If there are too few connections, the system contains few states (attractors) and very short state cycles - the system 'freezes' and is not able to adapt. If there are too many connections, the number of states and the length of the state cycles is so large that the system displays turbulent or chaotic behaviour and has insufficient stability to be productive. Systems with two connections per node can support many nodes while still maintaining a manageable number of states and state cycles, roughly the square root of the number of nodes. Studies of organism complexity compared to the amount of DNA suggests that a similar relationship holds: the number of cells (states) is related to the square root of the amount of DNA, with each cell performing a limited set of chemical steps (state cycles).
Evolution
Gribbin argues that evolution is a fact that can be observed in the fossil record and living organisms. Natural selection is a theory used to explain the process of evolution, where individuals best suited to the environment as a whole (which includes other species) are more likely to pass on their genetic characteristics. Natural selection is based on three key concepts:
- offspring resemble their parents
- inheritance is somewhat variable
- there are more births than reproducing individuals, creating competition within a species for resources
Game Theory has been used to model relatively stable environments which can lead to an Evolutionary Stable Strategy (ESS). In the case of 'hawks vs. doves', neither extreme (all hawks, all doves) is stable. Although 'all doves' optimizes the resource gain compared to energy expenditure, introduction of a single hawk variant will destabilize the situation. On the other hand, an 'all hawk' environment requires excessive energy expenditure. The model suggests that a specific dove/hawk proportion is stable although significantly less than the theoretical optimal state.
In the real world, relationships are much more complex than the pair-wise dove/hawk model. However, the interactions are limited, in the same way as Introducing additional species results in more complex interactions, including "Red Queen" co-evolution between predators and prey. Even in this case, natural selection occurs within each species, although both species are continually evolving due to their interaction. Beneficial mutations can 'open up' a Evolutionary Stable Strategy, creating a ripple effect that pushes the system further from equilibrium. Selection pressures that reduce the number of connections between organisms isolates them from change, pushing the system away from turbulence and chaos. <this parallels Kay's strategies of control, isolate and adapt> Under the right circumstances, systems can remain near the 'edge of chaos'.
Gribbin introduces the idea of a 'fitness landscape', with organisms scattered across hills (attractors), gradually moving up the hills towards greater fitness through natural selection. In a stable fitness landscape, these hills would represent local maxima - even through higher hills may exist, organisms cannot reach them without achieving lower fitness levels (crossing a valley). However, in dynamic systems, the landscape is constantly changing. No survival strategy says 'best' forever. The fossil record suggests that species die out at random, unrelated to how long the species had survived. No species achieves an insurmountable edge over others, because all species are co-evolving, constantly changing the fitness landscape. However, species do appear to become better at evolving over time (<relates to Kay's comments about design as a dynamic process?>). Sex could be seen as a way for slower-breeding organisms to keep up with faster-breeding microbes and parasites.
Gribbin argues that evolution can occur at many levels, from genes to species and collections of species (co-evolution involving "building blocks"). Lotka (p227-228) has suggested that considering the evolution of systems (organisms and their environment) may simplify the problem when compared to analyzing individual components. Part of the reason may be the influence of the 'power law' - simulations systems have resulted in behavior very similar to actual extinction patterns, regardless of what factors kill off species (internal pressures, external forces of varying degrees of intensity).
Lovelock (p216) proposed that the way to look for life on other planets is to look for the attributes of life: is the atmosphere in a state of low entropy far from equilibrium, as demonstrated by reactive gases (oxygen and methane) as compared to stable gases like carbon dioxide. His 'Daisyworld' model suggested a method by which interacting feedback loops can cause white and black daisies to create moderate and relatively stable temperatures in spite of variations in solar energy (solar output has increased by 33-43% over the life of the solar system). The book ends with various examples of complex systems create and regulate conditions on Earth such that life can flourish, including the interaction of algae with formation of clouds and dispersal of nutrients from windblown dust to parts of the ocean far from land. How these self-organizing and self-regulating systems arose is not explained.
