2:30 PM

Here are a few notes from "Deep Simplicity" (2004) by John Gribbin.

Introduction: The Simplicity of Complexity

• "An atom, or even a simple molecule like water, is simpler than a human being because it has little internal structure; a star, or the interior of a planet, is simpler than a human being because gravity crushes any structure out of existence. And that is why science can tell us more about the behavior of atoms and the internal workings of the stars than it can about the way people behave." [p. 2]
  
  
• "... some systems ... are very sensitive to their starting conditions ..." [p. 2 - 3]
  
  
• "... feedback ... what a system does affects its own behavior." [p. 3]
  
  
• "... surface complexity arising out of deep simplicity." [p. 3]

Chapter 1 Order Out of Chaos

• "... the importance of comparing theories and models with experiments and observations of the real world" [p. 9]
  
  
• "the value of deliberately simplified models as descriptions of particular aspects of the real world" [p. 9]
  
  
• "There is an arrow of time built into the everyday world, and it seems to be closely tied in with the laws of thermodynamics and statistical mechanics" [p. 22]
  
  
• "second law of thermodynamics: ... the natural world can be described in terms of a great engine which converts heat into work, ... but there must always be some heat dissipated in the process ... spread out into the Universe at large, raising its overall temperature by a tiny bit. ... That is, the amount of useful energy is always decreasing." [p. 25]
  
  
• "Entropy measures the amount of order in a system, with increasing disorder corresponding to increasing entropy." [p. 26]
  
  
• "One of the key concepts is that of an attractor." This is a particular state (i.e. a type of equilibrium) that a system will move toward. This is what we mean we talk about order out of chaos.[p. 28]

Chapter 2 The Return of Chaos

• "... the idea of phase space, arose from the work of the Irish mathematician William Hamilton (1806 - 65)." [p. 42]
  
  
• "Phase space can be thought of as like a landscape , with rolling valleys, deep potholes, hills and mountains. The Hamiltonian allows mathematicians to analyse how the overall system changes as time passes ..." [p. 44]
  
  
• "... if a trajectory through a phase space representing the possible states of, say, three bodies returns to the same point in phase space that is has been to before, then the orbits themselves, no matter how complicated they may look, must repeat periodically." [p. 45]
  
  
• "But the key thing to take away from Poincare's work is the realization that under some circumstances (not all circumstances, but not necessarily rare circumstances, either) systems that start out from very nearly the same state can very rapidly evolve in entirely different ways." [p. 48]
  
  
• "The important point is that this limits our ability to predict the behavior of such systems. With a linear system, if I make a small mistake in measuring, or estimating, some initial property of the system, this will carry through my calculations and lead to a small error at the end. But with a non-linear system, a small error at the beginning of a calculation can lead to a very large error at the end of the calculation." [p. 49]
  
  
• "It is the question of precise determination of initial conditions that Lorenz drew attention to and which lies at the heart of modern understanding of chaos." p. 56 - 57]
  
  
• "The weather, it turns out, is sometimes more chaotic than at other times. When meteorologists run the numerical simulation these days, they don't just take the exact data from their grid points of observations as the raw material for a single forecast. Instead, to find out if the errors and uncertainties inherent in the observations matter significantly they usually run each forecast several times with slight variations in the starting conditions. If all the forecasts come out more or less the same, they know that the overall pattern of the forecasts can be trusted." [p. 57 - 58]