Physics, Nature and Society: A Guide to Order and Complexity in Our World (The Frontiers Collection)
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This wide-ranging and accessible book serves as a fascinating guide to the strategies and concepts that help us understand the boundaries between physics, on the one hand, and sociology, economics, and biology on the other. From cooperation and criticality to flock dynamics and fractals, the author addresses many of the topics belonging to the broad theme of complexity. He chooses excellent examples (requiring no prior mathematical knowledge) to illuminate these ideas and their implications. The lively style and clear description of the relevant models will appeal both to novices and those with an existing knowledge of the field.
valid at many levels and in many contexts, which suggests looking at nature as a sum of systems or “objects” (galaxies, stars, organisms, macromolecules…) that, despite their diversity, have a lot in common. Each is made up of a very many parts—elements which are all the same or quite similar—that interact among each other and with the environment. Some questions then arise. Is the world we see a consequence of cooperation between the elements these objects are composed of? And if so, is there
appear is not uniform or even as before, but that it has a maximum (6) between two minimums (1), likened in this to a bell. Furthermore, if we repeat the game over and over, let’s say ten thousand times or more, using various die, let’s say ten or more, the histogram that we obtain ends up fitting perfectly to the Gaussian function with the mean and variance of the data. This is illustrated in Fig. 5.4. Fig. 5.4This histogram shows the number of times (vertical axis) that each total (horizontal
is Over The botanist Robert Brown (1773), in his efforts to understand fertilisation processes, was observing a suspension of pollen in water under the microscope, when he focused his attention on tiny jittering particles stored in the vacuoles of the pollen grains. Unexpectedly, those particles were describing an incessant and nervous movement, as in Fig. 5.6. The random strange dance, which he proved not to rely on external causes such as light or heat, also occurred with spores. Brown
Fig. 6.4. If we divide a segment of unit length in parts of length ℓ, we get n = 1/ℓ parts. In a square of unit area we can make n = 1/ℓ 2 small squares of side ℓ, and from a cube of unit volume we can get n = 1/ℓ 3 little cubes of side ℓ. In general, each case can be described by the general relation n = ℓ −D , where D = 1, 2, 3 is the corresponding dimension. That is, if we divide an object into equal parts with the same shape as the original one, a power-law relates the number n of parts we
(World Scientific, Singapore 1990); Pierre Peretto, An Introduction to the Modeling of Neural Networks (Cambridge Univ. Press 1992). For a comment on how recent theoretical and computational studies have contributed to our present understanding on how the brain works, see “Theory and Simulation in Neuroscience”, Wulfram Gerstner, Henning Sprekeler, and Gustavo Deco, Science 338, 60 (2012). 15.Warren S. McCulloch and Walter Pitts, “A logical calculus of the ideas immanent in nervous activity”,