{"product_id":"deep-simplicity-isbn-9781400062560","title":"Deep Simplicity","description":"Over the past two decades, no field of scientific inquiry has had a more striking impact across a wide array of disciplines–from biology to physics, computing to meteorology–than that known as chaos and complexity, the study of complex systems. Now astrophysicist John Gribbin draws on his expertise to explore, in prose that communicates not only the wonder but the substance of cutting-edge science, the principles behind chaos and complexity. He reveals the remarkable ways these two revolutionary theories have been applied over the last twenty years to explain all sorts of phenomena–from weather patterns to mass extinctions.\u003cbr\u003e\u003cbr\u003eGrounding these paradigm-shifting ideas in their historical context, Gribbin also traces their development from Newton to Darwin to Lorenz, Prigogine, and Lovelock, demonstrating how–far from overturning all that has gone before–chaos and complexity are the triumphant extensions of simple scientific laws. Ultimately, Gribbin illustrates how chaos and complexity permeate the universe on every scale, governing the evolution of life and galaxies alike.“Gribbin takes us through the basics [of chaos theory] with his customary talent for accessibility and clarity. [His] arguments are driven not by impersonal equations but by a sense of wonder at the presence in the universe and in nature of simple, self-organizing harmonies underpinning all structures, whether they are stars or flowers.”\u003cbr\u003e–Sunday Times\u003ci\u003e \u003c\/i\u003e(London)\u003cbr\u003e\u003cbr\u003e“Gribbins breathes life into the core ideas of complexity science, and argues convincingly that the basic laws, even in biology, will ultimately turn out to be simple.”\u003cbr\u003e–Nature magazine\u003cb\u003eJOHN GRIBBIN\u003c\/b\u003e trained as an astrophysicist at Cambridge University and is currently Visiting Fellow in Astronomy at the University of Sussex. His many books include \u003ci\u003eIn Search of Schrödinger’s Cat\u003c\/i\u003e, \u003ci\u003eStardust, Schrödinger’s Kittens\u003c\/i\u003e \u003ci\u003eand\u003c\/i\u003e \u003ci\u003eThe Search for Reality Fitzroy\u003c\/i\u003e (with his wife, Mary Gribbin), \u003ci\u003eScience: A History\u003c\/i\u003e, and \u003ci\u003eThe Scientists\u003c\/i\u003e.Chapter One\u003cbr\u003e\u003cbr\u003eOrder out of Chaos\u003cbr\u003e\u003cbr\u003eBefore the scientific revolution of the seventeenth century, the world  seemed to be ruled by chaos in a quite different way from the way the  term is used by scientists today, but in the same way that most people  still apply the word. There was no suggestion that there might be  simple, orderly laws underpinning the confusion of the world, and the  nearest anyone came to offering a reason for the behavior of wind and  weather, the occurrence of famines, or the orbits of the planets was  that they resulted from the whim of God, or the gods. Where order was  perceived in the Universe, it was attributed to the response of  physical objects to a need for harmony and order to be preserved  wherever possible—the orbits of the planets and the Sun around the  Earth (thought to be at the center of the Universe) were supposed to be  circles, because circles were perfect; things fell downwards because  the center of the Earth was at the center of everything, the center of  symmetry in the Universe, and therefore the most desirable place to be.  Even when the philosopher Aristarchus of Samos, who lived in the third  century b.c., dared to suggest that the Earth moved around the Sun, he  still imagined that it must follow a circular orbit.\u003cbr\u003e\u003cbr\u003eThese examples highlight an absolutely crucial difference between the  science of the Ancients and the science of post-Galilean times. The  Ancient Greeks were superb mathematicians, and in particular they were  superb geometers, who had a very good understanding of the  relationships between stationary things. This geometry had its roots in  even earlier cultures, of course, and it is easy to imagine how this  first science may have arisen out of the practicalities of life in the  developing agricultural societies of prehistory, through the problems  associated with building houses and laying out towns, and the need, as  society became more complicated, to divide up land into fields. But the  Ancients had no understanding at all of how things move, or the laws of  motion. You have only to look at how puzzled they were by Zeno’s famous  paradoxes, such as the soldier who can never be killed by an arrow. If  he runs away, then by the time the arrow reaches the position he was in  he has moved; in the time it takes the arrow to cover that extra  distance, he can move a little farther; and so on.\u003cbr\u003e\u003cbr\u003eIn spite of the existence of people like Aristarchus, the  Earth-centered Universe remained the established image (what scientists  would now call a “model”) even after Nicolaus Copernicus published his  model of a Sun-centered Universe (but one still based on circles) in  1543. His book, De Revolutionibus Orbium Coelestium, had been  essentially completed in 1530, and much of its contents were widely  discussed before publication, leading Martin Luther to comment in 1539,  “This fool wishes to reverse the entire science of astronomy; but  sacred Scripture tells us that Joshua commanded the Sun to stand still,  and not the Earth.” Responding to similar criticisms, Galileo later  riposted: “The Bible shows the way to go to Heaven, not the way the  heavens go.” It was Galileo’s contemporary Johannes Kepler, using  observations painstakingly compiled by Tycho Brahe, who established,  for those with open eyes, that not only did the planet Mars move around  the Sun, but that it did so in an elliptical orbit, pulling the rug  from under the notion that the kind of circular perfection beloved of  the Ancient Greeks ruled the cosmos.\u003cbr\u003e\u003cbr\u003eEven to people who know little about science, or the history of  science, Galileo (who lived from 1564 to 1642) is famous today as the  man who turned one of the first telescopes on the heavens, found  evidence to support the Sun-centered Copernican model, and had a run-in  with the Catholic Church, which led to his conviction for heresy and  the suppression of his books in Catholic countries—which (of course)  led to them selling like hotcakes everywhere else. But he did much more  than this. It was Galileo, more than anyone, who laid down the  principles of the scientific method of investigation, which involves  comparing theories (or models) with the outcome of experiment and  observation, and it was Galileo who first came to grips with motion in  a scientific way.\u003cbr\u003e\u003cbr\u003eThe key to Galileo’s work on motion was a discovery he made while a  medical student in Pisa in 1583. During a boring sermon in the  cathedral there, he watched a chandelier swinging to and fro, and timed  the swing with his pulse. Galileo realized that the time it took for  the lamp to complete one swing was the same whether it swung through a  wide arc or a shallow one, and later experiments showed that the time  taken for a pendulum to swing depends on its length, not on how far it  swings. This is the basis of the pendulum clock, but even without going  so far as to build a clock (he did design one, later built by his son),  Galileo was able to use a pendulum as an accurate timekeeper when he  later carried out experiments to study the behavior of balls rolling  down a ramp. These experiments provide another insight into both  Galileo’s mind and the scientific method. He wanted to study falling  objects, to investigate the effect of gravity on motion. But falling  balls moved too fast for him to keep track of. So he rolled the balls  down an inclined ramp, realizing that this gave him a stretched-out and  slowed-down version of the way balls fall under gravity. Through these  experiments, Galileo developed the idea of acceleration. The velocity  (or speed) of an object tells you how far it moves in a certain amount  of time—say, one second. A constant velocity of 9.8 meters per second  means that in every second the moving object covers a distance of 9.8  meters. But Galileo found that falling objects (or balls rolling down a  ramp) move faster and faster, with the speed increasing each second.  Crucially, his experiments showed that the speed increases by the same  amount every second. This is uniform acceleration, and a uniform  acceleration of 9.8 meters per second per second means that, starting  from rest, after one second an object has a velocity of 9.8 meters per  second, after two seconds it has a velocity of 19.6 meters per second,  after three seconds it has a velocity of 29.4 meters per second, and so  on. I have chosen this particular example because 9.8 meters per second  per second is, indeed, the acceleration caused by gravity for a falling  object at the surface of the Earth; because time comes into the  calculation twice, it is called a second order effect, while velocity  is a first order effect. And this acceleration due to gravity explains  why pendulums behave as they do.\u003cbr\u003e\u003cbr\u003eGalileo did something else—something central to the story we tell in  this book. He realized that the balls rolling down his inclined planes  were being slowed down a little by friction. In fact, what he measured  was not a perfectly uniform acceleration. But he took the dramatic and  influential leap, astonishing for his time, of extrapolating from his  actual observations to work out how his balls would move without the  effect of friction, on some idealized, perfectly slippery slope. This  kind of extrapolation would be at the heart of the scientific  investigation of the world for the next four centuries. When  scientists—physicists in particular—tried to describe the world in  terms of mathematical laws, they formulated those laws to describe the  behavior of mythical objects such as perfectly hard spheres, which  bounce off one another without being deformed and roll along surfaces  without feeling friction, and so on. But, unlike the Ancient Greek  philosophers, they knew that their image of perfection did not  represent the real world. Armed with those equations, they could then  try to put in extra terms, correction factors, to take account of the  imperfections of the real world, allowing, say, for the effect of air  resistance on a falling object. Air resistance explains why on Earth a  hammer and a feather fall at different rates, while on the airless  Moon, as the Apollo astronauts demonstrated, they fall at the same  rate.\u003cbr\u003e\u003cbr\u003eAll of this helped Galileo to cast out of science another aspect of the  geometrical perfection that his predecessors had imagined in the real  world. Before Galileo, it was thought that when a cannon fired its ball  at some angle above the horizontal, the flight of the ball would  consist of a straight line as it left the muzzle, then it would follow  the arc of a perfect circle for a time, and then it would fall  vertically to the ground. Only the imagined perfection of straight  lines and circles was involved in the motion. Applying his discovery  that gravity produces a constant downward acceleration on the  cannonball, and allowing for the initial velocity of the ball out of  the muzzle, Galileo showed that the flight of the ball must actually be  a single smooth curve, part of a parabola, all the way to its target.  The same calculations showed that the maximum range for the cannon  (assuming the same charge of gunpowder and weight of shot) would always  be achieved when it was fired at an angle of 45 degrees upward from the  horizontal. These were practical matters of great importance in the  turbulent times Galileo lived in, and this kind of military work helped  establish his early reputation. Whatever philosophers and theologians  might say about perfection, armies in the field had no time to quibble  about the desirability of circular motion; all they wanted to know was  which way to point their guns to achieve maximum effect, and Galileo  told them.\u003cbr\u003e\u003cbr\u003eIt was a combination of Kepler’s discovery of elliptical orbits and  Galileo’s insights into both acceleration and the scientific method  that paved the way for the greatest scientific discovery of the  seventeenth century, and perhaps of all time: Isaac Newton’s universal  law of gravitation. Newton was born in 1642 and died in 1727. His great  work Philosophiae Naturalis Principia Mathematica, or just the  Principia for short, was written from 1684 to 1687, and published in  1687, but was based on ideas that he had developed twenty years  earlier, when he was a young Cambridge graduate about to become a  fellow of Trinity College, and had been forced to spend months at his  mother’s home in Lincolnshire when the University was closed because of  the plague. Like Galileo, Newton stressed the importance of comparing  theories and models with experiments and observations of the real  world, and always carried out relevant experiments himself, whenever  possible, to test his ideas. This is so deeply ingrained as part of the  scientific method today that it may seem obvious, even to  nonscientists, and it is hard to appreciate the extent to which, even  into the seventeenth century, many philosophers would speculate about  the nature of the physical world in an abstract way, without ever  getting their hands dirty in experiments. The classic example is the  argument about whether two different weights dropped from the same  height at the same time would hit the ground together—an argument that  rumbled on for decades among those abstract thinkers even after a  Flemish engineer, Simon Stevin, actually did such experiments with lead  weights dropped from a height of about ten meters, found that they fell  at the same rate, and published his results\u003cbr\u003e\u003cbr\u003ein 1586.1\u003cbr\u003e\u003cbr\u003eNewton also embraced and refined Galileo’s insight into the value of  deliberately simplified models (such as Galileo’s frictionless planes)  as descriptions of particular aspects of the real world. It is a key  feature of Newton’s work on gravity and orbits, for example, that in  his calculations of the effects of gravity he treats an object such as  Mars, or the Moon, or an apple, as if all its mass were concentrated at  a single point, and that provided you are outside the object of  interest, its gravitational influence is measured in terms of your  distance from that point, the center of mass of the object (which is  also the geometrical center if the object is a sphere). The alternative  would be to carry out a separate calculation for each atom in the Moon,  or Mars, or whatever object you were studying. In the Principia, Newton  proved that this is the case for spherical objects. He knew that the  Earth is not precisely spherical (indeed, he was able to calculate how  much the Earth bulges at the equator because of its rotation); but he  felt it was reasonable to assume a spherical Earth (and a spherical  Sun, a spherical Mars, and so on) as a first approximation, and  calculate the orbits accordingly. As it happens, later calculations  have established that, provided you are far enough away from them, even  very irregularly shaped objects do act, gravitationally speaking, as if  all their mass were concentrated at a point, but this doesn’t diminish  the importance of the idea of using idealized approximations to reality  where it is necessary, or helpful, to make the calculations more  straightforward.\u003cbr\u003e\u003cbr\u003eThere is, though, rather more to this particular story than meets the  eye. In the Principia, Newton proved the validity of treating the  gravitational influence of a spherical object as if all its mass were  concentrated at its center, using geometrical techniques that would  have been understood by the Ancient Greeks, and were certainly familiar  to Newton’s contemporaries. These calculations were difficult. But we  now know that well before he wrote the Principia, Newton had developed  (or discovered) the mathematical technique now called calculus, and  that this proof is very easy using calculus. Some scholars suspect that  Newton actually solved the problem using calculus first, and then went  through the painstaking process of translating everything into  classical terminology, to make sure that his contemporaries would  understand it. If so, he may, in a sense, have shot himself in the  foot, because by keeping quiet about his new mathematical technique, he  paved the way for a bitter wrangle with the German Wilhelm Leibniz, who  invented the technique independently (and gave it the name by which it  is still known). Leibniz had the idea a little later than Newton did,  but had the good sense to publish his work, which is partly why there  were bitter rows about priority (the bitter rows were also partly  because both protagonists were unwilling to make concessions about  sharing credit for their discoveries, and Newton in particular was a  rather unpleasant person, who had an arrogant belief in his own  abilities and a spiteful reaction to anyone he perceived as an  opponent). But the arguments over priority are of little concern here.  What matters is that calculus is a technique that makes it possible to  break up problems into tiny components that can be manipulated  mathematically and the results added up to give a solution to the  overall problem. In the case of the gravitational influence of a  spherical object, for example, the sphere can be treated as being  divided up (differentiated) into an infinite number of infinitesimally  small pieces of matter, and an equation describing the gravitational  influence of such a typical piece of matter in terms of its position in  the sphere can be written down.Author of The Scientists","brand":"Random House","offers":[{"title":"Default Title","offer_id":48233079374053,"sku":"NP9781400062560","price":29.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781400062560.jpg?v=1767724950","url":"https:\/\/k12savings.com\/es\/products\/deep-simplicity-isbn-9781400062560","provider":"K12savings","version":"1.0","type":"link"}