Deep Simplicity by John Gribbin

• It’s only when many atoms are linked together in complicated and interesting ways that complicated and interesting things like people are produced. But this process cannot continue indefinitely, since if more and more atoms are joined together, their total mass increases to the point where gravity crushes all the interesting structure out of existence.
• 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 smaller than a human being because gravity crashes 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.
• Entropy measures the amount of order in a system, with increasing disorder corresponding to increasing entropy. Since we know that in the real world, disorder increases in any closed system (things wear out) as time pases, the inevitable increase in entropy defines a direction of time, an arrow pointing from the ordered past into the disordered future.
• The truth is, there is no such thing as an isolated system (except for the entire Universe), and no system is ever in perfect equilibrium. It may get very close to equilibrium--as close as you like, if you wait long enough--but the equilibrium is never literally perfect.
• A linear system is more or less equal to the sum of its parts; a nonlinear system may be either much more, or much less, than the sum of its parts.
• In essence we have already found the underlying simplicity from which chaos and complexity emerge--simple laws, nonlinearity, and sensitivity to initial conditions and feedback are what make the world tick.
• Resonance is a way of getting a large return for a relatively small effort, by making the effort at just the right time and pushing a system the way it “wants” to go.
• In a system that is sufficiently sensitive to initial conditions, it is always possible that, no matter how many digits we choose to work with, the entire future of the system may, as Lorenz discovered, depend significantly on the value of the next digit, the one we have in effect thrown away.
• The universe cannot, in principle, be predicted in all its detail; but, equally, time cannot, in principle, be reversed.
• The Peano curve is a line that is more than a line, “trying” to be a plane; the Cantor set is a line that is less than a line, “trying” to be a point.
• The key thing about complex numbers is that they are in a sense two-dimensional, whereas everyday numbers are one-dimensional.
• The very term “dynamics” tells us that it describes how systems change; yet ideas such as entropy were derived from calculations involving systems in equilibrium, where nothing changes. Equilibrium itself is of no intrinsic interest, because nothing happens there. But how things move toward equilibrium can be very interesting.
• The nearest a living thing ever gets to equilibrium is when it dies. The fact that something is dead is nowhere near as interesting as how it died--a premise on which the success of a whole genre of detective novels, the murder mystery, is based.
• If the objects were infinitely far apart, the total energy stored by the gravitational field linking them would be zero--essentially because the force is proportional to one divided by infinity squared.
• It is a fundamental truth about the way the Universe works that gravitational fields have negative energy, and the for matter concentrated at a point, this negative energy exactly cancels out the mass-energy of the matter.
• The most important fact about the Universe today is that it is expanding.
• If things are getting farther apart now, then obviously they were closer together in the past, and if we go back far enough into the past, everything was on top of everything else in a single lump, the Big Bang.
• By measuring the present expansion rate of the Universe and using the general theory of relativity, we can pin down the time that has elapsed since the Big Bang to around fourteen billion years.
• One of the greatest things about astronomy is that because light takes a finite time to travel through space, we see things far away as they were long ago. A galaxy ten million light-years away, for example, is seen by light that left it ten million years ago.
• Without going into details of how stars work, we can see that stars only exist because clumps of gas have been drawn together by gravity and became hot enough inside for nuclear fusion reactions to take place.
• A complex system is really just a system that is made up of several simpler components interacting with one another.
• When scientists are confronted by complexity, their instinctive reaction is to try to understand it by looking at the appropriate simpler component and the way they interact with one another. Then they hope to find a simple law (or laws) that applies to the system they are studying. If all goes well, it will turn out that this law also applies to a wider sample of complex systems (as with the atomic model of chemistry, or the way the laws of cogwheels apply both to bicycles and to chronometers), and that they have discovered a deep truth about the way the world works. The method has worked for more than three hundred years as a guide to the behavior of systems close to equilibrium.
• You do not need to invoke some special, rare, and peculiar, physical effect in order to explain why large earthquakes occur--they just do.
• Power laws always mean that the thing being described by law is scale invariant.
• Whenever new discoveries are made in science, there is a bandwagon effect, with people trying to explain everything in terms of their new enthusiasm.
• The same size triggers do not all cause the same size events.
• The point is that any single event might be a special case, and doesn’t on its own tell you anything much about the underlying cause of similar events, or likelihood of their recurrence, any more than studying a single earthquake tells you much about earthquakes in general or how often they occur.
• Interesting things happen at the edge of chaos, and feedback is an essential ingredient in what makes them interesting.
• Evolution is a fact, just as the elliptical shape of the orbit of a planet around the Sun is a fact. There is ample evidence of evolution at work, transforming one species into another, both in the fossil record and from studies of present-day life on Earth.
• The test of a good model is not how simple it is, but how well it provides insight into real systems. In atomic physics, for example, it is at first sight an almost ridiculous simplification to treat atoms as miniature solar systems, with electrons “in orbit” around a central nucleus.
• Spectroscopy is the process of analyzing the light from an object by splitting it up into the rainbow spectrum, using a prism or some other device, and looking at the lines in the spectrum produced by different atoms or molecules in the object being studied.
• The difference between a hypothesis and a theory is that while a hypothesis is an idea about how things might work, it has not been tested by experiment and observation. If a hypothesis makes a prediction (or better, a series of predictions) about the way a new experiment will turn out, or what new observations will uncover, and if that prediction is borne out by events, then the hypothesis becomes a theory.
• The story of life in the Universe is another example of surface complexity built upon foundations of deep simplicity. There is new compelling evidence that the Universe as we know it emerged from a hot dense state (the Big Bang) some fourteen billion years ago. The basic building blocks that emerged from the Big Bang were hydrogen and helium, almost exactly in the proportions 3:1. All of the other chemical elements have been manufactured inside stars and scattered through space when those stars swell up and eject material in the later stages of their lives.
• Carbon plays the key role in life, because a single carbon atom is able to combine chemically with as many as four other atoms at once (including other carbon atoms, which may themselves be linked to yet more carbon atoms in rings and chains), so that is has an unusually rich chemistry.
• Chaos: In science, chaos occurs when a small change in the starting conditions of a process produces a big change in the outcomes of the process.
• Complexity: In science, a complex system is one that is chaotic, and in which the way the system develops feeds back on itself to change the way it is developing.
• Emergence: The appearance of structure in systems as they become more complex. When the whole is greater than the sum of its parts.
• Entropy: A measure of the amount of disorder in the Universe or in some smaller system. Entropy always increases in the Universe at large. But order can arise in smaller systems that feed off energy from outside.
• Red Queen Hypothesis: A suggestion that in the living world, different species have to evolve as fast as they can in order to stay in the same ecological niche, because if they don’t, their competitors will evolve faster and displace them.