And as a result, it is reasonable to expect that this same mechanism should also occur in many systems in nature. Indeed, as I will discuss in this chapter and the chapters that follow, I believe that this mechanism is in fact ultimately responsible for a large fraction, if not essentially all, of the randomness that we see in the natural world.

But that is not to say that the other two mechanisms are never relevant in practice. For even though they may not be able to explain how randomness is produced at the lowest level, they can still be useful in describing observations about randomness in particular systems.

And in the next few sections, I will discuss various kinds of systems where the randomness that is seen can be best described by each of the three mechanisms for randomness identified here.

Randomness from the Environment

With the first mechanism for randomness discussed in the previous section, the randomness of any particular system is taken to be the result of continual interaction between that system and randomness in its environment.

As an everyday example, we can consider a boat bobbing up and down on a rough ocean. There is nothing intrinsically random about the boat itself. But the point is that there is randomness in the continually changing ocean surface that forms the environment for the boat. And since the motion of the boat follows this ocean surface, it also seems random.

But what is the real origin of this apparent randomness? In a sense it is that there are innumerable details about an ocean that it is very difficult to know, but which can nevertheless affect the motion of the boat. Thus, for example, a particular wave that hits the boat could be the result of a nearby squall, of an undersea ridge, or perhaps even of a storm that happened the day before several hundred miles away. But since one realistically cannot keep track of all these things, the ocean will inevitably seem in many respects unpredictable and random.

This same basic effect can be even more pronounced when one looks at smaller-scale systems. A classic example is so-called Brownian

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From Stephen Wolfram: A New Kind of Science [citation]