The Beginning of Infinity: Explanations That Transform the World

by David Deutsch

Fortunately, some of that complexity resolves itself into a higher-level simplicity. For example, we can predict with some accuracy how long the water will take to boil. To do so, we need know only a few physical quantities that are quite easy to measure, such as its mass, the power of the heating element, and so on. For greater accuracy we may also need information about subtler properties, such as the number and type of nucleation sites for bubbles. But those are still relatively ‘high-level’ phenomena, composed of intractably large numbers of interacting atomic-level phenomena. Thus there is a class of high-level phenomena – including the liquidity of water and the relationship between containers, heating elements, boiling and bubbles – that can be well explained in terms of each other alone, with no direct reference to anything at the atomic level or below. In other words, the behaviour of that whole class of high-level phenomena is quasi-autonomous – almost self-contained. This resolution into explicability at a higher, quasi-autonomous level is known as emergence.