by executing the appropriate sequence of machine instructions on whatever computer system one is using.

And having now identified the phenomenon of universality in the context of practical computing, one can immediately see various analogs of it in other areas of common experience. Human languages provide an example. For one knows that given a single fixed underlying language, it is possible to describe an almost arbitrarily wide range of things. And given any two languages, it is for the most part always possible to translate between them.

So what about natural science? Is the phenomenon of universality also relevant there? Despite its great importance in computing and elsewhere, it turns out that universality has in the past never been considered seriously in relation to natural science.

But what I will show in this chapter and the next is that in fact universality is for example quite crucial in finding general ways to characterize and understand the complexity we see in natural systems.

The basic point is that if a system is universal, then it must effectively be capable of emulating any other system, and as a result it must be able to produce behavior that is as complex as the behavior of any other system. So knowing that a particular system is universal thus immediately implies that the system can produce behavior that is in a sense arbitrarily complex.

But now the question is what kinds of systems are in fact universal.

Most present-day mechanical devices, for example, are built only for rather specific tasks, and are not universal. And among electronic devices there are examples such as simple calculators and electronic address books that are not universal. But by now the vast majority of practical electronic devices, despite all their apparent differences, are based on computers that are universal.

At some level, however, these computers tend to be extremely similar. Indeed, essentially all of them are based on the same kinds of logic circuits, the same basic layout of data paths, and so on. And knowing this, one might conclude that any system which was universal must include direct analogs of these specific elements. But from