Nevertheless, if one maintains the goal of performing specific well-defined tasks, there may still be a problem. For insofar as the behavior that one gets is complex, it will usually be difficult to direct it to specific tasks—an issue rather familiar from dealing with actual humans. … But a crucial point is that on their own such processes will most likely not be sufficient to create a system that one would readily recognize as exhibiting human-like thinking.

But does one really need a language that has the kind of sequential grammatical structure of ordinary human language? … Or perhaps it is a consequence of our apparent ability to pay attention only to one thing at a time. … At the outset, one might have imagined that human thinking must involve fundamentally special processes, utterly different from all other processes that we have discussed.

Thus, for example, the structure in codes 237 and 948 is the most common, followed by the one in code 1749. The only new structure not already seen in elementary rules is the one in code 420—but this occurs only quite rarely. … And indeed, even if one accepts this, there is still a tendency to assume that somehow what one sees must be a consequence of some very special feature of cellular automata.

But in one case a nested pattern is produced. … So this suggests that one might be able to get evidence about universality just by trying different possible encodings, and then seeing what range of other systems they allow one to emulate. In the case of the 19-color universal cellular automaton on page 645 it turns out that encodings in which individual black and white cells are represented by particular 20-cell blocks are sufficient to allow the universal cellular automaton to emulate all 256 possible elementary cellular automata—with one step in the evolution of each of these corresponding to 53 steps in the evolution of the original system.

But one of the major features of the new kind of science that I have developed is that it does not have to make any such restriction. … Knowing that universal systems exist already tells one that this must be true at least in some situations. … But before the discoveries in this book one might have thought that this could be of little practical relevance.

But as soon as one tries to think about them independent of the particular example of human intelligence, it becomes much less clear. … Indeed, as soon as one thinks of a system as performing computations one can immediately view features of those computations as being like abstract representations of input to the system. … And as it turns out this is quite similar to what happens if one tries to define the seemingly much simpler notion of life.

And normally this has made us assume that they must in effect just be some kind of radio noise that is being produced by one of several simple physical processes. … But if there are beacons that are intended to be noticed even if one does not already know that they are there, then the signals these produce must necessarily have recognizable distinguishing features, and thus regularities that can be detected, at least by their potential users. … And although I somewhat doubt it, one could certainly imagine that if one were to show data like the center column of rule 30 or the digit sequence of π to an extraterrestrial then they would immediately be able to deduce simple rules that can produce these.

And if one identifies a feature—such as repetition or nesting—that is common to many possible systems, then it becomes inevitable that this feature will appear not only when intelligence or mathematics is involved, but also in all sorts of systems that just occur in nature. … One might imagine that one could set something up—say the solution to a difficult mathematical problem—that was somehow easy to describe in terms of a constraint or purpose, but difficult to explain in terms of an explicit mechanism. … Can one perhaps use a signal that is a representation of actual data in, say, astronomy, physics or chemistry?

But if, as in the past, one tries to do computer experiments on continuous mathematical systems, then the situation can be different. For in such cases one must inevitably make discrete approximations for the underlying representation of numbers and for the operations that one performs on them. And in many practical situations, one relies for these approximations on "machine arithmetic"—which can differ from one computer system to another.

And starting with 1, the sequence of numbers one gets is 1, 3, 6, 9, 15, 24, 36, 54, 81, 123, 186, 279, 420, 630, 945, 1419, 2130, 3195, 4794, ... … But by changing the procedure just slightly, one can get much less regular growth. … If one starts with 1, then this procedure simply gives 1 at every step.