Posted by ProjectC

Complexity and science - from A New Kind of Science page 861 and 862.

Ever since antiquity science has tended to see its main purpose as being the study of regularities - and this has meant that insofar as complexity is viewed as an absence of regularities, it has tended to be ignoredor avoided. There have however been occasional discussions of various general aspects of complexity and what can account for them.

Thus, for example, by 200 BC the Epicureans were discussing the idea that varied and complex forms in nature could be made up from arrangements of small numbers of types of letters. And although its consequences were remarkably confused, the notion of a single underlying substance that could be transmuted into anything - living or not - was also the centerpiece of alchemy.

Starting in the 1600s successes in physics and discoveries like circulation of blood led to the idea that it should be possible to explain the operation of almost any natural system in essentially mechanical terms - leading for example RenĂ© Descartes to claim in 1637 that we should one day be able to explain the operation ofa tree just like we do a clock. But as mathematical methods developed, they seemed to apply mainly to physical systems, and not for example to biological ones. And indeed Immanuel Kant wrote in 1790 that "it is absurd to hope that another Newton will arise in the future who will make comprehensible to us the production of a blade ofgrass according to natural laws".

In the late 1700s and early 1800s mathematical methods began to be used in economics and later in studying populations. And partly influenced by results from this, Charles Darwin in 1859 suggested natural selection as the basis for many phenomena in biology, including complexity. By the late 1800s advances in chemistry had established that biological systems were made of the same basic components as physical ones. But biology still continued to concentrate on very specific observations -with no serious theoretical discussion of anything as general as the phenomenon of complexity.

In the 1800s statistics was increasingly viewed as providing a scientific approach to complex processes in practical social systems. And in late 1800s and early 1900s in effect avoided complexity by concentrating on propertiesand systems simple enough to be described by explicit mathematical formulas. And when other fields tried in the early and mid-1900s to imitate successes in physics, they too generally tended to concentrate on issues that seemed amenable to explicit mathematical formulas.

Within mathematics itself - especially in number theory and the three-body problem - there were calculations that yielded results that seemed complex. But normally this complexity was viewed just as something to be overcome - either by looking at things in a different way, or by probing more powerful theorems - and not as something to be studied or even much commented on in its own right.

(...)

With its strong emphasis on simple laws and measurements of numbers, physics has normally tended to define itself to avoid complexity. But from 1940, issues of complexity were nevertheless occasionally mentioned by physicists as important, most often in connection with fluid turbulence or features of nonlinear differential equations.

(...)

Watching the history of the field of complexity theory has made it particularly clear to me that without a major new intellectual structure complexity cannot realistically be studied in a meaningful scientific way. But it is now just such a structure I believe I have finally been able to set up in this book.

-- Stephen Wolfram.