Complexity and the paradigm of Wolfram's A new kind of science: From the computational sciences to the science of computation
Kovas Boguta · Complexity · 2005
echnological innovation often opens the door to new directions in science.When Galileo first turned a telescope to the heavens, he discovered that they could no longer be explained with simple arguments.When van Leeuwenhoek turned a microscope to a drop water, he unexpectedly found it teeming with creatures.In our present age, a new invention-the computer-is being used to explore the world of very simple computational systems.The unexpected complexity that is found in that world is the subject of Stephen Wolfram's A New Kind of Science [1].Its 1200 pages are a first pass at explaining all of the implications of this discovery.My goal here is much more modest: to trace out that branch which establishes a paradigm for making progress with complex systems.The extremely simple computational systems described in the book are capable of impressive complexity.And once one has seen the unprecedentedly clear examples of the kinds of computations and behavior they produce, one begins to wonder if the complexity we see in Nature is related.I believe it is.Nature, it seems, has been doing computation all along.It is only now that we have noticed.In retrospect, it is clear why complexity in nature is so common, whereas complexity as a subject of science is much more rare: the paradigm of science has since Newton systematically minimized the role of computation.In our present age, computer simulation is ubiquitous.But it is regarded as only a tool; otherwise available models are implemented on computers as a convenience.These models are uninformed by the computational realities of our universe and fail to leverage its power.This is because there is no core field dedicated to understanding what these realities are, nor has it yet been completely understood by science in general that they are relevant.A New Kind of Science is an effort at laying the groundwork for this field.It shows that there can be a pure science of empirically investigating simple computational systems.It argues that these systems are not somehow separate from the natural world, but in fact essential for understanding it.On a meta-level, it makes the case that the computational universe is an ultimately idealized analog of the natural one-just as rich, but in virtually every practical respect more suitable for basic research.Instead of being a science that only exists because of other fields, complexity theory can focus on the essence of the issue and stand on its own.