Biology Reference
In-Depth Information
When mathematics was introduced into science it provided for the first time an abstract
framework in which scientific conclusions could be drawn without direct reference to
physical reality. Yet, despite all its development over the past few thousand years, mathe-
matics itself has continued to concentrate only on rather specific types of abstract systems -
most often ones somehow derived from arithmetic or geometry. But the new kind of science
that I describe in this topic introduces what are in a sense much more general abstract
systems, based on rules of essentially any type whatsoever.
One might have thought that such systems would be too diverse for meaningful general
statements to be made about them. But the crucial idea that has allowed me to build a
unified framework for the new kind of science that I describe in this topic is that just as the
rules for any system can be viewed as corresponding to a program, so also its behavior can
be viewed as corresponding to a computation.
Traditional intuition might suggest that to do more sophisticated computations would
always require more sophisticated underlying rules. But what launched the whole computer
revolution is the remarkable fact that universal systems with fixed underlying rules can be
built that can in effect perform any possible computation
....
But on the basis of many discoveries I have been led to a still more sweeping
conclusion, summarized in what I call the Principle of Computational Equivalence
(PCE): that whenever one sees behavior that is not obviously simple - in essentially any
system - it can be thought of as corresponding to a computation of equivalent sophistication
...
it immediately gives a fundamental explanation for why simple programs can show
behavior that seems to us complex. For like other processes our own processes of percep-
tion and analysis can be thought of as computation. But though we might have imagined
that such computations would always be vastly more sophisticated than those performed by
simple programs, the Principle of Computational Equivalence implies that they are not.
And it is this equivalence between us as observers and the systems that we observe that
makes the behavior of such system seem to us complex [pp. 4-6]. (5.2)
The key unifying idea that has allowed me to formulate the Principle of Computational
Equivalence is a simple but immensely powerful one: that all processes, whether they are
produced by human effort or occur spontaneously in nature, can be viewed as computations.
...
it is possible to think of any process that follows definite rules as being a computation -
regardless of the kinds of elements it involves
.
So in particular this implies that it should be possible to think of processes in nature as
computations. And indeed in the end the only unfamiliar aspect of this is that the rules such
processes follow are defined not by some computer program that we as humans construct
but rather by the basic laws of nature
.
But whatever the details of the rules involved the crucial point is that it is possible to
view every process that occurs in nature or elsewhere as a computation. And it is this
remarkable uniformity that makes it possible to formulate a principle as broad and powerful
as the Principle of Computational Equivalence
...
. For what the principle does is to assert
that when viewed in computational terms there is a fundamental equivalence between many
different kinds of processes
...
. [pp. 715-716].
...
(5.3)
[This statement is almost identical to the idea of universal computation advocated
by S. Lloyd (2006).]
The traditional mathematical approach to science has historically had its great success in
physics - and by now it has become almost universally assumed that any serious physical
theory must be based on mathematical equations. Yet with this approach there are still
many common physical phenomena about which physics has had remarkably little to say.
But with the approach of thinking in terms of simple programs that I develop in this topic it
finally seems possible to make some dramatic progress. And indeed in the course of the
topic we will see that some extremely simple programs seem able to capture the essential
