Wolfram's book A New Kind of Science (NKS) appeared in 2002. The Principle of Computational Equivalence (PCE) (cf. Part 71), enunciated in this book, is a major component of Wolfram's NKS approach to understanding natural phenomena. He dares to go where no scientist would venture readily, namely attacking research problems of immense complexity. One of the ways he does this is by constructing his computational universe, which is an huge repertoire of 'patterns' generated by running all conceivable cellular automata, and then 'mining' this universe for possible solutions to the problem at hand.
'There are typically three broad categories of NKS
work: pure NKS, applied NKS, and the NKS way of thinking. . . Pure NKS is about
studying the computational universe as basic science for its own sake —investigating
simple programs like cellular automata, seeing what they do, and gradually
abstracting general principles. Applied NKS is about taking what one finds
in the computational universe, and using it as raw material to create models,
technology and other things. And the NKS way of thinking is about taking
ideas and principles from NKS — like computational irreducibility or the
Principle of Computational Equivalence — and using
them as a conceptual framework for thinking about things' (Wolfram 2012a).
The above figure gives a breakup of the various
subjects in which NKS has been applied. The impact of Wolfram's book has been
truly wide-ranging, with applied NKS emerging as the largest group of
applications. I quote Wolfram (2012a) again: 'Let’s start with the largest group:
applied NKS. And among these, a striking feature is the development of models
for a dizzying array of systems and phenomena. In traditional science, new
models are fairly rare. But in just a decade of applied NKS academic literature,
there are already hundreds of new models: Hair patterns in mice. Shapes of
human molars. Collective butterfly motion. Evolution of soil thicknesses.
Interactions of trading strategies. Clustering of red blood cells in
capillaries. Patterns of worm appendages. Shapes of galaxies. Effects of
fires on ecosystems. Structure of stromatolites. Patterns of leaf stomata
operation. Spatial spread of influenza in hospitals. Pedestrian traffic
flow. Skin cancer development. Size distributions of companies. Microscopic
origins of friction. And many, many more.'
The figure
below gives a glimpse of the impact of NKS on art.
While there
are many enthusiasts, there are also many critics of NKS (Jim Giles published in 2002 in Nature a review of the NKS book). Wolfram (2012b) has recently
reviewed the various responses to his work. I find the attitude of several
conventional scientists very intriguing, even disappointing. There are any
number of extremely complex problems challenging us for a solution. The
traditional approach in science has been to model the system under
investigation in terms of a few differential equations, and solve them under suitable
'boundary conditions'. We feel elated if our model embodies the 'essential
physics' of the problem, and even makes some predictions. And we feel absolutely
thrilled if the predictions also turn out to be true. But the wicked thing
about most of the real-life complex systems is that any simplifying
assumption for modelling them can kill the very essence of the problem.
You can do two
things when faced with such a situation. Either stay away from working on such
research problems, or do what NKS suggests. Staying away is not a very good
idea. For how long can you go on working only on simple or simplifiable
research problems? Complexity requires a radically new approach to how science
has to be done. NKS is one such approach.
Critics of NKS
tend to snigger at what has been achieved by it. I would take them seriously if
they had some better alternatives to offer. They have none.
A criticism
levelled against Wolfram's NKS is that his CA lack the predictive power of
theories developed around conventional, i.e. calculus-based, mathematics. Complex
systems are unpredictable, except possibly that one can sometimes
explain/predict the level of complexity in terms of the previous lower
level of complexity. In any case, is this criticism really valid? Suppose you
have succeeded in identifying some archived simple program from Wolfram's
computational universe as providing a reasonably good match with the complexity
'pattern' observed in Nature. Such a simple program is clearly giving you a
very good hint about the basic interactions involved. You can even create
'predictions' by tinkering with the simple program and generating the modified
patterns, and checking them against experiment. If such a prediction gets
confirmed reasonably well, you are on the right track so far as gaining an
insight into the basics of the complex phenomenon is concerned. What
more can you ask for? Getting on the right track is half the battle won. Just build
on that great start, by any means.
Nevertheless, I
quote from Wolfram (2012b):
'Another theme
in some reviews is that the ideas in the book “do not lead to testable
predictions”. Of course, just as with an area like pure mathematics, the
abstract study of the computational universe that forms the core of the book is
not something which in and of itself would be expected to have testable
predictions. Rather, it is when the methods derived from this are applied
to systems in nature and elsewhere that predictions can be made. And
indeed there are quite a few of these in the book (for example about repeatability of apparent randomness) — and many
more have emerged and successfully been tested in work that’s been done since the book appeared.
'Interestingly enough, the book
actually also makes abstract predictions — particularly based on the Principle of Computational Equivalence. And one very important such
prediction — that a particular simple Turing machine would be computation
universal — was verified in 2007.'
Kurzweil (2005) remarked that even the most complex CA
discussed by Wolfram do not have the evolution feature so crucial to the
question of complexity. This may be because the CA discussed by Wolfram are not
open systems. There is no influx of energy or negative entropy or information
into the CA running simple programs. The NKS should be extended to overcome
this deficiency. In fact, as we shall see in a later post, this is what Langton (1989) did to some extent in his pioneering work on adaptive
computation.
An interesting
comment about the efficacy or otherwise of the NKS as providing a theory of the
evolution of the universe is that of Lloyd (2006):
'The idea of
using cellular automata as a basis for the theory of the universe is an
appealing one. The problem with this argument is that classical computers are
bad at reproducing quantum features, such as entanglement. Moreover, as has
been noted, it would take a classical computer the size of the whole universe
just to simulate a very tiny quantum-mechanical piece of it. It is thus hard to
see how the universe could be a classical computer such as a cellular
automaton. If it is, then the vast majority of its computational apparatus is
inaccessible to observation'.
The debate
goes on.
What about the
future of NKS? Wolfram (2012c) gushes with optimism and expectation. And the
tribe of NKS enthusiasts continues to grow.
Want to attend a free virtual conference about the latest in NKS? Please click here:
Want to attend a free virtual conference about the latest in NKS? Please click here:
Here is recent lecture by Wolfram about our
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