Wednesday, July 20

Reflections on the book "A New Kind of Science," by Stephen Wolfram

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Stephen Wolfram was born in London and educated at Oxford where he received his Ph.D. in theoretical physics, aged 20 and subsequently made lasting contributions in the field of particle physics and cosmology. In the 1980’s he made a series of classic discoveries that ultimately yielded many new insights into physics, mathematics, computer science, biology and the operation of our universe. In 1986 he founded his own research company and began the creation of Mathematica, which has developed into the world’s leading software system for technical and symbolic programs. Hence he has been in the enviable position to use the income from his business to fully fund the pure research into those areas close to his heart. He has not let the wonderful opportunity of self-funding his own research slip through his fingertips and his dedication is readily evident in a “New Kind of Science”.

Consequently his writing represents 10 years work and research to be enjoyed by virtue of its easy style by both scientists and non-scientists alike. In fact the early crucial experiment and discoveries are easily checked on any modern computer Only later when these experiments are allowed to develop out into billions of cellular automation does he need the use of the greater computer processing power now available to him. Graphics further enhances the presentation and the reader’s easy ready grasp of the profound conclusions verifiable often by simple observation.

You cannot help but be swept along on this fast flow of fresh infectious writings, which quickly joins your mind and souls (if you will) with him on his journey of discovery. At times the path can become a bit of a challenge into this new land of understanding away from the safety of our present inbuilt intuition and way of thinking. A minor discomfort though to be quickly shrugged off with the realization of the exciting prospect of a glimpse for the first time of some new truths (or the substantiation of others) emerging from his discoveries.

In some respects the experiments provide evidence at odds to some degree with some of our traditional Darwinism, Mathematics and thinking in general about the world in which we live.

They also provide a much more solid foundation for future thought encompassing philosophy and substantiation in a different way of our religion for those who feel compelled by the spirit to follow down these new pathways.

Its structure

The Foundations of as New Kind of Science
The Crucial Experiment ( I will briefly reach this point on this posting )
The world of simple Programs
Systems based upon numbers
Two dimensions and Beyond
Starting from Randomness
Mechanisms in Programs and Nature
Implications for Everyday Systems
Fundamental Physics
Process of Perception and Analysis
The Notion of Computation
The Principle of Computational Equivalence.

The Crucial Experiment.

All of Wolframs experiments began by observing the behavioral output of simple programs on a computer. We are all familiar with the operation or at least the result of software that produces our pay, invoicing records or keeps information for us in vast quantities on modern computers. Wolfram in his experiments wrote very simple programs and observed the outputs.He uses black and white squares but you could use any items –blue and white shaped beads if they took your fancy as it only the output behavior that is the subject of the experiment. Each one of the items he calls a cell. He calls the output cellular automata. Why would he do this in the firstplace? His research found this aspect of computer programming had not been done to any degree anywhere. The early results were so entirely different to what he had anticipated he became very excited over his initial discovery and so began this labor of love encapsulated within the pages of this book. These computer programs can be described more accurately, as rules. The programs tell the computer to carry out some instructions for a specified interval. There is no intention to achieve a result other than to see what happens. He begins with basic programming rules and builds up to a very mildly complex instruction on page 27.


E.g. the so-called rule 30.Start with a single black square.(Cell) and repeat the rule line by line e.g. first, look at each cell and its right hand neighbor. If both of these were white on the previous step, then take the new color of the cell to be whatever the previous color of its left-hand neighbor was, otherwise, make the new color the opposite of that.

Your intuition would tell you there should be some sort of repetitive pattern to appear over the given cellular data output would it not? After all the same rule is being applied over and over again.

The effect of this program 500 steps later is shown on page 29 and after 1500 steps on page 30 (or after 2 million cells).
At this stage there are no signs of overall regularity and in the pattern obtained seem perfectly random according to standard mathematical and statistical tests.

It becomes almost impossible to predict –even approximately –what the cellular automation will do. The only answer is keep running the program and see what happens. We can observe the outcomes of a particular rule as it continues on pages 32-38 up to 3200 steps, which tells us we need only very simple rules to produce highly complex behavior. So what! You say! Well does this not go against some of our most basic intuition about the way things normally work? We would expect the initial simple instructions to produce a pattern. We have been all brought up on a diet that often expects complex things to be built up slowly from complex beginnings. Why is this so? Well our intuition tells us around us we are surrounded by complex systems crucial to our existence.

Wolfram’s experiments show very complex systems can be built up from very basic underlying instructions or beginnings. During the course of the book he shows the implications to many field of current knowledge and I will list just a few in abbreviated summary form from the section “The Foundations For A New Kind of Science “
Mathematics.

Essential enlargement is necessary to now include simple rules that create these complex systems.

Physics
Existing methods tend to revolve around ideas of continuous numbers and calculus-or sometimes probability. Wolfram involves just simple discrete elements with definite rules. In many ways the greater simplicity of the structure make it possible to identify new phenomena.

Biology
Wolfram's discoveries show simple programs can reproduce many features of biological organisms and seem to capture some of the essential mechanisms through which genetic programs manage to generate the actual biological forms we see.

Social Sciences
There is now a much better chance of capturing fundamental mechanisms for phenomena in the social sciences by using this kind of science based upon simple programs.

Computer Science
A dramatic broadening of the domain to which computational ideas can be applied.

Philosophy
Much has been written over the course of history about the ultimate limits to knowledge, free will, the human condition and the inevitability of mathematics but with the discoveries in this book we can look at these mysteries with a new intuition.

Art
Use of the simple programs to explore generalizations of the forms we see in nature.

Chaos Theory
Almost redundant, for all it shows is that if there is enough complexity in the details of the initial conditions, then this complexity will eventually appear in the large –scale behavior of the system. What wolfram s shows is that even if the initial conditions are very simple there are many systems that still produce highly complex behavior.

Conclusion
The experiments forms the beginning of Wolframs journey into this new way of thinking and offers explanations for the underlying complexity around us ending with his Principle of Computational Equivalence some 800 pages later and represenative of 10years passionate work.

Whilst it implies that many some of the wonders of the universe may be captured in simple rules it also goes on to show there can no way we can ascertain all of the consequences of these rules, except in effect just to watch and see how they unfold.

Perhaps this is yet another way of looking at the wonder of gods creation in everything. These discoveries may well help ultimately provide a much better framework to understand more about free will and determinism whilst changing markedly the more fundamental views of how beauty and complexity abound in nature.

I highly commend the book for review.

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2 comments:

Andy Dabydeen said...

You actually read the book? I'm impressed. It's BIG!

vanessa byrnes said...

this is helpful in thinking about why certain things happen. Humans I think try to make them selves feel better by saying "everything happens for a reason" or "it was meant to be" However, I think a lot of things are random and this theory is consistent with that