A New Kind of Science
I’ve managed to read Stephen Wolfram’s book (pdf version, 20 to 30 pages in a week due to a busy schedule). I can say that it was a new kind of experience.
First, all of the pictures were very interesting. I can recall several times when I was looking at only one picture trying to figure what is going there and what will change if one underlying rule is tweaked. I guess that it is in the figures that thing which makes this book so interesting to read.
However, the images have very little content. The most striking revelations came from the content. Implications in physics, systems where the Second Law of Thermodynamics doesn’t hold, short and simple explanations for everything, a simple model for the economy. Complex systems explained by means of simpler programs. This is the content of the first part of the book.
There are several pages covering our understandings of time and space. There are several fragments were Divinity is implied to exist. At least in a sense that there must exist an entity capable of omniscience and omnipresence.
Randomness and data compressions topics are also touched in this book. The fact that there can be no universal compression scheme is explained in a new way. Implications for perceptions are immediately extracted from this even though between these two topics there seems to be no links.
Cryptography has several pages allocated to it. Although rule 30 is presented as being a very complex one and suitable for encryption, Wolfram demonstrated that it too can be subject to cryptanalysis. However, he also presents a strategy which will make the key used for encryption hard to deduce. Maybe I will come back regarding this topic in a future blog post.
The most part of the book is focused on more general topics. This part begins with the Godel thesis. It is proved that among the cellular automata presented, there are some who can emulate all others. Thus, we arrive at the central point of the book: The Principle of Computational Equivalence (PCE).
According to this principle, any process that is complicated enough can emulate any other process. Moreover, the threshold between this kind of processes and the simpler one is lower, not higher as our every-day intuition would say. In the end, we will arrive to the conclusion that everything is a computation (compare this to Pythagoras’ idea that everything is a number)
The end of the book speaks about the PCE’s implications. The topic of Free Will is touched. Undecidability and intractability are discussed with a wide array of examples. The big problem of P and NP is touched on several sections of the book. Moreover, even intelligence itself is analysed using the PCE.
For more informations, please read the book. It will be an interesting lecture.