A New Kind of Science

After I watched the video, I borrowed the book "A New Kind of Science" in the library. Seriously, I couldn't read the who 1263 pages in a week; however, I took a look what's going on inside the book. Overall, it's a remarkable piece of experimental mathematics, together with considerable speculation about scientific applications of various degree of plausibility. Just like what he said in the video, Wolfram's book begins with examples, and that is a good starting point for a review as well. The simple example of his work is one-dimensional cellular automata. What he also shows in his speech, an infinite row of cells, each of which can be white or black.

Time jumping in discrete steps, and at each steps, the world is updated using fixed rule that determines the new color of each cell based only on its own old color and those of its immediate neighbor. All systems that reach this bound are equivalent. However, almost all system that are not obviously weak reach the bound and are thus equivalent to the halting problem. In fact, Wolfram also talked about this happens for most initial conditions, not just some. Anyway, what I feel about him is how amazing he could dedicate his whole life to investigate the science and write a remarkable book, also he is young comparing to the most well-known scientists.