I’ve just started reading “Determined” by Robert Sapolsky. I noticed that one of the chapters ahead (haven’t finished it yet) references Cellular automata. And I realized I forgot to share an interesting find—a book “A New Kind of Science” by Stephen Wolfram. I bought it earlier this year and have read about 60% of it.
“A New Kind of Science” is a voluminous tome of over a thousand pages that covers everything from physics to biology and neuroscience. Its author, Stephen Wolfram, a doctor of physical and mathematical sciences, is the creator and main developer of the scientific software Mathematica and also Wolfram Alpha. Having become incredibly wealthy, he dedicated his intellectual career to exploring what happens when simple rules are applied to cells on a plane or in space.
He discovered that even simple rules like “if the square to the right is black, be black; if it’s white, be white,” when repeated a million times, can generate surprisingly complex structures. To a human, this complexity does not fit well with the simplicity of the rules because everywhere in our world, it seems that simple rules generate simplicity, and complex rules generate complexity. Hence, his main idea is that often simple rules can generate very complex outcomes.
Essentially, this is how DNA works. After all, DNA is a program that receives a) the actual software code—a sequence of amino acids and b) the result of the previous execution (enzymes floating in the cell suppressing some fragments of the software code, as well as some initial state of enzymes floating in the mother’s egg cell). As a result, after 10 iterations, the same software code generates structures that simply did not exist before ten iterations. And at, say, the hundredth iteration, something else gets activated. And calculating what will activate if something initially goes slightly wrong—like if an enzyme isn’t present at a needed moment in the cell—is virtually impossible. This makes genetics a very complex field.
Wolfram has a whole system for such things. For example, for a simple algorithm – we choose the color of a cell in the next iteration based on the color of the cell in the current iteration and the colors of the immediate neighboring cells. Such rules are formulated as 8 transformations of three bits into one, which essentially gives a program that only needs 8 bits to fully describe its logic. These 8 bits define the program. For example, Rule 22, which can be formulated as: each cell in the next generation will be black if exactly one of its two neighboring cells or itself is black in the current generation. So, if you initiate this rule against some initial state, a random pattern of large and small triangles, which are simultaneously random and not, will form over millions and billions of generations. The most interesting part is that it’s unpredictable from the initial condition and by the rule—at least, science doesn’t know how, and observations can only be made by running simulations and examining the outcomes. For instance, it might be that somewhere at the billionth generation, the pattern begins to repeat. Or it doesn’t. Or an intricate trapezoid might appear in the pattern that hadn’t appeared before. Or after a certain step, everything might collapse into a completely white or black background.
But what’s interesting is that this complexity is determined from the very beginning. Essentially, the number (rule) + initial combination determines the infinite terabytes of the resulting pattern. Slightly change the rule or the initial combination, and everything changes to something else, but also determined.
By the way, almost 100% of Wolfram’s discoveries would have been understood even in ancient Greece, and nothing prevented them from being formulated and passed down to the next generations in ancient Greece. But for some reason, there hasn’t been a single attempt over thousands of years. Only in the 20th century did they gradually begin to dig into the topic. Well, try to think of any other branch of science that theoretically could have been invented in ancient Greece but was only conceived now.
In the book, he analyzes the biology of these resulting creatures, and even classifies them reasonably well. He identifies some common characteristics—the same triangles in the pattern, although neither he nor others can explain where they come from.
In general, the book is very entertaining.
Now about the oddities.
Wolfram claims that this is a new way of doing science: instead of mathematical modeling of physical processes, scientists can simply observe computer-generated patterns that accurately model phenomena. And that in many cases, this opens up new horizons. Well, that’s debatable. Well okay.
I’m also somewhat irritated by the speaking style “one of the most important discoveries that I made.” It’s practically in every chapter. It must be admitted that the topic Wolfram launched with this book around 2002 was already in circulation, but no one had systematized it quite like he has. And it must be admitted that since 2002, it has also not been particularly popular among scientists. Maybe there’s not much more to delve into than Wolfram did, or maybe they just don’t like him so much that no one wants to touch it 🙂
So, no doubt, this book must be incredibly irritating to industry practitioners who, reading it, seem to practically not exist compared to the self-proclaimed brilliant mind of Mr. Wolfram. Sometimes it almost crosses into parody. I remember from my school days programming Conway’s “Game of Life,” and I was amazed then, where the heck does the information to describe all this come from. But according to Mr. Wolfram, he was the first to think this way. That is, he of course refers to Conway, but unwillingly, cloaking all the references with self-praising statements. Possibly, Wolfram did indeed make many discoveries independently and helped revive the subject, but even if so, he needs to recognize the merits of others more in his texts and not boast about how smart he is.
The book, by the way, is available in public access—Wolfram has put it up on his website, well adapted for the web. In its printed version, it is also surprisingly affordable. So if you’re interested, I advise you to take a look and form your own opinion.
Hi, I'm Rauf Aliev. 