October 2025
This has to be the most poorly-written book I have ever read — and I have over 3,000 non-fiction books in my library. Here’s a sentence from Chapter One:
“Ultimately this is a consequence of what I call the Principle of Computational Equivalence, which states that above some low threshold, systems always end up being equivalent in the sophistication of the computations they perform.”
What does Mr. Wolfram mean by “systems”? Planets orbiting the sun? Molecules? Living cells? Pinball games? Anything? Everything? He never states his meaning. How do such systems perform computations? Does Jupiter have a big computer inside that directs its motions around the sun? How does a molecule calculate? I suspect his meaning is metaphorical, but it’s impossible to know.
What does he mean by the “sophistication of the computations they perform”? How do we evaluate the sophistication of a computation? Is it the number of steps that would be executed by a simulation program mimicking the system? Is it the length or complexity of the mathematical expression of the law determining its behavior? Is it the sophistication of the mathematical operators used; that is, do we rate exponentiation as more sophisticated than addition? Is a partial differential expression more sophisticated than a subtraction? Who knows? Mr. Wolfram doesn’t say.
Having battled with this sentence, we shrug our shoulders and move on to the next sentence:
“And this is why even our brains and our most sophisticated methods of scientific analysis can’t “computationally outrun” even something like Rule 30, so that we must consider it computationally irreducible.”
I have only three problems with that sentence:
What the hell does he mean by “computationally outrun”? Does he mean that our brains cannot compute as fast as Rule 30? Or that Rule 30 is just too complicated for our brains to understand?
What the hell does he mean by “Rule 30”? He never introduced us to this concept. He just started using it as if everybody knows about Rule 30, and anybody who doesn’t already know about Rule 30 is a worthless cretin doesn’t deserve to understand his celestial thoughts?
What the hell does he mean by “computationally irreducible”? Does he mean that no computer program could reduce Rule 30 to something smaller? In that case, what does he mean by “something smaller”? Since we don’t know what Rule 30 is, it’s kind of hard to imagine what would be smaller than Rule 30.
Those are just two sentences in Chapter One. The enigmas keep piling up, until by the end of Chapter One I was totally befuddled. I had no idea what Mr. Wolfram was trying to communicate.
The root of his failure could be metaphorically characterized as a kind of intellectual autism. In this metaphor, Mr. Wolfram has no conception of how other people think. He writes to himself, not to anybody else. He doesn’t care if anybody understands his writing. That’s only my explanatory metaphor; I have no idea what his real psychology is. What I do know is that his writing is incomprehensible. Each paragraph compounds the incomprehensibility of his book; the end result is a gigantic mountain of incomprehensibility. You could shuffle the pages and it would make almost as much sense.
But there is an important positive consideration. Mr. Wolfram has developed a completely new angle on our perception of reality. He uses cellular automata as a conceptual tool to understand phenomena. This is indeed a novel and, I must say, exciting way to approach reality. His book is plastered with hundreds of diagrams of a multiplicity of cellular automata. There’s no question that his approach can open our eyes to new ideas. I just wish that a competent writer had written this book; Mr. Wolfram has badly botched the job.
I was especially disappointed by the execrable writing because I too am something of a Second Law groupie. It’s fascinating that there are so many angles of approach to the Second Law. Originally it was conceived as a means of calculating the theoretical limits on the efficiency of steam engines.
Then there’s the statistical mechanics approach, in which we talk about the “accessible states” of a system and the definition of states that possess some desired attributes, then compare the number of desirable states to the number of accessible states. There are always many more accessible states than desirable states, so any system left to itself is more likely to end up in a non-desirable state. If we shake up a box containing ten coins, there are a lot more states with 6 heads and 4 tails than there are states with all heads, so we’ll be astounded if we end up with all heads.
My own approach to the Second Law hinges on three considerations: first, Maxwell’s Demon, who can violate the Second Law. Second, Leon Brillouin’s 1951 demonstration that Maxwell’s Demon cannot in fact violate the Second Law. Third, that Brillouin’s demonstration is dependent on Heisenberg’s Constant being greater than zero. This means that the Second Law is invalid in a classical world; to put it another way, the Second Law is a quantum-mechanical effect.
There are a number of other ways of thinking about the Second Law, and I was eager to see Mr. Wolfram’s approach, as from his reputation I knew that his thinking on the matter would be clever and novel. But, sadly, his skills as a writer fall far below his talent as a creative thinker. I hope that someday a more talented writer explains Mr. Wolfram’s thinking to the world.