Simple Rules, Complicated Behavior
Run the experiment — simple programs don't do simple things, and that's how nature builds complexity.
- Difficulty
- Advanced
- Time to result
- ~months to results
- Steps
- 5
- Confidence
- 85%
At the beginning of the 1980s Wolfram set out to formalize thinking about the world in a way that goes beyond what math provides. He realized that definite rules describing how things work don't have to be written in multiplications and integrals — they can be stated as 'you have this arrangement of black and white cells and then this happens'. He then asked what such simple programs typically do, and assumed a simple enough program would just do simple things. Computer experiments showed otherwise: use a simple rule and it does a complicated thing. This turned out to be interesting for understanding how nature works, because it seems to be the secret nature uses to make a lot of the complicated stuff we see — and it became A New Kind of Science in 2002.
Origin
Wolfram got interested at the start of the 1980s in how to formalize the world beyond mathematics, noticing math had worked pretty well in physics and pretty terribly in biology and the social sciences. He ran computer experiments on simple programs expecting simple output, was surprised, and took a solid bunch of years to absorb the point — the field took a few decades. He published the direction as A New Kind of Science in 2002.
Core principles
- 01The intuition that simple programs do simple things is wrong.
- 02You find this out by doing computer experiments, not by reasoning about it.
- 03Simple rules producing complicated behavior appears to be the secret nature uses to make the complicated stuff we see.
- 04Rules can be perfectly definite without being mathematical — arrangements of black and white cells, not integrals.
- 05Absorbing a result that contradicts intuition takes years, even for the person who found it.
- 06Where math failed as a description of a field, rule-based computation is the thing to try.
How to run it
- 1
Notice where math failed
Locate the fields where the 300-year mathematical program didn't deliver. Math worked pretty well in physics and gave us a lot of modern engineering; it worked pretty terribly in biology and the social sciences. People imagined a social physics of how society works and it never really panned out. Those gaps are the opportunity.
- 2
State rules without equations
Recognize that there are definite rules that describe how things work but aren't things you can write in mathematical terms. They look more like: you have this arrangement of black and white cells and then this happens. Definite structure without multiplications and integrals.
Pro tip The freedom from equations is the point — it's what makes the method reach fields calculus couldn't.
- 3
Do the computer experiment
Ask what these simple programs typically do, and then find out empirically. You just do these experiments — computer experiments — and look. Don't reason your way to the answer.
Watch out Your prior will be that a program simple enough is going to just do simple things. Wolfram held that prior and it was wrong.
- 4
Take the surprise seriously
You use a simple rule and it does a complicated thing. This was a big surprise to Wolfram and to everybody else. Don't explain it away — it's the finding.
Watch out It took Wolfram a solid bunch of years to absorb the point and the field a few decades. Budget for that.
- 5
Point it at nature
Apply the phenomenon to understanding how nature works. Simple rules producing complicated behavior seems to be the secret nature uses to make a lot of the complicated stuff we see — which turns the observation into a whole new direction for science.
Pro tip Wolfram's second-law-of-thermodynamics work — a question he first asked at 12 and published on ~50 years later — came from this direction.
In the wild
Wolfram's computer experiments on simple programs produced a result that contradicted the assumption that simple rules do simple things. He turned the finding into a whole big direction and a new understanding about how science works, published as a large book in 2002.
→ The book's title, he notes, kind of says what it is. The direction — understanding the world in terms of computational rules — became one of the two branches of his life's work, alongside building Wolfram Language.
At 12 years old Wolfram got interested in how the second law of thermodynamics works — something people had studied for 150 years. He finally figured it out and published a book about it roughly 50 years later, in 2023.
→ He calls it nice to tie up such things but also a little shocking how slowly big ideas move — a cautionary note on the timescale over which computational explanations of natural phenomena actually land.
Common mistakes
Reasoning instead of experimenting
The whole result is invisible to intuition. Wolfram's own prior was that a simple enough program would just do simple things. The only way through is to actually run the programs and look at what comes out — computer experiments, not argument.
Assuming complicated output needs a complicated cause
This is the intuition the result destroys, and it took Wolfram years and the field decades to give it up. As long as you hold it, you'll keep looking for elaborate mechanisms behind natural complexity instead of simple rules run long enough.
Is it for you?
Best for
Researchers and modelers in fields where equations never fit, and anyone trying to explain how complicated behavior arises from apparently simple systems.
Not ideal for
Domains where mathematics already works well (much of physics gave modern engineering exactly this way), and anyone unwilling to run experiments rather than reason from first principles.
From the transcript
“what one might have assumed is you have a program that's simple enough it's going to just do simple things this turns out not to…”
“you just do these experiments computer experiments and you find out yes you use a simple rule and no it does a complicated thing”
“it seems like that's kind of the secret that nature uses to make a lot of the complicated stuff that we see the same phenomenon…”
“those rules are more stated in terms of oh you have this arrangement of black and white cells and then this happens they're not things…”
From the episode
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