Simple Rules, Complex Behavior
A simple program can produce astonishingly complicated behavior.
- Difficulty
- Moderate
- Time to result
- ~ongoing to results
- Steps
- 4
- Confidence
- 85%
Through computer experiments on simple programs, Wolfram discovered that a rule simple enough to write down in a sentence can nonetheless produce highly complex behavior — a result that surprised him and, he says, everyone else. This overturns the natural assumption that simple causes yield only simple effects. He argues this same phenomenon is the secret nature uses to generate the complicated structures we see all around us. The insight became the foundation of his 2002 book A New Kind of Science and reframes how science can understand the natural world.
Origin
At the beginning of the 1980s Wolfram began studying what simple programs (systems defined as rules over arrangements of cells) typically do, expecting simple behavior; the repeated experimental finding of complexity from simplicity became A New Kind of Science (2002).
Core principles
- 01You might assume a simple enough program only does simple things — this is false.
- 02Simple rules can generate genuinely complex behavior.
- 03This is the secret nature uses to produce the complicated things we observe.
- 04Absorbing this point took decades for the field and years for Wolfram himself.
How to run it
- 1
Choose a minimal rule
Define a system by a very simple rule, such as an arrangement of black and white cells with a rule for how it updates.
- 2
Run it as a computer experiment
Actually execute the rule and watch what it produces, rather than assuming the outcome from the rule's simplicity.
Pro tip Empirical experimentation beats intuition here — the results are counterintuitive.
Watch out Your prior that 'simple in, simple out' will mislead you.
- 3
Recognize the emergent complexity
Note when a trivial rule yields genuinely complicated behavior, and treat that as a general phenomenon rather than a fluke.
- 4
Apply it to nature
Use simple-rules-complex-behavior as the mechanism explaining how nature manufactures the complex structures we observe.
In the wild
Wolfram describes doing computer experiments with simple rules and finding they do complicated things — a point that took the field a few decades and took him a solid bunch of years to fully absorb.
→ The finding became a whole new direction and his 2002 book A New Kind of Science.
Common mistakes
Assuming simple programs do only simple things
Wolfram calls this the big surprise: the natural assumption that a simple enough rule produces simple behavior turns out to be flatly wrong.
Is it for you?
Best for
Scientists and modelers trying to explain complex natural phenomena from minimal ingredients.
Not ideal for
Situations demanding an exact analytic shortcut, since these systems often can't be reduced (see computational irreducibility).
From the transcript
“you use a simple rule and no, it does a complicated thing. And that's that turns out to be pretty interesting if you want to…”
“it seems like that's kind of it's kind of the secret that nature uses to make a lot of the complicated stuff that we see…”
From the episode
Stephen Wolfram: How AI Works and How to Use It to Stay Ahead
Stephen Wolfram