A New Kind of Science
in a Nutshell
David Sehnal
QIPL at FI MU
Motivations
• How does anything complicated get
produced in nature?
• Traditional Science – i.e. calculus,
Newtonian physics, …
• What if there is a more general underlying
principle?
– Simple programs
1D Cellular Automata
Cell to be updated
Left neighbor
Right neighbor
New color
•
This type behavior is very surprising
1. Started from a single black cell
2. Used simple rules
3. Got something that looks to us
completely random
Is Complexity Special or Common?
Turing Machines
Substitution Systems
2D Cellular Automata
2D Turing Machines
3D Cellular Automata
To sum it up…
• Simple rules do not imply simple behavior
• It seems that complex behavior is a very
common phenomenon
Systems in nature
Snowflakes
• When a piece of a snowflake solidifies,
heat is released
• This heat prohibits ice nearby
• New rule: Piece solidifies if exactly on of
the neighborhood cells is solid
More systems in nature
•
•
•
•
Fluid flow
Patterns on shells
Fundamental physics
And many others …
Why can simple programs
produce complex behavior?
Computation
Computation
• All cellular automata can be though of as
doing computations
• One does not need to know the point of
the computation beforehand
Universality
• Some automata can simulate all others
• One only needs to specify the initial
conditions
Universality
• Once universality is reached, the behavior
is maximally sophisticated (from the
computational point of view)
More questions
• What about systems such as rule 30?
• Or systems in nature?
• How sophisticated are these?
Principle of Computational
Equivalence
Essentially any time the behavior of a
system looks to us complex, it will end up
corresponding to a computation of exactly
equivalent sophistication.
• Simple behavior (repetitive or nested)
corresponds to simple computations
• Complex behavior corresponds to
sophisticated computations
Threshold of Universality
• Rule 110 is universal
Where does all the complexity
come from?
… from the computational
sophistication of the system observed
compared to the computational
sophistication of the observer.
Thank you for your attention
Thank you for your attention