# Computational irreducibility

**computationally irreducible**

Computational irreducibility is one of the main ideas proposed by Stephen Wolfram in his book A New Kind of Science.wikipedia

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### A New Kind of Science

**Principle of Computational EquivalencedisagreeNKS**

Computational irreducibility is one of the main ideas proposed by Stephen Wolfram in his book A New Kind of Science.

For instance, he argues that the concept of computational irreducibility (that some complex computations are not amenable to short-cuts and cannot be "reduced"), is ultimately the reason why computational models of nature must be considered in addition to traditional mathematical models.

### Complexity

**complexdetailcomplexity theory**

### Stephen Wolfram

**WolframS. WolframStephen**

Computational irreducibility is one of the main ideas proposed by Stephen Wolfram in his book A New Kind of Science.

### System

**systemssubsystemsubsystems**

Wolfram terms the inability to shortcut a program (e.g., a system), or otherwise describe its behavior in a simple way, "computational irreducibility".

### Empiricism

**empiricistempiricalempirically**

The empirical fact is that the world of simple programs contains a great diversity of behavior, but, because of undecidability, it is impossible to predict what they will do before essentially running them.

### Fact

**factsscientific factaccurate**

The empirical fact is that the world of simple programs contains a great diversity of behavior, but, because of undecidability, it is impossible to predict what they will do before essentially running them.

### Behavior

**behaviourbehavioralbehaviors**

The empirical fact is that the world of simple programs contains a great diversity of behavior, but, because of undecidability, it is impossible to predict what they will do before essentially running them.

### Undecidable problem

**undecidableundecidabilitysemi-decidable**

### Prediction

**predictpredictionspredictive**

### Phenomenon

**phenomenaphenomenalphysical phenomena**

Wolfram states several phenomena are normally computationally irreducible.

### Free will

**freedomfreewillfreedom of the will**

Computational irreducibility may also provide a scientifically-based resolution for free will.

### Approximation

**estimate≈approximate**

Israeli and Goldenfeld found that some less complex systems behaved simply and predictably (thus, they allowed approximations).

### Chaos theory

**chaoticchaoschaotic behavior**

### Gödel's incompleteness theorems

**Gödel's incompleteness theoremincompleteness theoremincompleteness theorems**

### Computation

**computationalcomputationscomputing**

### Artificial intelligence

**AIA.I.artificially intelligent**

### Emergence

**emergentemergent propertiesemergent property**

### Holism in science

**holisticHolistic scienceHolism**

Natural systems can produce surprisingly unexpected behavior, and it is suspected that behavior of such systems might be computationally irreducible, which means it would not be possible to even approximate the system state without a full simulation of all the events occurring in the system.

### Cellular automaton

**cellular automataCACell games (cellular automaton)**

Additionally, during this period Wolfram formulated the concepts of intrinsic randomness and computational irreducibility, and suggested that rule 110 may be universal—a fact proved later by Wolfram's research assistant Matthew Cook in the 1990s.