Computational irreducibility is one of the main ideas proposed by Stephen Wolfram in his book A New Kind of Science. Wolfram terms the inability to shortcut a program (e.g., a system), or otherwise describe its behavior in a simple way, "computational irreducibility". 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. The idea demonstrates that there are occurrences where theory's predictions are effectively not possible. Wolfram states several phenomena are normally computationally irreducible.
- source: Wikipedia
The behavior of a living being or a man-made system will correspond to the computation of equivalence sophistication. For example, the brain of a child versus an adult will exhibit behavior based on the computation equivalent to the brain’s sophistication. Children’s brains are not developed so they behave differently than an adult’s brain. Wolfram explains as a result of the sophistication of the system, we can only reduce its computation to a certain point after which it is irreducible thus hampering our ability to predict its future behavior in full. Wolfram thinks this is why we are not able to explain the unique unpredictable nature (undecidability) of this natural world. Basically this is a fancy way of saying scientists don’t know everything.
Because science does not fully comprehend the idea of consciousness and is unwilling to admit it within mainstream learning, scientists are coming up with new kinds of science to explain the concept of free-will within our natural world. Computation irreducibility is one such deterministic theory to explain a non-deterministic natural world.
The video captures this idea in short.