Computational irreducibility is one of the main ideas proposed by Stephen Wolfram in his 2002 book A New Kind of Science, although the concept goes back to studies from the 1980s.
Many physical systems are complex enough that they cannot be effectively measured. Even simpler programs contain a great diversity of behavior. Therefore no model can predict, using only initial conditions, exactly what will occur in a given physical system before an experiment is conducted. Because of this problem of undecidability in the formal language of computation, Wolfram terms this inability to "shortcut" a system (or "program"), or otherwise describe its behavior in a simple way, "computational irreducibility." The idea demonstrates that there are occurrences where theory's predictions are effectively not possible. Wolfram states several phenomena are normally computationally irreducible.
Computational irreducibility explains observed limitations of existing mainstream science. In cases of computational irreducibility, only observation and experiment can be used.
Navot Israeli and Nigel Goldenfeld found that some less complex systems behaved simply and predictably (thus, they allowed approximations). However, more complex systems were still computationally irreducible and unpredictable. It is unknown what conditions would allow complex phenomena to be described simply and predictably.
Marius Krumm and Markus P Muller tie computational irreducibility to Compatibilism.[1] They refine concepts via the intermediate requirement of a new concept called computational sourcehood that demands essentially full and almost-exact representation of features associated with problem or process represented, and a full no-shortcut computation. The approach simplifies conceptualization of the issue via the No Shortcuts metaphor. This may be analogized to the process of cooking, where all the ingredients in a recipe are required as well as following the 'cooking schedule' to obtain the desired end product. This parallels the issues of the profound distinctions between similarity and identity.