Wolfram's A New Kind of Science takes the idea a bit too far, in my opinion. It's an exposition of the hypothesis that the underlying stratum of life and the universe is, like cellular automatons, discrete—and therefore can be understood in terms of discrete processes, which he views as analogous to real life. He points to emergence in cellular automatons as evidence that an analogous emergent phenomenon was the reason biological life came into existence.
Mathematically and philosophically, it's a very interesting idea, but I'd hope that at this stage in scientific history, we'd understand that step 2 to validating an interesting hypothesis is testing it.
yeah wolfram's famous idea (which is sort of the whole point behind a new kind of science) is this computational equivalence principle which is that most things that are at a certain level of computational complexity are equivalent to each other[1]. Which may be true in some limited sense but is definitely not true in the general sense that he tries to imply. This has led him to saying things like you can implement the whole universe "in 4 lines of the wolfram language" even though mathematica (which is in the universe and implements the wolfram language) takes more than 4 lines of code to implement.
Boring mathematicians of the school of actual concrete formalisations level the criticism that his Principle of Computational Equivalence is never given a formal definitive statement and is more of an aspirational feel good kind of fuzzy wuzzy thingy.
> which led to Stephen Wolfram's success etc etc.
Wolfram's A New Kind of Science takes the idea a bit too far, in my opinion. It's an exposition of the hypothesis that the underlying stratum of life and the universe is, like cellular automatons, discrete—and therefore can be understood in terms of discrete processes, which he views as analogous to real life. He points to emergence in cellular automatons as evidence that an analogous emergent phenomenon was the reason biological life came into existence.
Mathematically and philosophically, it's a very interesting idea, but I'd hope that at this stage in scientific history, we'd understand that step 2 to validating an interesting hypothesis is testing it.