This won't directly answer the question, but just to give some added context: Note that in abstract mathematics (which is what Conway was doing here) you’re kinda creating building blocks, and you're kinda playing for “street cred” among the rest of the abstract mathematics community.
This is kind of true in all academic publishing, that your success is due to your publications’ ability to inspire follow-up publications. But for abstract mathematics the “street cred” follows three rules: you get more cred based on,
• the wimpier the building blocks look
• the larger and more complex the structures you can build with them
• the more memorable or intuitive the blocks are (so like marketing... SK-calculus is the same as lambda calculus but lambda can say “I am the abstract mathematics of template substitution!” while SK-calculus can't, directly.)
All a way to say that the field is full of “fun little toys” and the key about criterion (2) is that we have figured out how to build structures of arbitrary complexity in Life, because we have discovered it is Turing-complete. It therefore is also NP-hard and a lot of other good stuff. Really revitalized work into cellular automata by giving some good marketing, 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.
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.
This is kind of true in all academic publishing, that your success is due to your publications’ ability to inspire follow-up publications. But for abstract mathematics the “street cred” follows three rules: you get more cred based on,
• the wimpier the building blocks look
• the larger and more complex the structures you can build with them
• the more memorable or intuitive the blocks are (so like marketing... SK-calculus is the same as lambda calculus but lambda can say “I am the abstract mathematics of template substitution!” while SK-calculus can't, directly.)
All a way to say that the field is full of “fun little toys” and the key about criterion (2) is that we have figured out how to build structures of arbitrary complexity in Life, because we have discovered it is Turing-complete. It therefore is also NP-hard and a lot of other good stuff. Really revitalized work into cellular automata by giving some good marketing, which led to Stephen Wolfram's success etc etc.