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Why is Conway's Game of Life so interesting? Does it prove anything or lead to insightful discoveries? The game itself seems to me, like a fun little toy at bes

Why is Conway's Game of Life so interesting? Does it prove anything or lead to insightful discoveries? The game itself seems to me, like a fun little toy at best.

TimTheTinker 2y ago
A simple set of rules leads to a fascinating array of emergent phenomena, which themselves can be utilized to do all sorts of interesting things. In fact, the game of life is Turing complete -- you can build whole processors[0] or programming languages in it. You can even implement the game of life in the game of life. Someone did that and implemented infinite zooming between GOL levels.[1] [0] https://github.com/nicolasloizeau/scalable-gol-computer https://github.com/nicolasloizeau/scalable-gol-computer [1] https://oimo.io/works/life/ https://oimo.io/works/life/
meschi 2y ago
It's a cellular automaton showing complex behavior emerging from very simple rules. Through especially crafted inputs you can simulate a Turing machine or Conway's Game of Life inside itself.
crdrost 2y ago
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.
- TimTheTinker 2y ago
  Excellent info. > 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.
  - seanhunter 2y ago
    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. [1] https://mathworld.wolfram.com/PrincipleofComputationalEquivalence.html https://mathworld.wolfram.com/PrincipleofComputationalEquiva...
    - defrost 2y ago
      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. eg: Lawrence Gray in his 12 page review: https://www.ams.org/notices/200302/fea-gray.pdf https://www.ams.org/notices/200302/fea-gray.pdf Cosma Shalizi's infamous Rare Blend of Monster Raving Egomania and Utter Batshit Insanity review: http://bactra.org/reviews/wolfram/ http://bactra.org/reviews/wolfram/
abetusk 2y ago
Conway's Game of Life (GoL) provides a clear demonstration that simple rules can lead to complex behavior. The complex behavior is deep in the sense that Conway's GoL is Turing Complete [0]. The local update rules provide an analogy to our universe with a kind of built in "speed of light" of how fast information can propagate in the system. Further, since there is a system clock of sorts, the system is massively parallel with further analogies to our universe. The game looks like a toy but note that many profound models are also "toy-like". Ising systems, precolation models, Bethe lattices, self avoiding walks, etc. all provide seeding grounds for deep insights into our physical world. Just as an aside, I heard a quote, which I can't find anywhere, about how Maxwell playing with magnets could have been considered him playing with frivolous toys but his setup was critical to him figuring out the underlying mechanics of electromagnetism. On one hand, I sort of agree that there's a lot of uninteresting exploration but on the other hand, taking a step back, GoL research is exploring the more general space of cellular automata and how it could potentially map to real world simulation. For example, how small can a system be before it can do arbitrary computation? Can all patterns emerge eventually (no, garden of eden style patterns)? What do rotationally invariant patterns looks like? Can you "copy" arbitrary patterns from some setup? If so, how fast? Is it dependent on how big it is, or how complex it is? etc. GoL provides a sandbox in order to answer these questions and potentially give insight into other systems as well. In my opinion, one of the reasons for the popularity of GoL is because it was created right when computers became commodities, allowing hackers, amateur mathematicians and others to program something simple, that could be heavily optimized for limited hardware, and create intricate and complex behavior. There was a quote somewhere, that I'm also having trouble finding, about how, at one point, GoL simulations accounted for a significant portion of wasted compute. [0] https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life#Undecidability https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life#Undeci...
- aj7 2y ago
  Just leave physics out, and you’ll be OK. God doesn’t play the GoL.
_akhe 2y ago
It shows that complex structures, importantly those with generative capabilities and other utilities, can evolve from a simple pattern. It's a fun toy because it's implemented in pixels with arbitrary rules, but the concept is exportable to other domains. The eeriness of it I think comes from that we still don't understand a lot about the world - concepts like consciousness, the origin of the universe, origin of life - or, any mystery where we don't understand how a whole became greater than the sum of its parts - when you see a model like this, it shows visually how such unknown complexities probably originated in far simpler forms. When I see those epic Game of Life videos where there's a giant stealth bomber looking structure steaming across the screen creating sub-processes in its wake, to me it's like a blue whale moving through the ocean, or a vast alien spaceship silently yet steadily barreling through the void of space. There's an ominous intelligence that seems to emerge out of what was once simple, binary, unconscious, incapable.

Why is Conway's Game of Life so interesting? Does it prove anything or lead to insightful discoveries? The game itself seems to me, like a fun little toy at best.

TimTheTinker 2y ago

A simple set of rules leads to a fascinating array of emergent phenomena, which themselves can be utilized to do all sorts of interesting things. In fact, the game of life is Turing complete -- you can build whole processors[0] or programming languages in it. You can even implement the game of life in the game of life. Someone did that and implemented infinite zooming between GOL levels.[1] [0] https://github.com/nicolasloizeau/scalable-gol-computer https://github.com/nicolasloizeau/scalable-gol-computer [1] https://oimo.io/works/life/ https://oimo.io/works/life/

meschi 2y ago

It's a cellular automaton showing complex behavior emerging from very simple rules. Through especially crafted inputs you can simulate a Turing machine or Conway's Game of Life inside itself.

crdrost 2y ago

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.

TimTheTinker 2y ago
Excellent info. > 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.
- seanhunter 2y ago
  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. [1] https://mathworld.wolfram.com/PrincipleofComputationalEquivalence.html https://mathworld.wolfram.com/PrincipleofComputationalEquiva...
  - defrost 2y ago
    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. eg: Lawrence Gray in his 12 page review: https://www.ams.org/notices/200302/fea-gray.pdf https://www.ams.org/notices/200302/fea-gray.pdf Cosma Shalizi's infamous Rare Blend of Monster Raving Egomania and Utter Batshit Insanity review: http://bactra.org/reviews/wolfram/ http://bactra.org/reviews/wolfram/

abetusk 2y ago

Conway's Game of Life (GoL) provides a clear demonstration that simple rules can lead to complex behavior. The complex behavior is deep in the sense that Conway's GoL is Turing Complete [0]. The local update rules provide an analogy to our universe with a kind of built in "speed of light" of how fast information can propagate in the system. Further, since there is a system clock of sorts, the system is massively parallel with further analogies to our universe. The game looks like a toy but note that many profound models are also "toy-like". Ising systems, precolation models, Bethe lattices, self avoiding walks, etc. all provide seeding grounds for deep insights into our physical world. Just as an aside, I heard a quote, which I can't find anywhere, about how Maxwell playing with magnets could have been considered him playing with frivolous toys but his setup was critical to him figuring out the underlying mechanics of electromagnetism. On one hand, I sort of agree that there's a lot of uninteresting exploration but on the other hand, taking a step back, GoL research is exploring the more general space of cellular automata and how it could potentially map to real world simulation. For example, how small can a system be before it can do arbitrary computation? Can all patterns emerge eventually (no, garden of eden style patterns)? What do rotationally invariant patterns looks like? Can you "copy" arbitrary patterns from some setup? If so, how fast? Is it dependent on how big it is, or how complex it is? etc. GoL provides a sandbox in order to answer these questions and potentially give insight into other systems as well. In my opinion, one of the reasons for the popularity of GoL is because it was created right when computers became commodities, allowing hackers, amateur mathematicians and others to program something simple, that could be heavily optimized for limited hardware, and create intricate and complex behavior. There was a quote somewhere, that I'm also having trouble finding, about how, at one point, GoL simulations accounted for a significant portion of wasted compute. [0] https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life#Undecidability https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life#Undeci...

aj7 2y ago
Just leave physics out, and you’ll be OK. God doesn’t play the GoL.

_akhe 2y ago

It shows that complex structures, importantly those with generative capabilities and other utilities, can evolve from a simple pattern. It's a fun toy because it's implemented in pixels with arbitrary rules, but the concept is exportable to other domains. The eeriness of it I think comes from that we still don't understand a lot about the world - concepts like consciousness, the origin of the universe, origin of life - or, any mystery where we don't understand how a whole became greater than the sum of its parts - when you see a model like this, it shows visually how such unknown complexities probably originated in far simpler forms. When I see those epic Game of Life videos where there's a giant stealth bomber looking structure steaming across the screen creating sub-processes in its wake, to me it's like a blue whale moving through the ocean, or a vast alien spaceship silently yet steadily barreling through the void of space. There's an ominous intelligence that seems to emerge out of what was once simple, binary, unconscious, incapable.