[HN Gopher] Learning about Innovation from Half a Century of Con...
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       Learning about Innovation from Half a Century of Conway's Game of
       Life
        
       Author : feelthepain
       Score  : 84 points
       Date   : 2025-03-19 10:52 UTC (12 hours ago)
        
 (HTM) web link (writings.stephenwolfram.com)
 (TXT) w3m dump (writings.stephenwolfram.com)
        
       | kccqzy wrote:
       | > if we want to get closer to the study of the pure phenomenon of
       | innovation
       | 
       | Innovation in the real world is often driven by the usual
       | incentives of capitalism, like the basic need to out-compete the
       | competitors by improving quality or lowering costs. I do not
       | really think Game of Life serves as a model for innovation in the
       | real world; it might serve as a model of the pure phenomenon of
       | innovation. In the real world, even things like pure math
       | research is motivated by applied math, by monetary factors like
       | NSF grants etc.
        
         | leepyaar wrote:
         | This is a myopic view.
         | 
         | How would we have gotten to the point of human history when
         | capitalism became predominant if innovation is driven by
         | capitalism?
         | 
         | Also, humanity is hardly an economy of capitalism any more.
         | More similar to oligarchical capital feudalism.
        
           | enslavedrobot wrote:
           | You're right, it's just a coincidence that the advent of
           | capitalism and an unimaginable increase in global wealth
           | happened at the same time.
           | 
           | Thousands of texts written by historians and economists who
           | dedicate their lives to understanding our past are totally
           | wrong.
        
             | nxobject wrote:
             | I'm not sure what you're saying is inconsistent with
             | parent's comment: you're both talking about different
             | points in time in humanity's history - the snark seems
             | unwarranted.
        
               | enslavedrobot wrote:
               | Calling the parent myopic while saying "Also, humanity is
               | hardly an economy of capitalism any more. More similar to
               | oligarchical capital feudalism." Is deserving of snark.
               | 
               | In the context of 5 centuries of capitalism we live in an
               | age of unprecedented equality, freedom, and opportunity.
               | 
               | Further, observed over the last 5000 years of human
               | civilization the stupendous rise of innovation under
               | capitalism is so dramatic that implying it is not
               | responsible for the wealth we enjoy today beggars belief.
        
           | kccqzy wrote:
           | Well the pace of innovation before the dominance of
           | capitalism was slow. It became much faster afterwards.
        
         | nickpsecurity wrote:
         | I agree. Going back further, we see the innovation drivers were
         | God providing for man (Bible), people providing for their
         | needs/wants at a societal level (most systems), individuals
         | pursuing what they enjoy, seemingly random acts that go against
         | reason, etc.
         | 
         | This was enacted via specific processes (human brain) using
         | resources and their environment within their constraints,
         | sometimes surplus. It involved local and global phenomenon that
         | were dependent and independent.
         | 
         | In short, it's nothing like cellular automata or most
         | simplistic models of the world. We'd have to model the above
         | within this world's laws to know what drives innovation among
         | humans in this world.
        
       | amai wrote:
       | Cellular automata are actually useful to learn something about
       | AI, too:
       | 
       | https://the-decoder.com/edge-of-chaos-yale-study-finds-sweet...
        
       | visarga wrote:
       | The cool thing about Conway's Game of Life is that you can't
       | predict it unless you do the full recursion, there is no
       | shortcut. It relates to external undecidability of recurrent
       | processes.
        
         | whatnow37373 wrote:
         | "Computation irreducibility"[0] is Mr. Wolfram's word for it
         | and I believe it has some relationship to his CA physics, but I
         | won't pretend I understand.
         | 
         | [0] https://en.wikipedia.org/wiki/Computational_irreducibility
        
           | jonahbenton wrote:
           | Yes. He relates an interpretation/definition of the second
           | law of thermodynamics- the increasing entropy thing- to his
           | irreducibility. And builds a computational theory about the
           | role and importance of the physics "observer" in these
           | analyses. Computational irreducibility is basically a
           | statement both about the intrinsic requirement for
           | computation to arrive at the future, and also about the
           | computational capability of the "observer"- a model, or our
           | brains- to arrive, or not, at the future more efficiently.
           | 
           | I am a computational person, not a scientist, and I think
           | science people find him to be speaking total garbage. That
           | seems a correct assessment to me. His model of the world from
           | physics perspective seems wrong. Nevertheless personally I
           | find his computational lens/bias to be useful.
        
             | kennysoona wrote:
             | > I am a computational person, not a scientist, and I think
             | science people find him to be speaking total garbage. That
             | seems a correct assessment to me. His model of the world
             | from physics perspective seems wrong.
             | 
             | I don't think it's that he is speaking garbage, he is
             | basically talking about digital physics which is a real
             | theory being considered and researched, not pseudoscience.
             | 
             | But he doesn't work with the scientific community at all,
             | he just writes his long essays and uses his own terms and
             | ignores anyone else doing similar work. He then gets upset
             | when scientists don't just defer to him.
        
               | cubefox wrote:
               | Though most academic disciplines have a strong "not
               | invented here" bias. It makes you ignore anything outside
               | your citation bubble or from different fields with
               | somewhat different conventions and terms. Even if the
               | other guys are academics as well.
        
         | shakna wrote:
         | Kaggle's competitions [0] do pull a lot of impressive little
         | pieces of code, a number of which actually do take shortcuts.
         | They do define a few things to make it more possible, and there
         | is luck involved not just deterministic results.
         | 
         | [0] https://www.kaggle.com/c/conways-reverse-game-of-
         | life-2020/o...
        
         | brzozowski wrote:
         | Wouldn't every Turing complete cellular automaton have this
         | property? What would be an example of a nontrivial (i.e.,
         | sufficiently expressive) CA that is "predictable"?
        
           | 1ewish wrote:
           | I believe this is part of Wolfram's general point around
           | computational irreducibility - there are none.
        
           | tromp wrote:
           | One example would be a CA that takes an exponential number of
           | steps to emulate n steps of a Turing machine. That allows you
           | to predict exponentially far into the future by running the
           | TM machine instead.
        
             | bob1029 wrote:
             | This insight is why I stopped trying to use CA as my
             | underlying computational substrate in genetic programming
             | experiments. It is _much, much_ cheaper to run something
             | like brainfuck programs than it is to simulate CA on a
             | practical computer.
             | 
             | A switch statement over 8 instructions contained in a
             | contiguous byte array will essentially teleport its way
             | through your CPU's architecture.
        
       | dvh wrote:
       | If you like game of life you gonna love this video about
       | backwards game of life: https://youtube.com/watch?v=g8pjrVbdafY
        
       | MattGrommes wrote:
       | I feel like I'm too dumb to understand whether these CA articles
       | of his are interesting or just numerology deep-dives like people
       | who spend their lives "investigating" the torah.
        
         | leephillips wrote:
         | He's been at this for decades, without a single prediction of
         | any phenomena in nature. His theories can't even reproduce
         | known physical phenomena correctly. So you can be dumb and
         | still correctly conclude that it's basically numerology.
        
         | jerf wrote:
         | From the article, for some context for what I'm about to say:
         | 
         | "And indeed, what we'll often see is that the more optimized a
         | structure is, the less modular it tends to be. If we're going
         | to construct something "by hand" we usually need to assemble it
         | in parts, because that's what allows us to "understand what
         | we're doing". But if, for example, we just find a structure in
         | a search, there's no reason for it to be "understandable", and
         | there's no reason for it to be particularly modular."
         | 
         | If I were going to sum up what I will politely call Wolfram's
         | Conjecture, it is that there is some other way to start with
         | some sort of understanding of cellular automata and derive from
         | that understanding the ability to model systems, and presumably
         | the ability to build systems in cellular automata, using that
         | superior understanding that are not characterized by the
         | modularity shown in human constructions. Something like chaos
         | mathematics, but for cellular automata, and presumably,
         | something that goes beyond statistical characterization into
         | some sort of deeper understanding that is somehow analogous to
         | our ability to deeply understand the modular systems.
         | 
         | For the purposes of what I'm saying here, I'm virtually
         | equating "understanding" with "ability to meaningfully
         | manipulate". You or I may not be able to manipulate one of the
         | human constructed systems in Life, but there is a path to learn
         | how that is observably human-comprehensible and capable of
         | being conveyed through human communication, because it has
         | been. By contrast, the article shows many cases of "humans
         | constructed this system with property X, and by random search
         | we found a much more efficient system with that property, but
         | it is not something a human could ever have reasonably
         | designed".
         | 
         | What I may less charitably call "Wolfram's Mistake" is that
         | there is at the moment frankly no evidence that I can see that
         | such a thing is true, despite him having been searching for it
         | for a very long time.
         | 
         | There's two angles on that, which are: One, is there any such
         | understanding that is _accessible to human cognition_? And two,
         | is there any such understanding _at all_ , without that
         | limitation, but with some sort of finite level of intelligence
         | significantly smaller than the level necessary to just brute
         | force the problem?
         | 
         | Or, to put it another way, it is not hard to hypothesize
         | intelligences that could just glance a description of Life and
         | then simply internally simulate systems directly looking for
         | whatever you like. You may consider them something like "What
         | if a human just had a modern computer built directly into their
         | brain?" They would have vastly, vastly more raw computational
         | power than a human without that for this purpose, but, is there
         | any sort of understanding of cellular automata in general or
         | even Life in particular that is meaningfully more compact than
         | simply running the automata?
         | 
         | If you want to dig more into what it means to "understand"
         | something, I refer you to "Why Philosophers Should Care About
         | Computational Complexity"
         | https://www.scottaaronson.com/papers/philos.pdf , rather than
         | trying to further elaborate in this post. An "understanding" of
         | this sort of cellular automata, whatever it may be, no matter
         | how alien the system that has this "understanding" may be,
         | should me meaningfully more computationally compact than the
         | exponential complexity of simply having a table of all
         | possibilities in memory.
         | 
         | From this perspective "Wolfram's Mistake" is that there is no
         | such understanding; there is fundamentally no way to create a
         | computational model for the phenomena in a cellular automata
         | system that is simpler than the cellular automata itself in a
         | general case.
         | 
         | Which means that rather than being the key to understanding,
         | they're actually a really bad lens to try to view the world
         | through for any sort of understanding by us finite beings. As
         | incomplete and simplified as our many other lenses may be, at
         | least they work in _some_ cases. Cellular automata don 't seem
         | amenable to compact theories of any utility. (And by "any
         | utility", I mean, _any_ utility; scientific, mathematical,
         | engineering, practical, all of them.) There 's a few places of
         | use, but not very many.
         | 
         | An interesting aspect is that while all Turing Complete systems
         | ultimately exhibit this behavior, they do not seem to all do so
         | _equally_. Lambda calculus, for instance, has all the same
         | chaos in some sense, if for no other reason than you can always
         | create the game of Life directly in lambda calculus. Yet lambda
         | calculus _also_ admits human understanding. I select lambda
         | calculus in particular as one of the most human-friendly Turing
         | Complete formalisms. Turning them into actual useful
         | programming languages is on the order of  "useful learning
         | exercise". Turing machines are sort of in between; we can work
         | with them, but they do tend to explode into chaos relatively
         | easily. Cellular automata, by contrast, require _extreme_ human
         | effort to work with, just to get them to halfway tame. There 's
         | an interesting study here about why that is, which is currently
         | well beyond me.
         | 
         | Again, looking at Wolfram's Conjecture another way is that this
         | is somehow not correct and we're just not looking at CAs
         | correctly, and if we did, they might become more useful than
         | Turing machines or perhaps even lambda calculus, and, again, I
         | just don't see the evidence for this.
        
         | IshKebab wrote:
         | Yeah I always felt his writing had the unmistakable aura of
         | quackery, despite being apparently correct maths. Weird vibe
         | for sure.
        
       | 1ewish wrote:
       | Whilst it is not framed as such, there are some interesting high
       | level takeaways in here for AI, particularly around e.g program
       | synthesis/induction and ARC.
       | 
       | I think Wolfram could contribute a lot if he shifted his focus
       | towards these domains.
        
       | dang wrote:
       | [stub for offtopicness]
        
         | Suppafly wrote:
         | [flagged]
        
           | moregrist wrote:
           | It's more like a continuous eye roll since 2002 when he
           | released _A New Kind of Science_.
           | 
           | I spent around 15 years working on stochastic lattice models.
           | They can be amazing. They can also fail to capture the
           | essence of the problem. Same with cellular automata.
           | 
           | They're definitely not _new_. They weren't new in 2002. I've
           | always viewed Conway's game of life as an interesting
           | deterministic variant of an Ising model, and Ising models
           | date back to the 1920s.
           | 
           | Most physicists I knew at the time looked at the book,
           | shrugged, and kept working on what they were doing. I love
           | lattice models, cellular automata, lattice fluid models, and
           | the like. But they're just one class of useful model.
           | 
           | And yet because Wolfram has a perpetual money machine called
           | Mathematica, he's got a huge megaphone to advocate for
           | himself.
           | 
           | I'll keep rolling my eyes. I don't hate the guy, but he is
           | just a little too into self-promotion for my taste.
        
             | MengerSponge wrote:
             | "Still not sure which will become self-aware first: Wolfram
             | Alpha, or Stephen Wolfram"
        
             | Suppafly wrote:
             | >I'll keep rolling my eyes. I don't hate the guy, but he is
             | just a little too into self-promotion for my taste.
             | 
             | That's fair, but a lot of the hate here is unreasonable.
        
             | nxobject wrote:
             | Not to weigh against Wolfram one last time, but he's
             | (finally?) renamed Mathematica just "Wolfram". Why he would
             | toss out years of brand-related goodwill is beyond me.
        
               | SubjectToChange wrote:
               | Have you opening Mathematica recently? Or visited the
               | product page for Mathematica[1]? The only change has been
               | branding the language itself as the "Wolfram Language"
               | where Mathematica is just one of their product offerings.
               | 
               | [1]: https://www.wolfram.com/mathematica/?source=nav
        
               | nxobject wrote:
               | Mathematica is open on my computer as we speak (or,
               | rather, now Wolfram.app). The "About" screen indicates
               | "Wolfram 14.2". I have a seat on an site licence.
               | 
               | https://imgur.com/a/WUpSsF8
               | 
               | (If you're interested in what I'm currently doing with
               | it, I'm playing around with Mathematica's neural network
               | library.)
        
               | SubjectToChange wrote:
               | _The "About" screen indicates "Wolfram 14.2"_
               | 
               | Mathematica (MMA) and the Wolfram Language (WL) used to
               | be the one and the same. But now a user could be using WL
               | in a web based notebook, through Wolfram Alpha, or even
               | on SystemModeler.
               | 
               | The brand name "Mathematica" isn't going anywhere, not
               | after nearly forty years. It's basically marketing being
               | like "how do we communicate updates to WL as not just
               | being updates to MMA?".
        
               | kgwgk wrote:
               | > The brand name "Mathematica" isn't going anywhere
               | 
               | But it's not what it used to be. Now you don't "run"
               | Mathematica - you "access" it running another program.
               | It's basically marketing to weaken one brand and
               | strengthen the other.
               | 
               | "Upgrading from Mathematica to Wolfram"
               | 
               | https://reference.wolfram.com/language/tutorial/Upgrading
               | Fro...
        
               | FilosofumRex wrote:
               | you got to be joking, do you play with slide rules and
               | abacus too
               | 
               | NN in Mathematica is a just a toy and artifact of a
               | bygone era. Try HuggingFace
               | https://github.com/huggingface/course
               | 
               | or Karpathy's intro https://github.com/karpathy/nanoGPT
        
               | Suppafly wrote:
               | >Why he would toss out years of brand-related goodwill is
               | beyond me.
               | 
               | I suspect that Wolfram is the bigger name ever since
               | Wolfram Alpha has been a thing. I'm sure way more people
               | interact with that than Mathematica. Besides, as far as I
               | can tell, it's still named and marketed as Wolfram
               | Mathematica, not really sure where you got the idea it
               | was renamed.
        
             | SubjectToChange wrote:
             | _And yet because Wolfram has a perpetual money machine
             | called Mathematica, he's got a huge megaphone to advocate
             | for himself._
             | 
             | Wolfram primarily posts to his blog and occasionally
             | publishes a book. He's not exactly buying a marketing blitz
             | with all of his money. Wolfram Research itself is primarily
             | focused on other things too.
             | 
             | I don't know what it is about Stephen Wolfram that drives
             | people crazy. Yes, he's self aggrandizing, but he's hardly
             | unique in that respect. Simply read past it or roll your
             | eyes and move on. But apparently there are more than a few
             | people who can't help themselves (even this thread is an
             | example).
        
         | InkCanon wrote:
         | Wolfram's problem is mindset IMO. There's a certain kind of
         | highly intelligent mind, but because of fame, money, habit or
         | personality, makes them intellectually lazy. Instead of doing
         | the proofs, research, careful discussion and reconceptualizing
         | that leads to useful theories and conclusion, they jump
         | straight to the end, because they think they're smart. This
         | produces some impressive sounding theory, but which upon closer
         | inspection proves to be to be too vague to actually be
         | testable, if not contain outright errors. People I put in this
         | group including Wolfram and his computational theories, Langan
         | and his Cognitive Theoretical model of the Universe, and the
         | Italian school of algebraic geometry. There's a kind of
         | interesting perception here. A reasonable person thinks one who
         | makes correct theories is an intelligent man. Others think they
         | are intelligent, so therefore their theories are correct.
        
           | hollerith wrote:
           | My impression is different: I think Wolfram is plenty hard-
           | working, but his internal mental life is so full of fantasies
           | of unlimited success and fame that he cannot manage an
           | impartial-enough evaluation of his own work output.
        
             | mentalgear wrote:
             | any specific source ? (fire time I hear that about Wolfram
             | )
        
               | hollerith wrote:
               | My impression is based on hearing him speak for a few
               | hours and maybe some biographical facts such as can be
               | gotten from Wikipedia.
        
             | FilosofumRex wrote:
             | "your impression", is true only in the Ruliad. Ask people
             | who knew him back in the 80's... he never worked on
             | anything on his own that has amounted to anything. He is a
             | real life crank, crackpot and all around charlatan.
             | 
             | Mathematica is the product of 30 years of work on Macsyma
             | and Maple systems at MIT and elsewhere, which he cracked
             | its codebase, usurped and sold to an unsuspecting academic
             | community back when only the likes of Bill Gates would do
             | such as thing.
             | 
             | He also missed the entire LLM wave because he refused to
             | open source WolframAlpha codebase and work with others in
             | the NLP community.
        
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