[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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