The Lasting Lessons of John Conway's Game of Life 84
Siobhan Roberts, writing for The New York Times: In March of 1970, Martin Gardner opened a letter jammed with ideas for his Mathematical Games column in Scientific American. Sent by John Horton Conway, then a mathematician at the University of Cambridge, the letter ran 12 pages, typed hunt-and-peck style. Page 9 began with the heading "The game of life." It described an elegant mathematical model of computation -- a cellular automaton, a little machine, of sorts, with groups of cells that evolve from iteration to iteration, as a clock advances from one second to the next. Dr. Conway, who died in April, having spent the latter part of his career at Princeton, sometimes called Life a "no-player, never-ending game." Mr. Gardner called it a "fantastic solitaire pastime." The game was simple: Place any configuration of cells on a grid, then watch what transpires according to three rules that dictate how the system plays out.
Birth rule: An empty, or "dead," cell with precisely three "live" neighbors (full cells) becomes live.
Death rule: A live cell with zero or one neighbors dies of isolation; a live cell with four or more neighbors dies of overcrowding.
Survival rule: A live cell with two or three neighbors remains alive.
With each iteration, some cells live, some die and "Life-forms" evolve, one generation to the next. Among the first creatures to emerge was the glider -- a five-celled organism that moved across the grid with a diagonal wiggle and proved handy for transmitting information. It was discovered by a member of Dr. Conway's research team, Richard Guy, in Cambridge, England. The glider gun, producing a steady stream of gliders, was discovered soon after by Bill Gosper, then at the Massachusetts Institute of Technology.
Birth rule: An empty, or "dead," cell with precisely three "live" neighbors (full cells) becomes live.
Death rule: A live cell with zero or one neighbors dies of isolation; a live cell with four or more neighbors dies of overcrowding.
Survival rule: A live cell with two or three neighbors remains alive.
With each iteration, some cells live, some die and "Life-forms" evolve, one generation to the next. Among the first creatures to emerge was the glider -- a five-celled organism that moved across the grid with a diagonal wiggle and proved handy for transmitting information. It was discovered by a member of Dr. Conway's research team, Richard Guy, in Cambridge, England. The glider gun, producing a steady stream of gliders, was discovered soon after by Bill Gosper, then at the Massachusetts Institute of Technology.
More context required! (Score:5, Insightful)
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I wouldn't call The Game of Life [wikipedia.org] an obscure game!!1
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I am pretty sure Mr. Gardner had a bigger purpose for this game. If he just wanted to waste time he would have been playing Dwarf Fortress. [wikipedia.org]
Comment removed (Score:5, Funny)
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Supplied on tape ... nah. Back in my day we had to write our own.
This was the final for my high school programming course. Implement Conway's Game of Life in Pascal. I believe we had one week if I remember correctly.
Now *I* feel old and depressed too counting the decades since. Thankfully we're still counting with one hand, but not by a whole lot .... Great.
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Correct. And you don't write it just once. I have written it many times, first literally as cells in a 2D array. I wrote it in assembly language too. I later wrote sparse list versions (since most cells are usually empty). I have written it using bit parallelism (generating 8x4 "bricks" of cells) with lookup tables, with lookup tables and with sparse representations. I wrote it as a Java applet for a now ancient web page (1995). I never implemented HashLife though.
Today https://sourceforge.net/projects/goll
Headline: "Lasting lessons" Summary: Nope (Score:4, Insightful)
The summary merely summarises the game, without even mentioning the "lasting lessons" in the headline.
You must be so proud of your work.
Editors, EDIT !
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Slashdot isn't a conventional publication and Slashdot editors aren't conventional editors. You might understand better if you think of them as people who... don't edit.
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That's so true. In fact it's so un-conventional that it still doesn't support UTF-8 in 2020.
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Maybe these people - who do, after all, call themselves "editors" - can take this short course ?
JOURNALISM 001:
- THE HEADLINE MUST DESCRIBE THE STORY IN AN ATTRACTIVE WAY, USING SIMPLE TERMS THAT THE VAST MAJORITY OF READERS WILL UNDERSTAND.
- THE SUMMARY MUST INCLUDE THE MAIN POINTS OF THE STORY AND ANY TERMS USED THAT WILL NOT BE UNDERSTOOD BY THE VAST MAJORITY OF READERS MUST BE EXPLAINED.
Too much to ask ?
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Too much to ask ?
Considering that "spend three minutes a day skimming the front page to make sure you're not reposting the same thing" is apparently too much to ask, I'm going to go with "yes."
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"Editors, EDIT !"
You must be new here.
complexity from simple rules (Score:5, Interesting)
For example:
DNA has very simple rules, but the resulting structures are incredibly complex.
https://www.scripps.edu/news-and-events/press-room/2020/20201223-krishnamurthy-dna.html/ [scripps.edu]
Re:complexity from simple rules (Score:5, Informative)
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I have yet to see emergence used as an explanation of "why something is so".
Emergent properties can be explained, but they cannot be inferred from the isolated component compounds of a system demonstrating emergence.
You misunderstand emergence, just as you (most likely) minstunderstand evolution.
Re:complexity from simple rules (Score:5, Interesting)
You could say that the rules of binary are also similar. DNA has A, T, G and C while binary has 0 and 1.
The resulting structures of DNA are incredibly complex, but the thousands of data/file formats and sub-formats and data chunks (etc) of different types of data are also extremely complex too.
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What might be interesting (likely someone has thought of it long before I did) would be a 'game' of life where you use 4 different color coded squares - call them A, T, G, and C - and then establishes "rules" like life, but recognizing synergies and having rules resulting therefrom.
Feels like that would be exponentially more complicated and might result in some insights.
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Setting that game in a 3D grid could be even more insightful.
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And beautiful to watch, honestly.
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If you unwind one strand of the helix you will be able to build its complement strand, based on what has to be on the "other side" to match up.
Evolution, operating on immense timescale and impossibly large permutations and experiments, seems to come down to binary systems. Male/Female , (AT)/(GC)
It is possible to come up with triple gender biomes (
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It's not really binary, because A-T isn't the same as T-A. It depends on which DNA strand the amino acid is on, so each 'bit' in the sequence still has 4 possibilities. For a particular sequence, the matching strand has only 1 possibility, but that's irrelevant to this discussion.
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And there are a fair number of organisms that can reproduce asexually, from bacteria to fish and reptiles. Single cell organisms at least are able to adapt pretty quickly this way, despite being almost copies of the predecessor. I was tempted to make an oblique reference to Jurassic Park, but that was changing
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The amino acid encoding in DNA isn't "the rules."
The rules are how that code gets translated into proteins. They're surprisingly simple, but lead to an incredible diversity of self-assembling chemical machines.
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Yes, that's kind of the same point. But Conway's Game of Life is extremely easy to study in silico and has much simpler rules than chemistry.
For astrophysics nerds... (Score:5, Interesting)
Stephen Wolfram's book A Project to Find the Fundamental Theory of Physics [amazon.com] basically hypothesizes that the universe is a gigantic game of life. He follows this hypothesis a long ways, reproducing a lot of results from physics. I've only read a summary and excerpts, but it really is a fascinating hypothesis. Even if not correct, it provides another way to look at some physical phenomena, and may well provide some valuable insights.
Re:For astrophysics nerds... (Score:5, Interesting)
Stephen Wolfram's book A Project to Find the Fundamental Theory of Physics [amazon.com] basically hypothesizes that the universe is a gigantic game of life. He follows this hypothesis a long ways, reproducing a lot of results from physics.
He doesn't really. He sketches outlines of things but since his whole thesis is digital, it falls apart when faced by quantum effects, so he has to start above that level. It also doesn't really work at the very large scale, so he has to stop below that level.
It's a cute idea, but it doesn't really say much about the real world, although it has some application in simulations (which of course are digital).
Re:For astrophysics nerds... (Score:4, Interesting)
> since his whole thesis is digital, it falls apart when faced by quantum effects,
Except that the Universe IS digital -- according to Physicists. i.e. Plank Length [wikipedia.org] (1.61 x 10^-35 m) and Planck Time [wikipedia.org] (5.39 x 10^-44 s) are quantized. As far as Modern Science knows nothing smaller or shorter exists and we (currently) have no way of measuring even anything remotely close to these small amounts.
The bigger problem is that Physicists pulled these fundamental physical constants out of their ass [wikipedia.org] because the math "works". Other "magic numbers" [wikipedia.org] such as the fine-structure constant [wikipedia.org] is proof that Physicists have no rational explanation for why THOSE particular constants have the values they do compared to a DIFFERENT set of constants. e.g. Why 1.61 x 10^-35 and not 1.62 x 10^-35 or 1.60 x 10^-35
for Planck Length??
As Feynman famously said the fine-structure constant:
Modern Science is a complete clusterfuck of hacks so the math conveniently "works out".
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Digital is not the same as granularity. Then if it is continuous "all the way down", the next question is at what level of transfinite set?
LOL no (Score:1)
Contrary to popular belief planck length may not be the shortest unit of length possible in spacetime
If only you or the moderators had bothered to read the first pargraph of your own link.
(or had a clue what they were talking about)
The Planck length refers to the internal architecture of particles and objects. Many other quantities that have units of length may be much shorter than the Planck length. For example, the photon's wavelength may be arbitrarily short: any photon may be boosted, as special relativity guarantees, so that its wavelength gets even shorter.
The Planck length is sometimes misconceived as the minimum length of space-time, but this is not accepted by conventional physics, as this would require violation or modification of Lorentz symmetry
Didn't this used to be a place where at least a few smart people came?
Re:LOL no (Score:4, Interesting)
While there's a theory that the wavelength of a photon can be arbitrarily short, that's not proof. I suspect that it can't. In fact, I would assert that if the energy contained within a photon gets large enough, the photon will collapse into a black hole. I've got to admit that I'm not sure what that wavelength would be, but it might well be around the Planck length.
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It's the Planck length.
Re: LOL no (Score:2)
The second paragraph directly supports the quoted statement.
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Planck length and time are related to Planck's constant which is related to the Heisenberg Uncertainty principle which represents an actual smallest unit of precise measurement... therefore the Universe IS Digital.
Didn't this used to be a place where at least a few smart people came?
Just because you are an AC doesn't mean you have to also be an ASS.
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Yes, it was once such a place.
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Standard Plank length is 8ft.
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Wrong question.
Correct question why is Plank time designed like this?
Plank length is the distance light passes during one tick of Plank time.
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While I get your point and to some degree agree, let's remember that "math" is a symbolic language meant to represent actual things. It's a question of teleology.
"3" merely represents a group of objects (or distance on a 1 dimensional line, etc) is an integer collection of objects that is more than a pair and less than 2 pair.
So, to use my favorite example, if you draw a perfect circle in our Euclidean perception of reality, pi is peeking out from it - every one. That doesn't mean pi is there, of course,
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"Quantized" doesn't mean "digital." It doesn't even mean "discrete" despite computer types jumping to that conclusion.
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> since his whole thesis is digital, it falls apart when faced by quantum effects,
Except that the Universe IS digital -- according to Physicists. i.e. Plank Length [wikipedia.org] (1.61 x 10^-35 m) and Planck Time [wikipedia.org] (5.39 x 10^-44 s) are quantized.
Not the same thing.
As far as Modern Science knows nothing smaller or shorter exists and we (currently) have no way of measuring even anything remotely close to these small amounts.
The bigger problem is that Physicists pulled these fundamental physical constants out of their ass [wikipedia.org] because the math "works".
Finding out that there's a formula that describes an observation is not "Pulling something out of your ass".
Other "magic numbers" [wikipedia.org] such as the fine-structure constant [wikipedia.org] is proof that Physicists have no rational explanation for why THOSE particular constants have the values they do compared to a DIFFERENT set of constants. e.g. Why 1.61 x 10^-35 and not 1.62 x 10^-35 or 1.60 x 10^-35
So what? Were you expecting a Teacher's Edition of the universe with all the answers already provided? Finding out why things are the way they are is what science is about and it takes time.
Modern Science is a complete clusterfuck of hacks so the math conveniently "works out".
You seem confused.
Re: For astrophysics nerds... (Score:2)
In a way that makes a case to see the universe as digital or discrete, but if placement of objects is not restricted I disagree with calling the universe, it reality, digital or discrete instead of co
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> since his whole thesis is digital, it falls apart when faced by quantum effects,
Except that the Universe IS digital -- according to Physicists. i.e. Plank Length [wikipedia.org] (1.61 x 10^-35 m) and Planck Time [wikipedia.org] (5.39 x 10^-44 s) are quantized. As far as Modern Science knows nothing smaller or shorter exists and we (currently) have no way of measuring even anything remotely close to these small amounts.
Planck time means that you cannot make meaningful distinctions about time units less than a certain amount - it does NOT mean that time is quantized at that amount. Likewise with other measurement issues, distances can come in quantities less than the Planck length, we just can't tell the difference between distances less than the Planck length.
More generally, we currently cannot tell if time is quantized. There are theories that it has to be quantized to reconcile general relativity with quantum mechanic
Re:For astrophysics nerds... (Score:5, Interesting)
Oh, so Wolfram has managed to turn 1,200 pages [amazon.com] into 2,100 pages, has he? Great, great. How far along is he at revolutionizing all of science and establishing himself as the single greatest mind in the history of intellectual pursuit? Any further than my retired step-uncle?
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...the universe is a gigantic game of life.
It's a cute idea, but it doesn't really say much about the real world....
The Game of Life is unlikely to resemble the universe at any scale, since it has almost no structural stability [wikipedia.org]. Changing A SINGLE CELL often demolishes whatever pattern you had going. If real life were like that, people would behave rationally almost all the time, but occasionally do things that make no sense at all. Oh wait...
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It's probably correct that you can model the universe that way. After all, you can model a (finitely limited) Turing machine that way, so you can model anything computable.
You might consider what it would mean to say that this model was more correct than other models that yield the same results.
the first few paragraphs of an article I read... (Score:1)
Let me copy/paste them for you, and then you can ponder about why the article was important afterward, since I left that detail out of the fucking summary.
Honestly, why was this posted at all?
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Because Ads.
Intelligent design (Score:1)
I've sometimes heard Conway's Game of Life referred to as an example of complexity arising from just a few simple rules, as evidence against creation or intelligent design.
The glider and glider gun are certainly interesting things that were apparently "discovered" rather than created. But, the most amazing things I've seen in the Conway's Game of Life, are evidently results of human construction, rather than randomly occurring.
The Game of Life rules themselves are "fine tuned" for the most interesting "life
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And the same set of rules would probably give completely different results (i.e. more/less interesting) in a 3D environment.
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Yes, some of the most interesting things in Game of Life were 'made', because people use their intelligence or understanding, rather than leaving it chance. But they do that because they can and it was not essential, so this is a trivial point. If enough random seeding had been carried out these interesting things would almost certainly have emerged at some point. Or possibly other even more interesting things.
You can crossbreed two selected living organisms to produce an interesting or more complex resul
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It would take many, many orders of magnitude more soup-searching before anything rivalling the most impressive "engineered" patterns is likely to appear,
Random results (Score:2)
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That would be fine except for the fact that no game of life can even begin until a designer has seeded the plane to be at some initial state.
Even if the state is such that it continues to run forever in some vastly long cycle, no application of Occam's razor can ever be used on a snapshot of an in-progress game to imply that there was never someone who initially seeded that game, yet it is almost invariably invoked to refute intelligent design.
I would suggest that the surprising complexity that arises
Chaotic patterns? (Score:2)
Just curious: are there patterns that are truly chaotic? Or can you only ever have patterns that repeat themselves after some point?
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As per this article [conwaylife.com], it's unknown. I suspect that proving whether or not a pattern is truly chaotic is fundamentally undecidable is equivalent in difficulty to the halting problem.
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Descendants of the original replicator will crash into each other with horrific results in the crowded center, making a chaotic mess of ever-increasing diameter, while the replicators at the ever-expanding frontier will
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It's possible to prove that patterns are non-periodic, e.g. Penrose tilings, which is what I assume the OP means by "chaotic." Determining whether a given seed evolves into such a thing is of course a much, much more difficult problem than proving such a thing exists.
Re: Chaotic patterns? (Score:5, Interesting)
I believe it's always one of two cases: either a pattern repeats with a certain order or given enough interactions it fizzles out to a steady state. Both can occur locally but there is no true chaos without further human input. This is why it can be simulated very officially. Once the localized patterns are computed and any interacting patterns, you are left essentially with localized events that can be played like a movie (I.e. recorded bits). It's turing complete so there are write ups about projects that simulate Tetris on a gameboy architecture, implemented in Conway's GoL. Pretty funny and interesting stuff.
We could ask the question backwards though, where would any chaos in the game arise from within the rules. This is actually the most interesting part of the Bible. Genesis presupposes the existence of chaos before the creation event which is a fun discussion to have with many religious types. Likewise any mathematical model that accounts for a generating event (e.g. The Big Bang) has to first presume the existence of Chaos, even if they model accounts for the emergence of physical forces... As such chaos is the most significant a priori in large scale physical modelsbut likewise is not something we can computationally model. At best a computer measures a chaotic event to generate a truely chaotic signal.
Chaotic patterns - $30,000 prize (Score:2)
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I think you misunderstand the purposed prizes (plural). Three problems and three definitions of randomness which should not be confused with chaos and likewise three different prizes. As such each of the work completed on each problem begins to highlight a bit more about the others.
For instance, the work done on problem 1 actually begins to illuminate potential tricks to problems 3. It's already clear that part of the set is periodic, as such, there is a virtual certainty that there exists a shortcut to co
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As such chaos is the most significant a priori in large scale physical models but likewise is not something we can computationally model
Really? How do you explain the emergence of the Mandelbrot set from a very simple generating rule?
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The complexity arises from the complex algebra. This is a good example that counters my point about easily computationally modeling it but it's also kind of an esoteric example and ultimately when we study fractals we find they are a kind of mathematics that comes out of chaos to bring order. Making this argument of "order" is a bit more challenging in terms of the mandelbrot set because it's abstract but we are now understanding through multi-fractal analysis that DNA uses fractal patterns to build resista
Youtube video explaining it much better (Score:2)
Explains the history, the types of creatures in the game, and how they can be used to build a computer
https://www.youtube.com/watch?v=Kk2MH9O4pXY
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Golly... (Score:2)
There are a few Conway's Game of Life programs out there - it looks like Golly [sourceforge.net] is the most cross-platform (yes, it's even on Android/iOS!), has a ton of options and comes with a bunch of useful examples you can load without having to start from scratch editing your own.
Re:Golly... (Score:4, Informative)
The first link goes to a complete self-constructing spaceship, the Speed Demonoid -- copy.sh/life is an online HashLife implementation that's fast enough to simulate the whole thing in a browser.
The second link shows a LifeViewer "Exploratorium" display of a number of Life discoveries, old and new. Point of interest #20 shows the new doo-dah spaceship, which is another of the discoveries from 2020 that the article mentions. LifeViewer also handles most of the animations in LifeWiki [conwaylife.com] articles, and on the conwaylife.com forums [conwaylife.com].
lacking detail (Score:2)
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My first C program project... (Score:2)
Lasting lessons? Well how to program, but working out the logic to make the program was the real learning experience.
Man, that was a long time ago....
Video on the subject (Score:2)
There's a fantastic video on the subject by a guy called Dylan Beattie. My wife is not into computer science or maths and she thought it was amazing.
It starts at 4:20. The rest of this video is also well worth a watch.
https://www.youtube.com/watch?v=6avJHaC3C2U&t=260s [youtube.com]
Conway did lots more (Score:2)
Here's just one other example of the wacky things he came up with.
FRACTRAN https://en.wikipedia.org/wiki/FRACTRAN [wikipedia.org]
I wrote an interpreter in R https://cran.r-project.org/package=Rfractran [r-project.org] ; there are interpeters in many other languages out there.
WATOR Was Another Example (Score:3)
Very interesting game, fairly simple code, could be ported to most anything. Source was originally in Scientific American Magazine, quite the surprise!
https://en.wikipedia.org/wiki/... [wikipedia.org]
https://www.cs.mcgill.ca/~carl... [mcgill.ca]
https://github.com/hauerCodes/... [github.com]
https://www.triplespark.net/si... [triplespark.net]
http://www.leinweb.com/snackba... [leinweb.com]
https://people.duke.edu/~ng46/... [duke.edu]
I played with it for a long time, adding more variety in the interactions. Even added dolphins (and a primitive AI), whales (browsing on plankton), starving sharks going cannibalistic. Very interesting indeed.
Trees in Slay (Score:2)
There's a strategy game called "Slay" that I enjoy. Available for Windows, Android, iOS
http://www.windowsgames.co.uk/slay.html [windowsgames.co.uk]
On Android, it's a one-player game, but you play it as if it was a a multi-player game; the AI plays all sides other than your side. But in addition to the sides, there are trees.
When a pawn dies, it is replaced on the next turn with a little cross; then on the next turn, the cross is replaced with a tree. Also, levels start with initial trees.
The trees grow according to simple ce
The Life game (Score:1)