Conway's Game of Life Extrusion | Hacker News Reader

Conway's Game of Life Extrusion

qotile.net

94 pointsbrunoc29 comments

Cellular automata, which includes Conway's Game of Life, is impressive because of the complexity that arises from simplicity. Starting from just a few simple rules and starting arrangements, structures can appear that you would never have expected.

Some people believe that our universe could be a type of cellular automata itself.

There are some interesting connections between our universe and the type of cellular automata like Conway's Game of Life. It is possible to predict events in the future by looking at the big picture. Various levels and hierarchies of structures are formed in Conway's Game of Life (e.g. gliders and glider guns) that seem to obey their own rules. However, these macro rules are nowhere close to the original micro rules of the simulation. While we can look at these macro rules to make certain predictions, the only way we can determine every cell's state in the future is by letting the simulation play out one generation at a time.

What I find interesting is that deterministic computation (like cellular automata) does not mean predictable results. Vast complexity, both in seemingly random/noisy patterns and repetitive twisting/scrolling patterns, can emerge from the simplest rules. This seems to indicate that a deterministic model of the human brain/mind (or for that matter, the entire universe) does not lead to the unsatisfactory dehumanizing implication that we're all predictable or lack free will.

And yet if a system is deterministic, it certainly is predictable (read: able to be predicted) and does lack free will. So if the universe is a deterministic automata the 'unsatisfactory dehumanizing implication' stands. Despite this, the only way to predict the state of a Conway system n iterations from now is to allow the system to run for n iterations. No one could actually model the universe precisely by creating a cellular automata. The automata would have to contain as much information as the universe, so it couldn't fit within the universe. Also even if the builder did know the system rules and a valid starting condition he could only compute as fast as 1 iteration per iteration of the actual universe...and hence not be able to outpace the universe and predict the future. I think solipsist is right about macro vs micro rules. And the macro rules themselves have macro rules ad infinitum. At some point you get to macro rules that try to describe human behavior (which apparently don't work very well). I don't think the cellular automata reductionist approach will help us too much in predicting the future in our universe for reasons mentioned above. We may be better off with macro rules like Newtonian physics and so forth.

Perfect explanation. I'm pretty sure that macro is the way to go. I have a theory that you can take anything and separate it into macro and micro levels (whether it be economics, science, etc.) You can look at systems at different scales and, while there is sometimes an intermediate, it's usually possible to separate the interpretations into two distinct categories.

As mkrecny stated, choosing to observe and predict the micro aspects of our universe is a lost cause. However, finding patterns in higher levels of systems is what makes science works. While micro systems are usually the areas left for theorists, macro systems have real life applications for scientists. We predict things every day and some things are simply easier to predict than others.

His explanation isn't perfect. It's quite flawed. Rice's theorem (and the more well-known halting problem) demonstrates that deterministic computation is absolutely unpredictable.

It does not follow that a deterministic system is predictable, depending on what you mean by "predictable", in theory or in practice. A Turing machine is deterministic, but predicting whether it will halt or not is not decidable.

Not true. Determinism does not imply predictability where predictability means "able to be computed faster than just waiting for the algorithm to play out." When the whole universe is performing a computation, even if it's deterministic, there's no way to "predict" in the sense of knowing a future event before it takes place. Any other definition of "predictable" doesn't make sense.

An additional (and perhaps stronger) argument is that Rice's theorem states that you cannot in general predict the behavior of deterministic computation. You can't know if a program will ever access the network card, output a letter "A," halt, etc. even though all of these programs are known to be deterministic.

I don't think anyone is saying that we can create a cellular automata (or any computer) capable of simulating the entire universe. That doesn't mean that the universe can't be modeled as one. You can't simulate an Intel i5 CPU in realtime in Windows 7 running on an Intel i5, but that doesn't mean an i5 isn't deterministic.

As a side node, the potential richness and unpredictability of deterministic computations is a major theme of many works by Rudy Rucker. Any investigation of cellular automata will reveal the unpredictability of deterministic computation, which is essentially the whole point behind cellular automata.

I feel like you stopped reading after the first sentence as we ended up saying the same thing. I certainly don't mean to say that determinism implies predictability in the first sense you define above. In the second, more general sense "knowing a future event before it takes place" predictability really could depend on the concept of emergence (or solipsists notion of macro-levels). Here's a thought experiment: It's conceivable that you could perfectly simulate a higher level of organization in a system (which would require less information). It's also conceivable that objects on that level (emergent properties of the lower levels) operate according to their own rules distinct from (but derived from) the lower levels. Here's the kicker: given that the higher level is an emergent property of the behavior of the lower level, when we look at it in isolation, it contains much less information than the lower level. In fact several state iterations of the lower level could pass before a state change percolates to the higer level. Thus, in such a thought experiment by having a perfect model of the higher level, you could outpace the lower level and know a future even before it takes place.

By your parenthetical I assume you know of chaotic systems. But yeah, its been some time since I read philosophy but I vaguely remember that you still aren't guaranteed free will just cause things are undeterministic. This is because since you cannot show that an event was caused you cannot prove that your actions led to the event. How do you know that it is because of your actions that some event occurred or you chose to act as you did if things don't necessarily lead from one another? And the other side is true too. Just cause things are determined does not necessitate free will be lost. It was usually sugar coated but I always took it as even with just the illusion of free choice, that ability to be able to seemingly choose what you would have anyways is free will.

I stopped thinking about such things as I always got stuck in a head wrenching recursive loop of futility.

: ) yeah I know how you feel

Why is determinism important to you? Why do you think humans would be any freer if they were governed by dice than deterministic laws?

I believe the human conception of free will belongs to an ontologically different category of concepts to physical determinism. That one is implemented in terms of the other is besides the point. It's like trying to argue about Turing completeness on the basis of quantum mechanics.

Consequences are what matter. I believe the most common practical impact of this free will pseudo-debate these days is in criminal trials; "my bad childhood made me do it", "I'm mentally ill", "look at my brain scans" or whatever. But these things need to be argued within their own categories. Either you argue at the level of morality and free will, and treat prison etc. as a punishment; or you argue at the level of determinism, and treat prison as a deterrent and corrective. You can't mix and match categories to suit your purposes, and argue against punishment on the basis of determinism.

I look at prison as separating people with anti-social behaviour from the rest of society. Rehabilitation/punishment for the individual is irrelevant.

Good for you. I'm fairly sure a majority of people in my own country disagree with you, not least because its logical implication is that any crime which deserves any imprisonment at all deserves life imprisonment, since you have excluded both mechanisms that justify release: rehabilitation (which would "fix" the person) and punishment (which would deter the person). If prison is neither rehabilitating nor punishing, it must be permanent.

But even then, it's more or less besides the point of the differences between consequentialist and deontological ethics, which seems to me to be at the heart of ideas about free will vs determinism, at least where they have a practical upshot.

>universe could be a type of cellular automata itself

The problem with this idea is that the universe, unlike any grid, is isotropic (or appears to be). That must be the reason why you don’t see examples of, for example, circular waves here.

>The problem with this idea is that the universe, unlike any grid, is isotropic (or appears to be).

Well that's just one hypothesis, albeit one that corroborates a lot of observations.

I would never have thought to take the licence of adding film grain, but it really makes the images tangible --- like bizarre long-ignored government surveillance photos.

I don't think the film grain was added separately. LuxRender uses path tracing, which inherently produces noise that decreases as the computation progresses.

There were similar renderings of Conway's Game of Life in Wolfram's A New Kind of Science, but by way of 1D-slices through time and grayscaling the second axis. These have the famous class 4 property that Wolfram raves about, leading to the principle of computational equivalence and such godless sentences.

Here are instructions for turning Blender files into RepRap instructions. I would pay to hang something like this on my wall.

http://objects.reprap.org/wiki/Using_Blender_for_making_prin...

You should get in touch with the artist (Paul Slocum). I'm sure he'd oblige.

What i found very nice is graphs of the population size through generations of metuselah's, with my favorite being the R-pentomino http://www.conwaylife.com/wiki/index.php?title=R-pentomino

Monitoring population size through generations in Conway's Game of Life was the premise of my state science fair project. I ended up going further and changing the rule parameters to see which were the most optimal ones, but if you want to see the population vs. generation graphs for the original rules, here they are:

12 pentominoes: http://i.imgur.com/wrO3o.png

Population over 50 generations graph: http://i.imgur.com/TIRgK.png

Thanks for the fascinating link. I never knew how much effort had been spent categorizing the various emergent phenomena in the game of life.

Reminds me of how the Tralfamadorians see things.

Amazing. These look like fantastic cities.

Yeah I thought the same thing too - on a larger scale with a couple of smoothing algorithms one could end up with some interesting city landscapes.

These would be amazing to build with a 3D printer. If I had the time I'd try building one by hand using legos.

These are amazing, Slocum is pretty great. But, I submitted this before. Can anyone explain how double-submits are moderated?

As I understand it, if the URI doesn't match exactly, or the story is no longer in Hacker News's RAM, the duplicate won't be caught. I could be wrong, but I seem to remember pg or someone saying that HN only checks the stories currently loaded in RAM for duplicates.

The benefit of this is that old stories can be rediscovered by new users.

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