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PaulGrobstein's picture
Your thoughts about The World of Langton's Ant?, as per assignment at the end of From Cellular Automata to Agent-Based Models? Maybe, to make it a little easier for me (and others) to find them, add them as comments to this post? or put a link here to things you're saying elsewhere?


DavidRosen's picture

I was thinking about the ideas of "free will" and "agency", and they do not make any sense to me. In any model of the universe, all processes can either be completely determined or they can have probabilistic elements. Proponents of "free will" seem to be trying to add a third option, without giving any kind of explanation of what it means.
SunnySingh's picture

One of the recurrent themes I noticed in the article, as well as throughout our class discussions, is the concept of free will. I recently found an interesting ‘proof’ concerning free will. Surprisingly enough, it was written by our friend, John Conway. Although I have not completely internalized the ‘proof’, I am a bit skeptical of it. Moreover, there seem to be problems with the axioms used and assumptions made. Regardless, Conway attempts to show that “if there exist experimenters with (some) free will, then elementary particles also have (some) free will.” I’m hoping this ‘proof’ stirs up some interesting discussion. As for Langton’s Ant, I am a bit curious as to how Langton discovered this interesting case. It takes roughly 10,000 frames before the ant begins to ‘build the road’. Was it just ‘chance’ that Langton happened to watch the system evolve that long? Why didn’t he stop after 100 frames? 1,000 frames? Could this imply that given any seemingly complex system, order will eventually arise given that we ‘watch’ long enough? Furthermore, could the mere act of observation affect the outcome of certain systems? I guess this somewhat goes hand in hand with Conway’s ‘proof’. If we watch a system of elementary particles, will they behave independently of their pasts? Or will they act in such a way as to comply with what we expect?
AngadSingh's picture

I like the distinction between 'free will' and 'free whim' and find that distinction to also be applicable to this notion of 'purpose' as it relates to Langton's Ant, real ants, or me. Langton's Ant makes only a couple determinations or judgements - and those are restricted to whether or not it should turn right/left or turn the space on/off. The more intricate road-building pattern emerges whimsically, in the sense that a decision or judgement was not made by the ant to engage in road-building activities at any moment. Whimsical in this sense does not retain the common-place understanding of 'unpredictability', 'randomness', nor 'spontaneous'. It is instead deterministic. In Part 3A , Langton's Ant (and general reality is alluded to) is characterized as containing an agent, an environment, and sequential steps in time. I think it may be useful to collapse the agent and environment categories into a single category, or at least make the claim that the agent operates whimsically as defined above. This is related to Wolfram's thoughts on a linear CA's ability to model reality. I am not convinced about this development of agents or agency. I suppose my reluctance in accepting the agency idea for the CA, the notion of of purpose for Langton's Ant, and PG's Conjecture all stem from the same source - which is my reluctance to consider any particular aspect or object as 'special' - or more appropriately, 'more special than the next'. It seems like all aspects and objects operate under the same rules and to confer extra-speciality upon one would be disingenuous.
Kathy Maffei's picture

There's a strong argument to be made for tossing the concept of purpose onto the sentimental, self-delusional pile of anthropomorphisms. There's no proof that purpose exists beyond our own intentions. I can create something for a particular reason, and using the word purpose in describing it helps us exchange ideas. Other than that, we can't honestly prove that anything has a purpose. Does a lion intend to stalk and kill the antelope, or is it acting purely from instinct to behave in a particular way when prompted by certain stimulus? Can it truly consider the implications of its actions? Doesn't having purpose imply intention? (That being said, I still can't help but believe that my cats really do love me.) These ideas and Langton's Ants remind me of Valentino Braitenberg's "Vehicles" – the first few pages are available for preview on Amazon. Braitenberg’s thought experiment uses simple robots with basic instructions that lead to complex behaviors that appear to demonstrate intention, emotions, and even intelligence. The experiments demonstrate how easy it is to suppose purpose in observing behavior when you have no idea as to how something works. Braitenberg explains the "law of uphill analysis and downhill invention," meaning that it is much easier to create something with complex behavior than it is to guess the underlying structure of something by observation.
DavidRosen's picture

"Does a lion intend to stalk and kill the antelope, or is it acting purely from instinct to behave in a particular way when prompted by certain stimulus?" Another question to ask is whether or not there is actually a meaningful distinction between these two possibilities.
Lisa Spitalewitz's picture

I agree with you; I think it's very important to keep our tendency for sentimentality and our viewpoint as humans as far away from this analysis as possible (though I don't see any reason to give them up in our personal and pet-owning lives!). I think it is important to keep this in mind with respect to the words we use and what we mean by them, especially with respect to words like "purpose" or "intention." I guess I'm not really saying anything new here, but at least I'm emphasizing that I think is an important point.
Laura Cyckowski's picture

On the concept of "purpose", I agree that it seems useful to attribute the idea as coming from and dependent on an observer, and following from that it may be independent of the agent and/or creator/fiddler. Similarly, it also seems acceptable to attribute the concept of "free will" as arising from an observer and not an actual entity/parameter within the system itself-- "What we see as human choice may in fact be a deterministic outcome of all of the forces acting on the individual, but it is 'almost in principle' impossible for us to predict what the decision will be, so there appears to be free will... what appears to us as our own ability to choose is really our inability to predict...". Also, is it not significant to acknowledge that some of the flip sides to points 8 and 9 are possible-- that in a system deemed "unpurposeful" or "random" to an observer that this is the purpose/intent of an existing mind/creator/fiddler? Randomness a purpose-- or would that defy the meaning of purpose? I'm just confused over why only when the ant was building organized paths was the observer supposed to suddenly identify the ant/system having purpose. But I guess that goes back to the fact that only through an observer could meaning be added. I guess I'm still trying to grasp the need for a dichotomy between determinism and randomness, and randomness necessarily implying indeterminism? Or maybe how randomness equates with no rules, because isn't "follow these rules versus don't follow any rules" a rule in itself? When randomness in the applet is turned on, there's still only a limited number of possible moves, save an enormous number in comparison to the relatively few the ant was following before.
DavidRosen's picture

Randomness and determinism are not compatible because if any rule in the system involves true randomness, then even with perfect knowledge we could not predict what state will come next.
Leslie McTavish's picture

I agree with Laura that the fact that the ant demonstrates a recognizable pattern does not constitute purpose. Based on simple rules, and the preceding results of those rules the ant generates a repeated action (loop) which is small enough for us to recognize as a pattern. In terms of taking some sort of direction (or having some purpose), it will continue to follow only one path until it runs into something else or comes full circle and is again influenced by its previous actions. Without some type of random behavior, how does one demonstrate intent? Purpose implies intent, and if intent is generated only by predetermined rules, that precludes free will. I don't understand Conway's 'proof' about free will, except that it starts with the assumption that at least one entity has free will to begin with. He is not trying to prove its existence, only that it also exists in particles that one would not normally associate 'will' or 'purpose' with.
Flora Shepherd's picture

I’m confused about the distinction between deterministic and random systems. If we impose purpose and if “Randomness can generate anything that can result from rules if you have enough time to wait,” then how easily can the line be drawn? “See how important even a passive observer is? It is the observer who creates a story that gives meaning to what is taking place in the world of Langton's ant. And it is the meaning that creates the new questions that we use to further explore the world, including by becoming a participant in it and hence altering it.” “That a world does things that are surprising to an observer does not establish whether it is deterministic or not.” I find myself quite interested in the importance of the observer. The observer is also important to one’s understanding of much of physics including Quantum Mechanics’ uncertainty principle and inertial reference frames in General and Special Relativity. I find the quantum correlation especially interesting because many claim that quantum is not satisfactorily explained in Wolfram’s book and related theories of emergence.
JesseRohwer's picture

I think it's fairly obvious from the applet (and just general intuition) that a deterministic system cannot have any random elements. However, can a random system have deterministic elements - that is, can it display deterministic behavior? I think not, because even if you create, within your random system, some subsystem which you attempt to isolate from random elements, that "virtual reality" environment exists within your random system, and so the randomness must eventually affect it. For example, if quantum uncertainty exists, then our "deterministic" CAs on our computer simulations are not, in fact, perfectly deterministic because there is always a chance that some particles in the computer will randomly change their state in such a way that a computing error results in a violation of the deterministic rules of the CA. Does this mean that determinism and randomness are mutually exclusive, in which case it would be impossible for us to create a truly deterministic system (IF quantum uncertainty is a part of our reality), or am I being illogical? This seems like an interesting implication of quantum uncertainty.
LauraKasakoff's picture

While fiddling with Langton's ant I thought back to Wolfram's cellular automata. A striking similarity is that both depend not only on a set of rules but also the starting environment. Of course with Langton’s ant it doesn’t stop there; the interaction between the ant and the environment is clearly evident. When the ant moves she changes her environment, and as a result, it changes what she might do at that spot in the future. Changing the starting environment changes what the ant does too, just like with cellular automata, there is this intrinsic connection between the rules and environment. An interesting difference between the CA environments we've seen and our ant world is the ability to change our environment during the middle of an ant run. By allowing us to produce or remove "road blocks", i.e. add more dark or light squares, we can change the system at any given time. This is something that increases the complexity of the system a great deal. The ant’s future is still deterministic, but it is harder to comprehend what is happening from the outside. (This seems more like real life to me then the CAs we have been playing with because in the world there are more changes in the environment that affect our behavior other than a simple starting point.) Of course we could introduce environmental changes in CAs at different time points by randomly adjusting zeroes or ones at a given step. Isn't that where randomness can take a part even in a system that is deterministic? Not only could the Prime Mover create randomness in a neatly packaged starting condition but also by meddling with the system along the way. One thing I find frustrating about all of these examples including the Game of Life as well, is the fact that we are in a finite dimensional space in our computer that we are treating like a torus so we don't have to limit the number of times we apply the rules. The limitations of this space lead me to wonder how our system would behave if we truly had infinite dimension to go with the infinite number of time sets we use to apply the rules. I understand that the ant’s life is deterministic, but will it always make a road? Since the computer is constrained by some boundaries, I found that adding in lots of extra dark squares at a certain point in time in a random distribution made it "hard" for the ant to construct a road. I'm not saying that I know whether or not it would be impossible for the ant to produce a road by some point, but it went for a great deal of time (until my computer froze) without reaching it’s road-making purpose. Is there an amount and positioning of squares in our finite java applet space such that the ant is forever stuck trying to create a space without ever making it? Even if our space was truly infinite would it ever encounter a setup where it couldn’t build road? An interesting thing I tried was to set the left half of the starting environment to black squares and leaving the other half light (like a black and white cookie, oh, those are so good). My thinking was that it might not be able to make roads if the starting plane had an equal distribution of light and dark squares. When I pressed go the ant proceeded to move to the dark side (he he) but did not act as erratically as it had with the starting condition of all white squares. In fact, the ant almost moved in a perfectly straight line but rather than a straight line it looked more like it was following a tangent curve up and down the dark left half (of course movement is in the eye of the observer). However once it made the toroidal jump to the right white side, it behaved erratically once again and started on road construction. Now I think that difficulty building roads must have something more to do with the positioning of the dark and light squares rather than just their density.