Chaos Theory
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Crosbyfan
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- Nov 27, 2003
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Absolutely. A hockey game is not a stable system in which minor "fluctuations" always diminish over time.
Both stable and unstable systems exist in nature. A close hockey game is certainly in the latter category.
Even a one-sided game can be chaotic from a certain perspective:
rookie makes a mistake, gets sent down to the minors, gets injured in a game he would not have otherwise played, takes time off with a trip to Australia, steps on a butterfly on the beach...
...massive hurricane avoided 6 weeks later in Carolina...
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An injury to a butterfly goalie in Edmonton can cause the Hurricanes to win the cup on the other side of the continent.
Pentothal
Listen with one ear
Of course. How many playoff overtime games are won right off a faceoff?
Every little puck battle, every bounce, every faceoff makes a difference.
Every little puck battle, every bounce, every faceoff makes a difference.
Rhiessan71
Just a Fool
Very nice.
Wait...I thought the only reason EDM was even there was because of Pronger
Hippasus
1,9,45,165,495,1287,
I don't think chaos theory pertains to a hockey game at all. It might be able to be considered an unstable system though. I'm not sure how one would mathematically categorize a hockey game, but I think it is either a non-chaotic deterministic system or a stochastic process. There would have to be exponentially large changes in the state of the hockey game, like the score, on the basis of relatively small ocurrences, like missing a pass, in order for it to be deemed chaotic. Instead there are rules, predictable behaviors, and predictable outcomes; not to mention the fact that the outcomes are greatly simplified by the relatively short duration of a game. Unpredictability and randomness are one thing, chaos is a whole other category of complexity.
Dennis Bonvie
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Chaos theory applies to deterministic systems also.
Taken from wikipedia (source: Stephen H. Kellert, In the Wake of Chaos: Unpredictable Order in Dynamical Systems, University of Chicago Press, 1993, p 32, ISBN 0-226-42976-8.)
"This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved."
In the OP I said that I was looking at this from more of a layman's view of chaos theory, rather than trying to do a strict mathematical analysis.
My question in the OP was most of what I was thinking of when I made the topic.
For example: (assuming an evenly matched game)
If team A wins the opening face-off, will it ultimately yield a completely different game than if team B had won, or would the game still follow the same general pattern?
ie: Does the pebble you throw into the stream divert the flow of the water, or does the water move past the pebble mostly unchanged?
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Hippasus
1,9,45,165,495,1287,
It's true that chaos theory can apply to deterministic systems as well, just not necessarily so. Part of the difficulty is that the initial conditions of a chaotic system are beyond us, so we can't predict a future state of the system even if it's deterministic. Anyways, I think it could be argued that players behave deterministically if one were hypothetically to take everything into account: personal upringing, equipment, etc. If they do then I think a hockey game is a non-chaotic deterministic system and if they don't then it's probably a stochastic process. I don't believe chaos is the proper term at least in the mathematical sense of chaos theory, but this is nonetheless a very interesting topic.
EDIT: This article says I'm wrong: http://www.athleticinsight.com/Vol2Iss2/ChaosPDF.pdf The high number, complexity, and interrelationship of the variables may lend credence to the thesis that a hockey game is a chaotic deterministic system. To eliminate ambiguity in the post above I should say that chaotic systems in the mathematical sense are necessarily deterministic as far as I know. It could be an issue of the number of salient variables in connection with a hockey game. If they are truly unlimited, then that would lend support to the thesis that a hockey game is a chaotic system. If not, then this would perhaps lend support to the notion that a hockey game is a non-chaotic process in some way, regardless of how complex it may be in terms of the details of how a game unfolds. It may also appear chaotic since we cannot grasp enough of the salient variables which constitute the unfolding of a hockey game. When there is that much speed, ricocheting, and other variables, there seems to be a great number of ways a game could unfold. I'm just not sure if this is sufficient to deem a hockey game truly chaotic in the mathematical sense.
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