What If

Protego
| Jan 31, 2009 at 3:29pm
| Posted in: Blog
| 462 reads
| 14 comments

Does anyone know the meaning of "The Butterfly Effect"? i keep thinking that with the chess is the same. The end is made by an option or a move but isn't that a little scary? Everything depents on a choice or our far future will be shown to everyone of us like it is written?

Comments

17 months ago
JacksRevenge

Yes, it is the same word chaos but with different meanings depending on the context. In Greek mythology it means nothingness and confusion. In philosophy it has usually similar meanings to that. But in Chaos Theory it has a different meaning.

Chaos Theory is a bad name for the theory since it's not a "theory of chaos" as we use the word routine speech. Its only connection to chaos is that systems described by Chaos Theory (Chaotic Systems) can appear to be chaotic since they are so very sensitive to initial conditions. And yet they are not "chaotic" in the everyday sense of disorder kind of chaos. They are absolutely deterministic and therefore predictable if we know enough about the system.
17 months ago
Protego

subject:chaos

" In Chaos (mythology) as a primary entity of Greek mythology."

"In Chaos (metaphysics) as metaphysical interpretation contrary to law, order. "

"In chaos theory as a scientific field. "
17 months ago
JacksRevenge

"Analyze the chess board you will see that there is a way to consider all the possibilities of the ending. By taking every opposite move pieces one by one with all their possible moves. By doing that we are having a number that show us that the one game can only “move” in the space with the limits of this specific number."

Yes, what you're talking about is exactly a subset, a branch of the phase space graph of chess that I mentioned in my last post.

"If every theory refers to everything like the atoms itself and the universe itself, then maybe this universe is not a chaos and has “lines” of beginning and ending and also our possible future has the same numbering limits"

Indeed we can imagine a universal phase space which has all possible universes according to some set of physical law, like the one we know. And indeed we can trace out different universe histories as the "line" you mention, and yes there are limits, especially due to the set of physical laws that constrain the energy of a universe as it evolves.

However, this does not contravene chaos. To understand the Chaos of Chaos Theory, you have to entirely forget about the everyday meaning of "chaos", which is really a different thing: Chaos in everyday terms means there is no order, no predictions can be made, no rules by which to understand something. Chaos in Chaos Theory means that these "lines" in the phase space that describe exactly the past, present and future of a chess game or universe or whatever, can be very, very, very close together. So close together that we can't tell which one we're on and if somehow the path we're following along that line gets "bumped" then we don't know which one we got bumped onto. Even the lines that are as close together as you like, lead on to very different futures. That's the point of Chaos Theory. There are lines, but tiny changes in which line result in enormous changes in future outcomes.
17 months ago
Protego

That is why "the butterfly effect is a metaphor that encapsulates the concept of sensitive dependence on initial conditions in chaos theory.namely a small change at one place in a complex system can have large effects elsewhere. Although this may appear to be an esoteric and unusual behavior, it is exhibited by very simple systems: for example, a ball placed at the crest of a hill might roll into any of several valleys depending on slight differences in initial position. The butterfly effect is a common trope in fiction when presenting scenarios involving time travel and with "what if" cases where one storyline diverges at the moment of a seemingly minor event resulting in two significantly different outcomes."

But if you look close enough:

Analyze the chess board you will see that there is a way to consider all the possibilities of the ending. By taking every opposite move pieces one by one with all their possible moves. By doing that we are having a number that show us that the one game can only “move” in the space with the limits of this specific number. If every theory refers to everything like the atoms itself and the universe itself, then maybe this universe is not a chaos and has “lines” of beginning and ending and also our possible future has the same numbering limits
17 months ago
JacksRevenge

There is some background necessary to discuss the Butterfly Effect.

First, we have to understand what a deterministic system is. Imagine an idealized situation of a ball thrown in the air, no air friction for simplicity. Is it a mystery how the ball will behave? No. There are rules which will describe the motion of the ball, given we know the initial conditions of the situation, i.e. the position and velocity of the ball along with the strength of gravity. We have what are called the kinematic equations which are a set of rules that take an exact numerical description of the situation at the current instant of time as an input and give us a single, exact numerical description of the situation at the next instant of time. These numerical descriptors of the situation are the position of the ball, speed, direction, gravity strength. All of these descriptors considered together are called the 'state' of the system. Now we can understand what it means to say that a deterministic system is one whose state is described explicitly through time by a set of rules; given we know the starting conditions, there is exactly one future for the ball and we know exactly what that is.

Second, we have to consider something called a Phase Space. A roadmap is a 2-dimensional space. A room can be described as a 3-dimensional space. Both of these are perfectly natural because a physical length in any dimension in these spaces describes a physical length in reality. There is no reason that the length in an abstract space such as a map should describe physical length. Indeed, we are familiar with "maps" that describe things such as your heart rate as time goes by. This space has a dimension for heart rate and a second for time. We can add more dimensions to a space if we like, and why not add a dimension for every single Degree of Freedom (think of the numerical descriptors of the ball system above) of a system? That way we could have a space where each point is a precise description of every single aspect (degree of freedom) of the system in a single state. For example, we could have a phase space for the ball, which is described by (x-position, y-position, z-position, speed, direction, gravity strength), then the point at the coordinates (0,0,1,4,v,9.8) would be a ball located 0m forward, 0m sideways, 1m upwards, 4m/s speed, going direction v, accelerating down at 9.8m/s. Our rules to describe how the system changes (kinematic equations) tell us exactly which point in phase space will describe the system at the next instant of time. In such a way, we can continue along instant by instant, tracing the path of this point through phase space, therefore yielding a precise description of the system through time. If you know where you are in phase space, you know exactly where you will be next.

Third, we need to talk about what a Chaotic System is. Now, given that we have a system like the ball above that is deterministic, it may seem rather simple to predict the future of the ball (in this case it is because an idealized ball is not a chaotic system). We can simply predict precisely the entire future of the ball system, that is to say, trace the line in the phase space graph of the ball system which our initial conditions told us where to start and kinematic equations told us the path to follow instant by instant to create the entire graph. Some systems are unfortunately much more complicated in a very strange way.

A double pendulum is one of the simplest systems that can exhibit chaotic motion. If you look at its phase space graph, you can see that it has areas where the graph is very, very dense. So you might have trouble pinpointing where to "start from" (initial conditions). If you take a magnifying glass and look closer, you see that it's still incredibly dense, and you aren't sure where to place your imaginary pencil so you can play the game of "know where I am now --> trace graph to show where I will be therefore describing the future of my system". If you then take a microscope and look many times closer at the graph, a bell will ring in your head and you might think "uh oh", and it really is uh oh. The reason for this is that the phase space graph of a chaotic system has areas of infinite density. That is, the lines are infinitely close, no matter how close you look, you will never be close enough to see where exactly you should put your pencil and trace out your system's future and each of these infinitely close lines describes a different future for the your system.

Now we can make sense of what it means to say that a chaotic system is Deterministic and yet Unpredictable because we can't know its initial conditions with perfect precision. The tiniest uncertainty in initial conditions gives enormous uncertainties in longer term predictions. This is exactly where we should introduce the butterfly effect: in an ongoing chaotic system, we can perturb the state of the system the tiniest little bit, as in a butterfly's wings disturbing the air in a breeze. We have nudged the trajectory of the point that describes the system in phase space off its course just the tiniest bit. We have knocked if off track onto another line in the phase space, but which one? We don't know, but the important point is that even though we just barely knocked it off track, the new line that it is now travelling on may yield an incredibly different future for the system than the one it would have had without the butterfly's flap. This enormous change in future outcomes due to incredibly tiny changes in the system is the famous Butterfly Effect.

Now we must consider chess and the butterfly effect. Why are they similar? First, the chess system can be described precisely at an instant of time, in fact, the chess board itself stamped out along many, many branches which describe every possible legal game of chess would form the phase space graph of chess. Now we hit a difference. The problem here is that it's not really the same as above. We cannot predict exactly what the future of a chess game will be given its current state; the players have a choice to make different moves.

Still, the main point of your idea is quite correct. A very tiny difference earlier in a game can lead to very different outcomes in the future of the game. Probably the earlier the difference, the more magnified the change in outcome; different openings often lead to very different midgames and endgames.

Now, when you say "our far future will be shown to everyone of us like it is written?", you are talking about a clockwork universe, if I understand correctly. One where there are no options, no possibilities. There is only one path for the future and we are stuck on it, unable to effect any change. Don't feel spooked out, we are certainly rescued in real life by the probabilistic, undeterministic fundamental nature of Quantum Physics. As for the chess board, we escape being trapped on a single line of destiny because we have the freedom to choose by our own will.

The short of it is, one small choice may have huge effects on the future but don't feel trapped, you still have the power to affect the outcome.
24 months ago
Protego

i am reaaly sorry, there is something i don't understand. can you be more clear?
24 months ago
Nightcastledup

we like your anology of the buterfly effect to the game of chess peices like that, you see the supptleties, is insufficiently spoken up, if you notice the suptleties of that statements, like that we want to talk to you, for many reasons, but the question here is can you play chess by a statemented systemcheck list, if you notice these other peices don't know what they are talking about in simple terms is a little more direct but don't worry about it we have protectionals up
3 years ago
Utopia

Everything affects everything ...
3 years ago
Protego

MrDLB, the butterfly refers as an example to a complicated theory . The "what if" is it a tittle on your book?
3 years ago
MrDLB

That is interesting... I live in Pacific Grove, California... the home of the Monarch Butterfly... so I use that symbol in my AOL.com Instant messanger... And, I am writing a book called "Life is a Journey ... A Heavenward Transformation" which my Part Two of my book is based on "What If?"
3 years ago
Protego

you wrote down some philosophical questions and your references are out of subject, but still very good effort. Thanks for sharing your thoughts !
3 years ago
Vance917

A philosophical question has often been posed -- if a tree falls in a forest, and nobody hears it, then did it make a sound? At first, this seems like a fairly stupid question. Of course it made a sound, even if nobody heard that sound; one does not "validate" a sound by hearing it. With further thought, the question takes on no additional meaning, because certainly every forest has some living creatures in it, even if not human ones. Certainly somebody heard that tree fall, and it made some sort of indelible mark on them. Maybe it scared them, and, as a result, they moved further from the center of the forest, and closer to (human) civilization. Maybe this mass migration caused interations that otherwise would not have occurred, some good, some violent. Yes, I think I hear the ripple effect of that tree loud and clear now.

Maybe a boat from the Ukraine to Italy (I hope I am remembering this correctly) carries rats which themselves carry pests and leads to the great epidemic of 1918. Today, it is the bird flu. Also today we have all these idiots who have to drive junior to the bus stop in the SUV instead of -- gasp -- walking the half a block. This seemingly local effect is a contributing factor in global warming, with the emphasis on that word "GLOBAL".

This butterfly effect would seem to be messing up our world. But, alas, there is another side to it too. Maybe we lose a loved one to some dread disease, and carry this tremendous loss with us until we can unburden ourselves by feeling compassion for someone else now going through what we went through before. Maybe the butterfly effect reduces the degrees of separation from six to some smaller number. Maybe all it really means is that we are all connected, for better or for worse.
3 years ago
Protego

yes, i know about all these you just wrote, you are rephering to the theory of chaos. But if you analyse this the conclusions are: our life depents on how a butterfly moved its wings?? Do you ever thing where would you be now if that day you didn't do that, or the opposite? Still is scary...
3 years ago
THCCKINGJON

humm.

Does this help...?

First discovered when investigating the weather.

Other examples: one grain triggering a landslide in a sandcastle. one footprint triggering an avalanche.
if a butterfly flaps its wings on one side of the earth it is said to cause a hurricane on the other side . How one little thing can snowball into a huge thing.
The butterfly effect has been most commonly associated with the Weather system as this is where the discovery of "non-linear" phenomenon.
The phrase refers to an idea that a butterfly's wings might create tiny changes in the atmosphere that may ultimately alter the path of a tornado OR delay, accelerate or even prevent the future occurrence of a tornado in a certain location.

The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale alterations of events. Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different. While the butterfly does not cause the tornado, the flap of its wings is an essential part of the initial conditions resulting in a tornado..
(physics) In a chaotic system, the ability of miniscule changes in initial conditions (such as the flap of a butterfly's wings) to have far-reaching, large-scale effects on the development of the system (such as the course of weather a continent away).
1. Major events can be caused by surprisingly unrelated minor forces, apparently distant from any particular event. (butterfly effect)
On a person note The Monarch is my favorite Butterfly..

Have they an effect on you ??

I bet there is..

http://www.youtube.com/watch?v=oe1YRC18U7E

http://www.youtube.com/watch?v=oe1YRC18U7E&feature=related