How about a date with disorder ?
A post after a long time.I gonna take you for a ride about disorder which in the view of a sect of people is strangely in order. I keep wondering at people who keep their imagination in high gears looking to model random process. Can we ever model the shape of clouds or think about replicating the contours that are seemingly crazy figments in our perception?
To understand the observed's behavior, it needs lots of intellectual courage and a smart brain to identify the variable tweaking it.Onething for sure; most of nature's system is non-linear. That leads to the inevitable question, are things so complex that it cannot be modeled or is it that, we have camouflaged ourselves to simplicity by overlooking simple rules?
Have you heard of Chaos theory? Well if you have not, then I shall take the liberty to confuse you. Chaos theory refers to an apparent lack of order in a system that nevertheless obeys particular laws or rules. The two main components of chaos theory are the ideas that systems - no matter how complex they may be - rely upon an underlying order, and that very simple or small systems and events can cause very complex behaviors or events.
There was crazy guy who was trying to study the cotton prices a trying to predict the cotton prices, the more he tried the more he failed.Atlast he came across a great observation, there was an underlying similarity between the change in monthly and change in yearly cotton prices adjusted for scale.
Each particular price change was random and unpredictable but the sequence of changes was predictable independent of scale. Curves for daily and monthly price changes matched, the degree of variation had remained constant over a tumultuous 60-year period that saw two world wars and a depression. Although it was almost next to impossible to predict the local price the system's behavior as a whole was close to deterministic. In Sierpinski's lingua the system is locally random and globally deterministic.
Have you ever wondered how the fern/pine tree looks similar to its branches, they in turn are similar to the leaves and they are in turn similar to the veins of the leaves. I don't know if this inspired somebody to think of fractals. Fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced/size copy of the whole.
Fractals have something very important to say, that things are self-similar. May that is the geometry of nature and to be more refined what is in the microcosm in the macrocosm. Nature has simple elements which create complex elements using very simple rules. No better example than basic genes which are self similar but create complex beings like humans. How fascinating isn't it? The moral of the story, what is apparently envisaged as disorderly is in fact very orderly, just that we don't understand them.
Whenever things comeback and remind us of similar things, we are confounded by the perception that life's a full circle but we feel that they are not exactly the same. Fair enough, true they had some other interesting observation about dynamic systems.
In dynamical systems, an attractor is a set to which the system evolves after a long enough time. For the set to be an attractor, trajectories that get close enough to the attractor must remain close even if slightly disturbed. Geometrically, an attractor can be a point, a curve, a manifold, or even a complicated set with fractal structures known as a strange attractor.
Look at the trajectory of a ball tied to the end of a thread which is slowly winded around our finger. It never repeats its path nor does it overlap but the paths traced are self-similar and it has the centre of the spiral as the "strange attractor”. This is the example of a simple dynamic system. Think about the complexities perceived, if the ball traverses a path which has two centers and the paths are never repeated nor overlapped and yet self similar which is nicknamed "Lorenz attractor".
That’s how most things in life and nature are, disorder seamlessly falls in love with order. So the next time you think things are complex, we need to acknowledge that we did not understand certain simple rules.
To understand the observed's behavior, it needs lots of intellectual courage and a smart brain to identify the variable tweaking it.Onething for sure; most of nature's system is non-linear. That leads to the inevitable question, are things so complex that it cannot be modeled or is it that, we have camouflaged ourselves to simplicity by overlooking simple rules?
Have you heard of Chaos theory? Well if you have not, then I shall take the liberty to confuse you. Chaos theory refers to an apparent lack of order in a system that nevertheless obeys particular laws or rules. The two main components of chaos theory are the ideas that systems - no matter how complex they may be - rely upon an underlying order, and that very simple or small systems and events can cause very complex behaviors or events.
There was crazy guy who was trying to study the cotton prices a trying to predict the cotton prices, the more he tried the more he failed.Atlast he came across a great observation, there was an underlying similarity between the change in monthly and change in yearly cotton prices adjusted for scale.
Each particular price change was random and unpredictable but the sequence of changes was predictable independent of scale. Curves for daily and monthly price changes matched, the degree of variation had remained constant over a tumultuous 60-year period that saw two world wars and a depression. Although it was almost next to impossible to predict the local price the system's behavior as a whole was close to deterministic. In Sierpinski's lingua the system is locally random and globally deterministic.
Have you ever wondered how the fern/pine tree looks similar to its branches, they in turn are similar to the leaves and they are in turn similar to the veins of the leaves. I don't know if this inspired somebody to think of fractals. Fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced/size copy of the whole.
Fractals have something very important to say, that things are self-similar. May that is the geometry of nature and to be more refined what is in the microcosm in the macrocosm. Nature has simple elements which create complex elements using very simple rules. No better example than basic genes which are self similar but create complex beings like humans. How fascinating isn't it? The moral of the story, what is apparently envisaged as disorderly is in fact very orderly, just that we don't understand them.
Whenever things comeback and remind us of similar things, we are confounded by the perception that life's a full circle but we feel that they are not exactly the same. Fair enough, true they had some other interesting observation about dynamic systems.
In dynamical systems, an attractor is a set to which the system evolves after a long enough time. For the set to be an attractor, trajectories that get close enough to the attractor must remain close even if slightly disturbed. Geometrically, an attractor can be a point, a curve, a manifold, or even a complicated set with fractal structures known as a strange attractor.
Look at the trajectory of a ball tied to the end of a thread which is slowly winded around our finger. It never repeats its path nor does it overlap but the paths traced are self-similar and it has the centre of the spiral as the "strange attractor”. This is the example of a simple dynamic system. Think about the complexities perceived, if the ball traverses a path which has two centers and the paths are never repeated nor overlapped and yet self similar which is nicknamed "Lorenz attractor".
That’s how most things in life and nature are, disorder seamlessly falls in love with order. So the next time you think things are complex, we need to acknowledge that we did not understand certain simple rules.
Labels: attractor, chaos theory, disorder, fractal
Back to one of ur mathematical articles eh....i think we already had a discussion on serpinski's triangle..I guess it is this obsession to unfold the fundamental patterns that has taken us inside the so called indivisible part called atom and futhere into quarks etc....
Posted by
Sudarshan |
8:29 pm
the desire to go to the basics never subsides in the human mind.. what if things are self similar ?
Posted by
Sara |
9:24 pm