Topologist's Sine Curve and life

posted Jun 19, 2012, 2:38 PM by Abhishek Ojha   [ updated Jun 19, 2012, 2:39 PM ]

I love some mathematical concepts..  this is one of them...

 

Okay... so Sine curve is a nice, smooth, periodic and well-behaved wave function. Everything is perfect as it should be. Goes on as it should... perfect !!

 

...symmetric, well behaved... looks lovely.

 

...but change a little. Flip x to 1/x and then comes the madness... 

 

Its still the same sine function but becomes a function of function... dependent on other function...

you just flip a little of it and it becomes connected but not connected (mathematically speaking - connected but not path connected and not locally connected).

 

It also reaches 0 but not as smoothly as original sine curve... It is not as nice as it was... in fact, not even comparable.

 

Initially, it becomes painfully slow... starting from an asymptote which never touches x axis.. then as it approaches 0 it behaves madly... faster and faster going up and down... oscillating like never before !

 

That’s how life is sometimes.. a small trigger, a small flip, a small change, a small interference, a single moment, a single person... can makes it painfully slow as well as madly fast... just a matter of time.. :) …don't worry if it suddenly becomes painfully slow by an event... a time may come when it will become madly fast like never before :)

 

 

(Graphs made using Wolfram Alpha)

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