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BUTTERFLY EFFECT - REVISITED



 DAILY LIFE:
 One fine morning, you left the house a little late and you missed the bus.  On the way, your friend showed you a advt. for a new job.  Then your life changed for ever.  This is the butterfly effect.

     " A flap of butterfly wing on one side of the planet may trigger tornado on the other side of the planet".  This is the famous quote.

ORIGIN:
    In 1960, American Mathematician and meteorologist wrote computer code to predict weather.  He rounded off some numbers manually and fed into the computer.  For example, 0.123456 was  rounded off as 0.123.  This tiny rounding off error produced unpredictable, drastic change in the weather report.  This is the origin of 'butterfly effect'.

MATH:
     Consider the equation
 P next = P previous   * r * (1-Previous)
 Let  P previous = 0.25
 Let r = 1.5
     Let us calculate 'P next'and feed it back into the equation and again calculate P next; Repeat the process again and again and see what happens.

P pre *r * (1-Pre)  = P next
0.25 * 1.5 * (1-0.25)  = 0.2812
0.2812 * 1.5* (1- 0.2812) = 0.3032
0.3032 * 1.5 * (1- 0.3032 ) = 0.3169
.
.
0.3310 * 1.5 * (1-0.3310) = 0.3322
0.3322 * 1.5* (1-0.3322) =  0.3327

For r = 1.5; the value settled down at .333 as you have seen.
When r = 2.5; it settles at 0.6
If the r= 2.5 to 3.5, the answer never settles down, but oscillates between
two or more values.
     Something exciting happens when r is above 3.57.  The values run into
chaos- totally unpredictable.

   Take r = 3.9 and initial P = 2.5.  We get some random pattern of output values.
     Take again r = 3.9 and initial P=.2501.  Run the calculation.  We get totally different pattern of output this time even though the initial P is changed as little as 0.0001.  This is the butterfly effect in Math. (see figure)

ECONOMICS
     Today we live in global village.  All economics of different countries are interlinked.  Rise or fall of oil price will affect global economy.  A little fall of blue-chip stock value in one country will affect international economy.

IN HISTORY
     The US initially intended to bomb the Japanese city of KUROKO and not the Nagasaki.  Because a munitions factory was there in Kuroko.  But the pilots were not able to see the factory due to cloudy weather even though they flew three times over it.  But Nagasaki was clearly visible.  Hence they bombed it.  The split-second decision changed the course of history.

     In 1900, young Hitler applied for Art school.  But it was rejected by a professor.  Had he been admitted into the school, we would have different world history.  We might have got a great water colour painter.

     We understand minuscule can manifests into monumental.  Sometimes, we are puppets in the hands of fate.
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