MI: Linguistics

Mind-Boggling Exponential Growth

twelfth century scholar Ibn Khallikan is credited with
a story that demonstrates the mind-boggling nature
of exponential growth (base with continuous powers) 

In mathematics, exponential growth occurs when
the growth rate of a function is always proportional
to the function's current size . . .

the general principle behind exponential growth is
that the larger a number gets, the faster it grows
- Wikipedia

Ibn Kallikan's story is based on a legend about the
origin of Chess; it goes like this -

Grand Vizier Sissa Ben Dahir invented the game of
chess to please his King, Shirham of India;

and Shirham was more than pleased; in gratitude,
he told the Grand Vizier to name his reward

expecting a request for gold or jewels, Shirham was
surprised to hear that his Vizier wanted nothing more
than grains of wheat on a chessboard

the Grand Vizier asked that a single grain be
placed on the first of the board's squares

then 2 on the second; 4 on the third; 8 on the
fourth and so on -

each time doubling the amount added until grains
of wheat were placed all 64 of the board's squares

shaking his head in disbelief, King Shirham granted
the Vizier's seemingly modest request

the story ends, of course, with a shocked King
who could not make good on his promise

the Grand Vizier's request entailed exponential
growth; in other words, his reward grew at a
progressively faster rate as grains of wheat were
added to each successive chessboard square

in total, the number of grains needed to grant the
Vizier's request would be

(2^64) - 1

or, in words, two the sixty fourth power minus one

that's 18,446,744,073,709,551,615 grains of wheat -

a quantity far greater than a thousand years of
U.S. wheat production



more and more today we are hearing about the
concept of exponential growth

it is applied to such phenomena as the yearly
increases in computing power and the world's rapidly
growing demand for energy

and we may be hearing and re-hearing the story of
the Vizier, the King, the chessboard and the grains
of wheat

but Ibn Kallikan's 13th century tale is a good one;
one that can provide the mind needed boggle

http://www.ponderabout.com/archives/972/mind-boggling-exponential-growth.aspx

Assignment: Your assignment is to create a short story just like the one you just read above. You will take the idea/s presented in this short story and create a story in a time and setting of your choice. Meaning you will recreate the above story in any setting you want and time. The story must be at least a paragraph long and must be submitted through the weblog.