Wednesday, May 6, 2009

Double Trouble

As writers strive to tell a good story, Dr. Bartlett retold this classic at the 2009 EntConnect conference to illustrate why sustainable growth is such an oxymoron.

In the 6th century AD, Indian King Balhait was concerned about the prevalence of gambling games based only on luck. He tasked his mathematician Sissa to create a game which would sharpen mental acuity and encourage virtue. Thus, the first game of chess was invented played on a 8 x 8 checkered board, totaling 64 squares.

So pleased with this new game, the king wished to reward his mathematician. Legend has it Sissa only asked for one grain on the first square of the board, then two grains on the second square, four on the third square, eight on the fourth square, etc., so that the next square doubled the amount of grain on the previous square till the board was filled.

This request seemed like a modest amount of grain, but the table below shows how this doubling scheme worked out.

-- Square # --Grain on Square -- Total # Grains--

------1 ------------- 1 ---------------------- 1 ----------
------2 ------------- 2 ---------------------- 3 ----------
------3 ------------- 4 ---------------------- 7 ----------
------4 ------------- 8 --------------------- 15 ----------
------5 -------------16 --------------------- 31 ---------
------6 -------------32 --------------------- 63 ---------
------n ---------- 2**(n-1) --------------- 2**n - 1 ------
------… -------------…-------------------------…--------
------64 --------- 2**63 ----------------- 2**64 - 1------

From the table we see the eight grains on the 4th square are more than the total of seven that are on the previous three squares. The 32 grains on the 6th square are more than the total of 31 on the previous five squares.

The trend is clear. The growth in any doubling time is greater than the total of all the preceding growth. So by the 64th square, the number of grains on the board is 18,445,744,073,709,551,515. That is 400 times the world wheat harvest in 1990 and possibly more wheat than humans have harvested in the entire history of the earth!

A modest percentage growth (7% growth per year, doubling time of 10 years as discussed in the previous blog) can equate to huge escalations over a short periods of time.

Double trouble? Just ask Captain Kirk. In the original Star Trek episode – The Trouble with Tribbles - those small furry creatures seemed to multiply without end!

For screenshot of Captain Kirk half-buried in Tribbles: click here

Dr. Bartlett links:

Chess links:
Origin of Chess:

Star Trek links:
Trouble with Tribbles, plot summary:
Screenshot of Captain Kirk half-buried in Tribbles:

Photos from
Ancient chess board:
Wheat grains:


  1. Interesting Susan! And though I am not a Star Trek fan like my husband, I remember those Tribbles! :0)

  2. wow, those are some fascinating thoughts. I am definitely not a number/analytical person. Sounds like you are. Lucille

  3. Thanks Robbie & Lucille. This next set of blogs are key ideas from Dr. Bartlett's Energy speech - and he is a nuclear physicist. Some are my ideas. I hope I can make it understandable to the lay person.