Of Butterfly Wings and Compound Interest…

How Small Changes Can Produce Large Effects Sooner Than You Might Think


This is the tale of a college professor, a financial consultant, and a Ph.D. research scientist who saw something few, other than themselves, seemed to have noticed, i.e., how small changes can produce large effects. They have applied this observation in  distinct ways producing a new field of science, significant returns on invested capital, and a revolutionary approach to behavior modification, respectively.

While the applications are different, the powerful, underlying core principle is the same.

The Professor


A nearly infinitesimal data entry error followed by the pursuit of a fresh cup of coffee led to a pioneering effort in a new branch of mathematics, Chaos Theory. This ultimately challenged over 300 years of conventional wisdom based upon Isaac Newton’s deterministic model of our supposedly “clockwork universe.” That led to a profound insight about how nature works, i.e., small changes can produce large consequences. As you will see below, that insight likewise applies to each of us in our daily pursuit of matters ranging from the casual to the consequential.

The caffeine deficient typist was Edward Lorenz, an M.I.T. professor of meteorology. He was repeating a computer simulation of weather patterns he had run recently. After inputting the variables and restarting the program, he left his office to get some coffee while the computer was running the new simulation.

Upon returning to his office, Professor Lorenz discovered the new run of the simulation was producing significantly different results than those of the prior simulation. The new run was altering the entire weather pattern simulated earlier, even though all the input variables in the two runs were supposed to be identical.

Upon examination, he discovered his input error in the second simulation. He had rounded one variable from .506127 to .506. This single minuscule error accounted for the entirety of the vast variance between the two runs of his weather simulation.

Professor Lorenz realized that a small change, such as the error he made, could lead to a vast difference over time. He recognized this sensitivity to initial conditions as chaos, not randomness. He demonstrated this through a series of equations. When their results were plotted on a graph, they appeared as two linked ovals, somewhat resembling a butterfly (as overlaid in the image above). This led to the quip, ”Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?,” now referred to as the Butterfly Effect, a metaphorical expression of Lorenz’s observation that small changes can have large consequences.

The Financial Consultant


Andrew Kahr was a consultant to the credit card industry.  He had what proved to be a profitable insight at a time when the interest rate charged on a credit card was typically 18% per annum, and the outstanding balance a consumer owed to the credit card companies was about $7,300.

He proposed the policy change, adopted by the credit card companies, to reduce a consumer’s minimum monthly payment from 5% of their outstanding balance to 2% of their outstanding balance.  On the face of it this was an accommodation to the consumer, reducing their monthly payment burden somewhat in months they happened to be short of cash.  In practice, this small reduction in the minimum payment required became the new norm of monthly payments made.  Consumers paid dearly for the convenience.

Before the policy change making only minimum 5% payments monthly to liquidate the typical credit card balance would require a little over ten years at an interest cost of approximately $3,000 for a $7,300 balance (assuming no further charges).  After the policy change making only minimum 2% payments monthly to liquidate the typical credit card balance would require over 50 years at an interest cost over $20,000 for the same $7,300 balance (assuming no further charges).

The point here is not to argue the merit of the credit card companies’ policies or the choices made by consumers, but simply to illustrate another arena in which small changes can produce large effects.

In fairness to Mr. Kahr, here is a link where you can hear him speak for himself, if you like, in an interview he gave about the credit card industry and his role in it.

The Ph.D. Research Scientist


B.J. Fogg is a Ph.D. Research Scientist and Founder of the Persuasive Technology Lab at Stanford University.   He has studied human behavior for twenty years, mostly at Stanford.

In December 2011 he launched a program he calls Tiny Habits® to “…tap the power of environment and baby steps.”  The program is based on only three steps:

  • Get specific
    • What behavior do you want?
  • Make it easy
    • How can you make the behavior easy to do?
  • Trigger the behavior
    • What will prompt the behavior?

Over forty-thousand people have completed the online course.  It’s free and requires only a small time commitment.

This link will take you to a page with further information, including a video of B.J. Fogg’s Tedx Talk.

Full Disclosure: I’ve taken the course, derived benefit, and otherwise have no relationship with B.J. Fogg or his program.

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