Talking About Systems: looking for systems in the news (and not)
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Archive for the ‘Complex Systems’ Category

Talking to Kids About Exponential Growth During COVID-19

When kids ask, “Why do I need to wear a mask?” it’s helpful to have a good understanding of exponential growth. Here are a few ideas for ways to unpack this powerful force.

Start by reading What does exponential growth mean in the context of covid-19?, a short article in the Washington Post. Then grab a chessboard (or draw the same number of squares on a large piece of paper).  Get some cheerios, jelly beans or something desirable and small.  


Look at the graph in the article.  Why does it look like a hockey stick?

To make it real, put one Cheerio on the chessboard and say: “Pretend these are jelly beans.  You win a bet and as your prize, I have to pay you one jelly bean on the first day. For the next 63 days, I give you double the jelly beans I gave you the day.  Sounds like a good deal?  There’s only one requirement:  you have to agree to eat the jelly beans you get each day.  Deal?”

Who wouldn’t accept that deal?  (Turns out, it’s not a good deal).

“On the first day, you get one jelly bean, the second day you get two and on the third day you get four. Then ask your kids to fill in the rest.  “On the fourth day I get eight jelly beans and on the fifth I get 16 and then I get 32!”

Things are looking good. The squares are too small and the Cheerios are too big so you’ll need to pull out a piece of paper and calculate that on the 10th day though, he or she will have 512 jelly beans to eat.  Are they phased yet?

Double that number on the 11th day. That would be 1,024 jelly beans.

By the 20th day, the number is over 500,000 jelly beans.  On the last day, the 64th day, he would have 18,446,744,073,709,551,616 jelly beans. 

Draw a simple graph like this:


Talk about how sneaky doubling can be. And how once it gets going, it can be unstoppable.  Think of other examples together. If you are talking to teens, they may know examples of a small party that spiralled out of control (true story here) Another simple example is compound interest. Take two sticky notes. On one write “Money in the bank” on the other write: “Interest”. Say: If you leave your money in the bank (draw a link to interest), you received interest on that amount. The more money in your bank account, the more interest you accrue, (draw a link from interest to money in the bank) the more money in your bank account. 

If you leave your money in the bank, you are leveraging a simple closed loop of cause-and-effect known as compound interest, one Albert Einstein once may have called, “the most powerful force in the universe.”  

Now, go back to the question: Why do I need to wear a mask? Staying home. Not visiting friends.  Your behaviour multiplied by a lot of kids doing the right thing, can help “flatten” an exponential growth curve. Perhaps this is the simple lesson:  Our individual actions can combine to have positive or devastating impact on the whole.

Here are some other great resources for talking with kids about exponential growth:


Stories are a great way to learn about anything, even exponential growth. Here’s a system-based review I wrote about  One Grain of Rice by Demi (good for young and old) for the Waters Foundation.

For a similar story, try “Sissa and the Troublesome Trifles.  See I. G. Edmonds, Trickster Tales (Philadelphia: J. P. Lippincott Co.,1966) pp. 5-13.


For a classic, hands-on example of underestimating the power of exponential growth see the Paper Fold game in the Systems Thinking Playbook and John Sterman’s original version below.

From “Business Dynamics”, John Sterman, p.268

The Infection Game

See The Shape of Change and the Shape of Change Stocks and Flows, by Rob Quaden, Alan Ticotsky and Debra Lyneis, illustrated by Nathan Walker.  This paper-and-pencil game simulates the spread of an epidemic.  Best when played by a larger number of students – 35 is ideal.  


This youtube clip by Dr. Albert Bartlett of U Colorado is worth every minute, more for teens and adults.

There are also some wonderfully clear examples of exponential growth on the Khan Academy site that explore compound interest and bacteria.

Websites/Blogs: Search “exponential growth” on the Water’s Center for Systems Thinking and Creative Learning Exchange websites.  Lots of great curriculum ideas.

Really good explanations, visuals and video clips on these two blogs:

Zimblog:  Understanding Exponential Growth

Growth Busters:  check out the documentary film and the blog

Got Complexity?

Surgeon and author Atul Gawande looked at the extreme complexity of knowledge in a range of fields from medicine to disaster recovery. He found that avoidable failures could be dramatically reduced with a simple tool: a checklist. AtulGawandeChecklistManifesto Simple surgical checklists such as those described in Gawande’s book, The Checklist Manifesto, have been adopted in more than 20 countries and are considered the biggest clinical invention in 30 years.

In almost every profession, we deal with complexity. If you’re working to ensure food security, create a zero-carbon future, foster a healthy democracy, cultivate healthy communities and safe school environments, eliminate slavery in supply chains, safeguard water sources, resolve sectarian conflict, protect endangered species, restore forests or other seemingly intractable issues, you are likely challenged on a daily basis to help others see the impact of our actions on the often tightly interconnected systems of which we are a part. In the case of climate change, a systems view shows us the link between politics, policy (for example, legislation related to carbon emissions and deforestation), the natural sciences (particularly forests, which help stabilize the climate by absorbing heat-trapping emissions from factories and vehicles), and a person’s own consumption habits. Without a systems view, the complexity can be daunting, and the result is often policy resistance or, worse yet, polarization and political paralysis.

In my work as a complex systems coach and teacher, I often hear people say: “But where do I start?” To answer that question, my colleague Michael Goodman and I created this simple checklist as a guide for framing complex issues. There are of course more “checklists” for enacting systems change. But this is a good place to start. We hope you find this helpful.

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For those of you who are familiar with the iceberg model, you will some overlap with this checklist.  Here Mike Goodman explains:  “While there is some overlap with the six steps, this checklist is meant to highlight some important elements of systems thinking not very visible in the six steps alone. The six steps were based on traversing the iceberg from top to bottom with some amount of iteration:

1. Tell the Story

2. Draw Graphs

3. Draft Focusing Question

4. Identify the Structures

5. Apply the Going Deeper Questions

6. Plan an Intervention

In contrast, the checklist focuses on identifying the change, thinking about boundaries, making structure visible using closed loops, delays and archetypes and power of language. The two go together but are different.”


We would love to hear from you. Comment here, or join the conversation on LinkedIn.



The Most Needed Skills in the 21st Century


Recently, McKinsey and the World Health Organization both asked the same question: what are the most needed skills in the 21st century?

McKinsey looked at the top 10 job skills for adults.

The World Health Organization looked at 16 life skills for K-12 students.

Both came up with same #1 skill:  complex problem solving.

The key word is complex. It’s a word that’s worth revisiting. A broken arm or a flat tire is a problem, but not a complex problem. Most complex problems like attracting the right talent, reducing a community’s emission levels, improving a company’s safety culture — all involve multiple parts and processes interacting over time. Said simply, they all involve systems. And more specifically, complex systems.

At the mention of complex systems you might be tempted to run for the hills. Stick with me. This will be worth your time. I promise.

Complex doesn’t just mean complicated.

A complex system means:

  • it changes over time,
  • it’s open to influences from outside of itself,
  • it’s capable of being chaotic and
  • it’s non-linear, meaning small inputs have large and difficult to predict results.

If you’re dealing with a complex problem, it may mean refreshing the tools in your tool box. Bullet points, matrices and flow charts can help to organize our thinking.

Yes. But we need other frameworks, habits of mind, tools and even new language (like feedback loops) when we’re dealing with the type of dynamic, interconnected, complex problems Russ Ackoff called “wicked messes.”

So, where do you start?

If you are looking for tools, consider those that are designed to make visible the often hidden connections in complex systems. Tools such as the iceberg, hexagon grouping, causal loop diagrams, stocks and flows, and systems modeling software (like Vensim, Kumu and many others).

What have you found most useful for both understanding and solving complex problems?   Join us on LinkedIn to add your thoughts and questions

(Definition of complex system adapted from Daniel Siegel, author of Mindsight).