Musings of an Analyst

Years ago, one of my favorite mentors shared his view that if you don’t understand an idea well enough to explain it using an analogy, you don’t understand it.  In hindsight, I think this was his version of the quote attributed to Einstein that “if you can’t explain it simply, you don’t understand it well enough.”  Over the years, I have thought about what that means for me.  It often comes home for me when I try to explain difficult concepts to elementary school kids.  Others have wrestled with the same idea in ways that I find interesting.

Feynman implicitly applied this idea throughout his famous series of physics lectures.  He stressed that the reason for studying certain types of differential equations was because of their broad applicability to a range of physical phenomena.  Similarly, he talked about a range of conditions where the wave equation applied.  In both of these cases, there are insights to extract from studying the equations and thinking about what they mean.

In contrast, Feynman also commented on the impossibility of explaining how quantum mechanics works by using an analogy because, in his opinion, it didn’t work like anything else we know about.  Was this a reflection of the inherent differences between quantum mechanics and everything else?  Or was this a reflection of how much we have left to learn about quantum mechanics?  Did even Feynman not know enough about it to explain it simply?  I don’t know.  That may be because I do know that I don’t understand quantum mechanics well enough to explain it simply.  Personally, it helps me to think about things in terms of analogies.  It helps me to better understand the topic I am thinking about, and it helps me to think about where the tools I know might help be to better understand the limits of both my knowledge and the tools that I know and like to use.  Admittedly, there are limits to where this technique can be applied.  Feynman commented on this in an interview he did after he had won the Nobel prize in physics.  In response to a question, he responded “if I could explain it to the average person, it wouldn’t have been worth the Nobel prize.” 

Two of my other mentors and former bosses gave me advice that has shaped me over the years.  One told me “The value isn’t in the answer.  The value is in the struggle.”  During a conversation about analyzing the data from a structural test, I shared my initial opinion on what the results were implying.  My boss at the time and long-term mentor told me “That may be.  But you don’t have enough agony points invested yet to be sure.” Taken together, the advice from my personal mentors has helped me understand the importance of seeking to deeply understand what is going on and that it helps me personally to try to understand things well enough to explain it using an analogy.  When I can’t, I benefit from the struggle of trying to understand it well enough to explain it using an analogy.  The value is in the struggle.  I learn as a direct result of the agony points that accrue from seeking to explain things via an analogy.  I don’t always recognize what I don’t know until I try to explain it using an analogy.  For me, seeking to understand things using analogies helps me be appropriately rigorous in my efforts to understand.

There are limits to the applicability of any analogy.  Understanding those limits is part of the understanding of the analogy and the topic.  For me Lorenz’s equations and his famous observation on the sensitive dependence on initial conditions helps illustrate this idea.  Lorenz found that the dynamics described by the equations that bear his name were extremely sensitive to small differences in the initial conditions.  How do you explain that mathematical idea in a way that makes sense to people?  Do you say, “if the equation is simulated for an extended time, the difference between starting the first state at a value of 1.0 results in a qualitatively different outcome than if you start the first state at a value of 1.00001?”  Or do you say “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?”  Obviously, a butterfly flapping its wings in Brazil does not cause a tornado in Texas.  But, the difference in how well we understand the current state of the weather everywhere right now is the difference between predicting very different weather in just a few days.  This underlying behavior in the equations that describe the weather is why three-day weather forecasts tend to be much more accurate than seven-day weather forecasts.  That is because small differences compound over time.  In my opinion, Lorenz quote enables a more meaningful understanding of the phenomena.

What does this mean to me?  There is value in seeking to understand topics in a way that you can explain them using an analogy.  This helps the person seeking to understand. And, it often helps when you are trying to communicate a difficult topic to someone who has not invested the same number of agony points seeking to understand it.  But, for this to be most useful, the person using the analogy and the person hearing the analogy need to understand where the analogy applies, what it means, when it doesn’t apply, and what it doesn’t mean.  Butterflies don’t cause tornadoes.  But, understanding that things as small as a butterfly’s wings flapping mean the difference between predicting a tornado or not helps people understand ideas.  And, mutual understanding helps people communicate effectively.  Whether this communication is in a business environment where better mutual understanding leads to better team decisions or when seeking to teach a new idea to someone of any age, mutual understanding leads to better outcomes.  For business decisions, people need to understand both the analogy and the limits of the analogy to use them effectively when they are making decisions.