Tuesday, October 17, 2017

Electronic Screens, Adventure, and the Cultivation of Intuition

It is all the rage these days to cast aspersions on the ubiquitous electronic screens that seem to rule our lives now.  Often, we write them down and then post them via those same devices, that others may partake of our rants.  But, contrarian that I am, I would like to say some things in defense of the screens.

When I was seeking my Texas Teacher Certification back around 1984, I took a class in Math Methods from the department head of the School of Mathematics at Texas A&M.  It turned out to be one of the most revolutionary courses I ever took, not only for my teaching career, but for life in general.  The professor spoke convincingly about the efficacy of guessing in Mathematics (though he recommended we use the word conjecture in place of guess, for pragmatic reasons).  Often, the best and fastest way to solve a problem is to adventurously step out into the void with a guess, a first approximation of the answer.  How that approximation stacks up against the constraints of the problem (e.g., governing equations) very often leads to a way to achieve a much better second guess, if not an exact solution.

Later, in my automotive engineering career, it occurred to me that (though powerful computers now did most of the "thinking" for me) nearly 100% of the problems I solved at work were solved through making an initial guess, and then making successively better approximations to the solution.  The world is a complicated place.  Engineering school (even at the graduate level) can give you a false impression of this, because an inordinate amount of time is often spent on one or two of the very few problems which have derive-able, closed-form solutions.  In truth, it is a statistically insignificant number (i.e., basically 0%) of the world's problems for which a closed-form solution may be found.  Almost always, engineering problems are solved by some method of iterative guessing (I mean, conjecture), such as Newton's Method.

In that Math Methods class, our professor emphasized the importance of developing mathematical intuition.  This cuts against the grain of the old, now largely defunct "just show me the exact steps to solve this kind of problem" approach, and you can see this in the obscene anger expressed against (so-called) Common Core math methods on the internet, from people who are apparently too timid to guess, or whose Math teachers a few decades ago told them never to do so.  But intuition is extremely powerful.  It can be developed.  But you have to be brave, to get out of your comfort zone to do so.  You have to have the temerity to experiment, to guess.  You have to risk being "wrong."

If you are old, as I am, did you ever stop to wonder why four-year-olds seem quicker to pick up new technology and more agile at operating electronic devices than we oldsters?  It is often chalked up to the idea that young people have more nimble minds, and I won't try to dispute that.  But I think there is a greater reason:  kids are not afraid to guess.  They are not afraid to push the wrong button and see what happens.  And what happens, eventually, is that they develop very good intuitions about how the electronic world operates.

Or, if you will, consider the opposite end of the spectrum.  Have you ever had occasion to help an elderly relative adapt to a newly-acquired electronic device?  I have a friend whose parents didn't understand where to type an internet address into their internet browser.  Instead, they made Google their home page, and then typed the web address into the Google search field.  It worked often enough that they could usually find what they were looking for.  But any four-year-old could have shown them a better way.  It is even worse if you need to teach a complex, multi-step task, such as:

1.  Go to a certain website.  Fill out the fields there.
2.  Use a button on the website to export your answer to a PDF file on your computer.
3.  Find the PDF file in your Downloads directory (wherever that is!) and move it to another directory.  CTRL-C and CTRL-V may help here.
4.  Rename the file.  Click the current name until the entire name is highlighted and then type in the new name.  Hit "RETURN."
5.  Open Outlook and send the renamed PDF file to two different addresses in your Outlook address book.  (Oh, but you'll have to know how to navigate to the folder where the PDF file now resides.)

Depending on the task at hand, there can be dozens or even hundreds of steps.   If one does not develop an intuition about these things, complex tasks can be very daunting indeed.  And that's for identical, repetitive tasks.  When faced with a brand new task, and without calling someone else in to help, you have nothing but intuition upon which to rely.  Your screen is filled with a few hundred tiny icons, perhaps, some of which may not be visible at first.  Where to begin?  You just have to make a guess.  You have to adventurously click on something, do some poking around, and see what you can find.

I submit to you that all of these electronic screens have done a fabulous job of developing our intuition.  They have made our minds more nimble, more resilient.  They have required us to be better problem-solvers, braver souls, better at guessing.  This leads us to be better thinkers in the final analysis.  It can help us to find a globally optimum solution rather than being satisfied with a locally optimum one.  In some of the Math and Physics classes I taught, I used an exercise that works to do this same thing.  There was a problem.  Say, estimate the height of a tower.  The students were required to come up with the craziest, zaniest ways to do this.  There is the obvious Trigonometric method.  There are Physics-based solutions (e.g., drop a ball from the top of the tower, and time how long it takes to hit the ground).  Maybe you chop down the tower and stack pennies from one the base of the tower to the tip.  Then, you multiply the number of pennies by the diameter of a penny.  There are so, so many ways.  And humanity is greatly enriched by cultivating the kind of imagination that does not stop at the first method found.

So, I submit to you that all of these electric "screens" everyone is so distressed about are actually making us better thinkers, and giving us more agile minds.  It is something to be thankful for.