The More You Know…

From teaching undergraduates, I’ve come to believe the following:

• As a freshman, you get overwhelmed by the simple.
• As a sophomore, you think you know everything.
• As a junior, you think you know nothing.
• As a senior, you don’t care what you know.

But, as the Preacher reminds us, “there is no new thing under the sun” (Eccles. 1:9b). Meaning…? I guess my belief above wasn’t as original as I’d hoped.

In 1999, Cornell psychologists David Dunning and Justin Kruger described a rather interesting pattern in human thinking. They conducted experiments showing that, essentially, as someone learned more and more about some topic, he would become more and more aware of just how much there was to learn about that topic and, consequently, became more and more aware of how little he actually knew in relation to the entirety of that topic. This phenomenon became known as the “Dunning-Kruger Effect.”

In essence: knowledge up –> confidence down.

But a much more “fun” part of Dunning and Kruger’s findings is that the inverse also holds: knowledge down –> confidence up. In other words, the less that someone knew about some topic, the more he thought that he knew.

Once you really think about it, it just makes sense.* The smaller some “world,” the less there is to know about that world.

*I know…I know…”making sense” doesn’t prove anything. But Dunning and Kruger have experimental evidence to support the idea.

Consider a kindergartner who is just learning basic addition: 1 + 1 = 2, 2 + 3 = 5, etc. To that child, the whole “world” of mathematics is just that simple addition. To that child, “mathematics” equals “simple addition.” To that child, mastering that little bit of addition means having mastered mathematics. That child literally thinks that he knows everything there is to know about mathematics. Why? Because he knows everything there is to know about what he perceives is mathematics.

Of course, the child soon gets into subtraction, multiplication, and division, and that child soon realizes that the “world” of mathematics is bigger than he originally thought.

But, even then, the actual world of mathematics is far, far bigger than he can possibly conceive. It is not unusual for a child to ask me what it means to be a mathematician: “Do you multiply really big numbers?”*

“No, you sweet innocent…no. I usually just cry myself to sleep wondering if I’ll ever nail down that proof of the Third Sylow Theorem.”

To be honest, the more I learned about math, the more I learned that I was hopelessly lost if I wanted to learn everything there is to know about mathematics–even learning about something as “simple” as multiplication. Borrowing from my example above, the seemingly simple “world of multiplication” is far larger than you or I could possibly imagine.

To get a sense of this, I invite you to visit the https://mathworld.wolfram.com/ website (I know you won’t, but you’re still invited…), and plug the word product into the search bar. You will get 91 pages of results. Page 1 alone lists links to the following:

• dot product (very familiar to those studying vectors)
• inner product (ditto)
• Cartesian product (familiar to those beginning to study sets)
• direct product (familiar to those studying abstract algebra)
• Jordan product (ditto)
• cup product (“Huh?”)
• Hadamard product (“OK, now you’re just making stuff up.” “Am not!” “Are, too!” “Am not!”…)

And that’s just the first page…out of ninety-one…just dealing with multiplication!

Consider your own line of work. Don’t you get a slight, sly–and certainly irritated–smile when someone else mentions how easy your job is?* Of course you do because you know that there are 100 things about your job that the other person doesn’t know…and probably doesn’t even know that they exist.

*Either that, or you want to punch him square in the face. But this blog is called Quiet Contempt, so we’ll keep it to just the sly smile.

The whole point is that we all need to develop an awareness that we don’t know everything…especially if we are just beginning to study the topic (or, far worse, if all of our “study” is reading posts from our isolated bubble of social media friends).

Even the Bible makes a big deal out of this very thing. In I Timothy 3, Paul lays out the qualifications for a pastor (a “bishop”). In verse 6, the given requirement is “Not a novice, lest being lifted up with pride he fall into the condemnation of the devil.” The prospective pastor is expected to spend a great deal of time transforming from a “novice” in the faith to one with much more maturity.

Paul himself sat at the feet of Jewish masters for years. However, once he was saved on the road to Damascus, he recognized that he was still a “novice” Christian even though he was highly experienced in Judaism. In Galatians 2:1 (see chapter 1 for context), Paul notes that he spent some 14 years in private study before moving into his public ministry.

In my next post, we will take a slightly deeper look into the Dunning-Kruger Effect and see what it means as we slowly but steadily learn more and more about different topics.

But, to conclude, let me return to my starting illustration and show how the Dunning-Kruger Effect neatly describes my observations about undergraduates:

• Freshman are typically in awe as they are introduced to the basic concepts of their chosen majors. But, being basic, those concepts aren’t typically too difficult to grasp, leading to…
• Sophomores that think they have a pretty good handle on their major (and college life in general). But this is when they usually take their first deep, year-long courses. Thus, especially in the second semester, they begin to realize that there’s a LOT more our there than they possibly imagined, leading to…
• Juniors that come to realize that learning everything about their major is futile. Often, their second deep, year-long courses go even deeper, and they realize that the rabbit hole doesn’t just keep getting deeper and deeper–it drops all the way to Wonderland. (For the record, juniors are often my favorite students. They’ve learned enough to speak knowledgeably about their majors, but have a healthy respect for just how much their majors entail.) This finally leads to…
• Seniors that just want to finish. They probably still have a love for their major (though it is a far more mature and respectful love than that shown by eager freshmen) and still want to learn more about it, but they are just too burned out on formal learning and are just wanting to begin to apply what they now know is a just a fraction of what their major really holds in store.

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Then come graduate students…