Connecting the Dots Backwards: Not Knowing What We Don’t Know, Part 1
Note from the author: This article is based on a previous article published online by Math Horizons magazine. That version can be accessed here: https://www.maa.org/sites/default/files/pdf/Mathhorizons/supplement/MH-CoreyWeb.pdf
About a year ago my 20-year-old son came to me with a sketch of a body suit that was designed to help the wearer do some pretty remarkable things. I don’t think flying was one of them, but I could tell my son had carefully thought out what he wanted the suit to do. He said he really wanted to make this suit, but then he said something that caught me off guard, it was something close to: “I don’t want to go get an engineering degree because that will take a long time and I will spend a lot of time learning things that I don’t need to know to build this suit.” Well, to be clear, it didn’t surprise me that my son didn’t want to spend more time in school, it was this idea of learning just what he needed to know to make this one item.
On the surface nothing seems wrong with the idea of learning just what you need to know to accomplish a certain task. If you don’t play the piano and you really want to learn one song that you love, you can just work hard and long to learn that one song. But when it comes to design and engineering, things are not as straightforward as just finding a way to get your fingers to hit the right keys at the right time. An engineering or design task is a problem solving process that requires background research, brainstorming, testing out prototypes, working within constraints, trade-offs, etc. This process is a process of discovery and exploration, not a straightforward application of known solutions, especially to create something as cutting edge as the suit my son was designing. So the reason his statement caught me off-guard is that even a team of expert engineers couldn’t sit down and write out all of the things my son would need to know to make his suit a reality.
No, in engineering and design, as in so many other fields, the work is much more fluid and dynamic, and rarely is there the problem of learning too much you “don’t need to know”, but instead, it is not knowing enough. In the same way that the team of engineers could not write out what my son needs to know, they could also not write out what he might learn in an engineering degree that he would not need to know! Yet my son thinks it would be a simple thing to decide what information/knowledge/skills/understandings he would need to accomplish the goal and which ones he does not. That is the problem, and it is not just a problem when trying to design a cutting edge, powered, body suit. Thinking that we can decide before hand what we need to know and what we don’t need to know is one of the great fallacies of learning.
Connecting the Dots
The difficulty in this fallacy, that we can decide beforehand what we need to know to accomplish a goal, lies with an implicit assumption. That assumption can be summarized as: we know what we don’t know. But this is a fraudulent assumption. Why? Because in the vast majority of life, we don’t know what we don’t know.
Viewing learning from the I-KNOW-what-I-don’t-know perspective is fine for certain kinds of knowledge. Simple tasks for example. If you lose the taskbar on your computer, you use your phone to search for the solution. There is usually a simple fix and a simple reason why you lost it (usually some accidentally hit combination of keys).
But these situations are few compared to all of the other situations where we could use knowledge. In most cases we don’t know what we don’t know. This makes it very hard to predict what kind of knowledge we will need in the future. It also makes it very hard to see how we could use knowledge that we don’t have. Here are a few stories to illustrate this point.
This is a segment from Steve Job’s commencement address at Stanford University where he was telling a story about dropping out of college [1].
“Reed College at that time offered perhaps the best calligraphy instruction in the country. Throughout the campus every poster, every label on every drawer, was beautifully hand calligraphed. Because I had dropped out and didn't have to take the normal classes, I decided to take a calligraphy class to learn how to do this. I learned about serif and san serif typefaces, about varying the amount of space between different letter combinations, about what makes great typography great. It was beautiful, historical, artistically subtle in a way that science can't capture, and I found it fascinating.
“None of this had even a hope of any practical application in my life. But ten years later, when we were designing the first Macintosh computer, it all came back to me. And we designed it all into the Mac. It was the first computer with beautiful typography. If I had never dropped in on that single course in college, the Mac would have never had multiple typefaces or proportionally spaced fonts. And since Windows just copied the Mac, it's likely that no personal computer would have them. If I had never dropped out, I would have never dropped in on this calligraphy class, and personal computers might not have the wonderful typography that they do. Of course it was impossible to connect the dots looking forward when I was in college. But it was very, very clear looking backwards ten years later.
“Again, you can't connect the dots looking forward; you can only connect them looking backwards.”
I had a colleague attend a national conference for technology teachers; school teachers who taught such things as cabinetmaking, auto repair, welding, multimedia production, computer animation, etc. The keynote speaker was a medical doctor who led the team that developed the artificial lung [2]. As part of his talk he told the teachers something he hadn’t told people before. He told them the most important experience he had had that allowed him to develop the artificial lung. The teachers were amazed when he confessed that the key experience was rebuilding an old car when he was 16 years old. During that experience he learned how many components of a car worked and how they worked together. The artificial lung, he admitted, is really just a fancy radiator.
What I find most interesting about this story is that if any of us, or about anybody in the world, was faced with a task of developing an artificial lung we would not think – “I know what I need to do, I need to rebuild an old car!” Similarly, if it had been you and Steve Wozniak creating a computer in your parents’ garage, you would not have turned to Steve and say “Steve, I think one thing that we really need is for one of us to go take some calligraphy classes. That will really help us make our computers stand out.” You cannot connect the dots forward, or in other words, you don’t (usually) know what you don’t know. Yet that is exactly what my son is expecting to be able to do.
Just Look It Up
Because we have so much information at our fingertips via smart devices and the internet many students complain at having to learn (especially memorize) anything. The common response by students is that this is a waste of time and that these things can always be looked up in the future. Well they certainly can. That isn’t the point I am debating. The problem is that you can only look up things that you know you don’t know.
This quickly leads to a great fallacy in knowledge: you don’t need to learn things that you can look up. But now we can look up about anything online or in a university research library. This leads to the quick conclusion that you don’t have to learn anything once you can look up information online or in the library. What then becomes of the knowledge that we form our everyday thoughts with? We can only think with ideas that are already formed in our minds. That is how we make sense of what we experience. With those ideas in books, websites, videos, etc. then they are not free for us to think with until we have digested them and made them a part of us.
Here is an experiment. Take the time to memorize a quote. Here is one I have always liked by Thomas Edison, “We often miss opportunity because it is dressed in overalls and looks like work.” Memorize it really well and repeat it every morning and evening. Do this for two weeks and pay attention at how many times that quote comes to your mind throughout the day when it might be applicable to the situation you are experiencing. For the vast majority of you it will come to mind multiple times. But here is the interesting part. You could have always looked up the quote and read it, you didn’t have to memorize it, but without it being memorized (and fresh) you probably would have not stopped at those occasions when it came to mind and thought, “I wonder if there is a quote that I could use right now.” It just would have never occurred to you. The quote will have come to mind because something you experienced would have connected with it. This experiment readily illustrates this fallacy of being able to look things up. We think thoughts with what we know – not what we could know. We make sense of the world around us much more with what knowledge and beliefs are in our mind, not with what we can look up on a smartphone.
Editor’s note: This is part one of a two part series. Click here for part two.
References
Jobs, S. (2005, June). Stanford University Commencement Address. Palo Alto, CA. Text retrieved from http://news.stanford.edu/news/2005/june15/jobs-061505.html
Zwischenberger, J. (2011, March). Teacher-Excellence General Session Keynote. Presentation given at the International Technology and Engineering Educators Association Conference. Minneapolis, MN.
