The Wonder Years, You Know? — July, 2007
I have a few strange, but related, questions to ask...
·As a youngster, did you watch The Wonder Years? Me too.
·Did you have a crush on Winnie Cooper or Kevin Arnold? Me too.
·In school, did you ever take a calculus course?
·Were you geeky enough in school to care that its proper name is The Calculus?
It's goofy, I know, but that's what it's called.
So what do The Calculus and The Wonder Years have in common? I was reading a book on calculus the other day and was dumbfounded to see that the book's introduction was written by Danica McKellar—Winnie Cooper to you and me. It turns out that cute little Winnie went off to UCLA for a few years. While there she earned a degree in Mathematics and co-authored the proof of a new math theorem. Who'd have known—sexy and geeky? Nice.
Anyway, the whole discovery got me to thinking about all the little surprises that are hiding out there in the world, just waiting for us to stumble upon them. This got me to thinking about what we know in relationship to what we don't. I've heard people categorizing the things we know and the things we don't know into three categories: 1—The things you know you know; 2—The things you know you don't know; 3—The things you don't know you don't know.
The things you know you know are those things of which you have an awareness and are certain you know a thing or two about.
The things you know you don't know are those things of which you are aware and are more or less certain you don't know a thing or two about.
The things you don't know you don't know are those things of which you have no awareness and therefore certainly don't know a thing or two about.
I've always liked this theory of knowledge because it's simple, poetic, and it highlights all that's left to learn. But I spent some time thinking about it recently and began to suspect it was too ambitious. Then I started chatting about it with a geeky friend of mine at the coffee shop, Kris, and really began to feel it was too ambitious and oversimplified. Kris and I started drawing a few pictures of this and a graph or two about that. I'd scribble something. She'd correct it. She'd ask a question. I'd blather for a few moments. She'd dive into some statistical analysis on bell curves of knowledge and ignorance. It was fascinating, but we didn't settle on anything conclusive.
So, I chewed on it for a few more days and finally came to some thoughts.
If we dare to accept the above theory of knowledge and take disgustingly oversimplified stock in it, we can optimistically say that the average astute person knows little to nothing about two-thirds of all things. Hopefully the adverbs I threw into that sentence reinforce my newfound lack of faith in this ambitious theory of knowledge.
The more I thought about the theory, the more I came to believe that our intellectual interaction with the world relies on three factors: awareness, knowledge, and certainty. Awareness describes whether or not we are even familiar with the existence of a particular subject matter. Knowledge describes whether or not we know anything about the subject matter at hand. Certainty describes whether or not we think we know anything about the subject matter at hand.
Once I settled on these three factors, I started to think about how they interact with one another to describe our knowledge. With respect to awareness, we can either be aware or unaware that a subject matter exists. With respect to knowledge, we can either have knowledge of a subject matter or no knowledge of a subject matter. With respect to certainty, we can be certain in our knowledge of a subject matter or uncertain.
Take these three factors, each with two possible states, and do some simple math. You arrive at eight theoretical states describing our knowledge of the world instead of three. To ease the pain I was suffering thinking about all this, I threw the factors into a chart, and the eight theoretical states look like this:
As can be seen, considering all mathematical interactions of our three knowledge factors yields eight theoretical states of knowledge. Remaining simplistic, we can say that each state can describe 12.5% of our knowledge of the world.
But the more I looked at this chart, the more I began to find things. For instance, states 5 through 8 all begin with an unawareness of some subject matter. If we begin with no awareness of a subject matter at all, our knowledge and certainty with respect to that subject are irrelevant. We don't even know the subject matter exists. Relaying this back to the original theory, I believe we can say comfortably that these four states involve the things we don't know we don't know. With this, I modified my chart a little and came up with this:
So, straight away, we can simplistically say that 50% of all things are quite certainly unknown to each of us.
Then I began to consider more heavily states 1 through 4 to see what other understanding I might find. Number 4, it seemed to me, described a state in which we are aware of a subject matter but know nothing about it and are uncertain about our knowledge of the subject matter. I think we can call this state the things we know we don't know. So, we're aware, but fuzzy at best. With this, I modified my chart a little and came up with this:
Add 12.5% to the 50% of things we're unaware of and we've climbed to 62.5% ignorance. This is almost, but not quite, the 66.66% the original theory described. So, I kept chewing on the whole thing.
I pondered state number 3 a little while and found a state not described by the original theory. These are subjects that we are aware of and are certain we know a thing or two about, but don't. That is to say, these are the things we think we know, but really don't know. These are the cases when we try to sound smart, but blow it big time. We all do it, probably more frequently than we'd like to think. With this, I modified my chart a little and came up with this:
Add 12.5% to the 62.5% of things we're either unaware of or stupid about and we arrive at 75% ignorance. We're now more than 8% dumber than the original theory suggested we are. Aren't you glad I started thinking about this? And don't forget, I think both of these theories are too ambitious about our intellect anyway.
But there's some good news! I started pondering state number 2 and found another state of knowledge not described by the original theory. This one works in our favor, though. State number 2 describes a scenario in which we are aware of a subject matter and feel we're ignorant about it, but really know a thing or two about what's going on. That is to say, these are the things we think we don't know but do know. With this, I modified my chart a little more:
So we know, but don't believe we know, about 12.5% of things.
And of course, state number 1 describes the things we know we know, and really do know. So we have to give ourselves 12.5% more credit and the chart comes out looking like this:
To summarize clearly, this new theory describes the things we know we know; the things we don't think we know but know; the things we think we know but don't know; the things we know we don't know; and the things we don't know we don't know. With an aggressively optimistic application of this theory of knowledge, and weighted scoring of the five states of knowledge, we should know about 25% of the things there are to know, whether we know we know or not. That was clear, right?
Personally, I'd be surprised if each of us knew 2% of what there is to know, and we're not likely confident in more than 25% of that. Don't let that be daunting. Let that be inspirational. Get out there and learn something new today. Then pass it on.
So, with that, I'm off to try and discover something new myself. Maybe Kevin Arnold wrote an introduction to a book on relationships that I can read. I don't think I know if he ever ended up with our beloved Winnie or not. Do you?
~ topher
Footnote: The Complete Idiot's Guide to Calculus — W. Michael Kelley, introduction by Danica McKellar. © Alpha 2002