I’ve been thinking about knowns and unknowns ever since my first exposure to the concept of an unknown unknown, but this is the first time I’ve put those thoughts to writing. The number of kinds of knowns and unknowns, like all binaries, increases twofold per level of meta-knowledge (knowledge about your knowledge). If you are at all familiar with bits (binary digits) then this idea should hopefully click right away. In this piece I’ll explore in detail the meaning of knowns and unknowns at the first and second levels of meta-knowledge. Then I’ll try to convince you that from the third level onwards, there is no useful distinction from the second level.
Let’s start by examining the most basic case. At meta-knowledge of level one, there are two possibilities: either known or unknown. You should already be pretty familiar with these two. Nothing fancy is going on here; these are simply pieces of information that you either know or do not know.
Some knowns might be
- Your age in years
- The value of 2 + 2
And some unknowns might be
- How to fly a plane
- Exactly how many hairs you have
Moving a step forward, we arrive at meta-knowledge of level two. Now we have four possibilities. Intuitively, this is because at level two, we are know either knowing or unknowing about our knowns and unknowns. I’ll use italics and boldface to contrast meta knowledge descriptors with the subject being described.
| Kind | Example |
|---|---|
| Known known | Your age in years |
| Known unknown | How to fly a plane |
| Unknown known | How to throw a flick frisbee |
| Unknown unknown | The name of Louisiana’s capital |
At level two, we see some of the same examples from level one, under the kind of knowledge that is known. While unknown knowns and unknown unknowns do qualify as plain old knowns and unknowns, I purposefully excluded the level two examples from the level one examples in order to drive home the point that we don’t know them to begin with. And yet they are still as fundamental as the knowns and unknowns that we do know.
As I mentioned earlier, I’m going to be as detailed as I can, so let’s go over each example and explain why it’s in the category that it’s in.
The known known: Your age in years.
- You know the fact that you are of a certain age and you know that you know the fact. Therefore you know that you know your age in years.
The known unknown: How to fly a plane.
- You don’t know how to fly a plane and you are aware of your not knowing it. Given the chance to fly a plane, you’d decline—assuming you’re not crazy.
The unknown known: How to throw a flick frisbee.
- Imagine you came out of the womb knowing how to throw a flick. Up until you actually throw one for the first time, the fact that you know how do this remains unknown to you.
The unknown unknown: The name of Louisiana’s capital.
- Imagine you’re playing United States trivia and somebody calls on you to name Louisiana’s capital city (Baton Rouge). You realize that you don’t know the answer. Right as you realize this, the name of Louisiana’s capital turns from an unknown unknown into a known unknown.
Now that we’ve covered level two, we can move onto level three and onwards.
| Kind | Example |
|---|---|
| Known known known | Your age in years |
| Known known unknown | How to fly a plane |
| Known unknown known | Does not exist |
| Known unknown unknown | Does not exist |
| Unknown known known | Does not exist (besides trivially) |
| Unknown known unknown | Does not exist (besides trivially) |
| Unknown unknown known | How to throw a flick frisbee |
| Unknown unknown unknown | The name of Louisiana’s capital |
Again, as I said earlier, I’m going to try to convince you that the kinds of knowledge described by 3+ levels of meta-knowledge are functionally equivalent to that of two levels. To be clear, I’ve done no research on this besides thinking about it myself, so this could be completely wrong, but intuitively it feels right to me.
As we increase the levels of meta-knowledge, notice how there are only ever four valid kinds of knowledge. For level three, these valid kinds are
- Known known knowns
- Known known unknowns
- Unknown unknown knowns
- Unknown unknown unknowns
If you know that you know something, then you can know that you know that you know that thing. Ad infinitum. The same goes for unknowns.
Let’s break the other four kinds down case by case and see what makes them invalid.
The known unknown known.
- One cannot know an unknown known because that implies one knows said known, making it a known known.
The known unknown unknown.
- Similarly, one cannot know an unknown unknown because it would imply that one knows said unknown and thus it is a known unknown.
The unknown known known.
- Suppose you know that XYZ. Also suppose you do not know what meta-knowledge is. The only situation in which I see you being able to truthfully say, “I didn’t know that I knew that I knew that XYZ” is right after I describe meta-knowledge to you for the first time. This is a rather trivial case, and I believe it is the only case in which an unknown known known can exist.
The unknown known unknown.
- Same as above but replace unknown known known with unknown known unknown.
So there you have it. I think this topic warrants deeper thinking into the general case with arbitrarily deeply leveled meta-knowledge, but I’ll leave it at this because my brain is a little fried thinking about it.
I hope you were able to learn something after reading this. Apologies if I have made meaningless the string of characters that spells out “known” by repeating it so many times in this post.
I’ve wanted to write down my thoughts on this topic for some time now. Hopefully this is the start of a long line of posts. If you have any questions or concerns or corrections you’d like to send me, my email is available on the home page.
That’s it for now. Bye!