We are aware of the boundaries of our knowledge, and thus we have a pretty good idea of what to expect just beyond that frontier. In other words, there's a pretty big set of things that we *know* that we don't know yet.
Beyond what we know we don't know lies an infinitely larger set of things that we're completely unaware of; in other words, things that we don't know that we don't know yet.
The more we learn, the further we extend the frontier. As the frontier expands, we become aware of even more of what we don't know yet. Many things that we didn't know that we don't know thereby become things that we know we don't know.
So in that sense, the more you know, the larger the set of things you realize you don't know yet.
As Albert Einstein phrased it: "The more I learn, the more I realize how much I don't know."
Then there's the anonymous popular phrasing: "The more you know, the less you understand".
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