From Communications of the ACM - October 2000, Volume 43, Issue 10:
...and their opposite, the FourLevelsOfCompetence. (The first two of which are levels of ignorance.)
The various orders of ignorance can be seen as increasing levels of Risk. Various techniques of knowledge acquisition can be categorized as targeted toward reducing Nth order ignorance to N-1 for some fixed number N. For example, some might regard UnitTests as a way of reducing 1st order ignorance to 0th order ignorance. A successful test shows you something that you didn't know about either the code you wrote, or what that code was supposed to do (or where). (I would be inclined to regard UnitTests as a way of reducing 1st order ignorance to knowledge. Or is 0th order supposed to be 'you know something'?)
TomDeMarco says something like (paraphrasing): it isn't what you don't know that causes trouble, it is what you are absolutely sure is true (but isn't) that you have to worry about. I think this is a variation on the 4th order.
I'll bet WillRogers? didn't know that TomDeMarco had said that.
Is Ignorance really this orderly? ;) Let's separate being ignorant from our attitudes about ignorance.
Attitudes fall into a continuum with:
At one end, "I am not ignorant!" (I can't accept being ignorant).
And at the other, "I understand ignorance is part of the human condition" (I accept that no one person can know everything-even about a single topic!).
Perhaps the "orders" are more like a process.
One positive aspect of ignorance is expressed in the quote: Ignorance is fixable, stupidity is forever
This all reminds me of the CapabilityMaturityModel somehow...
"If knowledge is the contrary of ignorance... and knowledge is power... then ignorance is lack of power?"
Simplified yes. But knowledge 'is' not power (i.e. a synonym or identity). But more like knowledge 'leads-to' power. And 'not' or 'contrary' doesn't distribute over 'leads-to' I guess.