“As long as a thing is unknown, it belongs to us in a way that well-known things do not. For we have the opportunity to fill the empty, unknown spaces for ourselves, and in them there is room for imagination and for hope.”

Aldous Huxley, using the term "the doors of perception" which originated with William Blake in The Marriage of Heaven and Hell. It is sometimes credited to Morrison because he cited it in interviews as the inspiration for the name The Doors and without always crediting Huxley as the source.
Misattributed

Quote in a letter to Sherwood Anderson, October 1923; as quoted in Georgia O'Keeffe: A Life, Roxana Robinson, University Press of New England, 1999
1917 - 1929
Context: I have been thinking of what you say about form... I feel that a real living form is the natural result of the individual’s effort to create the living thing out of the adventure of his spirit into the unknown.... and from that experience comes the desire to make the unknown known. By unknown I mean the thing that means so much to the person that he want to put it down - clarify something he feels but does not clearly understand... Making the unknown known.... if you stop to think of form as form you are lost.

Introduction
The Female Eunuch (1970)
Context: The fear of freedom is strong in us. We call it chaos or anarchy, and the words are threatening. We live in a true chaos of contradicting authorities, an age of conformism without community, of proximity without communication. We could only fear chaos if we imagined that it was unknown to us, but in fact we know it very well. It is unlikely that the techniques of liberation spontaneously adopted by women will be in such fierce conflict as exists between warring self-interests and conflicting dogmas, for they will not seek to eliminate all systems but their own. However diverse they may be, they need not be utterly irreconcilable, because they will not be conquistatorial.

Department of Defense news briefing (12 February 2002)
Variant:
Now what is the message there? The message is that there are no "knowns." There are things we know that we know. There are known unknowns. That is to say there are things that we now know we don't know. But there are also unknown unknowns. There are things we do not know we don't know. So when we do the best we can and we pull all this information together, and we then say well that's basically what we see as the situation, that is really only the known knowns and the known unknowns. And each year, we discover a few more of those unknown unknowns.
:It sounds like a riddle. It isn't a riddle. It is a very serious, important matter.
:There's another way to phrase that and that is that the absence of evidence is not evidence of absence. It is basically saying the same thing in a different way. Simply because you do not have evidence that something exists does not mean that you have evidence that it doesn't exist. And yet almost always, when we make our threat assessments, when we look at the world, we end up basing it on the first two pieces of that puzzle, rather than all three.
:* Extending on his earlier comments in a press conference at NATO Headquarters, Brussels, Belgium (6 June 2002) http://www.nato.int/docu/speech/2002/s020606g.htm
2000s

(Cambridge: 2002), Book 9, Chapter 1, p. 24
On the Trinity (417)

Source: History of Mathematics (1925) Vol.2, p. 430; footnote

Physics and Philosophy (1958)
Source: Physics and Philosophy: The Revolution in Modern Science
Context: Whenever we proceed from the known into the unknown we may hope to understand, but we may have to learn at the same time a new meaning of the word "understanding."