Pascal  said, "Scientific learning is composed of two opposites which nonetheless meet each other. The first is the natural ignorance that is man’s lot at birth. The second is represented by those great minds that have investigated all knowledge accumulated by man, only to discover at the end that in fact they know nothing. Thus they return to the same fundamental ignorance they had thought to leave. Yet this ignorance they have now discovered is an intellectual achievement. It is those who have departed from their original condition of ignorance but have been incapable of completing the full cycle of learning who offer us a smattering of scientific knowledge and pass sweeping judgments. These are the mischief makers, the false prophets." (Pensees V:327)

 The passage would seem to suggest that the purpose of science — and indeed all education — is to arrive at a state of ignorance, but an ignorance that is aware of itself . It took almost three centuries for Pascal’s insight to become the common view of scientists. The philosopher Karl Popper wrote: "The more we learn about the world, and the deeper our learning, the more conscious, specific, and articulate will be our knowledge of what we do not know, our knowledge of our ignorance. For this, indeed, is the main source of our ignorance — the fact that our knowledge can be only finite, while our ignorance must necessarily be infinite." The physician/essayist Lewis Thomas went further: "The greatest of all the accomplishments of twentieth-century science has been the discovery of human ignorance."

Science writer Timothy Ferris agrees: "Our ignorance, of course, has always been with us, and always will be. What is new is our awareness of it, our awakening to its fathomless dimensions, and it is this, more than anything else, that marks our coming of age as a species." It is an odd, unsettling thought that the culmination of the scientific quest — the long slow gathering of reliable knowledge — should be the confirmation of how little we understand about the universe we live in.

This new awareness of our ignorance should not be taken as permission to indulge the superstitions we are born into. Rather, it should cause us to be modest and skeptical, parsimonious in our creeds, ever richer in reliable knowledge but ever more demanding in the caliber of proof.

On the other hand, consider all the questions for which we have answers. As long as our answers to these questions invoked the gods — as they did for thousands of years — no reliable public knowledge was possible. Only when a few curious people said "I don’t know" did science begin. Admission of ignorance is a prerequisite of scientific discovery, and by the same token, the more we learn, the more we are aware of what we do not know.

From an article in Science Musings:

 http://www.sciencemusings.com/2006/09/through-glass-darkly.html