In his short essay “Meditation in a Toolshed” C.S. Lewis makes an extremely helpful distinction between the two fundamental ways of knowing.
He calls them looking along and looking at.
His introductory example is also the origin of this formulation. He describes how, in a pitch-dark toolshed, he sees a beam of light falling through a crack in the door. First, he sees the beam of light itself; he looks at it. Then he positions himself so that the beam of light falls into his eye. Now he sees things (trees, etc.) through it; he sees along it.
Seeing is a deeply embedded metaphor in our languages for “understanding”, “knowing”, or at least “having a conviction”. We paraphrase a sudden, momentous realization as “Now it has dawned on me”. Or, more modestly, when you understand something, you say “I see.” Very intelligent people are called “bright” or “luminaries”. The list could be continued indefinitely. The point, which C.S. Lewis also makes, is that we can metaphorically apply our experiences of looking at and along the light beam to our understanding in an unusually direct way. “Looking at something” becomes understanding an object solely by rational analysis, without direct experience being involved. The classical scientific way of knowing is nothing but “looking at” (but this is not limited to science, as we shall see). “Looking along something” is then, analogously, understanding – or let us better say knowing by acquaintance – a thing or person through direct experience.
Lewis gives some examples: for instance, that of a young man in love with a woman. His experience of being in love with this woman is an instance of “looking along”; the analysis of the neurophysiologist measuring his brain activity during a conversation with the young lady and in her absence, a case of “looking at”
It is important to note that the purely rational analysis of “looking at” is not, or not necessarily, in tension with, or even contradictory to, the direct experience of “looking along” In the example cited, the neuroscientist’s findings do not constitute a refutation of the young man’s golden feelings (or rather, a refutation would only obtain if certain metaphysical theories such as eliminative materialism or reductive physicalism were true); even more, they easily complement each other to form a harmonious overall picture (for example, if emotions are properties of the soul caused by brain states and/or in turn trigger brain states).
All of the examples that Lewis gives draw the contrast between the two ways of knowing as that between a scientific observation and direct, first-person experience. This is undoubtedly true, but it does not go far enough for me. For, strictly speaking, the natural scientist and the young man do not “see” the same thing in two different ways – they see two different things. Qualities of experience (called “qualia” in philosophy) cannot be derived from brain states or built from them. Although the former are related to the latter, they are quite different kinds of states. But it seems to me, and Lewis would probably agree with me, that both ways of knowing could apply to one and the same thing. This is the case, for instance, with the young lovebirds. They experience their psychological states of infatuation firsthand. A psychologist could – if he believes in the existence of mental states – describe and analyze exactly these states, albeit in the sense of “looking at” (after all, he does not make the infatuation experience).
 Physicalist philosophers usually disagree.