To use the same example as Lewis, a man in love feels certain specific feelings when thinking of that special someone. But a scientist can come in and explain all of his feelings as mere biological stimuli. The basic problem arises: which of these explanations of the same thoughts is true? Lewis finally concludes that though neither picture is complete on its own, both must be used to truly describe anything.
This idea made me think of vision in a literal sense. We all know that we have two eyes, which collect data. This data is sent to the brain as a signal which is translated into an image which we "see". But think for a moment. If one eye is closed, the image our brain receives is slightly off. The picture is, for the most part, the same, but an apparent shift occurs. In other words, both eyes are needed to make a complete observation of the scene.
Now consider thinking from "outside" and from "inside". It is a similar case. Though only one view or perspective will give an adequate representation of the situation, the true observation relies on both views.
Why is this so necessary? Things like science or mathematics attempt to only look at objects, situations, and occurrences. This grounds thought and almost restrains it to a certain realm of reality. For example, no matter how many times a farmer insists that two female sheep can reproduce, by science (and common sense) we know this is outside the realm of possibility. But experiences make those same objects, situations, and occurrences more real to an individual. These experiences must also be trusted to explain. If they were not, it would be rather difficult to explain anything, given that experiences help even a scientist explain his or her work.
How does observation help us? Observation is the key to learning. By observing as Lewis suggests, one gains knowledge from experiences and science, from being an outsider and an insider, from looking at and looking along all at once. This form of learning will give the most complete and accurate view of the world.