In this interesting transcript from a talk by Lama Yeshe, he explains that refuge isn’t simply an act, but a way of thinking. He mentions:

When you take refuge in Buddhadharma, the important point is that you have recognized your own profound potential, and from the beginning can see that, “I can do something, I can take the responsibility of liberating myself.” This is different from the attitude we normally have: “I’m hopeless, I’m hopeless; maybe God, maybe Buddha, maybe Lama can do something for me.” This sort of human attitude is wrong. From the Buddhist point of view it is wrong to think, “I’m hopeless, Buddha can do something for me.” That attitude is wrong because it’s not true. By believing that you are hopeless you have already decided that you are nothing, you have already put a limit on your profound quality. The important thing in taking refuge is to have the understanding that you can do something to solve the problem of everyday life by relying, with confidence and trust, on the Buddha’s wisdom—or you can also call it your own activated wisdom—to liberate you from confusion and suffering. So it is really worthwhile. The real significance of taking refuge in Dharma wisdom is that it is the entrance to the path to enlightenment.

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