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Western medicine is often found by trial and error too. Scientists perform tests of thousands of compounds just in case one of them happens to do something that might turn out to be useful. Some drugs are used to treat different diseases than what they were originally developed for because we noticed that patients with those other diseases mysteriously showed improvements. I can't think of which off the top of my head but perhaps a heart medicine that stopped baldness.

The key difference is western medicine is tested objectively, while traditional medicines are based on belief. A million people getting sick and taking a treatment and recovering doesn't mean the treatment does any good, but they'll believe it does because everyone else believes it too.