Bowing to the king’s statue is not considered worship, since he did not accept the idol upon himself, whereas bowing to the idol due to love or fear is considered avodah zarah (according to Abaye) – what is the difference between these two cases?
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The question is what he is doing, not his motive for doing so. Bowing to a king’s statue is not idol worship. Bowing out of fear is idol worship, albeit with an motive.