The figure of a dove symbolizes the work that Jesus will do through the Spirit. The idea that the Spirit descended in the manner of a dove1 is incorrect: the form of the dove symbolizes the Spirit.2 There is no reason to think especially of Noah’s dove (whereby the olive leaf would be the sign of the Spirit3): this dove does not return to Jesus, but descends from above, not with a sign of new life on earth but with the sound of a heavenly voice. That shows that the work of the Spirit is not the work of a bird of prey, but of the peaceful dove. This matches the tenor of Isaiah 11:6–10, Isaiah 42:2–7, and Isaiah 61:1–3. The Messiah comes to bring peace (see Acts 10:36).4
10 And when he came up out of the water, immediately he saw the heavens being torn open and the Spirit descending on him like a dove.