Question: Does Luke 1:35 infer that the Holy Ghost is the Power of God?
And the angel answered her, “The Holy Spirit will come upon you, and the power of the Most High will overshadow you; therefore the child to be born will be called holy—the Son of God. (Luke 1:35 ESV)
Not necessarily: Spirit (Greek pneuma) and power (Greek dynamis) are two different things. See this example from the Old Testament:
Then he said to me, “This is the word of the LORD to Zerubbabel: Not by might (Hebrew khayil), nor by power (Hebrew hoakh), but by my Spirit (Hebrew ruakh), says the LORD of hosts. (Zechariah 4:6 ESV)
(Note that the Greek Old Testament, the Septuagint here has dynamis for might, and pneuma for spirit).
What about Matthew?
The argument that “power” and “spirit” are the same thing in Luke is suggested by Matthew’s use of only “spirit” in “pregnant through the Holy Spirit”:
18 This is how the birth of Jesus the Messiah came about: His mother Mary was pledged to be married to Joseph, but before they came together, she was found to be pregnant through the Holy Spirit. … 20 But after he had considered this, an angel of the Lord appeared to him in a dream and said, “Joseph son of David, do not be afraid to take Mary home as your wife, because what is conceived in her is from the Holy Spirit. (Matthew 1:18-20)
The problem is that Matthew does not supply the information that “spirit” means “power”, Matthew’s main concern is to underpin the legitimacy of Jesus’ descent. Matthew is only saying what Matthew is saying in the context of Matthew. Remember that Matthew does not even give the physical genealogy of Christ (from Solomon’s brother Mary, through Mary, found in Luke 3) but the legal descent via Solomon to Jesus’ adopted father Joseph. This is the context of his statement in 1:18-20.
Power for miracles, spirit for inspiration
In the Old Testament power is generally associated with miracles, while spirit is generally associated with inspiration. This distinction continues in the New Testament. For example when Jesus sends out his disciples it is with “power”, and John 7:39 tells us that the Holy Spirit “was not” until after the resurrection (John 20:22).
Therefore (A) “The Holy Spirit will come upon you”, and (B) “the power of the Most High will overshadow” you are describing two different things. It might look as though they are both related to the physical conception because there appears to be only one consequence: “therefore the child to be born will be called holy—the Son of God.” But the Holy Spirit did “come upon” Mary both in the special state she was in – not just physically – as a very special person, the virgin mother of the Son of God, but also in Mary having herself been inspired to prophecy after her (probable) maternal aunt Elizabeth prophesied:
41 And when Elizabeth heard the greeting of Mary, the baby leaped in her womb. And Elizabeth was filled with the Holy Spirit, 42 and she exclaimed with a loud cry, “Blessed are you among women, and blessed is the fruit of your womb! (Luke 1:41-42)
Mary’s Song of Praise: The Magnificat
46 And Mary said,
“My soul magnifies the Lord,
47 and my spirit rejoices in God my Savior,
48 for he has looked on the humble estate of his servant.
For behold, from now on all generations will call me blessed;
49 for he who is mighty has done great things for me,
and holy is his name.
50 And his mercy is for those who fear him
from generation to generation.
51 He has shown strength with his arm;
he has scattered the proud in the thoughts of their hearts;
52 he has brought down the mighty from their thrones
and exalted those of humble estate;
53 he has filled the hungry with good things,
and the rich he has sent away empty.
54 He has helped his servant Israel,
in remembrance of his mercy,
55 as he spoke to our fathers,
to Abraham and to his offspring forever.”
This “Holy Spirit” which “came upon” Mary is a different use of the two words from the way Paul, for example, later uses “Holy Spirit” in verses such as Romans 5:5 in the context of the new life. This use is much more akin to inspiration, which came and went. Mary’s later state, doubting her son and listening to his younger half-brothers, was evidently not inspired. But at this point in Mary’s life, about to bear the Son of God (and through her also Son of Man) we can understand why the Holy Spirit would “come upon her”. But that is different from “and the power of the Most High will overshadow you”, the pregnancy. Which is why it says it.