The Memorial as Abiding Presence
Yahweh has testified through His apostles and prophets that the Law of Moses was spiritual (Romans 7:14), being a shadow of the true image, which is Christ (Colossians 2:16-17) (Hebrews 8:4-5) (Hebrews 10:1). In this way, we can use the Law to help us discern the spiritual truths being obscured, that are brought out through the holy Son of God, Christ Jesus the Lord.
Although known since the beginning of creation, to Adam and Eve, Yahweh gave His Name once more to His servant Moses, to be shared with the children of Israel. As He was questioned about Who Moses should say had sent him, and what was His Name, God replied thus:
15God said moreover to Moses, “You shall tell the children of Israel this, ‘Yahweh, the God of your fathers, the God of Abraham, the God of Isaac, and the God of Jacob, has sent me to you.’ This is my name forever, and this is my memorial to all generations. Exodus 3:15
This Name, which had been known to their fathers, was now set down as God's Memorial to all generations, His Name for eternity.
As He continued to deal with the nation of Israel, He and His prophets would repeatedly refer to His presence as His Name being present. The desecration of the Temple was so much so because He said, "in Jerusalem shall My Name be forever." Thus, the people there were promised that their God, Yahweh, would always be present with them. God's Memorial was to be His presence among His people.
This corresponds directly with the Memorial given in the New Covenant to God's people, that of the Lord's Supper. Lord Jesus told His disciples to "do this for the remembrance of Me." That word translated "remembrance" is from the same root word as the one used in the ancient Greek translations of the Hebrew scriptures translated "memorial.." This Greek root word from which they both come means "to abide," which is seen in the article about the Remembrance of Jesus.
As the presence of Yahweh remained in Israel because His Name had been called upon the city and especially the Temple, so does the presence of Yahweh remain in the Assembly because we participate in the Supper that His Son left for us.
Christ is present with us in the Supper just as Yahweh was present through His Name in the Temple. It is this idea of Memorial that enables us to enter into that intimate experience of the personal presence of God.
Even more so, the Greek word used in the New Covenant for this "Memorial of [Jesus]" is intensified by the prefix, giving it a sense of repetition. Whereas God's Name was called once upon the City and Temple dedicated unto His Name, this Memorial of the Lord's Supper is often repeated as Jesus revealed to Paul, "as often as you eat this Bread and drink this Cup..."
We are guaranteed the presence of God in this New Covenant in many ways, including through His Spirit which He promised to give those who ask. But there is only one thing called Jesus' Memorial, and that is His Holy Supper.
Just as the Name of Yahweh was the Memorial for Israel, both a reminder of Who their God was, and that He was present in their midst in Jerusalem, so is the Body and Blood of Christ present in the Bread and Cup of His Supper the Memorial for His Body, the Assembly. He reminds of Who He is (the Son of God and Man) and what He does (gives Himself freely and completely to redeem the lost), and He is present with us as often as we eat and drink according to this blessed and powerful memorial. HalleluYah, for our God is love and He abides with us!