How does Protestantism explain Matthew 18:20 in this technology age?

The verse you quote does not specify exactly what "gather in my name" means, whether that includes cell phone conversations or Internet chat rooms or whatever. I'm not aware of any other verse that you could drag in to specify.

That hardly makes this verse unique. People often think of the Bible as a big book, but there are plenty of novels that are longer, lots of government bills are longer, etc. The Bible isn't anywhere near long enough to say exactly what every person who will ever live should do in every moment of his life. It just gives some general principles, and it's up to people to use their intelligence to apply them.

Do three people having a conference call count as "gathered in my name"? I can't give a definitive answer. Given the general nature of Jesus' comment here, I'm not sure what difference it makes.

In short, yes, Jesus is talking about a physical gathering of two or three people (or in one instance, two or three individuals, one united congregation, and one sinner). In our technological age, NOTHING can fully replace face-to-face meetings between people, especially the Lord's people at the grass roots level of a healthy local church, or an assembly of God's people.

What precedes Matthew 18:20

In context, Matthew 18:20 is preceded by Jesus' teaching on three things: 1) the inevitable occurrence of sin among God's children, and the responsibility of God's children to resist sin; 2) God's outgoing love for one of His children who goes astray (the one lost sheep from a flock of 100); and 3) Jesus' teaching on church discipline, the kind of which is rendered necessary by a sin of one member against another.

Then comes Matthew 18:20

This verse is really a conclusion of the passage on church discipline, a topic addressed in three ways:

1) the protocol of church discipline

2) the assurances that what is either bound or loosed on earth will be bound or loosed in heaven, and whatever two believers agree upon in prayer on earth will be done for them by their heavenly Father

3) the promise of Christ's presence in a gathering of as few as two or three believers who meet in Jesus' name

What follows Matthew 18:20

Jesus' teaching on forgiveness, which comprises an answer to Peter's question about how many times he is to forgive a brother who sins against him. Jesus' teaching includes the famous locution, "seventy times seven." Notice, too, that Peter's question is certainly relevant in light of verse 15, which begins with the words

"'If your brother sins against you . . ..'"

Contextualizing Matthew 18:20

In summary fashion, this verse simply continues the notion of "two or three" which begins in verse 15, proceeds through verse 18, and then continues in verses 21 and following.

In other words, the repetition of "two or three," whether in the context of church discipline (viz., one-on-one; two or three on one; one singular--the sinned against person--and one plural--the entire congregation--on one--the sinner), or in the context of binding, loosing, agreeing in prayer, and finally, meeting together in Jesus' name, all those repetitions are simply, in context, a continuation of what came before and what comes after. In discursive fashion, then, we have the following themes:

• the inevitability of both sin and sin's punishment, as well as the importance of a radical resistance to sin, whether it comes from without (i.e., an external-to-us stumbling block) or from within (an internal-to-us cause of stumbling, symbolized by our own hand, foot, or eye).

• the Father's heart of love for the one sheep in a flock of 100 who goes astray or is led astray by sin or a sinner

• an instance of sin within a local assembly of believers, and the protocol for dealing with that sin through a three-step process

• the assurance that whatever decision the church makes, whether to bind the accused sinner or to loose the accused sinner, it will also be either bound or loosed in heaven

• the assurance that an agreement by two believers in prayer on earth will result in their request being granted by their Father in heaven

• the assurance that even if church discipline does not reach the "court of final appeals" (viz., the church), Jesus' presence is guaranteed where just two or three are gathered together in His name in sincerity and simplicity

• the necessity of forgiving others who sin against us, and to do so in the light of the great debt of which we ourselves have been forgiven (basically an application of the part of the Lord's prayer which says, "and forgive us our debts as we forgive our debtors"), even if after repenting, they sin against us again

In conclusion, as good as our technological tools are today for communicating around the world at the speed of light, nothing can replace the face-to-face interactions of God's people (whether for church discipline, prayer, or simply fellowship) who desire to

"walk worthy of the vocation wherewith [they] are called, with all lowliness and meekness, with longsuffering, forbearing one another in love; endeavouring to keep the unity of the Spirit in the bond of peace" (Ephesians 4:1b-3).