The Lord invokes the law of witnesses as justification for this second written text. The Book of Mormon as a second witness of Jesus Christ is fulfillment of this ancient law of testimony.
The Lord indicates that "I speak the same words unto one nation like unto another." Clearly the differences in the types of Messianic knowledge in the two hemispheres at the same time suggests that the Lord is not literal here. There are differences in the specifics that relate to the time and place of those who receive the word of God. Nevertheless, it is the same God, and the same message, even when the specifics may vary with time and circumstance.
This verse also speaks of two nations that "shall run together." This is the reference for the modern shrinking of the world. The discovery of the New World by the Old initiated the inevitable "running together," a process that historically was more of a violent collision that a confluence. The Lord indicates that as the nations that were once separate (having separate revelations from God) become united through contact, their separate revealed knowledge will also come together. In the New World this clearly refers to the Book of Mormon. However, there is also applicability for the modern discovery of other valuable texts, such as the Dead Sea Scrolls and the Nag Hammadi Library. While not suggesting that they equal the doctrinal value of the Book of Mormon, they are nevertheless important sources of information about the way in which man has perceived his relationship to the God we worship.