Replies

The Sanhedrin was wondering by what power St. Peter and St. John converted thousands. "Now seeing the constancy of Peter and of John, understanding that they were illiterate and ignorant men, they wondered; and they knew them that they had been with Jesus (Acts 4:13)". Peter and John converted men not because they made from time to time vague references to the scripture which they could not read. They converted men because they, Peter and John, were with Christ.

Saint Catherine of Siena was illiterate most of her life. Yet,

For three years, Catherine lived a life of prayer, silence, and austerity in her tiny 9-by-12-foot room. During the Carnival of 1366, she experienced a mystical betrothal to Christ.
[...]
Catherine lived the life of a dozen women. She was an ambassador and peace-maker, a nurse and a healer and a powerful evangelist whose very presence triggered innumerable conversions. She served as a counselor to Popes, queens, priests, housewives, and condemned prisoners, while composing one of the great works of Christian mysticism. Importantly, it was her status as a single laywoman that set Catherine of Siena free to answer a call from God that would alter the course of Western history and result in her becoming the first lay Doctor of the Church
Saint Catherine of Siena

The girl was was with Christ, that's all.

Peter and John converted men...

The Holy Spirit converts men.

"Ye have not chosen me, but I have chosen you, and ordained you, that ye should go and bring forth fruit, and that your fruit should remain: that whatsoever ye shall ask of the Father in my name, he may give it you." -- John 15:16

"And when the Gentiles heard this, they were glad, and glorified the word of the Lord: and as many as were ordained to eternal life believed." -- Acts 13:48

Christian mysticism

Outside of the vastness of God, the life and resurrection of Jesus Christ, and the miraculous nature of the Trinity, the term "Christian mysticism" can be a loaded, misguided phrase.