Making the sign of the cross

Here's a snippet of the transcription of a fascinating talk given by Dom Cassian Folsom, prior of the Benedictine Monastry of San Benedetto and well known liturgical scholar:

... I had occasion to talk with a young Greek layman, who pointed out to me that Catholics make the sign of the cross backwards. That's not the most ecumenical way to put it! But there's something behind what he said. You know how the Byzantine tradition makes the sign of the cross: with the thumb, forefinger and middle finger held together and the last two fingers held together against the palm.
The three fingers symbolize the Trinity, and the two fingers symbolized the double nature of Christ: divine and human. Making the sign of the cross then, becomes a mini-catechesis, a self-reminder of the most basic mysteries of our faith.
But the way of holding your fingers is not the only difference. The eastern tradition makes the sign of the cross from right to left, whereas we make it from left to right. Why?
It's interesting to note that in the 13th century, Pope Innocent III (contemporary with St. Francis of Assisi) instructed the faithful on the meaning of the sign of the cross in these words: "The sign of the cross is made with three fingers, because the signing is done together with the invocation of the Trinity. This is how it is done: from above to below, and from the right to the left, because Christ descended from the heavens to the earth, and from the Jews (right) he passed to the Gentiles (left)."
Note that Pope Innocent is describing what the custom was in the West. In the 13th century the East and the West still made the sign of the cross in the same way. The pope goes on to say: "Others, however, make the sign of the cross from the left to the right, because from misery (left) we must cross over to glory (right), just as Christ crossed over from death to life, and from Hades to Paradise. [Some priests] do it this way so that they and the people will be signing themselves in the same way. You can easily verify this - picture the priest facing the people for the blessing - when we make the sign of the cross over the people, it is from left to right."
So the people, imitating the blessing of the priest, began to sign themselves from left to right. Be that as it may, centuries have gone by since then, and we in the West make the sign of the cross from left to right, with the palm open.

The whole, very interesting transcript is here