Orthodox cross themselves from right to left. first we will describe the mechanics of making the cross, then explain why it is indeed important that we make the sign of the cross correctly.
"Placing the cross on oneself"
The act of "Placing the cross on oneself" is a request for a blessing from God. We make if from right to left to mirror the actions of the priest when he blesses us. The priest, looking at the parishioners, blesses from left to right. Therefore, the parishioners, putting on the sign of the cross on themselves, do it from right to left.
Because the Lord separated the sheep from the goats, putting the faithful sheep on His right side, and the goats on the left, the Church always treats the right side as the preferred side. We only cross ourselves with our RIGHT hand. The priest, when blessing a person, first touches or points to their RIGHT side, then their left. Also the censing of the Holy Table in the Altar is always done from the RIGHT side first; censing of the Ikonostasis, the Congregation and of the Church itself always begins with the right side. The priest always gives communion with his RIGHT hand, even if he is left handed. There are other examples of this right side preference.
When a parent makes the sign of the cross over a child, they will cross them from left to right, just as the priest blesses. When they make the sign of the cross over themselves, they would do it, logically, the other way.
The Catholic Encyclopedia states that in the Roman Catholic Church, the faithful crossed themselves from right to left, just as the Orthodox do, until the 15th or 16th century. They must explain why they have changed an ancient and apostolic tradition? We cannot answer as to their motivations.
Is it important to cross ourselves a particular way? In a word, YES. We do not have the authority to choose willy-nilly what parts of the Christina Tradition we want to follow. Our fathers, and countless saints crossed themselves from right to left. Ancient icons show Christ or bishops beginning a blessing from right to left. the right side is referred to in a preferential way many times in scripture and our sacred hymns What should we want to change?
Thanks for Fr. Alexander Lebedev for providing the majority of the ideas in this answer.
There are also several interpretations, according to Church Fathers: the forehead symbolizes Heaven; the stomach, the earth; the shoulders, the place and sign of power.
SequenceTheodoret (393–457) gave the following instruction concernign the sign of the Cross
This is how to bless someone with your hand and make the sign of the cross over them. Hold three fingers, as equals, together, to represent the Trinity: God the Father, God the Son, and God the Holy Ghost. These are not three gods, but one God in Trinity. The names are separate, but the divinity one. The Father was never incarnate; the Son incarnate, but not created; the Holy Ghost neither incarnate nor created, but issued from the Godhead: three in a single divinity. Divinity is one force and has one honor. They receive on obeisance from all creation, both angels and people. Thus the decree for these three fingers.
"Dogmatic Sarcophagus", AD 350, Earliest known depiction of the Trinit Vatican Museums, Rome, Italy.
You should hold the other two fingers slightly bent, not completely straight. This is because these represent the dual nature of Christ, divine and human. God in His divinity, and human in His incarnation, yet perfect in both. The upper finger represents divinity, and the lower humanity; this way salvation goes from the higher finger to the lower. So is the bending of the fingers interpreted, for the worship of Heaven comes down for our salvation. This is how you must cross yourselves and give a blessing, as the holy fathers have commanded.
Peter of Damascus (12th Century) gave the following instruction:
Then we should also marvel how demons and various diseases are dispelled by the sign of the precious and life-giving Cross, which all can make without cost or effort. Who can number the panegyrics composed in its honor? The holy fathers have handed down to us the inner significance of this sign, so that we can refute heretics and unbelievers. The two fingers and single hand with which it is made represent the Lord Jesus Christ crucified, and He is thereby acknowledged to exist in two natures and one hypostasis or person. The use of the right hand betokens His infinite power and the fact that He sits at the right hand of the Father. That the sign begins with a downward movement from above signifies His descent to us from heaven. Again, the movement of the hand from the right side to the left drives away our enemies and declares that by His invincible power the Lord overcame the devil, who is on the left side, dark and lacking strength.
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