January 3rd is the Tenth Day of Christmas. The ten lords a-leaping stand for the Ten Commandments:
I am the Lord your God, who brought you out of the land of Egypt, out of the house of slavery; you shall have no other gods before me.
You shall not make for yourself an idol, whether in the form of anything that is in heaven above, or that is on the earth beneath, or that is in the water under the earth. You shall not bow down to them or worship them; for I the Lord your God am a jealous God, punishing children for the iniquity of parents, to the third and the fourth generation of those who reject me, but showing steadfast love to the thousandth generation of those who love me and keep my commandments.
You shall not make wrongful use of the name of the Lord your God, for the Lord will not acquit anyone who misuses his name.
Remember the sabbath day, and keep it holy. For six days you shall labour and do all your work. But the seventh day is a sabbath to the Lord your God; you shall not do any work-- you, your son or your daughter, your male or female slave, your livestock, or the alien resident in your towns. For in six days the Lord made heaven and earth, the sea, and all that is in them, but rested the seventh day; therefore the Lord blessed the sabbath day and consecrated it.
Honour your father and your mother, so that your days may be long in the land that the Lord your God is giving you.
You shall not murder.
You shall not commit adultery.
You shall not steal.
You shall not bear false witness against your neighbour.
You shall not covet your neighbour’s house; you shall not covet your neighbour's wife, or male or female slave, or ox, or donkey, or anything that belongs to your neighbour. (Exodus 20:1-17)
January 3rd is the feast of Jesus' Holy Name. Whychristmas.com writes of this feast, "This remembers when Jesus was officially 'named' in the Jewish Temple. It's celebrated by different churches on a wide number of different dates!"
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I do not seek to understand that I may believe, but I believe in order to understand. For this also I believe, –that unless I believed, I should not understand.-- St. Anselm of Canterbury (1033-1109)