In Deuteronomy 4:13 why were the Ten Commandments written on two tablets?

Dr. Meshulam Margaliot points out that Midrashic tradition is divided about what was written on which tablet. The options seem to be:

1. 1–5 on one and 6–10 on the other. (This is the tradition interpretation that is most common in art and synagogue decoration.)

2. All 10 on each tablet.

Even numbered on one and odd on the other (as suggested by Mike Bull), does not seem to be a Jewish interpretation represented in the Midrash. The commandments have traditionally been paired 1 and 6, 2 and 7, etc.

The tablets themselves were likely to be fairly large¹, so there would have been plenty of room to write all ten commandments on each one, if the Lord chose to do so. In fact, there was likely room for the commandments that follow the ones listed in Exodus 20 (and Deuteronomy 5). Therefore, there's no particular reason to split the commandments across the tablets at all.

We do, however know of a good reason to suspect both tablets contained the same text:

Having journeyed from Rephidim, they entered the wilderness of Sinai and encamped in the wilderness. Israel encamped there in front of the mountain, and Moses went up to God. The Lord called to him from the mountain, saying, "Thus shall you say to the house of Jacob and declare to the children of Israel: ‘You have seen what I did to the Egyptians, how I bore you on eagles’ wings and brought you to Me. Now then, if you will obey Me faithfully and keep My covenant, you shall be My treasured possession among all the peoples. Indeed, all the earth is Mine, but you shall be to Me a kingdom of priests and a holy nation.’ These are the words that you shall speak to the children of Israel."—Exodus 19:2-6 (NJPS)

God is entering into a suzerain/vassal agreement with Israel and the Ten Commandments were the terms and conditions of that treaty. As with other legal documents, both sides would get a copy of such an agreement. Clearly God's copy would be stored in the Ark of the Covenant, which was stored in the presence of God. Dr. Margaliot explains further:

But what about the Israelite's copy, on the second Tablet, where was that copy placed? Here we note a common practice in the ancient Near East. When a treaty was made between parties of unequal status, the lesser partner, or vassal, would place his copy of the pact in the temple of his god, the reason being that the vassal had then to take an oath in the name of his god to "the great king." (See Ez. 17:11-19. The reference here is to the king of the Hittites, who made treaties with the rulers of smaller kingdoms in northern Syria during the first half of the first millennium B.C.E. This custom, however, undoubtedly dates much further back.)

...

Since the Israelites had the status of vassal vis-à-vis G-d and were the lesser partners to the Covenant, it was reasonable for them to file their copy of the Pact in the Holy Ark of the Lord their G-d. Thus we conclude that both Tablets were placed together in the Ark in the Tabernacle, and later in Solomon's Temple: "There was nothing inside the Ark but the two tablets of stone which Moses placed there at Horeb, when the Lord made [a covenant] with the Israelites after their departure from the land of Egypt" (I Kings 8:9).

As Canaanites, the Hebrew people were surrounded by the great Egyptian and Hittite civilizations. As it turns out, copies of a peace treaty between those rivals have survived to this day:

Each copy has nearly identical language and binds each nation to various obligations. It was witnessed by each side's gods and contained blessings for keeping it and curses for breaking it. Very likely treaties similar to this one were the model (or type) of the covenant between God and His people.

Footnote:

1. According to the Babylonian Talmud:

   The tablets were six handbreadths in length, six in breadth and three in thickness.—Bava Batra 14a.

   That's wider and thicker than the props Cecil B. DeMille used, but about the same height.

   

   Originally the tablets would have had squared-off tops; the rounded tablets mirror medieval wax tablets not ancient clay and stone tablets.