Binary search in the Old Testament
August 10th, 2015
The lot is cast into the lap,
but its every decision is from the Lord.
(NIV Proverbs 16:33)
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| …“Lux et Veritas”… Seal of Yale University image from Wikimedia Commons. |
The seal of Yale University shows a book with the Hebrew אורים ותמים (urim v’thummim), a reference to the Urim and Thummim of the Old Testament. The Urim and Thummim were tools of divination. They show up first in Exodus:
Also put the Urim and the Thummim in the breastpiece, so they may be over Aaron’s heart whenever he enters the presence of the Lord. Thus Aaron will always bear the means of making decisions for the Israelites over his heart before the Lord. (NIV Exodus 28:30; emphasis added)
Apparently, the Urim and Thummim worked like flipping a coin, providing one bit of information, a single binary choice communicated from God.1 Translations of Urim as “guilty” and Thummim as “innocent” indicate that the divination was used to determine guilt: “Thummim you win; Urim you lose.” An alternate translation has Urim “light” and Thummim “truth”, hence “Lux et Veritas” in the Yale seal’s banner.
Saul, King of Israel and father-in-law of King David, uses the binary choice provided by Urim and Thummim divination in 1 Samuel to unmask the party who violated the king’s oath:
Then Saul prayed to the Lord, the God of Israel, “Why have you not answered your servant today? If the fault is in me or my son Jonathan, respond with Urim, but if the men of Israel are at fault, respond with Thummim.” Jonathan and Saul were taken by lot, and the men were cleared. Saul said, “Cast the lot between me and Jonathan my son.” And Jonathan was taken. (NIV2 1 Samuel 14:41-42)
Saul executes a small (and highly unbalanced) binary search. He first divides the population into two parts. He and his son Jonathan are assigned Urim and all the rest get Thummim. God responds with Urim. Then to decide between Saul and Jonathan, the process is repeated, and Jonathan is fingered as the guilty party. (The method apparently works; the preceding verses of 1 Samuel give the story of Jonathan’s transgression.)
The universality of binary as an information conveying method has a longer history than one might have thought.
- The Old Testament Urim and Thummim should not be confused with the “higher bandwidth” device of the same name that Joseph Smith claimed to use to receive the translation of a now lost 116 pages of the Book of Mormon. This device purportedly resembled a pair of spectacles with transparent rocks for lenses, a kind of “oraculus rift”. For the extant Book of Mormon, Smith changed his method to scrying with a “seer stone” placed in his hat. A photograph of the stone, coincidentally, has just recently been released by the LDS church.↩
- The use of a Septuagint-based version of the Bible, here the New International Version, is important, as this verse is considerably shortened in versions such as the King James based on the Masoretic text, leaving out the use of Urim and Thummim to make a binary decision.↩
