{"id":2298,"date":"2015-08-10T10:00:02","date_gmt":"2015-08-10T14:00:02","guid":{"rendered":"http:\/\/blogs.law.harvard.edu\/pamphlet\/?p=2298"},"modified":"2015-08-10T08:53:22","modified_gmt":"2015-08-10T12:53:22","slug":"binary-search-in-the-old-testament","status":"publish","type":"post","link":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/2015\/08\/10\/binary-search-in-the-old-testament\/","title":{"rendered":"Binary search in the Old Testament"},"content":{"rendered":"

The lot is cast into the lap,
\nbut its every decision is from the Lord.
\n(NIV Proverbs 16:33<\/a>)<\/em><\/p>\n\n\n\n\n
\"\u2026\u201cLux<\/a><\/td>\n<\/tr>\n
\u2026\u201cLux et Veritas\u201d\u2026<\/span>
\nSeal of Yale University image from Wikimedia Commons<\/a>.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The seal of Yale University shows a book with the Hebrew \u05d0\u05d5\u05e8\u05d9\u05dd \u05d5\u05ea\u05de\u05d9\u05dd (urim v\u2019thummim), 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:<\/p>\n

Also put the Urim and the Thummim in the breastpiece, so they may be over Aaron\u2019s heart whenever he enters the presence of the Lord. Thus Aaron will always bear the means of making decisions<\/em> for the Israelites over his heart before the Lord. (NIV Exodus 28:30<\/a>; emphasis added)<\/p><\/blockquote>\n

Apparently, the Urim and Thummim worked like flipping a coin, providing one bit of information, a single binary choice communicated from God.1<\/a><\/sup> Translations of Urim as \u201cguilty\u201d and Thummim as \u201cinnocent\u201d indicate that the divination was used to determine guilt: \u201cThummim you win; Urim you lose.\u201d An alternate translation has Urim \u201clight\u201d and Thummim \u201ctruth\u201d, hence \u201cLux et Veritas\u201d in the Yale seal\u2019s banner.<\/p>\n

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:<\/p>\n

Then Saul prayed to the Lord, the God of Israel, \u201cWhy 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.\u201d Jonathan and Saul were taken by lot, and the men were cleared. Saul said, \u201cCast the lot between me and Jonathan my son.\u201d And Jonathan was taken. (NIV2<\/a><\/sup> 1 Samuel 14:41-42<\/a>)<\/p><\/blockquote>\n

Saul executes a small (and highly unbalanced) binary search<\/a>. 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\u2019s transgression.)<\/p>\n

The universality of binary as an information conveying method has a longer history than one might have thought<\/a>.<\/p>\n

\n
\n
    \n
  1. The Old Testament Urim and Thummim should not be confused with the \u201chigher bandwidth\u201d 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 \u201coraculus rift\u201d. For the extant Book of Mormon, Smith changed his method to scrying with a \u201cseer stone\u201d placed in his hat. A photograph of the stone<\/a>, coincidentally, has just recently been released by the LDS church.\u21a9<\/a><\/li>\n
  2. 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.\u21a9<\/a><\/li>\n<\/ol>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

    The lot is cast into the lap, but its every decision is from the Lord. (NIV Proverbs 16:33) \u2026\u201cLux et Veritas\u201d\u2026 Seal of Yale University image from Wikimedia Commons. The seal of Yale University shows a book with the Hebrew \u05d0\u05d5\u05e8\u05d9\u05dd \u05d5\u05ea\u05de\u05d9\u05dd (urim v\u2019thummim), a reference to the Urim and Thummim of the Old Testament. […]<\/p>\n","protected":false},"author":2110,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"New post: Binary search in the Old Testament","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[380,145],"tags":[],"class_list":["post-2298","post","type-post","status-publish","format-standard","hentry","category-computer-science","category-other"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p5pLfN-B4","jetpack-related-posts":[{"id":247,"url":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/2009\/07\/06\/as-library-budgets-collapse-authors-need-to-take-responsibility-for-access\/","url_meta":{"origin":2298,"position":0},"title":"As library budgets collapse, authors need to take responsibility for access","author":"Stuart Shieber","date":"Monday, July 6, 2009","format":false,"excerpt":"Jonathan Eisen at The Tree of Life writes If you need any more incentive to publish a paper in an Open Access manner if you have a choice - here is one. If you publish in a closed access journal of some kind, it is likely fewer and fewer colleagues\u2026","rel":"","context":"In "libraries"","block_context":{"text":"libraries","link":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/category\/scholarly-communication\/libraries\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":2104,"url":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/2014\/06\/04\/how-universities-can-support-open-access-journal-publishing\/","url_meta":{"origin":2298,"position":1},"title":"How universities can support open-access journal publishing","author":"Stuart Shieber","date":"Wednesday, June 4, 2014","format":false,"excerpt":"To university administrators and librarians: ...enablement becomes transformation... \"Shelf of journals\" image from Flickr user University of Illinois Library. Used by permission. As a university administrator or librarian, you may see the future in open-access journal publishing and may be motivated to help bring that future about.1 I would urge\u2026","rel":"","context":"In "libraries"","block_context":{"text":"libraries","link":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/category\/scholarly-communication\/libraries\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":712,"url":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/2011\/02\/14\/dissertation-distribution-online-my-comments-at-the-aha\/","url_meta":{"origin":2298,"position":2},"title":"Dissertation distribution online: my comments at the AHA","author":"Stuart Shieber","date":"Monday, February 14, 2011","format":false,"excerpt":"I spoke at a panel last month at the annual meeting of the\u00a0American Historical Association devoted to the question of electronic dissertations and intellectual property rights entitled \"When Universities Put Dissertations on the Internet: New Practice; New Problem?\" My co-panelists included Edward Fox, professor of computer science at Virginia Tech\u2026","rel":"","context":"In "open access"","block_context":{"text":"open access","link":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/category\/scholarly-communication\/open-access\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":720,"url":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/2011\/03\/01\/institutional-memberships-for-open-access-publishers-considered-harmful\/","url_meta":{"origin":2298,"position":3},"title":"Institutional memberships for open-access publishers considered harmful","author":"Stuart Shieber","date":"Tuesday, March 1, 2011","format":false,"excerpt":"Some open-access publishers offer institutional memberships, whereby a fixed annual fee, often based on the size of faculty or expected number of submitted articles, covers all or a percentage of article-processing fees for the institution for the year. The issue of OA publisher memberships is interesting and fraught. Harvard University\u2026","rel":"","context":"In "open access"","block_context":{"text":"open access","link":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/category\/scholarly-communication\/open-access\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1552,"url":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/2012\/10\/17\/guide-released-on-good-practices-for-university-open-access-policies\/","url_meta":{"origin":2298,"position":4},"title":"Guide released on good practices for university open-access policies","author":"Stuart Shieber","date":"Wednesday, October 17, 2012","format":false,"excerpt":"I'm pleased to forward on the announcement that the Harvard Open Access Project has just released an initial version of a guide on \"good practices for university open-access policies\". 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