Abu Rayhan al-Biruni: measurement, calculation and scientific accuracy

In science, Abu Rayhan al-Biruni placed one habit above all else: write down what you measured, not what you heard. There are few more useful lessons for a statistician.

Key points

1. Origins. According to Britannica, al-Biruni was born in Khwarazm in 973; sources give his birthplace as the outer part (birun) of Kath, the capital of Khwarazm. He was later taken to the court of the Ghaznavid ruler Mahmud and spent most of the rest of his life in Ghazna (Britannica).
2. He studied India with his own eyes. Taking part in Mahmud's campaigns in northern India, he learned Sanskrit. In his work "India" ("Tahqiq ma li-l-Hind"), completed around 1030, he brought together in an orderly way the information he had gathered about the science, religion, literature and customs of that land.
3. A great compendium. In his work "Al-Qanun al-Mas'udi" he gathered in one place the astronomical knowledge up to his time, including the data in Ptolemy's "Almagest", and dedicated it to Mas'ud, the son of Mahmud (Britannica).
4. Coordinates of places. His work "Tahdid nihayat al-amakin" ("The Determination of the Coordinates of Positions for the Correction of Distances Between Cities") was translated into English by J. Ali in 1967 and published by the American University of Beirut Press. Its essence is calculating an unknown quantity (the longitude and latitude of cities) on the basis of known points.
5. Measuring density. According to Chemistry World (Royal Society of Chemistry), al-Biruni determined the density of substances by placing a stone in a vessel of water and weighing the water it displaced; the accuracy of his values amazed 19th-century scientists. The method has come down to us mainly through the works of his follower al-Khazini.
6. International recognition. In 1973 the 1000th anniversary of the scholar's birth was celebrated, and the UNESCO Courier devoted its June 1974 issue specially to him. An article in that issue by academician B. Gafurov was titled "A universal genius who lived in Central Asia a thousand years ago".
7. A bridge to statistics. The three pillars of al-Biruni's method, repeated measurement, comparison of sources and arranging the results in a table, are still the basic requirements of statistical observation today.

Example: checking the warehouse scales the al-Biruni way

At the "Oltin Tola" spinning mill, sacks of raw material are weighed on scales. The storekeeper Shohruh weighed one control sack five times (kg, prepared by the author, hypothetical figures):

Four results are close to each other, while the fifth differs sharply. Following al-Biruni's approach, the first question is: "What changed the fifth time?" It turned out that the sack had been placed on the edge of the scales. If this measurement is excluded, the average is (50.2 + 49.9 + 50.1 + 50.0) ÷ 4 = 50.05 kg. The average of all five, however, is 50.4 kg: a single faulty measurement shifted the average by 0.35 kg. If thousands of sacks are weighed in a year, this difference turns into a noticeable shortage or surplus in the warehouse balance.