The Support of the Needy on the Legal Ruling of Chess

I harbored some doubt regarding this report until I encountered one of the clever travelers original: sahab al-kudiya; referring to a class of wandering scholars and witty beggars known for their ingenuity, who described a method to me that proved the accuracy of what had been claimed. He presented a paper confirming it, demonstrating that if one doubles the numbers up to the sixteenth square, the total reaches thirty-two thousand, eight hundred and sixty-eight grains Mathematical note: The actual calculation for the 16th square ($2^{15}$) is 32,768; the author's source contains a slight discrepancy. He told me to consider this sum as the volume of one qadaha traditional dry measure used for grain, and it was indeed so. I tested the calculation, and the result matched what he said.

Then, he doubled the seventeenth square up to the twentieth, which resulted in a waybaa larger unit of measure, typically containing several qadahs. From the waybas, he moved to the ardebsa major Egyptian unit of dry volume, continuing the doubling until he reached the fortieth square. At this point, the total reached one hundred and ninety-four thousand, seven hundred and sixty-two and two-thirds ardebs. This amount constitutes a shunaa large granary or storehouse for grain.

He then doubled the shunas up to the fiftieth square, and the sum was one thousand and twenty-four shunas. This amount constitutes a "city" an analogy used to visualize the massive quantity of grain as the storage capacity of an entire city. He continued doubling until the sixty-fourth square—the final square of the board—where the total reached sixteen thousand cities and eighty-four and two-thirds cities original: wa-thulthi burr; likely a scribal error or specific fractional notation for wheat. It is a known fact that there are not even this many cities in the entire world, for the circumference of the Earth is only eight thousand miles.

When Al-Salah bin al-Safadi a famous 14th-century historian and biographer mentioned this in his commentary on the Lamiyyat al-Ajam a celebrated poem by al-Tughra'i, he noted that the final calculation for the chessboard requires eighteen quintillion, four hundred and forty-six quadrillion, seven hundred and forty-four trillion, seventy-three billion, seven hundred and nine million, five hundred and fifty-one thousand, six hundred and fifteen The text expresses this in a repetitive Arabic format: "eighteen thousand thousand thousand [six times]..." to indicate the scale of quintillions. He then recited a verse by another author that uses a mnemonic system to record this massive number:

18,446,744,073,709,551,615
If you wish to double the chess squares, their sum is:
Ha-Wahah li-ghina bidd naww dadkha This mnemonic uses Abjad—an alphanumeric system where each letter has a numerical value—to encode the digits of the final sum

If we were to measure the dimensions of this number as a single cube, its length, width, and height would each be sixty miles. This is measured by the mile that equals four thousand cubits, with a cubit being three moderate spans of a hand. This calculation assumes that the Egyptian ardeb is sixteen cubic cubits in weight...