JF Ptak Science Books Post 2812

I found a very unusual paper^{1} in the *Journal of the Franklin Institute* for 1863 promoting moving from base-10 to base -16...for almost everything. It was written by John Nystrom^{2}, an engineer who practiced across several fields and wrote textbooks about more. (Including in this very volume, where he contributes two other papers.) The paper in mind is a very early entry in the history of the application of the hexadecimal system. Nystrom's plan included converting to a hex arithmetical system, and then expanded the idea to the calendar, musical notation, geography, time—an overall shift in metrology. His idea did not extend to calculators, and his name does not seem to be referenced by any of the modern compsci folks (with the major exception of Donald Knuth^{3}). Probably base-16 was not employed in programming until, I guess, around the early 1960's. All that said, this is still a remarkable paper. Also: the paper is illustrated with a beautiful color-highlighted folding plate of divider-like instruments that translated hex to denary.

The Nystrom ideas did not take hold, and it seems that he was a bit cranky about the idea of its not being accepted, perhaps because it was left to the hands of people who just couldn't see its value. He ends his book of 1862 with the following few observations: “If the Arabic notation employed in our present decimal arithmetic had been suggested to Moses when he wrote the ten commandments on Mount Sinai he would surely have made similar remarks as that made on the tonal system that such curious looking characters could not be understood by his people....My manuscript on the tonal system has been sent to a great many places for publication. The Franklin Institute thought it would have a very serious effect on the number of subscribers of their journal. The Smithsonian Institute would not publish it because they had so much of the same kind before. The US Coast Survey stated they would publish it if recommended by a member of Congress. And lately the Society of Philadelphia has rejected it perhaps on the remarks herein replied to but Mr D recommended its publication.”--John William Nystrom, *Project of a New System of Arithmetic, Weight, Measure and Coins: Proposed ..*.(1862)

As for me, I just don't understand what he was driving for, or at.

**Notes**

1. John Nystrom, “A New System of Arithmetic and Metrology, called the Tonal System”, pp 263-275, 337-348, 402-407 (concluded), and illustrated, including a folding plate. In* Journal of the Franklin Institute*, third series vol 46 overall vol 76, July-December 1863, 432pp.

2. “John Williams Nystrom (Swedish: Johan Vilhelm Nyström) (1825–1885) was a Swedish born, American civil engineer, inventor, and author. He served as an assistant Secretary and Chief Engineer of the United States Navy during the American Civil War. Nystrom received many patents for inventions such as a marine steam engine, a refrigerator, and calculating machines...Nystrom is most notable for his proposal to switch from decimal to hexadecimal as defined in his 1862 publication titled . In 1859, Nystrom proposed a hexadecimal (base 16) system of notation, arithmetic, and metrology called the Tonal system. In addition to new weights and measures, his proposal included a new calendar with sixteen months, a new system of coinage, and a hexadecimal clock with sixteen hours in a day.”--Wikipedia

3. “...a prominent Swedish-American civil engineer named John W. Nystrom decided to carry Charles XII’s plans [radix-8 arithmetic] a step further, by devising a complete system of numeration, weights, and measures based on radix-16 arithmetic. He wrote, “I am not afraid, or do not hesitate, to advocate a binary system of arithmetic and metrology. I know I have nature on my side; if I do not succeed to impress upon you its utility and great importance to mankind, it will reflect that much less credit upon our generation, upon our scientific men and philosophers.” Nystrom devised special means for pronouncing hexadecimal numbers; for example, (C0160)16 was to be read “vybong, bysanton.” His entire system was called the Tonal System, and it is described in J. Franklin Inst. 46 (1863), 263–275, 337–348, 402–407. A similar system, but using radix 8, was worked out by Alfred B. Taylor [Proc. Amer. Pharmaceutical Assoc. 8 (1859), 115–216; Proc. Amer. Philosophical Soc. 24 (1887), 296–366].--Donald Knuth, *The Art of Computer Programming* section 4.1 (which is in volume 2).

A last note on the Nystrom calculator: “In an article of* Scientific American* the device was hailed as the most important one ever brought before the public. Despite all of the accolades however, it was never widely accepted, and no more than 100 devices were ever produced. This may have been because the cost (there were $10, $15, and $20 models, a huge sum in 1850s), or because the instrument was never well advertised or marketed. --history-computer.com