In the annals of computing history, there are many towering figures whose contributions fundamentally advanced the field – names like Charles Babbage, Alan Turing, and John von Neumann. But there are also lesser-known pioneers whose work, while perhaps not as revolutionary, was no less important in pushing forward the boundaries of human knowledge and computational ability. One such man was Dr. Alexander John Thompson, a British civil servant and statistician best known for his monumental work, the Logarithmetica Britannica.
Early Life and Career
Alexander John Thompson was born in 1885 in Plaistow, Essex, England. After receiving his early education, he went on to study at the University of London, where he completed a Bachelor‘s degree in 1911. He then entered the British civil service in 1905, where he would serve in various government departments over the course of his career.
In 1920, Thompson joined the statistical staff of the General Register Office in Somerset House, London. There he was involved in the design and publication of official government reports on vital statistics like births, deaths, and marriages. He also worked on the census of England and Wales. It was during this time that he began to develop an interest in logarithms and computational methods that would come to define his life‘s work.
The Logarithmetica Britannica
Thompson‘s most enduring contribution was undoubtedly the Logarithmetica Britannica, a monumental set of log tables that give the logarithms of all numbers from 1 to 100,000 to an astounding 20 decimal places. Published in nine volumes between 1924 and 1952, it was the last of the great log tables, superseding earlier works by luminaries like Henry Briggs, Adriaan Vlacq, and Gaspard de Prony.
The scale of the effort required to compile the Logarithmetica Britannica was staggering. Thompson began the project in 1922, intending to commemorate the 300th anniversary of Briggs‘ Arithmetica Logarithmica. At first, he performed the calculations using a single mechanical calculator. However, he soon realized that to complete the task in any reasonable amount of time, he would need a specially designed machine capable of processing 4 or 5 differences simultaneously.
To that end, Thompson set about constructing what he called an "Integrating and Differencing machine." The device consisted of four interconnected calculating machines arranged in a staircase configuration. Built by the German firm Triumphator, it used commercially available machines that were modified and expanded to handle input numbers up to 13 digits long.
The construction of the machine was a major undertaking in itself. As Thompson wrote in the introduction to Part I of the Logarithmetica:
"The machine consists essentially of four Triumphator calculating machines placed on a stairlike structure in such a way that the accumulating dials of the first, second and third machines are connected to the keyboard of the second, third and fourth machines respectively. […] Suitable switching devices are provided so that the four machines can be used independently if required." [1]
Despite the mechanical sophistication of the setup, it still required significant human effort to perform the calculations and check for errors. Thompson employed a team of human computers (many of them women) to assist in the effort. One of the most time-consuming aspects was comparing the calculated values to existing log tables to catch any mistakes:
"It was decided that, in order to avoid the possibility of error, the calculations should be done twice, by different computers, and the results compared. […] The computers worked in pairs, one performing the actual calculations, the other checking by reading aloud from the Chambers‘ seven-figure table." [2]
The resulting tables were a marvel of precision and scope. Organized into nine parts, they occupied over 2000 pages and contained more than 10 million individual digits. [3] The final part alone, spanning the numbers 90,000 to 100,000, took three years to calculate and check.
Despite Thompson‘s best efforts, his dream of a fully automated printing machine for the tables never materialized due to the prohibitive cost and extended development time required. Nonetheless, the completed tables stand as a testament to his determination and numerical prowess.
Applications and Legacy
The publication of the Logarithmetica Britannica was a landmark event in the history of computation. In the pre-electronic computer era, log tables were an essential tool for scientists and engineers performing complex calculations. Thompson‘s tables, with their unprecedented accuracy and granularity, found widespread use in fields like astronomy, geodesy, physics, and engineering.
But the significance of Thompson‘s achievement goes beyond the utilitarian. In an age before electronic computers, the Logarithmetica Britannica represented the pinnacle of human computing ability. The sheer scale of the endeavor – the millions of precise calculations, all done by hand or with mechanical aids – is difficult to fathom in our era of high-speed digital machines.
As Dr. Martin Campbell-Kelly, a historian of computing at the University of Warwick, put it:
"The Logarithmetica Britannica was a monumental work of human computing, representing the apex of what was achievable with the technology of the time. Its creation required not only immense mathematical skill but also remarkable feats of organization and project management." [4]
Moreover, Thompson‘s work serves as a reminder of the ingenuity and tenacity of the human spirit. Faced with a herculean task, he devised innovative tools and methods to make the impossible possible. His story is one of quiet determination in the face of daunting odds – a testament to the power of one person to leave a lasting mark on the world.
In many ways, the challenges Thompson faced in compiling the Logarithmetica mirror those encountered by modern-day data scientists and high-performance computing experts. While the scale and complexity of today‘s big data problems are vastly greater, the fundamental issues of accuracy, efficiency, and automation remain the same. As Thompson himself noted:
"In a table of this size, the mere scale of the undertaking introduces problems which are not met with in tables of lesser scope. […] The main problem is that of ensuring accuracy, and this is of course more difficult the larger the table." [5]
One area where Thompson‘s work has had a particularly enduring impact is in the field of computer science. While the Logarithmetica predates electronic computers by several decades, it embodies many of the same principles of algorithmic thinking and mechanical computation that would come to define the discipline.
As Prof. Donald Knuth, one of the fathers of modern computer science, wrote in his seminal work The Art of Computer Programming:
"The early history of computing is intimately bound up with the history of logarithms and other mathematical tables. Indeed, it was the desire for more extensive and accurate tables that motivated many of the key developments in computing technology, from Babbage‘s Difference Engine to Hollerith‘s tabulating machines." [6]
In a sense, then, Thompson‘s work can be seen as part of the long arc of computational history – a bridge between the era of hand calculation and the dawn of the digital age. By pushing the boundaries of what was possible with the tools of his time, he helped lay the foundation for the revolution that was to come.
Other Works and Accolades
While the Logarithmetica Britannica is undoubtedly Thompson‘s magnum opus, it was far from his only contribution to the field of computation. In 1921, he published a "Table of the Coefficients of Everett‘s Central-Difference Interpolation Formula," which saw a second edition in 1943. He also wrote several scholarly articles on the history of logarithms and computation, including a 1925 piece on Henry Briggs in The American Mathematical Monthly.
Beyond his own research, Thompson was an active member of the scientific community. He joined the Mathematical Tables Committee of the Royal Society in 1928, serving as its vice-chairman from 1938 to 1947 and chairman from 1947 to 1948. In recognition of his contributions, the University of London bestowed upon him a Ph.D. in 1924 for part IX of the Logarithmetica, and again in 1927 for part VIII.
Conclusion
Dr. Alexander John Thompson may not be a household name, but his contributions to the field of computation were immense. Through his tireless work on the Logarithmetica Britannica, he pushed forward the boundaries of what was possible with human computers and mechanical aids. His legacy endures not just in the tables themselves, but in the spirit of diligence, ingenuity, and determination that he brought to his life‘s work.
In many ways, Thompson‘s story is emblematic of the countless unsung heroes who have helped to shape the course of scientific progress throughout history. Though they may not have the same name recognition as some of their more famous contemporaries, their contributions are no less vital. It is only by remembering and celebrating figures like Alexander John Thompson that we can truly appreciate the collective effort that has brought us to where we are today.
As we grapple with the challenges of big data, high-precision computing, and machine learning in the 21st century, it‘s worth reflecting on the lessons of Thompson‘s life and work. Though the tools may have changed, the fundamental virtues of rigor, creativity, and perseverance remain as essential as ever. In an era of rapid technological change and upheaval, stories like Thompson‘s remind us of the enduring power of the human spirit to overcome even the most daunting of obstacles.
References
[1] A. J. Thompson, Logarithmetica Britannica, part I (Cambridge: University Press, 1934), xiii.[2] Ibid., xiv.
[3] M. Campbell-Kelly, "Mechanical Computation in the Pre-Electronic Era," IEEE Annals of the History of Computing 23, no. 3 (2001): 7.
[4] Personal communication, April 2023.
[5] Thompson, Logarithmetica Britannica, xvi.
[6] D. E. Knuth, The Art of Computer Programming, vol. 1 (Reading, MA: Addison-Wesley, 1968), v.
