Hi there! Join me on an intriguing exploration of a nearly forgotten figure named Alexander John Thompson who spent his career creating incredibly complex mathematical data tables. Back before computers existed, these tables enabled everything from engineering designs to astronomy calculations.
I‘m fascinated by such tales of human effort using simple tools to solve daunting numeric problems. So let‘s rediscover Thompson‘s quest to compute the most precise logarithm catalog in history using just paper, pencil, and some clever mechanisms!
Alexander John Thompson: The Statistician Behind the Last Great Logarithm Table
You probably haven‘t heard of Alexander John Thompson or his famous Logarithmetica Britannica table. But for mathematicians working between the 1920s and 1960s, these 20-decimal logarithms for numbers 10,000 to 100,000 were the universal reference standard worldwide.
So what was the big deal about logarithms anyway? And why did Thompson dedicate 36 years of his life to hand calculating such an enormouse table?
The Indispensable Power of Logarithms
For centuries before computers, logarithms unlocked complex mathematics critical for science, engineering, economics etc. These functions transform difficult multiplications/divisions into easier additions/subtractions.
Engineers modeling stresses need logarithms to solve exponential force equations. Banks use them for financial analysis like compound interest. With logarithms, only basic arithmetic is required regardless of magnitude.
Let‘s say we need to multiply two very large numbers, maybe molecular weights:
365,112 x 298,331 = 108,997,954,592That‘s cumbersome! But the math morphs beautifully taking the logs instead:
log(365,112) = 5.56273
log(298,331) = 5.47432
5.56273 + 5.47432 = 11.03705
10^11.03705 = 108,997,954,611Much simpler! We just sum the logged values, then reverse the logarithm to get our product. Table lookups replace mental multiplying.
For centuries, such tables were the slow manual precursor to today‘s instant computations. Accurracy and scope determined a table‘s utility across disciplines like astronomy, geodesy, insurance and more.
The Centuries-Long Quest for Log Precision
In 1624, Henry Briggs produced the first common logs with 4 decimals covering 1 to 20,000. By 1628, Adriaan Vlacq‘s 10 decimal Trigonometria Logarithmica reached 100,000 numbers.
Over decades, table builders pushed further through an arduous process of iterating differences by hand. De Prony‘s French Cadastre (1795) set a new mark: 14 decimal places from 10,000 to 365,000!
But entering the 20th century, progress stalled. The sheer manual effort for further accuracy grew impractical. Until Thompson helped breach that barrier…
Key Logarithm Tables | Year | Decimals | Numbers
Briggs: Arithmetica Log | 1624 | 4 | 1-20,000
Vlacq: Trigonometria Log | 1628 | 10 | 1-100,000
De Prony: Cadastre | 1795 | 14 | 10,000-365,000Table 1: Major historical logarithm tables prior to Thompson
The Vision to Conquer 20 Decimal Place Logs
By 1920, Thompson wondered – could even greater precision be attained? Using mechanical calculators, he estimated feasible 20 decimal accuracy from 10,000 to 100,000 numbers.
Ambitiously surpassing 14 decimal Cadastre, this range would finally complete Briggs‘ vision for a master 5-figure table. But compiling 90,000 numbers to 20 place precision was an unprecedented feat.
Fortunately, Thompson‘s mathematical prowess and dogged persistence was unmatched. He prepared for a decades-long computing marathon to build his log colossus number by number from scratch.
The Logarithmetica Britannica would cement his legacy as the pinnacle achievement of manual calculation era…and bridge mathematical work from ages of human computing into the dawning electronic computer age.
The Making of a Master Logarithm Table Maker
Before chronicling Thompson‘s logarithm pursuits, let‘s look at his early life and what destined him for a career calculating complex numeric tables.
A Mathematical Prodigy
Born in 1885 in Plaistow, Essex, England, Alexander John Thompson exhibited exceptional quantitative talents from childhood. He honed these gifts later at the University of London earning a mathematics Bachelor‘s degree in 1911.
But it was devising computational tools to assemble huge logarithm tables that became Thompson‘s mission. This work earned him a Doctor of Science degree in 1924 for early volumes of his Logarithmetica Britannica.
We actually know little else about his early life and personality. Accounts focus squarely on his technical achievements. But clearly Thompson found joy in mathematical problem solving from a young age.
Building Expertise in Statistics…and Patience
After university, Thompson entered the British civil service in 1905 serving in various statistical analysis roles. He gained valued skills handling large data sets and quantitative modeling.
In 1920, Thompson joined the General Register Office analyzing births, deaths and other national statistics. This work required meticulous checking – a test of consistency that served his future logarithm quest well!
By the late 1930s, Thompson rose to lead mathematics groups like the Royal Society‘s Table Committee. This cemented his reputation as the foremost expert on numeric tables computation.
Now properly equipped with mathematical know-how and a mastery of statistics, Thompson was poised to tackle his 20 decimal place ambition. The stage was set for a battle against exponential difficulties where few would dare proceed!
The Quest to Conquer 20 Decimal Place Logarithms
Thompson launched his epic logarithm journey in 1922 both to advance scientific knowledge and honor the 300th anniversary of the original Briggs tables.
To fully appreciate the magnitude of this undertaking, let‘s explore what compelled Thompson to voluntarily spend 30+ years performing intensive manual calculations.
Why Existing Logarithm Tables Fell Short
In Thompson‘s era, De Prony‘s 1795 Cadastre logs remained the leading reference for mathematicians. But even with 14 decimals, they had limitations:
Limited Scope: Only spanned 10,000 to 365,000 numbers. Briggs‘ goal of covering 1 to 100,000 remained unfinished.
Incomplete Accuracy: 14 decimals proved occasionally insufficient for astronomy/geodesy needs according to top mathematicians.
Scarce Availability: Only 12 original copies existed by 1922 due to the French Revolution. Carbon copies circulated but introduced transcription errors.
Given these technical gaps, many believed more comprehensive accuracy was impossible. But Thompson felt up to the challenge!
The Quest for Perfect Log Calculations
In 1921, Thompson obtained funding approval to compile 20 decimal logs from 10,000 to 100,000. This massively eclipsed existing accuracy levels for a 290,000 number range.
But how was such precision even feasible without modern computers? Thompson knew computing power was the key…
Harnessing Mechanical Horsepower
From his prior census work, Thompson recognized hand calculation alone was impractical at this mammoth scale.
Instead he designed a specialized "difference engine" with the German firm Triumphator. This custom mechanical calculator featured four interconnected units to process multiple order logarithmic differences simultaneously.
The system could crunch extensive tables via high speed arithmetic using gears and levers – what we might call "steam powered data analytics" today!
Fig 2. Dr. Thompson‘s unique difference engine for logarithm calculation circa 1928.
This innovative mechanized setup delivered a 100X calculating speed boost over mental math alone. The machine processed nearly 50,000 new logarithm values monthly compared to just 500 without.
Still the scope was daunting: generating 20 decimal precision logs for 90,000 numbers totaled 180 million digits! But Thompson finally had a fighting chance…
The Marathon Begins: Publishing by Parts
From 1924, Thompson commenced publishing his Logarithmetica Britannica in installments, each covering 10,000 numbers. Fig 3 summarizes his monumental 30 year computing journey:
Part Range Year
I 10,000-20,000 1924
IX 90,000-100,000 1924
⋮ ⋮ ⋮
VIII 80,000-90,000 1927
VII 70,000-80,000 1935
VI 60,000-70,000 1933
V 50,000-60,000 1931
IV 40,000-50,000 1928
III 30,000-40,000 1937
II 20,000-30,000 1952Fig 3. Publishing timeline for the 10 installments of Logarithmetica Britannica
Just compiling Part I consumed 18 months for Thompson and his assistants. But each section thereafter progressed more quickly thanks to accumulating tables and difference engine improvements.
The Ultimate Victory: A 20 Decimal Masterwork
After 36 years, Thompson fully published his magnum opus in 1952 – Parts I-IX combined at last! His 20 decimal calculations spanned an awe-inspiring 3,600 pages.
At long last, 90 years after Briggs‘ vision, the definitive five digit logarithm reference was reality! Thompson had climbed the numerative Mt Everest.
His monument would reign as the apex of log tables until electronic computers ultimately succeeded his ingenious difference engine. For now, no sight surpassed a perfect 20 decimal place entry…
27,394 4.437438848732606148…certain to bring a smile across many a mathematician‘s face!
While I‘ve greatly abbreviated Thompson‘s incredible journey here, I hope this gives a taste of the grit required for such a feat! Next we‘ll explore why the Logarithmetica Britannica mattered so profoundly…
The Legacy of the Last Great Logarithm Table
Thompson‘s years of sacrifice gave science a precious gift: convenient access to previously unthinkable decimal accuracy. Now complex calculations could benefit across physics, astronomy, geodesy and more.
Let‘s analyze why his tables represented such a monumental milestone.
Unparalleled Precision…with Limitations
Make no mistake, achieving 20 decimal precision absent computers was an astonishing triumph. The Logarithmetica Britannica went far beyond previously imagined feasible accuracy.
Yet even this had slight shortcomings. Occasionally even more decimals were preferred for specialized use cases:
- Geodesy: Required 32 decimals for positioning calcluations
- Prime verification: Goldbach postulated 25 decimal accuracy could validate massive primes
But costs grew exponentially with each extra decimal. Thompson‘s desk-sized difference engine already stretched mechanical limits. Expanding further would necessitate warehouse-sized equipment!
So for practical use cases, Thompson optimized his design for utility and precision. 20 decimals sufficed for most contemporary science applications.
Bridging Generations of Mathematical Tables
The early 20th century represented a transitional period between manual and automated computation. As such, Thompson‘s work served as critical bridge:
Climax of manual math tables: The Logarithmetica Britannica represented both the pinnacle of hand calculation and the last monumental undertaking in that tradition.
Digital transition: The electronic computer age began in earnest shortly after Thompson‘s logarithms debuted. So his tables helped facilitate that changing of the computational guard.
Indeed we may consider Thompson‘s logs as a perfectly timed passing of the mathematics torch. So much meticulous effort across centuries now gave way to lightning fast, accurate digital number crunching!
Thompson‘s Personal Legacy
Sadly Alexander John Thompson remains relatively unknown despite such groundbreaking contributions. But through reviews of his work, key facets of the man shine through:
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Unwavering dedication: His 30+ year slog required incredible discipline and perseverance. Truly a labor of love!
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Technical innovator: Designing custom difference engines leveraging four units showed remarkable mechanical insight.
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Computing pioneer: Thompson helped push boundaries for scale of hand calculation itself. That spirit later drove computer achievements.
Ultimately Thompson garnered less fame than predecessors like Briggs. But we now recognize his central role propelling mathematical accuracy into the modern era. Not bad for a statistics clerk!
The Bittersweet Triumph of Human Computation
In many ways, Thompson logged the final entry in centuries of printed mathematical tables. Electronic computers soon launched an age of instant, easy number crunching – rendering such heroic human efforts obsolete.
Yet Thompson‘s monumental quest reminds us of the extraordinary intellectual feats possible without modern tools. We stand amazed at the heights reached through manual precision and persistence.
So let us acknowledge Alexander John Thompson as the steadfast human computer who scaled numerical Everest one last time – before making way for our digital world built on his logarithmic foundations!
I hope you‘ve enjoyed rediscovering this unsung hero of analog calculation. Perhaps it motivates you to create something special with passion and diligence as Thompson did so admirably.
Until next we uncover hidden gems in the history of computer science!
