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When Computers Were Human
The most important of these teams was the Mathematical Tables Project, organized by the Work Projects Administration in the United States during the Great Depression. WPA rules required the hiring of people with virtually no skills, so much of the definitive work of the Mathematical Tables Project was computed by people who had mastered only addition. They were not authorized to subtract, let alone delve into the mysteries of multiplication or division. The algorithmic steps assigned to them sometimes produced negative numbers, and it goes almost without saying that these computers had no idea what these were or how to handle them. Gertrude Blanch, the mathematician who oversaw their work, had devised a scheme whereby positive numbers would be written in black, negative numbers in red. On the wall in front of her human computers hung a poster that encapsulates much of the era of human computing. It read:
Black plus black is blackRed plus red is red
Black plus red or red plus black, hand the sheets to team 2
Grier has written a history of human computing. It begins in the 1760s and continues through the two hundred years until digital computers ended the industry.
From the start, computers were dedicated to projects in astronomy, cartography, and navigation. Grier describes the nature of these problems and why they required numerical solutions. He touches on the alternating competition and cooperation between teams of computers in different countries, and the different organizational models they employed. Perhaps the most memorable fact from the early years of human computing is that the very first team of French computers, assembled by Gaspard Clair Francois Marie Riche de Prony in the early 1790s, was composed entirely of wig-makers left unemployed by the French Revolution. They created trigonometric tables required by France's experiments with the decimalization of trigonometry (an abandoned effort to do for angle measure what the metric system was doing for the measurement of mass, length, and so forth).
Their work, though of little ultimate relevance to the modern world, illustrates aspects of human computing that would not change. Major computing efforts were always sponsored by governments. A small number of planners oversaw work by people who themselves knew little math. And the bulk of the work was done by people who were marginalized, perhaps otherwise unemployable, and who would do the repetitive calculations. This work conferred no prestige, and many were skeptical even of the conclusions drawn from it. If an equation could not be properly solved, how could one take confidence from any numerical approximation? Even Henry David Thoreau worked a dig at human computers into the manuscript for Walden, dismissing the mathematics that might allow an astronomer "to discover new satellites of Neptune but not detect the motes in his eyes, or to what vagabond he is a satellite himself."
Women emerged as the most important computers. Demand for computing spiked in wartime, when young men were off fighting and therefore unavailable, and the economics of hiring women was compelling even in peacetime. They would work for half of what similarly skilled men would. By World War II, in the United States, computing power was measured not in megahertz or teraflops, but in kilogirls.
By the 20th century, the work of human computers was augmented by mechanical or even electrical calculators that automated certain steps of their work, but these were expensive and prone to breakdown, and did not significantly change the nature of the work.
Grier devotes special attention to the Mathematical Tables Project run by the WPA, later taken over by the National Bureau of Standards, and to the mathematician Gertrude Blanch who ran that team. She is fascinating, a woman who arrived in the United States at the age of 11, who had worked to support her family and not been able to get her Ph.D until she was 39 years old. It was then 1936, the middle of the Great Depression, and the job prospects for female, Jewish mathematicians were bleak. Through luck and hard work she found her way to the Mathematical Tables Project, where she assumed a role that combined mathematician, schoolteacher, and coach. Her fanatical attention to error-checking resulted in tables good enough to win the support of those who were skeptical of work by a government relief organization. She also led by example, and solved certain problems personally when she thought that would be easier than breaking down the algorithms for her computers. Grier says that Blanch in this way personally did work that backed Hans Bethe's Nobel prize-winning model of solar evolution, though it is unclear if Bethe ever knew that the math had been done by one mathematician, rather than her computers. After the war, Blanch was hampered by FBI suspicions that she was secretly a communist. Their evidence for this was nearly nonexistent, and in what must have been a remarkable showdown, this diminutive fifty-year-old mathematician demanded, and won, a hearing to clear her name. She worked productively in numerical mathematics and algorithms for the rest of her life, but remained forever suspicious of digital computers and never adopted them herself.
Grier does excellent research, tracking down surviving computers and sorting through family letters to tell the stories of an entire industry that is being forgotten. He even finds evidence for the working environment for the women computers at Harvard Observatory in the late 1870s in the lyrics to a satire of Gilbert & Sullivan's HMS Pinafore, written by a junior astronomer there at the time.
The book is beautifully printed and has a comprehensive index. Kudos to the Princeton University Press for taking such pride in their work.
When Computers Were Human is weak in several areas. First, Grier glosses over technical aspects of human computing. What were the algorithms that these people used? How was error-checking implemented? He never tells us. Clearly, Grier's goal was to write a work of history, not math, but the people likely to read it are people who care about the math, or about computers, and he omits material that such readers would expect. Second, this is a bureaucratic story. The best human computing was done by large teams sponsored by government in wartime, and the story of these teams revolves around the politicians or bureaucrats who arranged for their funding, and the various acronym-labeled groups that gave them work or provided their employees. At times, it reads as much like a history of agricultural policies as a text about the prehistory of computers.
Grier's story follows his sources: he devotes space to the groups where he has the most material, even if others may have been larger or done more important work. Finally, his discussion of digital computers, where they play a role in the story, is cursory, and may not give credit to those who deserve it.
Is it worth reading? Yes. Consider the reviews of the final tables published by the Bureau of Standards at Amazon.com: In comments as recent as 2004, people who are still using these 50-year-old volumes comment in several languages on which chapters of the books are most useful, where to beware of errors or outdated methods, and on the special emotional role that these volumes play for those who use them, or who needed them in the past. "I probably would never have gotten my Ph.D without this book, and it is a stupendous classic." "Nearly every time you need a mathematical relation or information you will find it on this book." "If you work with mathematical research or numerical computing, you must have this book," and so forth. This praise, and Grier's book, are fine testaments to the world's first computers.
You can purchase When Computers Were Human from bn.com. Slashdot welcomes readers' book reviews -- to see your own review here, read the book review guidelines, then visit the submission page.
You can have my circular slide-rule when you pry it from my cold dead fingers.
I want a new world. I think this one is broken.
Now what's the percentage of the businesses/governments that used open source software/algorithms on their human computers?
...a beowolf cluster of those!
(p.s. I'm not wasting perfectly good karma on this)
But can they boot up with Linux? And when the supervisory mathematicians added a new table for them to use, did you have to recompile them? :D
Did he write this book before or after his seminal work on "In Living Color": When Television Was Funny.
concrete5: a cms made for marketing, but strong enough for geeks.
The more interesting part is the title rather than the blurb though. It sounded almost like when men were men, women were women and small furry creatures from Alpha Centauri were small furry creatures. Sadly this seems to be a story about the people who bothered the so called computers rather than a story of grit and glory - a story of buearacracy and communist witch hunts ?.
Quidquid latine dictum sit, altum videtur
The Sandiego Supercomputer is made of people! You've got to tell them! Sandiego Supercomputer is people!
Starsucks
So if computers are originally human, does that put the brain under the GPL liscense or are we stricly proprietary hardware?
Perfecting Discordia
www.stevenvansickle.com
My mother was one of those computers - she worked in England during WWII, using a 'comptometer' and had no idea what she was computing, despite hearing random roaring noises from elsewhere in the facility, until one fine day she was introduced to a Mr. Whittle, who had designed one of the first jet engines for Great Britain.
You can't talk about Wikipedia's flaws on Wikipedia
This sounds like a demeaning, brutal job. Almost like a factory for addition. Can you imagine what these folks talked about when they went home at night?
"Had a bunch of sevens at the plant today. Thought we never add them all up."
There's a slide-rule connection here. Oddly enough, numbers that couldn't be computed on a slide rule were deemed irrational. For those interested in slide rules, Here's a short history of the slide rule and here's a guy's collection of slide rules
Microsoft Taken To Task On Hiring Practices
http://www.gwu.edu/~elliott/facultystaff/grier.cfm
I used to read Caltizzle. I was a lot cooler than you.
Did they feed them pi?
Reminds me of "Souls In The Great Machine", a book I read a little while ago. In it, a giant computer is made in a similar way that this describes, sort of, although not all the components are there voluntarily.
http://wsulug.org
So instead of asking a hunk of plastic and metal for answers to math problems, I would have been asking a room full of educated unmarried women?
This is progress!?!?!
In Capitalist America, bank robs you!
Well I take that back, George Bush has scheduled the next Depression in about 8 years. See you there in the computer room or the breadline. Your current skills will be worthless during the depression.
Dont believe me? the national debt had doubled under George. For the current generation that's a debt of about $150,000 per head.
Some drink at the fountain of knowledge. Others just gargle.
Tables calculated by humans also contained a lot of human errors - I understand Charles Babbage was so frustrated by errors in human calculated tables that he wished for some way they could be calculated "by steam" (engine/machine).
try { do() || do_not(); } catch (JediException err) { yoda(err); }
Feynman is credited with an early application of parallel processing in the way he divided up his "girls" to do the yield calculations for the first atomic bomb, while they were waiting for IBM machines to be set up at Los Alamos during the Manhattan Project. Instead of each girl doing one whole equation herself, he divided the work so that one girl would only do a single kind of operation (such as cube roots.) In his memoir, "Surely You're Joking, Mr. Feynman," he writes that with this scheme he was able to get the predicted speed of the IBM machines out of his human computers. "The difference was that the machine didn't get tired and could work three shifts. But the girls got tired after awhile."
Most of the tedious calculations in wartime Los Alamos was done by "clever boys with engineering skils and high school diploma" that were drafted into army and then assigned to Los Alamos duty.
Everybody there was doing the calculations on simple electromechanic calculators "Merchant" which had the unpleasant tendency to break down a lot. (They also used slide rule to get quick fist aproximations). Eventualy they purchased a great number of card-punching machines from IBM (designed for bank account tabelations) and adapted them for iterative numerical calculations by putting them into a *cycle* - a revolutionary idea at the time.
This stil required lots of people to feed the cards into the machines at each step and the stacks of cards was going round very very slowly. The biggest problem of these calculations was that at this point the boys were pretty bored with the job. When they were told what they were actualy working on, their productivity increased ninefold!
A very entertaining re-collection of this computing history is in "Los Alamos from bellow" in "Surely you are joking Mr. Feynman"
I doubt that we will ever figure out - and I suspect that even if we did figure out we couldn't do much about it
There is a great short story by Asimov, in which many years in the future, man has forgotten how to do math without an electronic computer. It then happens one day that a young man figures out a process for doing addition and multiplication on paper, and shows off his new methods to a bunch of government big wigs. The military planners are overjoyed, and they begin to redesign their rockets so they can fit a man, who will then be able to calculate his trajectory and pilot the missile to its target by using pencil and paper. This is a huge win for all involved, because humans are much cheaper than computers, of course. :)
Actually there's a good scifi novel called "Dune" in which a class of humans, called "mentats", receive intensive training to be able to perform complex computations.
From what I remember, there's hardly any machine-computers in Dune. The empire has great technology and all, but it's all manned (space travel by the members of the spacing guild, calculations by mentats, telepathy by the bene gesserit)...
"A door is what a dog is perpetually on the wrong side of" - Ogden Nash
By World War II, in the United States, computing power was measured not in megahertz or teraflops, but in kilogirls.
For what it's worth, I still measure a computer's ability in 'kilogirls' but its not necessarily related to the processor power...
People wihout much of a background in physics would trall through the images, looking for patterns that they'd been told to look out for.
I think its important that someone is documenting the work of these heroes of maths and physics. Without them, advancements would have had to wait for the computer revolution. If we don't remember how important their contributions were, I'm sure it will only be a generation before they're forgotten.
During World War I, Naval Ships, mainly battleships relaying on long range artillery such as the Dreadnought used human computation for projectile of artillery. Dreadnought having eight 15-inch guns capable of firing a 1,920-pound projectile 35,000 yards (or 16 miles) and steam turbines reaching a speed of twenty-one knots, gave the extra edge to win the battle through precision of ballistic projectile from far distance.
Having said that, I believe, some of the points which the article brought up downplayed the importance of those "human computers" in some way.
I believe, those who filled the occupation as "human computer" led the way for greater precision and more reliable and faster computation if not life saving.
"Don't let fools fool you. They are the clever ones."
Reminds me of an Asimov story "The Feeling of Power" written by Asimov in 1958. People of the future, who are totally reliant on personal computers, experience the wonder at being able to do arithmetic by hand.
Are we there yet?
If anyone's interested, there are several sites with instructions on creating your own slide rule.
h tml
http://www.sphere.bc.ca/test/build.html
http://solar.physics.montana.edu/kankel/math/csr.
etc.
Coder's Stone: The programming language quick ref for iPad
Yes, it was a result of the Butlerian Jihad. There was a big war about "thinking machines" and they were banned. Thus, mentats. I'm not sure, however, if the machines were combattants in the war, or just the subject of it.
Even Star Trek treats the idea in Insurrection. One of the guys living on the paradise planet says, "When you create a machine to do the work of a man, it diminishes the man".
The people on this project were not mentat-like. They're more like an op-amp in a funky human computer.
clicky
Technoli
Is that when laptops were pretty secretaries?
Humans have such a good sense of humor!
People could add but not subtract? They could know what a positive number is, but not a negative?
There was a time when this was true of YOU, y'know.
Granted, these days most of us in industrialized nations move on and grok subtraction and negative numbers by second grade, but it doesn't seem unreasonable that 3/4ths of a century ago, some unskilled works might have made it to adulthood without getting that far.
Feynman isn't credited with that or indeed a lot of things in "Surely you're joking Mr Feynman" and the other one the title of which escapes me. Feynman credits himself with many of those things. I'm not disputing his credentials as a great scientist, for sure he is universally recognised for those things, and as an influencial thinker (especially in self-professed "geek" circles) but even the man's best friends would and indeed on many occasions have pointed out his proclivity for self-promotion and tendency to portray himself in a certain light that might not be entirely accurate in his books.
Plays violent online games as: Nerfherder76
The Smithsonian has a great interview with Ida Rhodes, who assisted Blanch.
Here.
The last few years of school I went to waldorf school. We actually learned to use log tables (still got my table book here) and calculators were forbidden.
We'd draw roots using them and all.
The reasoning was that anyone can keypunch but understanding what log actually mean is a differn't thing and requires getting your hands dirty. It was at that time when I started programming on my first computer - a PC 1402 Sharp Pocket Computer. Amongst my friends I was the only one that actually understood what these symbols really meant.
I'm gratefull for our teachers taking us that way. I'd actually do the same. Once you've really understood what logs are all about (and when you do your A levels with log tables you have understood what they're about) tackeling larger math problems is a piece of cake.
Take this advice: If you have kids, don't let them near/use an electronic calculator to early. Give them log tables or a slide ruler. It's the best was to learn higher math.
We suffer more in our imagination than in reality. - Seneca
If you run more electricity through them, do they work faster?
HA! I just wasted some of your bandwidth with a frivolous sig!
The opening paragraph reminds me of a fiction book, Souls in the Great Machine by Sean McMullen. Wherein exists technologies that do vast mathematical computations by way of people acting as logic gates and functions. Much in the way that computers worked as described in that paragraph.
Mill Avenue Vexations
Your example IS the example of why sigfigs are inherently tricky. Your answer is right - and in addition, decimal places will always get you a reasonable answer. But you've actually increased the number of significant figures (from 3 to 4) - AND that's actually the right answer.
.5 - so your "dp" thing doesn't work at all - we added a dp of precision.
.5 as a shorthand for the integer 1/2, then 2.5 is absolutely the right answer.
.5 in a calculator and got 3, I would return it immediately.
.5, it has no way of displaying or expressing fractional significant figures.
You get into really, really big problems when you mix flop and integer math, and the calculator couldn't know which one you're doing. The basic problem comes from the fact that "integer" precision is commonly notated the same way as "no precision at all"
Here's some interesting examples:
If I divide 1 by 2, the answer should be
If I multiply 5 x.5 as decimals 3 is probably the right answer IF you can guarantee there are no additional sigfigs. But if I entered
If I entered 5 x
Furthermore, 2 1/2 is _probably_ the right answer, because 1/2 is only a small fraction of a significant figure. But your calculator only knows how to display "1/2" as
Going the other way is even worse - unless you're going to make everyone enter everything in SI - which will never happen - there's DEFINITELY no way to differentiate between estimated and real values. What's the right answer to 80 x 90? 7200? or 7000 ? It depends on whether those zeros were significant zeros or placeholders...
Finally, some really, really crazy things start to go on when you have exponents and the like - very commonly you get cases where you probably meant the base of the exponent to be an integer even if some part of the exponent itself is a decimal - because 2.0 ^ 32.0 has NO significant digits unless the 2 is actually an integer. (even if the 32 DOES have infinite precision. (for instance: 2^32 ~ 4 bil. 1.96^32 ~ 2 bil; 2.04 ~8 bil )
But nonethless not EVERY exponent is supposed to be an integer - especially when you're simply squaring something (pythagorean theroem on an arbitrary length, anyone? )
You really need a calculator that is very advanced - not to do the math, but to have input and display that can reasonably interact with how poorly the PEOPLE using them know sigfigs - and how poor an idea the PEOPLE usually have about their input method.
I've never seen a calculator with an _interface_ that could handle it. I actually think it might be easiest to do in a software calculator (even if my hardware calculator was better at some of the actual math)
Looking for freelance Actionscript (Flash/Flex) or ColdFusion work and/or freelance developers. Email me, put Slashdot
Wikipedia contains more information on why there are no machinal computers in the Dune universe. There was the Butlerian Jihad in the Dune universe, which was a crusade for the destruction of computers, robots, and anything that tries to replace the human mind with a machine (artificial intelligence).
This battle for supremacy of humans and sentient machines is described in Dune: The Butlerian Jihad, one of the prequels by Brian Herbert and Kevin J. Anderson.
Morality is usually taught by the immoral.
My mom was employed by NASA (aka NACA) as a "computer" during the Mercury space program. In those days, each engineer had his computer and the computers wore skirts (as they liked to say). She did the calculations for the rescue rocket that was mounted on top of the capsule.
I always enjoy telling people that my mother was a computer. The response I normally get is an understanding and condescending nod.
I remember the early years of computer science as being a secretarial/trade school kind of thing. I remember MIT and Stanford faculty debates as to whether they should even offer an undergraduate major in computer science because it considered too "vocational". If you were a Stanford student in comp sci you got a "stealth degree" as a minor in the math department. At MIT they hid it in electrical engineering and STILL HAVENT granted it independent department status even though at the height of the computers science boom one third of undergraduates majored in this option. Even now MIT refuses to teach a practical introductory computer science course. Their first course has been based on LISP since the late 1960s and still uses the version called SCHEME.
ironically the only reason we have low interest rates right now is the influx of chinese trade dollars into our debt markets. That will dry up ten seconds after the chinese dollar floats. The debt however will remain and have to serviced on the backs of the next generation of income earners.
Some drink at the fountain of knowledge. Others just gargle.
I was one.
/hr. + 0.12 shift premium. (Gas
In the summer of '57, at the Southern California
Cooperative Wind Tunnel, swing shift. Pay
was $1.60
was about 30 cents / gallon).
Punching an electromechanical "square root Frieden".
Weight about 50 lbs., price about $1600.
The "system" featured overlapped I/O:
remember previous result
Left hand:enter new caclulation, start
Right hand: write down previous result
while the gears churned...