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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.
When women were locked by the dozen in rooms calculating projectile trajectories like they were meant too.
What the hell is he doing writing about computers? Or is this a comedy book?
http://www.imdb.com/name/nm0004979/
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
I thought David Alan Grier was a comedian? Ive seen him on Comedy Central...hmmm.
...am glad to see that David Allan has moved onto other things after his long career with M.A.S.H. in the 70s. ;P
-"...bad old ideas look confusingly fresh when they are packaged as technology" - Jaron Lanier (Digital Maoism on Edge.o
that's what I'd call "distributed computing"
The Chronic *WHAT* les of Narnia!
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.
I loved him on the show In Living Color!
Get a FREE Sony PS3
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
In case anyone was confused by the lack of the line break.
-dave
http://millionnumbers.com/ - own the number of your dreams
Who knew that Mr. Grier, the hall monitor with the short leg on "In Living Color" was a closet math geek? :-)
Reminds me of Dune.
The Sandiego Supercomputer is made of people! You've got to tell them! Sandiego Supercomputer is people!
Starsucks
I wonder if he'll get 'Twan to write another review for his book.
The reviewer clearly should have rated this book "Two snaps in a Z formation"
/. ++
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
Someone could write a bad futuristic sci-fi novel about the human race being extinctk succeeded by a human-computer hybrid thingamajig, and title it "When Humans Were Human". Hardy har har. Or not.
I caught the Mountain Wumpus! He gave me his treasure chest ($100) to let him go free again.
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
Did they feed them pi?
Agile Artisans
i don't have hard drives. i just keep 30 chinese teenagers in my basement and force them to memorize numbers
The laws of probability forbid it!
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!
I'm betting that this procedure involved a fair amount more violence than it does today...
This sig used to be really funny...
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.
My high school math teacher had worked on Concorde. He mentioned how they also had a roomful of women "computers" to do various calculations for them.
There's probably a bunch more Dune references that could be made. Insert all here. Now that we're done with that, we can get on with the Soviet Russia, ...Overlords, and other staples.
Just wanted to get that out of the way.
Besides, anyone who had a martinet of a high school math teacher has had a taste of being a human computer. "You want how many digits of the square root of pi? What are you smoking Mr. (blipped)? No, no, no, I am not writing them longhand. You can take a dot matrix print like everyone else."
If my grammar and spelling are off, I am [distracted/tired/careless] (take your pick)
...where the average poster will be lucky to get 0.001 of a kilogirl.
The next title in the series will be: When Computers Were Machines...
Soylent Green Computing
Irrational, meaning unable to be expressed as a ratio of whole numbers.
Nice try though.
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
Sean McMullen wrote a very nice series that used this as a plot element. The first book is Souls in the Great Machine . Takes place in Australia about 2000 years in the future.
The man who never alters his opinion is like the stagnant water and breeds Reptiles of the Mind -- William Blake
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. :)
Irish children are forbidden to use electronic calculators in school for maths until late teenage years (and even in exams where calculators were permitted, you had to write "E.C." (electronic calculator) in big letters next to the answer to say you used a calculator - exam supervisors kept an eye out for that...), so that Irish people have the mental arithmetic abilities to rebuild Irish civilisation when stranded in a post-nuclear-holocaust hell world filled with the zombies or something like that.
e arch=LOG+TABLES
Actually, I think it helps in day-to-day life: when I lived in the UK for a while, a thing that really stood out was that shop assistants AND customers would quite often believe the cash register before their own brains, whereas in Ireland, people just spot the mistakes. Basic arithmetical "common sense" was anything but common in the UK. I don't actually know when UK children are allowed calculators, but I bet it's earlier than Irish children.
So anyway, in junior cycle of secondary school, when begin you do trigonometry and logarithms etc, we still used trig and log table books. I couldn't find a good picture on line, but they are EUR1.90 from here for a standard-issue copy:
http://shop.schoolboox.ie/Product/Products.aspx?s
in support of the parent:
next up, a book review of an obscure work 'the first folio' a timeless classic! I can't believe I found this!
like you jackasses even fucking read books that don't have anthropomorphized tenticle rape of impossibly drawn women.
yeah math.. done by people... before digital computers.. thanks.. was your PhD in 'fucking useless observations' as well?
I liked it.
On an old episode of Dr Who, the Doctor went to a planet of human calculators (to try to get the TARDIS chameleon circuits working again, I think). Everybody on the whole planet was sitting around with an abacus in their hand.
"I'm not impatient. I just hate waiting." - My Dad
I've heard from older physicists that in those early years the scientist-computer match was quite popular.
(It still is, but, well...)
Any sufficiently advanced libertarian utopia is indistinguishable from government.
We already know humans back then were subject to all kinds of viruses, just like Windows today.
The book is a bit expensive for $35 USD on Amazon. It's bad enough that you have to pay $50 USD or more for a good technical book. But $35 USD for a history book?! Sheesh... I'll wait for the paperback.
Did they spank them?
If you want to read great sci-fi about human computers, try Sean McMullen's GreatWinter triology. In his books, overlibrarians develop primitive computers called "Calculator" using human power to help them control their world. They even have portable battle calculators, made up of around 50 man and help commanders make decision on the battle ground.
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...
I find it unlikely, but is this the same David Alan Grier -- the comedian -- who was on "In Living Color" and such? I haven't been able to find anything definitive yet, but I'm assuming it's just a coincidence.
That's got to be a pretty rare name, though...
"Destroy science and religion. Science would re-emerge exactly the same; but not religion." - Penn Jillette, paraphrased
This post reminded me of the last Tom Baker Dr. Who episode, in which the Doctor traveled to the planet Logopolis to fix the Chamelion circuit in the Tardis. It's basically a planet entirely populated by "humananoid" computers, who constantly calculate complex mathematical computations in a vast distributed environment. Their calculations supposedly helped to hold the framework of space/time together. The Master threw a wrench into the works by strategically killing off specific Logopolis citizens, thereby weakening the space/time continuum. Seems clear to me that either the Logopolians hadn't thought enough about error checking/correction, or that the Master truly was a master of distributed networks.
By World War II, in the United States, computing power was measured not in megahertz or teraflops, but in kilogirls.
WOW!! On side note, repetitive jokes involving 'kilogirls' are going to haunt /. for years to come just like beowulf jokes!!!!
- mritunjai
This 23rd edition features upgraded interest rate information in the financial section, with compound interest and associated material from one quarter of a percent through twenty percent in intervals of one quarter of a percent.
Brilliant!
The neat thing with this one is that not only do you get the tables, you also get all the formulas and breakdowns of dozens of proofs!
All in one handy volume!
.. pa-ra-bo-la, pa-ra-bo-la, 2 pi R, 2 pi R, where's your latus rectum, where's your latus rectum, 2 pi R
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.
You mean this guy wrote a book about computers and mathematics??
I give it pi snaps up and a big ol greek sigma snap...
Once being an engineer had dignity, skills and nifty curled up bendy ties. Now it's downgraded to menial tasks Ceramics Engineer [Dishwasher], or even worse like getting your MCSE. [Minesweeper Consultant And Solitaire Engineer]
Sorry about the writing. Robot fingers, you know? Cliff Steele in DOOM PATROL #23
Jenn #2
Yeah. I know that -- p/q and all that. Didn't mean to imply that the numbers were irrational in the other sense of the word. Honestly, I don't know if that's true or not. I do know we're talking about the same latin root, ratio. The derivatives mean "to think" or more recently "to calculate" -- so it might be close enough for government work. For a nice history of the term, try this site Also try this site.
Marketing in RSS? Heavens To Betsy!
The first book (Souls in the Great Machine) is almost entirely focused on the creation and operation of the calculor and should be very well received by programmer types. By the timeline of the other books, calculors are just another tool, and McMullen is off steampunking other inventions -- which is still entertaining, but has nothing to do with computers.
This is how I finally explain myself the presence of the word "computator" in latin dictionaries - that is, B.C.
gtkaml.org
Did they run Linux?
These aren't the sigs you're looking for.
I wonder how stacktraces were obtained back then. Must've been popular events too!
When I first read the value for Pi, I comprehended that it was the only universal value for solving all equations; and thus, there is somthing wrong in the the founding of the number system, and not this most derelict-appearing irrational number. Flip the world right-side up, even if it means all other numbers are irrational and Pi is not irrational. Is an apple rational? A bannana? I would think that Pi is natural, but it is unlike apples and bannanas because its current usage today is in a man-made number system; thus today, the interpretation of Pi is unnatural. It needs to be changed to give Pi a more rational standing.
Does anyone know of any recent experiments on changing the number system into this mode? I can say the same for the value of Pi as well as charts such as Sine, Cosine, and Tangent. Charts have no basis for mathematics. Man-made measuring equipment needs equal criticism; Protractors should be shunned like the plague because all math theory is built upon knowing absolute and rational values to discover unknown and irrational values. With the current number system, I think Pi needs never be expressed because it can't be measured honestly; it is currently slandered as being infinity when it truly is not infinity, and needs to be un-adjusted as such.
Does anyone know of a number system that tries to correct the devoid of variables incorrectly declared and represented by irrational numbers? I think it is self-evident failure of a number system expressing such as irrational; 10 fingers is what our number system was made for. What is the more logical number system? I have yet to seek any articles in google, because the phrases are too difficult to search without collecting yet more treatise and university work on the same number system that I am debating.
(I've endured much libel and slander, and can't post logged-in anymore after two successful recorded posts on account. http://slashdot.org/~SlashdotTroll)
these computers were effected by viruses as well, but the virus started by taking out a single general purpose register then it would spread to any register that shared an instruction with an infected one, the registers didn't suddenly stop mind you (if they did the virsu could not spread) instead they functioned fine part of the time, poorly the rest.
virus that bOrks registers... fun.
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."
Since "thinking machines" were naturally forbidden, the hrethgir used human slaves to compute their equations. The upside was that humans sometimes made mistakes, and mistakes sometimes had beneficial consequences (but usually the slaves fared no better).
Not as good as his dad's stuff, but OK. Get it in paperback.
There exists no way of exchanging information without making judgments. --Bene Gesserit Axiom
I was fortunate to find in a used book store an 1868 Pocket Websters Dictionary. On a lark, after looking for all the dirty words (there were none), I looked up "computer". Sure enough, there it was as "one who computes".
Monday:
...
- How was work today?
- 3.1
Tuesday:
- How was work today?
- 3.141
Wednesday:
- How was work today?
- 3.141592
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?
...for making some of us feel not-too-old:
"In the not-so-distant past..."
Bring up not the name of the worst Doctor to wear the title. We were lucky to ditch Addric about then too, but the doufus-that-took-over-from-Tom-Baker's very name hurts my ears.
Sorry about the writing. Robot fingers, you know? Cliff Steele in DOOM PATROL #23
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
clicky
Technoli
... developed to speed up the deployment and computation of algorithms when you needed results quicker than a single Computer could handle, were lost due to the introduction of the microprocessor.
also:
there are sci-fi books and short stories about this sort of thing.
one of them is "the end of eternity", by isaac asimov - Computer Harkan (Computer as in a title like Doctor) is the main character.
also there's a short story - by greg bear, i believe - about a space expedition that got lost in deep space: the entire crew learned how to do sines, cosines etc. it took months, and by the time they were far enough along to plot a reasonable course home, the crew were doing the calculations in their heads.
fascinating but only enough material for a _short_ story...
so would a beowulf cluster of those be considered an orgy?.... imagine the viruses!1111
I'd like to see the same thing at an even lower level....instead of requiring that these computers add numbers....why not just make them perform the simple task of a binary logic gate. We can hand out hats with:
-|>-, =|)-, =)>- on them, and you can just hand giant heads/tails coins around a room in a particular pattern. A full adder is what, 3 or four gates, something like that? I'll be heralded as having quadrupled the number of jobs in the sector!
The comedian? :)
Red and black numbers,
France,
1790,
Is there a connection between this and the configuration of the roulette wheel?
Guess it's just not my lucky day
Is that when laptops were pretty secretaries?
Humans have such a good sense of humor!
However, your work since "In Living Color" leaves much to be desired.
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
Yes. But mostly in the stool though
had something else to say about it
... computer evolved out of man? wow! but ... I don't get something, does that prove or disprove the existance of God?
Tristan
is this the same David Alan Grier from In living color?
computing power was measured not in megahertz or teraflops, but in kilogirls... a term now used only in reference to basketball star's recreational activities.
I've abandoned my search for truth; now I'm just looking for some useful delusions.
The Smithsonian has a great interview with Ida Rhodes, who assisted Blanch.
Here.
Claim 1: A process of developing and verifing rules for the manipulation of symbols;
Claim 2: certain operations can be used to model real world effects, saving the effort of real-world implementation.
Hmmmm - I still think the crustless peanut-butter and jelly sandwich was a more profound.
No, I don't trust in god. He'll have to pay up front, like everybody else.
So the mentat really exists!! Where are the Navigators?
That's decimal places.
But 1.00 is 3 significant digits, so the final answer would be 44.7 (three significant digits), not 44.74 (2 decimal places).
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!
Humans that calculate are called calculaters while machines that calculate are calculators.
Thus, computers should be people, and the machines call computors.
Or do I have it completely backwards?
Mike
All ideas^H^H^H^H^Hprocesses in this post are Patent Pending. (as well as the process of patenting all postings)
In my first research job, and although I have an unusual name, there was someone else of my name in the company (even the same middle initial though they stood for different names.)
As the other guy had a PhD and I only have a Masters, our titles became part of our namespaces. So although your idea is presented humorously, it actually makes good sense.
Panurge has posted for the last time. Thanks for the positive moderations.
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
And people say those who read slashdot don't get girls! There's 5 billion kilogirls sitting in a beige box next to me right now~
When computers were humas spyware had a whole different meaning.... or should we say Mr Bond!
I might as well try an example...
Using just the first three terms of the infinite summation for the cosine function:
cos (0.3 radians) = 1 - x^2/(2!) + x^4/(4!) (easy pattern, nice for memorizing)
So -> cos (0.3 radians) = 1 - 0.3^2/2 + 0.3^4/24 = 0.9553375
Comparing to calc.exe's cos(0.3) = 0.9553365
So it was quite a good approximation, and easy to calculate too! (easier than I thought, actually)
The AACS key is NOT 0xF606EEFD628B1CA427BEA93A9CA9773F
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
I remember a chapter on human computers in Feyman's autobigraphic essays Surely You arent Joking .
Wikipeadia mentions this too in Feynman's bio.
This sounds familiar. Was it IBM's first attempt at the Power architecture? Were the male supervisors the Mac Daddies? Was GCC 0.1 the Girl Computer Co-ordinator?
I am a
You agree with me, that it is idiotic to use such a system arbitrarily used without questioning its accuracy. My point ex-actly. Everyone counts what they think and thus know is countable, and often give strange illustrations to what is infinite whereas Pi is just that. If you were to measure a stick with a tape-measure, how would you know the tape-measure was correct unless you measure the tape-measure? Then you get into a infinite circular reasoning crisis when trying to audit and arbitrary system with another arbitrary system. The same can be said about the verry evolution of language; how do you know you can actually count somthing or measure somthing; are they not approximations of infinite value expressed expressed rationally? All mathematics theory is being expressed with finite values in an infinitely unhindered universe. It's not applicable when you leave a civilized world and enter the real world where what can happen will happen. An infinite world defies probability and all matter of precision with recursive parallel existance. The verry moment a number is written on paper to rationalize and express a thing's value is already untrue because of CONVERTION. The man mechanism that separates people is their language; a CONVERTION; but given all language has a common ancestor it turns moreso as a code of the beginning. Nothing can be represented mathematically because the universe is infinite. Some people express value in calories, others in parsecs, some count you by how many years old or years young; it is quite silly, when you get down to it. Mathematicians use CONVERTION because they can't solve an equation using same terms; thinking that equal exchange will provide an answer; sure, in a world turned upside down where every irrational value is rationalized. I suppose we all can harp about how geometry truly is an inacurate form; Calculus addresses just this matter I intend to exhibit. A symbol can represent somthing, but when you bring mathematics into the equation you are mixing finite with infinite. Calculus is the key.
I fear the day is fast approaching when no one living will understand my very favorite joke, the one about Noah that ends with the amazing triple-pun punchline:
"The snakes were adders and couldn't multiply without their log tables."
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.
Standard Form is wonderful, you're guaranteed that your 1.00x10^0 is exactly 1 to all the accuracy you need. But like your major point was, interfacing with a calculator to just tell it if your number is absolute, or to x significant figures, is horrible.
How many people can read hex if only you and dead people can read hex?
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.
Hmmm...
whattofix.com 127.0.0.1
consideryourselfadded
I can now reveal its called "What do YOU care what other people think?". I believe it was supposed to be a rhetorical question though...
Plays violent online games as: Nerfherder76
Many businesses and the governement employed "warehouses" of clerks to process business paperwork like accounts receiveable and inurance claims. Some of this was computerized this fairly early on around the 1960s. However, I still suspect much medical insurance is still transcribed from paper forms- among the last holdouts. Jim Clark's Netscape successor Healtheon and a joint Congressional bill from B. First & H. Clinton are trying to modernize this.
She is my great-grandmother, David's grandmother. Only met her once or twice; I was too young to remember. It's great that David wrote this, I feel so proud!
Hosting a World of Warcraft server powered entirely by educated unmarried women would outright KILL your ping times....
You think lootlag is bad NOW? And don't even THINK of ever going to the auction house again...
If they were primarily men, you know that Truman and Eisenhower would have been blamed for the massive unemployment in the computing field. I'm out of work, blame the administration! Smash a vacumn tube, save a job!
Don't blame me, I didn't vote for either of them!
Yes, but could they run Linux?
OSGGFG - Open Source Gamers Guide to Free Games
My 1953 copy of Webster's Unabridged has an entry for "Computer (noun, archaic) One who computes".
Do not mock my vision of impractical footwear
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.
Only once you've proven that the methods you used to calculate the numbers in the log tables are correct all the way up from the fundamental axioms of set theory, and confirmed the derivation of each and every element in your log table can you be said, in an absolute sense, to really "understand what they're about".
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.
Nonsense. Teach them to use the tools they need to get the job done. Better still, teach them to build the tools themselves.
It's pretty easy to build an arbitrary precision adding device out of a series of graduated cylinders (or other measuring devices). Add something to measure (water, sand, flour), and you've got an highly effective, if somewhat primitive, adding machine. It has the added bonus of being intutively comprehensible to five year olds.
After all, almost all of our little grade school tricks are just attempts to simplify rote computations: shortcuts to avoid repeatedly applying the successor function to 0. To really understand mathematics, you need to understand problem solving, how to identify patterns, and most especially how to avoid rote calculation whenever a more powerful abstraction is available.
Real mathematicians use calculators whenever appropriate. Teach the students useful, basic abstractions about mathematics, and forget all the fussing over calculators. It didn't make sense thirty years ago, when I was in school: it makes even less sense now.
Adding numbers in your head isn't something you ever do very much in your adult life. When the total needs to be correct, even professional accountants break out the calculators. Nothing important is done by hand.
Give me a child who can't add or multiply very quickly without a calculator, but who knows why integer multiplication be reduced to repeated addition, integer addition can be reduced to a form of repeated counting, and why "decimal places" can be understood as a form of repeated grouping by tens, and I'll give you back a budding young mathematician.
Give me a kid who has learned by rote, reading tables, and following rules, one who can operate a slide rule and knows his times tables cold; but doesn't know anything else, and I'll give you back someone who doesn't really understand what mathematics is all about yet.
So, I disagree with your contention that giving children access to calculators "too soon" can damage their ability to understand "higher math".
Log tables and a slide ruler are just a more arcane form of calculating devices; rote learning, be it by rote memorization of tables, rote use of a calculator, or rote use of a slide rule is generally bad. You need students to know something of the why; and not just the how, before you can say they really understand.
Give me the kid who can't remember what eight times seven was, but can build a device to get the right answer. You take the kid who has memorized the answer, but doesn't know why it's right, or what to do if he ever forgets. I know which one will be the greatest mathematician; and it's not the kid with the good memory.
--
AC
We still look up the numbers in primitive hardware like the Game Boy, where it's just too slow to computer this stuff. It not as taxing though when you can access the numbers with electrons.
Doc Smith used the term "computer" in this context in his Lensman and other stories. The concept of an artificial computer shows up only in (that I know of) Children of the Lens.
Current Generation != total population. it's the children being born in the next 15 years that will have to pay this off. that comes to 150,000 a head. (figure 30 years to pay off the note at a reasonable interest rate)
by the time george bush leaves office the debt will have doubled
Some drink at the fountain of knowledge. Others just gargle.
you call someone a retard then cite not one ecomonic element to back your case. You are the retard
Some drink at the fountain of knowledge. Others just gargle.
I'm too young to have used them, but my older geekier friends wax nostalgic about their slide rules - analog (though nonliving) computers.
"All it takes to fly is to hurl yourself at the ground... and miss." - Douglas Adams
"What an awful nightmare! Ones and zeroes everywhere...and I think I saw a two!"
"It was just a dream, Bender. There's no such thing as two."
i'd hit it so hard, if you pulled me out you'd be the king of britain [bash.org]
Linus was a fire direction officer in his military stint. In the US Field Artillery, they still teach slide rules and tables to the Lieutenants and Soldiers in their training. (Well, the cannon guys.) So, did Linus learn it, too? My bet is yes.
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.
Nice try, but if you would reference article 1, sec. 8 of your constitution, you will see it is Congress who has control of the nations purse strings. The president will submit a budget, but congress can alter it or circular file it. Every budget Reagan ever submitted was declared DOA by Tip O'neill, Democratic speaker of the house. They gave him his defense increases, but cut nothing, in fact spent exponentially more every year, ballooned the deficit, and blamed the republicans for it. If he were to veto it the solidly democrat congress would override him.
+1 Funny?
+1 Insightful?
+1 Flamebait?
I have a cute little one I carry in my pants pocket, comes in very handy.
What is this? Some sort of pick-up line?
"Would you like to see what I have in my pocket? It slides! It RULES! And you don't need batteries!"
Time flies like an arrow. Fruit flies like a banana.
I use a slide rule rather than a calculator or computer in situations where it's appropriate. I have a cute little one I carry in my pants pocket, comes in very handy.
Is that a slide ruler in your pocket or are you just happy to see me?
Do not be alarmed. This is only a test.
Well, I way too often see questions on 8051 MPU (8-bit microcontroller) forum: "How to multiply two 16-bit numbers?" "How to get a fixed-point instead of integer from division?" "How to add two numbers bigger than 256?"
These all just boil down to writing the basic stuff you learned in school, taking bytes as digits of the numbers and adding, multiplying or dividing just like you would do on paper. But well, they didn't learn how to solve 10:3=? without a calculator, so they don't know that plain MOV A,B, incrementing pointers and repeating the basic division with modulo will solve their problems. Maybe these things should be learned later, not in 3rd or 4th year of school. But they are needed, and calculators and other solving devices take them away from kids.
Anagram("United States of America") == "Dine out, taste a Mac, fries"
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...
There is an excellent SF novel (first in a series, actually), by Sean McMullen, called "Souls in the Great Machine"5 344572
http://www.amazon.com/exec/obidos/tg/detail/-/076
It involves a very large-scale version of "human-component" computing. It is set in Australia in the far future, when there are orbiting satellites that destroy any electrical devices (the satellites are left over from some long-past world war). So to have a "computer", one is constructed of conscripts, each of whom does a small part of the large program.
The whole series is good, and full of interesting extrapolations on this idea- including a "battle calculor", which is a trainload of people to perform calculations on-the-go. A little more cumbersome than a pocket calculator...
Well, I way too often see questions on 8051 MPU (8-bit microcontroller) forum: "How to multiply two 16-bit numbers?" "How to get a fixed-point instead of integer from division?" "How to add two numbers bigger than 256?"
Well, I have two objections to that point of view.
First of all, those are engineering questions, not mathematical ones. You're complaining about a student's inability configure a pre-existing computing device to compute the answer they want.
A perfect valid answer is "use a more powerful existing computing device". It doesn't scale well, but it may well solve the problem at hand. For engineering problems, that's a valid line of thought.
Secondly, from a mathematical point of view, the right answer is to formally prove the algorithm that you're applying is correct, and then worry about coding it.
You sound like you're decrying a lack of basic creativity in your students, though, and drilling division problems is unlikely to solve that. I submit that you can make a student do all the rote computation that you like, but if (s)he doesn't understand why the algorithm works, then (s)he won't see how to abstract it. I don't think calculators are to blame for this; rather, the fact that poor teachers equate mathematics with mere computation, and who therefore assume calculators are a substitute for a formal education are the real culprits.
Maybe these things should be learned later, not in 3rd or 4th year of school. But they are needed, and calculators and other solving devices take them away from kids.
Your whole problem involves building a form of calculator to begin with: if we taught children how to understand, problem solve, and build computing devices to implement math problesm, I think they'ld both appreciate calculators better, and apply them more correctly.
--
AC
A perfect valid answer is "use a more powerful existing computing device". It doesn't scale well, but it may well solve the problem at hand. For engineering problems, that's a valid line of thought.
No, that's a perfectly wrong answer.
A budget USB controller chip based on '51 is something like $0.80 in bulk. The next "more powerful device" is like $5. Multiply by 10 mln devices sold. Saving one passive, like a resistor or a capacitor is several hundreds of dollars in savings. Stuffing complete driver into 2K of EEPROM of a TUSB* instead of including a dedicated DSP on the same board will decrease the final price by about 40%, cost by about 60%, power consumption by 70% (allowing the device to be running from USB cable power instead of requiring a separate power supply, another $5 in bulk) and making it the size of a USB plug, instead of a box of cigarettes (plus another similar box - power supply.) Embedded devices is still a market where a good smart algorithm and ability to implement it is way better than "taking a bigger chip", assembly is still more valuable than high level languages and knowing how to implement various algorithms better than knowing theory behind them without knowledge how to apply them in real life.
Anagram("United States of America") == "Dine out, taste a Mac, fries"
In World War II, analog computers (electrical and mechanical) were widely used for computing firing solutions for torpedoes and naval guns. Some of these systems were quite complicated. I've never been able to find a book that described them in detail. Probably because they were considered to be very sensitive military secrets. See here for an example.
Mea navis aericumbens anguillis abundat