A Daily History of Holes, Dots, Lines, Science, History, Math, the Unintentional Absurd & Nothing |1.6 million words, 7500 images, 4 million hits| Press & appearances in The Times, Le Figaro, MENSA, The Economist, The Guardian, Discovery News, Slate, Le Monde, Sci American Blogs, Le Point, and many other places... 4,200+ total posts
The small $25 miracle/godsend to number crunchers everywhere was this small, nine-place, sliding-digit chain-adder mechanical calculator, set in nickel-plated metal, and which we see in this fantastic and half-bizarre ad in Illustrirte Zeitung for June 1922. The instrument was about eight inches long and came in its owns hard case, and was a very good instrument for the lowish-end market. The add of course is fantastic. ("Die Erloesung" could I guess be transliterated as "Deliverance!" from the drudgery of making calculations by hand.)
Out of the many references I've seen for war gaming in early-ish computer journals and reports from the RAND corp (and other such places before, say, 1962) I don't think I've ever since a direct visual connection between three-dimensional gaming objects and a computer. But here are two examples,in the same journal and within a few dozen pages of each other, one featuring chess pieces and the other featuring toy soldiers. Both are obvious selections, but not used very often at all in illustration.
[Source: Communications of the Association for Computing Machinery, volume 2, number 10 and 12, October and December, 1959. Another image follows below.]
Games of war and capture go far back, with chess many hundreds of years old and Go older still. Early war games as "war games" appeared in the late 18th and early 19th century, developing past Strategoes (in the 1880's) with other iterations, and then famously in two mass culture works by H.G. Wells, Little Wars (1911) and Floor Games (1913).
[The two Wells works may be found here and are well worth looking at: http://www.gutenberg.org/ebooks/3691 (Little Wars, though fair warning here of the unfortunate but time-laced subtitle, "(A Game for Boys from twelve years of age to one hundred and fifty and for that more intelligent sort of girl who likes boys' games and books") and then http://www.gutenberg.org/ebooks/3690 (Floor Games)]
The U.S. Strategic Bombing Survey was a massive intelligence operation composed of a 1000-person team. It attempted to establish the successes and failures of American bombing operations during WWII, resulting in a 208-volume set of findings for the war in Europe and another 108 volumes for the war in the Pacific. Atomic bombing was another matter. I am not going to address the effectiveness issues of different sorts of bombing here--it is a very large and complex issue, and just outside the scope of what I set down to down just now and the amount of time I have. What I did want to do was share this typed/manuscript material (below) that was kept by a member of the analytical team serving in the Pacific. It is interesting to see how the form of the final reports took shape from some of the original notes.
This small archive—from the estate of J.D. Coker, who served in the U.S. Navy on the US Strategic Bombing Survey Ships' Bombardment section, and who later became a leading official in the U.S. Atomic Preparedness programs (such as the President's Committee on Emergency Preparedness)—are mimeographs and manuscripts that comprise what seems to be the summary of the Navy's bombardment of Kamaishi, Muroran, Hitachi, Kushimoto, Shimizu and Hamamatsu. This was about the extent of the Allied naval bombardments against Japan, as it was not possible for battleships to maneuver close enough to the Japanese homeland to fire against industrial and production centers. (It may have also been the case that the aircraft used to protect the assaulting ships could have perhaps done as much damage to the targets as the ships themselves.)
It is worth reporting on these two perhaps-forgotten (outside of the specialty area) classics in the early history of computation. The first was written by a powerhouse married team of Andrew and Kathleen (Britten) Booth—Andrew was the inventor of the magnetic drum memory and the Booth multiplication algorithm, and Kathleen was the creator of the first assembly language, for starters).
The book was a superior effort and was a survey of the state of computation via digital computer for the Post WWII-1953 era. The 17 chapters are geared mainly as an instructional--an advanced "how to", if you will, with plenty of diagrams and illustrations. After a few historical chapters, we have: the overall design of a computing system; the control; the arithmetic unit; miscellaneous operations; input-output; gates; single digit storage; miscellaneous components, storage devices. From this point on, from p136-196, the book deals primarily with programming issues: definitions of a code and discussion of its form and controls (!), pp 136-151; the techniques of coding; the use of subroutines in coding; program design; some applications of computing machinery.
Earlier in this blog I posted a magnificent illustration of the fabulous new comptometer adding/calculating machine, here. I wanted to include this unusually designed ad for the machine somewhere on the blog before I lost it (again), and so here it is:
In my experience the use of diagonal black-and-white lines like this for illustration or advertisements was really very uncommon.
"The Fingers as an Aid in Multiplication" is another wonderful find coming from a general browse in the great Scientific American (October 22, 1898, page 265). It is an interesting article, using the fingers so that the multiplication tables didn't have to be memorized by kids--I think that they absolutely should be--but the images taken out of context can also be regarded in some sense for this blog's "Found Absurdist" series. (We are told that the system was devised by "a Polish mathematician", Procopovitch--he is repeatedly referred to as "the Polish mathematician".)
See "Digital “Computers 1450-1750: Memory and Calculating on the Fingers and Hands", a post on this blog from 2008, here.
The "Proportior" (sounding somewhat like an exclamation, like Excelsior!, and looking for all the world like it should be spelled some other more appropriate way) a fabulous desktop/tabletop calculator, as seen in the Science, October 4, 1889:
Thanks to Ray Girvan for the link to a successful download of images for this!
The idea behind this extraordinary image below is the construction of an 8x8 magic square capable of describing BOTH the Knight's tour (" a sequence of moves of a knight on a chessboard such that the knight visits every square only once...if the knight ends on a square that is one knight's move from the beginning square) WITH the resulting moves forming a series of magic squares. It is the product of a Kiwi engineer named Sturmer, and appeared in the Scientific American Supplement for 1888.
Eric Weinstein says in his article "There Are No Magic Knight's Tours on the Chessboard" on Wolfram's Mathworld site says, well, such a thing is not possible. "After 61.40 days of computation, a 150-year-old unsolved problem has finally been answered. The problem in question concerns the existence of a path that could be traversed by a knight on an empty numbered 8 x 8 chessboard."
Weinstein is concise: "Not surprisingly, a knight's tour is called a magic tour if the resulting arrangement of numbers forms a magic square, and a semimagic tour if the resulting arrangement of numbers is a semimagic square. It has long been known that magic knight's tours are not possible on n x n boards for n odd. It was also known that such tours are possible for all boards of size 4k x 4k for k > 2. However, while a number of semimagic knight's tours were known on the usual 8 x 8 chessboard, including those illustrated above, it was not known if any fully magic tours existed on the 8 x 8 board."
Reckoning time from city to city before the adoption of Standard Time (1883/4) was a difficult and confusing process. Local time was local, and usually dominated by a central timepiece located in a public area, as in a church steeple or town hall. The problem is is that the foundation for this timekeeping--the zenith of the sun during the day--would be different from area to area. That's not so bad when communication over periods of days was involved, bu tit was very noticeable to train travelers who would find their home-reckoned pocket watches to be not-quite-right when moving hundreds of miles over the course of a day.
And that's where these charts come in. They were made before the institution of a standardized system for keeping time worldwide, and so the "Dresden Time" of new was actually equal to about 10:48 in Madrid or 12:02 in Vienna. In the U.S. in the 1870's there were hundreds of time zones (whittled down somewhat to 100 towards the end of that era) which made it a bit of a nightmare for maintaining railroad schedules. Stanford Fleming fixed all of that (the end of a long line of people who attempted standardized systems) in 1884, and did away with the need for these beautiful but confusing time arrangements.
On the other hand the displayed results for dealing with the pre-standardized chrono-confusions are beautiful things...
Image Source: Johnson's New Illustrated Family Atlas of the World, (1874). Source: David Rumsey Map Collection, here
(Note: we'll deal with square root of 3 at another time...)
The author of this manuscript, Charles Fisher, took a solitary pleasure in calculating the square roots of numbers from 2 to 589, not bothering to write down the 24 perfect squares to 576. (The sqrt being r2 = x for every non-negative real numberx.)From the few bits that I have checked the man seems to have done a good job back there in the 1830’s.
I cannot determine where this book was written or who Mr. Fisher was, though it is possible that he was a (Baptist) Minister from the few short textual notes that pop up here and there.
[This 140pp manuscript is being offered for sale at our blog bookstore, here.]
His work is pretty elegant.Take for example his solution (and proof) for the square root (hereafter sqrt(x)) 309,
which the calculator living under this page says is 17.578395831246947Mr. Fisher’s answer is 17 10/17 = 799/17=89401/989=309 100/989, and after some more involved arithmetic comes t the lovely proof number of
4121989960986322995025 /13339773336525317136 or
Which is getting pretty close.
The only note that Mr. Fisher makes on his calculations is for the sqrt(193), which he notes as “the hardest number to find the approximate root of any between 1 and 200. I have found it after repeated trials and have this evening wrote it in as above. March 1st, 1833. CF.”
I found these extraordinary magic squares lurking in the September 1915 issue of Himmel und Erde--seeing them was a shock to me, especially since I was expecting articles dealing with more technical and also astronomy-related issues, though treated as a history of astrology/astronomy aspect I guess that I should've have been too surprised. The author, W. Ahrens (of Rostock) had written on different aspects of the magic square in the South Pacific ("Etwas von magischen Quadraten in Sumatra und Celebes") and more extensively on the Kabalah and magic squares (in "Hebraeische Amulette mit Magischen Zahlenquadraten" for example), and in general in his Mathematische Unterhaltungen und Spiele (1901).
(An interesting example of a "Venus" magic square, with seven cells).
(This magic square, a "Moon" or "Lunar" square, has nine cells, and also has a form of a "T" world map. The names of the magic squares were adopted by Cornelius Agrippa (1486-1535) who constructed squares of 3,4,5,6,7,8 and 9 cells, naming them for the seven "planetary" astrological symbols, Saturn, Jupiter, Mars, the Sun, Venus, Mercury and the Moon. The magic square as an idea seems to have been introduced in the west by Moschopulus of Constantinople in the earlier 15th century--the magic square itself though is ancient, alive and well in India more than 1500 years before its arrival in Europe).
A magic square amulette from East India.
Another 9-cell magic square, indentifying itself with "Lunae" and "Luna".
This thinking stick comes to us via the courtesy of the Scientific American Supplement (19 August 1876, page 542), and shows a lovely Victorian non-SteamPunk answer to on-the-run calculation. It is an almost-elegant device, and seems as though it should work just fine. Its utility as a writing instrument seems a bit limited, as seems the calculator part, but the whole of it seems to be full of possibility--and a very nice piece of dedicated thinking.
[Text describing the invention below.]
Other nice examples of adding/writing found in the U.S. Patent Office via GooglePatents are seen below:
QUESTON: If great but not-popularly-known scientists could be represented as a chess piece, and that chess piece was on a game board opposite Popularly-Known-Celebrities-Not-Known-to-Scientists (and etc.), what piece would the great and dusty Robert Hooke be? And conversely, (on that opposite side), what piece would someone like, say Paris Hilton be?
I wonder about poor old Robert Hooke. He was such a tremendous thinker, a terrific rush of ideas, with revolutionary insights in many fields; he was a leading architect, a physicist, a microscopist, a chrononaut, a mathematician, an everything. He carried the Royal Society for years, carried on hundreds if not thousands of experiments, and of course was famously on the other side of a bad series of arguments with Isaac Newton. At the end of his long life, Hooke was afraid of not being remembered, of not having enough money to see
himself through hi sold age, afraid of others taking credit for his
work. He just seemed not to matter, anymore, in the last decade of his
life (and a period in which he was still doing significant work), and I
just wonder why he managed to become so semi-invisible.
He was so dedicated. I have an image of him scurrying with a friend, removing the estimable library of a patron and donor to the Society, trundling the books in wheelbarrows across a mile and then-some of bumpy London streets finding a home for these great treasures. He was an older man at this point, marching these books across parts of the city that he helped to restore after the fire, passed buildings that he helped to build and design, bumping his way through London, a great and famous scientist, saving books by the handful. [An idealized portrait of Hooke, at right.]
He was a tireless,
relentless observer and experimenter, who lost little effort in a stranded idea
and pursued interesting and problematic questions relentlessly. More than others too he chased his won glory—minor
but long and insistent—the years of which wore thin on many people in the
scientific community. But there were
many characteristics of the man that made him not quite so lovable and
endearing—not that Newton was any of those things, as he was not, but if you
are going to be a secondary luminary to a super nova you’ve got to have
something else going for you that the other man doesn’t have—sharing, helpful,
greatly generous—to get you into the long pre-dusty pages of history. Also it would’ve
helped if Hooke chose his battles with a little more aplomb and ingenuity—the
war which began in 1672 with Newton went very badly for Hooke and followed him
to the grave (and far beyond).
He just didn't "catch on", I think--at least he not for the long term. His brain teemed with ideas, but perhaps by the last decade of his long life, his tireless brain still working on innumerable bits, he just sucked the air out of a room.
He also never had his likeness recorded during his lifetime. And that is saying a lot. And I still don't know why.
Back to chess: I figure Hooke to be a Knight. I prefer Knights. He moved like a Knight. He importance was "higher" than that of a Knight, but, well, the Knight seems a good fit (and so he seems to get downgraded, in a way, even in this game). And Paris Hilton? I think she might be a queen (with a small "q")--as someone who is ultra-well-known but not for anything in particular except for the quality of being well-known.
The title of this quick post seems both irresistibly attractive and horribly repelling in an oh-g_d-is-this-what-we're-down-to dissertation for a moderately-good university. But really all this post is is a title--I stumbled upon this table looking for emigration figures to illustrate a dot-matrix map from the United States Industrial Commission (printed in 1900), volume 3, which concentrated on the statics and sociology of prison labor. So what this table shows is the effect of prisoners' labor on the price of pork and pork fat in the Chicago market for a ten year period at the end of the 19th century, and what we see is that the "free" labor in prison in this area produced cheaper prices in the fat market. There you have it. [Source: Internet Archive, here.]
Can We See More or Less than We Used To Be Able To See?
An early study of attention and perception (or “How Many Items Can it Embrace at Once?”) popped out at me while muscling my way through another year of Nature magazine for 1871. The article was by the polymatic W. Stanley Jevons ("The Power of Numerical Discrimination," in Nature volume III, 18711) who contributes an interesting and very early experimental bit on the success of the brain to correctly formulate an accurate memory when in a flash shown a number of items. (That is to say, when shown a certain group of X-number of items instantaneously and then removed, how often will the mind be able to remember the correct number upon recall--and without committing them to memory per se or counting them?) In this fascinating study Jevons records not only right/wrong answers but how "close" the remembered fit is to the original number, and in effect is a pioneering scientific effort towards understanding our abilities and limits in information processing. And as it turns out the ability to precisely recognize and remember groups of objects with success and without counting stops at about four items for the vast number of people texted. (It is another display of a famous four, including the four faces of Brahma, directions, Gospels, minute mile, playing card suits, seasons, corners of a square, virtues, color problem and of course four- letter words, to name a few.)
[Source: University of Wisconsin Digital Collections, here.]
Its important to distinguish Jevons’ experimental work on apprehension from earlier (and much earlier) philosophical
and semi-scientific work on memory formation and retention. This of course goes back as far or as deep as you want to go—taking a stab at random we’ll use Simonides who while trying to organize poetry and other data in his head came upon the idea of using Mnemonics and using associative processes in art and poetry to establish his own history of memory. (I should point out that one of the early-modern experimenters in the formation of memory was Giordano Bruno (at right) who wound up being tortured and burnt at the stake for other offense against The God while trying to formulate a truthful approach to science; evidently the memories that would be threatened by his scientific approach proved to be too much for the righteous in power, and he was removed before he could threaten corrective memory any further.)
It is interesting that many of the crimes of science punished by the Catholic Church during this period (1450-1650) were as much crimes against memory than they were crimes against the future—changing and challenging collective memory often proved fatal.
Getting back to Jevons—who was a very smart guy and who applied himself to a number of fields, not the least of which was constructing a logic machine: his experiment proved to be a springboard for a host of others, some of which didn’t do Jevons justice, misreporting his finding, misrepresenting the stuffy, and so forth. Perhaps the greatest of these was the greatest of the efforts based on his—Raymond Cattell —who for some reason stated in his very influential textbook of 1907 that humans can remember around 7 things (without counting) when the objects are flashed before their eyes. And for a hundred years this figure stuck, even though the Jevons report issued a more complex summation, and saying, anyway, that the number was around 10.
And what bothered me a bit with the Jevons experiment is what people remembered when shown the objects (beans)—would his results have varied if subjects were asked how many were shiny or odd-colored or deformed or whatever rather than just a simple number, the results could’ve been more interesting. (I don’t doubt that these issues have been taken up in the 20th century but haven’t looked). Sometimes people are just looking in the wrong places—for example operant psychology labs tested rats via visual stimuli until it was discovered that rats were olfactory geniuses and that humans were using them wrong all along.
It would be interesting to know what the history is of human capacity for image formation. Considering the growth of distractions and the enormous amount of true and trash stimuli—visual bombardment from television, outdoor advertisements, the sheer amount of growth of human construction and interaction—have humans enhanced this spatial/memory information processing capacity? Consider the growth of (just) eye movements over the last few hundred years, with the visual sense being subjected (for all classes of people) to enormously and fractally-expanded print sources, television, digital communication and so on—has this expanded this neural capacity? Has "space invaders" aided bean counting?
I don’t know, though I do wonder (literally) what the effect exponentially-growing mass input of (mostly junk) data might be doing to our noggins. Maybe the effects lean more towards dissolving privacy and reflective time—when does a person think if interruptive stuff is coming into your head at all points of the day, with the brain trying to interpret incomplete and ambiguous strings of sensory inputs?
Seems scary to me. Maybe memory is affected, maybe it makes it go away, shriveled because recollection is being eliminated. Or demented like the wonderful Yossarian (his first name is John, btw) from Joe Heller’s beautiful Catch-22 who develops for himself a condition in which he remembers everything twice (whatever that means).
It would be interesting to see a war of societies in which the sides were a culture that remember
nothing versus a culture that remembered everything. The unspeakably lovely Jorge Borges wrote something touching on this in "Fumes the Memorist," in which the humble narrator is capable of forgetting nothing, being able to recall explicitly everything within eyesight, perfectly—the problem is though that it takes a day to remember the events of another day. What would happen in such a culture where everyone forgot nothing?
And I’ve just been dealing here with visual memory, really—and as Proust makes plainly clear (and Borges and other prove), vision isn’t everything.