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
I was very surprised to come across this illustration while browsing the (3 April) 1870 volume of Punch, or the London Charivari .
I cannot think of any particular peculiar or unusual edition of Euclid that was published at about this time to demand such an unusual illustration. (The only newish edition that comes into any possible play here is Oliver Byrne's semi-insane First Six Books of Euclid, published by the Chiswick Press in 1849 and one of the most unusual and beautiful books of any sort printed in the 19th century--but then again that was 21 years before this volume of Punch.) And by "unusual" what I really mean to say is "highly unexpected" , as this all-angular depiction of a woman appears for all the world to be a Cubist- or Expressionist-like image, predating those movements by four decades.
But the Angular Woman just seems to be happenstance, a happy precursor to a revolution-in-the-making, an accident forty+ years too early. She is extraordinary--and for some reason she is smoking a cigarette.
[Below--an illustration from Oliver Byrne, illustrating the propositions of Euclid via the use of color rather than words, a beautiful but non-functioning work.]
An interesting appearance of lines in art that seemingly crosses several disciplines and chronological development is Jean-Baptiste Camille Corot's The Dreamer and the Large Trees (1874). It is vivid artwork full of motion, expressing itself in an impressionistic sense that seems almost more abstract expressionist than mid-early Impressionist. (As an Impressionistic work it would be well into the second decade of the movement; if Abstract Expressionist, it is three decades early.) It is a brusque, almost savage portrayal of a somber person in a deep wood, though the lines that is is composed of say anything but that.
The print was made via the cliche verre process1--Corot used a semi-photographic medium in which there was no camera, as it was the artist who drew the negative, who created the image from nature without a lens and without a camera body (thus eliminating lensless photography like pinhole), drawing directly on the medium (which in this case is glass, insinuated by the cliche) and then exposed/printed onto a photo-sensitive paper (the verre). The artist is in a sense making a photograph directly of the image in their mind, recording it on the medium, and then printing it from there.
Of course there are other important lines in the history of art: Vincent Van Gogh Starry Night (1889), Giacomo Balla, Street Light (1909), Umberto Boccioni States of Mind (1911), Michael Larionov's Rayonist Painting (1913), Robert Delaunay Windows, (1912), Roberto Crippa (1921-1972), Jackson Pollock (1912-1956, particularly Number 1, 1948), and any numbers of works by Barnet Newman. And of course the Cubists: Braque, Gris, Picasso, and the rest; the Constructivists like Malevich, and on and on into the sunset. But the reason I've chosen Corot is because of the unexpected, wildish impressionist qualities that seem so far out of place, even with the movement.
1. Cliche Verre was quite popular with French artists of this period, used by Theodore Rousseau, Charles Daubigny, Charles Jacques, Francois Millet and others. The process itself appeared very early on in the history of photography, being described in Robert Hunt's technical manual on artistic photography as early as 1841, two years after photography's beginning.
I was struck by the mosaic possibilities of the image (below) found in Thomas Baldwin's Airopaidia (printed in 1786) and so made it into one. But what the engraving is,m really, is a view from a balloon, looking straight down.
We're looking straight down, through the clouds, seeing two towns (at bottom-left and top-center)--why the rivers are red, I don't know.
There are other posts on this blog on looking straight down, which is an attractive subject--to me, at least. First-hand images of looking straight down fro a balloon are rare things, even through the early 19th century, and offer a prospective seldom seen in human history.
Another view from this work attempts to show some depth:
Here's another view of that same image from the Baldwin experience, reprinted around 1810, and left in black-and-white:"
Halton Tuner makes these observations on Baldwin's flight in his iconic Astra Castra: Experiments and adventures in the atmosphere 1(published in 1864 in London):
JF Ptak Science Books Post 1578 [Part of this blog's History of Lines series}
The post dedicated to Patti Digh, brilliant writer and birthday girl, who wrote a lovely, image-filled essay on Desire Lines back in December 2005 on her award-winning blog, 37days. I think the idea of Desire Lines is one of her favorites, and so I tried to imagine my own in her honor, a small Festschrift for the birthday girl. Happy Birthday, P.D.!
William Blake had a hard time of things, what with being thought of in unflattering terms of crazy vs. insane by many people rather than, say, being though of as "creative". He led a good and relatively long life (1757-1827), and by his artistic and poetic creations inspired generations of other creatives, though he was very little recognized during his lifetime. He was a seeker, and was somehow able to do his art and printmaking and poetry without a substantial income, living mostly on adequate income and patrons, slowly advancing to semi-poverty as he aged , but dying without a debt to his name.
The "line" that I site above to his unusual work, The Gates of Paradise--not the Baptistery doors by Ghiberti--, was actually a ladder and a collection of lines, but with the application of perspective becomes one combined line quicker and longer than it could ever be a ladder. Blake's character, as with Blake himself, wants whatever it is that he can have, conceivable or not; and som, if he wants the Moon, he just goes to get it. This version of The Gates of Paradise, which is largely a story of pictures and a few words as legend, was intended for children, perhaps--or at least that's what the title says. In any event, its an interesting message to send to children whether it was actually intended for children of the chronological age, or not. The "I Want, I Want" legend really wasn't necessary, as the image stands on its own.
Blake liked to tell a story with lines like this, as we see in this famous image of Newton:
Blake was an impossible anti-Newtonian--at least in my limited reading of the man--making a career of being a spectacular and beautiful anti-rationalist, a weaver of smoke, playing with and distorting images like a theramin player of words, using language to produce dichotomies in even the most standard of sensate ideas. Blake was the poster child for thing anti-tech, an anti-scientist out to save the world from its scientific self, the rationalist world set to destroy imagination, the “Antichrist science” hell bent on destroying the soul of art and religion.
“Art is the tree of life; Science is the tree of death” wrote Blake, and so he chose the “Athesistic” Sir Isaac to stand for the beast, depicting him in art as a naked geometer intent on subjugating the world with a compass and a keen brain, reducing glory to quantification, the work of Satan.. For most of my life I thought that this image by Blake was celebrating Newton—I knew little of the poet/artist/poet, and thought the painting a reverence. When I understood Blake a little, I saw that the image was intended as a mockery of Newton and the idea of science—this was an unusual sensation, because absent the unspoken intention of the artist, you could still take the subject matter of the artwork two ways.
And of course the Creator:
God is presented as the Great Geometer, the creative power of the universe issuing forth with compass/dividers, was perhaps a kind of Greek conception of the rule of the universe and its interaction with all things on Earth.
But it is interesting that in the end, Blake displays the sublime reasoning powers of Heaven and Earth, in the forms of God and Newton, both with desire lines. I think he enjoyed doing that.
The history of lines is full and rich with symbols, some of which have absolutely nothing to do with the extension of trust and belief and hope and fear--unless you're a young student studying math or chemistry or physics. One symbol in the maths that seems to have no exact age except to say that it is semi-ancient is the addition sign. (It will be interesting in this series on the history of lines to address the origins of other symbols like the sign for pi, division. multiplication, percent, inequality, equality and so on.)
I say "semi-ancient" because the symbol for addition is a hieratic form of the Egyptian hieroglyphic, looking like a capital "A" in a way, without the horizontal crossbar. The earliest appearance of a symbol for addition in Europe was in the 13th century, with the letter "p", appearing in various forms, as well as the word "plus", "used in connection with the Rule of False Position"1. The concept also appears as the word itself, as "et", or "and", which just so happens to closely resemble the symbol that the concept would become a few centuries later. The earliest appearance of the symbol we would recognize instantly today as an addition sign came in the 1489 book by Wideman, the Behenunde und kuepsche Rechnung (seen above in detail and in full, from the 1532 edition of the work), while the first time the "+" appears in an algebraic equation for the first time 25 years later, in a work by Vander Hoecke.
It is interesting to think of the life of these symbols before they became themselves.
I am not certain of this, but it seems that the first "+" printed in the United States did not occur until the 20th edition of James Hodder's2Arithmetic3 was printed in Boston in 1719, and this at the press of James Franklin (1697-1735), the fourth child of ten in the Franklin family that included Benjamin (1706-1790). So it is entirely possible that 13-year-old Ben helped his older brother print the first addition sign in the British Colonies.
1. D.E. Smith, The History of Mathematics, volume II, p. 397
2. Hodder in 1672 wrote "note that a + (plus) sign doth signifie Addition, and two lines thus = Equality, or Equation, but a X thus, Multiplication," no other symbols being used." (Smith p395)
JF Ptak Science Books Quick Post (Edited-and-added version of Post 1019)
“My car gets forty rods to the hogshead, and that's the way I likes it!"--Grandpa (Abe) Simpson, from The Simpsons (That's about 500 gallons to the mile.)
A line, a connection of two points in space, is about as basic an imaginary thing as we have here on earth. Humans have used these creations to build all sorts of straight things, from roads to building to ships to literature to mathematics and on and on. What doesn't happen very often, at least not in Western art in the last 500 years or so, is for people to be represented in art in a straight line that is not a processional (including military, religious, political venues), or that is not along a bench next to a table, or not supported by another artificial structure like a fortress wall (to give their waiting or standing a form to accommodate). That weakens the line field considerably--after all, what else is there to line up for? They're not queuing up for a sale at Gimbels, and they're not waiting patiently for a place on the bus. There's just not that much to form a line for, evidently.
There is, on the other hand, this (above and below), what I take to be rare representation of my odd requirements: a delightful woodcut from Jacob Koebel's 1522 Von Ursprung der Teilung, Mass und Messung dess Ertrichs, der Ecker, Wyngarten, Krautgarten und anderer Velder..., an early surveying handbook (probably the first ever printed in Germany) that could be used to measure and set out (as stated in its title) herb gardens, vineyards, farms and the like.
I'm not 100% sure of this, but I think what is going oin in this image is the measruing of a rod (or "rute" in German), which is about 5.5 meters or 16 feet; and what we have in the picture is 16 men being positioned over a measuring device and beign overseen by the powers that be, at rear. On the other hand, maybe not: the English rod was 16.5 feet, while the rod measurement for Saxony, Rhineland, Bavaria and Baden were different as well; Sweden also came in at 16 feet to the rod. The other big question was: how long was a "foot"? Since that measure also chnaged (varing between 23.51 cm in Wesel and 40.83 cm in Trier and 31.387 cm up north in the Rhineland) the measurement of anything with variable units of measure seems to have been problematic, or at least in a post-facto measure. [The whole issue of "absolute" units of measurement is another post for another time (and a much bigger and moire compelx story).] For right now I'm content to have found this pretty image, which in the end was probably the work of the author Koebel (1470-1533), who seems to have been a jack-of-all-trades; and while he was concerned with property and measurement, he also showed his flair with charm, as this group of men atest.
This woodcut cosmological illustration from a 1526 Bible is a subtle and very late printed rendition of a great and classic Medieval idea. At the center(or thereabouts) of the globe of the Earth there is a seeming confluence of two great rivers, but what it reminds me more of is the T-O map, the orbis terrarum, the direct descendant of the
Greco-Roman map making. The T-O map makes distant and deep calls into the past, finding a home in Macrobius (around 400 CE) and Orosius (5th century )and more famously with Isidore of Seville (ca. 600), a work known to most folks today because of its appearance in Seville's Etymologarum of 1472, which is also the first map printed in Europe (pictured below). (Why is took almost 20 years after Gutenberg to print a map is mysterious to me.)
Generally Jerusalem would appear at the center of this sort of map, which would have appealed to the necessary people that the publication needed to have the appeal of. The Mediterranean would separate Europe and Africa from Asia, while all of the land masses (the stuff outside of the "T" structure" were surrounded by the great "O", the ocean(s).
Sixteen years later a remarkable map of the world would appear in Ptolemy's Geographia, an Ulm-printed masterpiece that appeared in 1486.
But I think that the crossed lines from the Luther Bible of 1526 was really just a suggestion of the past, not meaning to lean on the Medieval world at all. Still, though there they are.
I think that if I had a sense for design and some artistic talent that I could perhaps make something interesting out of bits and pieces of the details of a hundred famous lines. Or two hundred. Unfortunately, I don't possess those talents, so I'll just have to write about it as though it has been done, already. If we could whisk ourselves away 50 years into the past to the great world of early broadcast television, back into the days of glorious black and white, it would be interesting to present the details singly and first on a game show like the lovable "What's My Line" show. (Another guest, another one of the hundred or two that could appear, can be seen below*, though I think this one is a dead giveaway.)
Today's line section from this blog's History of Lines series comes to us from William Harvey, being an illustration in his epochal Exercitatio anatomica de motu cordis et sanguinis in animalibus (orOn the Movement of the Heart and Blood in Animals). It was in this book that Harvey published his experimental results on how blood moved through its course in the body, showing that the 1400-year-old Galenic idea concerning the movement of blood was all wrong.
Harvey had conducted experiments via the scientific method--and was among the earliest to do so--and established early on, by 1615 or thereabouts, that the Galen theory regarding the movement of the blood was incorrect. He found that contrary to long-established belief the liver did not convert food into blood, and that the lungs did not push the blood through the body, and that blood was not continuously generated. Why wait until 1628 to publish his results? I suspect that he was not looking forward to the problem and notoriety of publishing results that went against the medical grain--actually some of which were the exact opposite of the accepted practice--which in fact was the case for decades after the first edition appeared. But Harvey presented his results in his short book in a concise way, explaining how it was that the heart and arterial systems functioned, and then in a second section of the work displayed how the blood was circulated rather than produced. (He was able to establish that if Galen's theory was correct that the liver would have to produce 540 pounds of blood every day--a simple impossibility.)
Harvey's work had a revolutionary effect on the study of physiology and medicine at the same sort of level as Copernicus or the use of the telescope by Galileo--I think that there is little doubt in that. Harvey was able to produce his results through experimentation and without the benefit of the microscope, which would have helped him enormously had he been able to identify capillaries--something that would have to wait for Marcello Malpighi and his publication in 1673, sixteen years after Harvey's death.
The detail from the big image in Copernicus' De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres), 1543.
This lovely river/tree appeared as a woodcut in Franciscus Maria Pecchius' Tractatus de Aquaeductus, which was printed in 1670-1673. It actually is nothing of the sort, as it depicts the construction of a dam in a busy river and forms part of a four volume work on the building of aqueducts--ranging from the selection of sites, to financial considerations and of course engineering and materials studies. Pecchius' work was the standard of its day, and it also was the cornerstone work on the (Roman) law of such things, presenting a jurisprudence that stretched back a thousand years.
But the way that the flow of the river is represented makes the image look very much like a tree, in a lovely, naive way. It might seem a horrible sleight to a work of this importance, but, well, sop it goes--the images, removed from their appropriate context, take on a life of their own...
This picture tells as much about the making lines--railroads pushing their way towards one another, the Union Pacific and the Central Pacific, pushing on towards one another to complete a rail line that connected the American coasts--as it does in covering them up. The photograph is of a Union Pacific supervisor named Samuel Reed, who was inspecting the rail bed--in 1868/9 it was not uncommon for one team to clear the land and lay down the ties miles ahead of the track layers. Miles of bits of wood, waiting for their iron.
But most roads, or at least most early roads, were in their places for a reason, and generally that reason was because it was a good way for getting from Point A to Point B. This photograph, along the way of the Old Platte Valley route, seems to be a mid-way point between the old and the new, or between the old and the old, lines of communication and lines of travel. These timbers are laid down on top of the old immigration route from the east to California and Oregon, which in turn were laid on top of the trails of fur traders, which were on top of those of Indians, which were on top of those of the buffalo herds, and so on, all the way down.
I'm about to start a series on this blog on a great constituent part of the concerns here of two other series: the History of Lines. This new bit will sit along next to the History of Dots and the History of Holes, and will begin to mention just some of those things that will bridge the gap among the three categories.
A lot of that--the History of Lines business--has to do with the interpretation of things on paper: heart rate, "brain waves", the motion of a bumble bee, navigation, and of course, words. (The great Kickapoo tracker Famous Shoes in Larry McMurtry's Streets of Laredo, one of the Lonesome Dove tetralogy, found that the one thing he couldn't track in this world were the marks on the pages of a book.)
The business of lines is like that of dots and circles, together describing much of the physical world. For "lines" alone there's just so much, an entire encyclopedia waiting to be written. There are unique lines, such as we see below from The Scientific American for 28 March 1885, in a line of workers for the Edison Electric Company holding an (electric) torchlight parade, the men attached by electrical wires that were in turn attached to the electric light bulbs on their helmets.
There are lines of succession, code and graphs; Battle Lines, the Maginot Line; fishing lines, units of poetry, lines of a play; there's waiting on lines, breaking the line, party lines; lines of fortifications, the lines on which music is written, and the foundations of geometry, and much more.
There were lines that occupied only a minute percentage of the landscape in which they were found, but were among its major controlling influences--such was the case in controlling the American West, except that one of the greatest of these lines, once completed and seemingly impenetrable, was briefly destroyed by its builders.
The story of the West getting filled up in the 1870s is a story of lines—railroad track, telegraph wires, barbed wire fences, and words on a page; big changes from disparate but related areas in technology and legislation, but when you looked at them from a distance and in the proper perspective, they all looked exactly the same.
The greatest of these lines may have been the invention of barbed wire in 1873, with Joseph Glidden, Jacob Haish and Isaac Elwood all managing to independently come upon the idea at about the same time. What barbed wire brought to the West was control and settlement. Prior to barbed wire there was open range grazing of cattle and extensive cattle drives, mainly because there was no fencing. There were also few farms due to this sort of grazing—the only thing a farm was here was in the way, and there was no recourse for the farmer to protect his
lands from a grazing herd. There was no fencing because there were no materials for the fence. Fencing was made almost entirely with lumber and stone, and on the treeless plains and the vast non-New England tracts of land, it was simply an impossible task. The introduction of barbed wire changed all of this very quickly, with thousands of miles of new fencing strung in the 1870’s alone. Fencing meant control, restriction of the use of land, of access to water, and to a way of life. It also meant that the farmer was now free to make a claim at a way of life on the plains, beginning a torrent of settlement and farms.
Another big line element of settlement were the texts (lines-on-paper) of three major acts of legislation which, over a period of just sixteen years, were responsible for moving more people than just about anything else in American history. The first of these was the Homestead Act of 1862. This was a revolutionary concept, legislated in 1358 words, effectively turning over 270 million acres, or about 8 percent of the country, of public lands to private citizens (“actual settlers of the public domain”). A claim could be made for a farm of 160 acres, for free, provided a structure was built on the land and it was maintained for five years. One could buy the parcel outright for $1.25 an acre as well. Next was the Desert Land Act of 1877 which opened drier lands, selling 640 acres at $1.25 an acre with three years to pay, so long as the land was irrigated by the end of the three years. Land that was deemed "unfit for farming" was sold to those who might want to "timber and stone" (logging and mining) upon the land with the third major piece of legislation, the Timber and Land Act of 1878. The act was used by speculators who were able to get great expanses declared "unfit for farming" allowing them to increase their land holdings at minimal expense. The Homestead Act alone accounted for the creation of almost 400,000 farms in the West by 1890. Farms meant parceling out land, "settling" it, having people on it, waiting when they weren't working.
Settlement was dramatically increased by the written and published promises and speculations of mineral wealth—not necessarily just by the introduction of miners, but by securing the lands from and removing its Indian owners. The Custer expedition into the Black Hills in 1873, for example, reported some hope for finding gold in the sacred mountains of the Sioux. Thousands of miners responded to possibility of wealth, and Custer was again dispatched to secure safety for them in the restricted lands. This in turn lead to more settlers and coincidentally to the debacle of the Little Big Horn, which was the beginning of the end of the Siouian control over vast amounts of land. From prospectors to protection to conflict, ultimately making land more available for more people.
The spread of the railroads was also an enormous settlement factor, with the number of miles of track being laid in Texas and the Great Plains doubling in just 5 years. Not only could you get West more easily, and quickly, and with less pain and suffering, but you could also be much more easily re-supplied.
Telegraph wires tripled, making it easier to control events: and this means from being able to respond to Indian attacks more quickly to ordering boxes of nails, or beer, or shipments of newly-invented canned food.
One of the greatest and most infamous of these lines-controlling-the-West concept were the pieces of legislation and agreements and other legal and binding documents, between the U.S. government and every Indian tribe in the U.S. Promises were made to the Indians and of course not one of these treaties were ever actually realized. It was these written lines that even the greatest of Indian intentions could not penetrate, and that in the end, after everything was said and done and written, after hundreds of treaties, not one was ever followed.
And at the end of tying the first metal ribbon across the country, the meeting of the Central Pacific and the Union Pacific railroads at Promontory Point (Utah) in 1869, after the locomotives Jupiter and No. 119 touched cowcatchers, after the driving of the golden spike, after the completion of the massive effort to complete the railroad line, some men of the 21 U.S. Infantry (and others) hammered away at the rail to chip away some souvenir pieces of the occasion. So, the moment the great undertaking was finished, it was put out of commission, possibly by a coronet player from the regimental band, or whomever. Of course the line was only very briefly pu tout of service, and the damaged rails quickly replaced, but the folks celebrating the completion of the uniting of the rail line were the only ones who were really able to also prevent its completion.
Of course in the end all of the lines applied and enabling the closing of the West were personified by smaller and more precise lines: maps.
The full text of the "Millions of Acres" (seen above) broadside is as follows: