Ptak Science Books

History of Lines--Big Lines, June 1944

JF Ptak Science Books   Quick Post 

[Source:  the Library of Congress, here.]

The idea of being on the receiving end of these lines on 6 June 1944 is terrifying.  General Rommel pretty much figured out what was going to happen, and sort of when it was going to happen, but he was kept out of the strategy loop even though he was in charge of the German defences here, unable to convince Hitler to move men and machines southward to meet the invasion where he thought it was going to come rather than strengthen the position of defence in a place where he knew the invasion wasn't coming, which was Pas de Calais. The pull of war by this time had destroyed the Luftwaffe, and German high command had been destroyed by Hitler--or at least communications and straegy within the command system of the German army was very highly compromised.  In any event, once the invasion had begun, there was not much hope for the Germans--it had been a complete surprise, with the huge efforts of misdirection playing themselves out beautifully. So beautifully, as a matter of fact, that once the invasion was well underway it was still a matter of no small debate as to where the "real" invasion would take place.  Even after the airborne divisions began landing some hours before the assault began, it was only the elderly and problematic General von Rundstedt who reacted appropriately, believing that the airborne assault was far too large to be a feint, and ordered two reserve panzer divisions to Normandy.  the amount of men and materiel moving onto Normandy was gigantic, impossible, overwelming, as some part of this map makes clear. 

The Mathematical Garden--Alexander Pope and Found Geometries

JF Ptak Science Books

(Revisiting an earlier post from 2008 with a added details).

While sitting at the edge of a stream in a flowing dress and shading herself with a yellow parasol, my wife and  the jewel in the crown, the brilliant Patti Digh, wrote a superb essay on following the paths less marked. (Maybe I'm making up the parasol bit. And the stream. And flowing dress.) I've always been a happy observer of found geometries, and her essay heightened my awareness to them, along with the conscious efforts that we may daily make to enforce these lines or follow a new, multi-dimensional geometric path. 

So when I stumbled across this map of Alexander Pope's garden and noticed the odd paths  winding their way through it, and  how much in contrast this was to the very sniffy upper  crust English garden of the 18th century, Patti's essay  lit instantly to mind—and also because in addition to being a geometer of emotion and thought she was in a past life a U VA English Master. 

Pope's garden was an irregular path in an irregular garden, that garden being his leased property at Twickenham, where he came to live in 1717, along with his mother and his boyhood nurse, Mary Beach, and his dog Bounce. 

Pope's garden was an irregular path in an irregular garden, that garden being his leased property at Twickenham, where he came to live in 1717, along with his mother and his boyhood nurse, Mary Beach, and his dog Bounce.  (Actually that would be a series of dogs as he named them all "Bounce".)  Pope was a poet and satirist and
critic and general taste-maker-the social influence extending even to garden-making, as his was famous even during his lifetime, and not for the reasons that most English gardens were famous.

His was not the planned regularity of the gentility (and far of course  from the suffocating, critically flawed gardens at places like Versailles,  "Is there anything more shocking than the regularity of a planned  garden?" asks Batty Langley in his New Principles of the Gardening… 1728), and were removed from the "normal", more articulated garden.  I've never really understood the formal garden, especially as it relates  to the ancient analogies of gardens and paradise-the Garden of Eden, Pliny's Garden of Venus, Lucretius' Earthly Paradise, seem as though  they might be some sort of paradisical thing (though we won’t address  Bosch’s Garden of Earthly Delights) , but the formal gardens and its  paradise relationship seems odd, what with the removal of nature's "chaos" and all, unless that was indeed the Master Plan.

But the mathematical garden was a desirous thing—still is—and none  other than Christopher Wren wrote that it was “naturally more beautiful than any irregular figure” (1750).  There were some critics of the math garden, like Mr. Langley, but most garden  designers wrote and argued in favor of it, coming to the similar  conclusion of John Dennis, in that the Universe, being “regular in all its parts”  would dictate that its beauty be found as regular  in other things too,  “and it  is that exact regularity that [the mathematical garden] owes its admirable beauty” (1704). 
Pope didn't seem to address (in print) the garden idea formally except for a few places--  Pope praised 'the amiable simplicity of unadorned Nature' in a famous essay, published  in The Guardian in 1713, and then again in his message to Burlinton in 1731.

The plan of Pope’s garden was somewhat irregular, but to me the  most appealing aspect was  the irregularity of the paths that curled and snaked their way through the garden. 
And particularly,  what about the lower part  of the path along the bottom of J. Serle’s 1725 engraving?  What was that path in Pope's garden  leading to, or from?  Was there a particularly nice tree there, a  favorite spot, a cool shade, an odd bit of sunshine at sundown?  Or was this  wall-clinging path just the workman's route? 

Perhaps these weren’t Pope's principal desire lines in the garden—in fact, the garden desire lines  weren’t the garden at all— they might’ve been under it.  Pope’s famous grotto at Twickenham  may be better known than his garden-it certainly sounds  much more interesting. Followed his  own desire line, underground, in his famous grotto, which he began to build shortly after arriving at  Twickenham, and which was still under construction at the time of his death. 

The unseen desire lines of  Alexander Pope seem more fitting to me, more poetic, what with  Pope needing to dig out the earth in order to find what  he was looking for, rather than a more  simple wandering around his fine, rustic garden. 

Have a look at the materials house in the grotto/cabinet of curiosity here, along with a  commendable plan of the grotto itself.

Exercise in Irony: the Usually-Invisible Chinese Rail Worker and the Highly Visible Photographer, 1869

JF Ptak Science Books   Post 1903   Part of the series on the History of Blank, Empty and Missing Things:  Chinese Rail Workers, 1869. 

One thing that you seldom see so juxtaposed in the photographic history of the American West are the people who were so important to it placed in proximity to those who were no well disposed to recording their existence. 

For example:  this image by J.B. Silvis, "China Section Gang Promontory", a photograph published as a stereocard between  1869 and 1870, shows a small group of Chinese workers setting two rails in Utah--they are the ubiquitously missing elements in historical images of transcontinental railroad construction. There were many thousands of these workers who were set to notoriously difficult tasks in bad situations and under time constraints with little liberty or pay (and not well-afforded much protection under the law), and in the history of documenting the expansion of the railroad across the West these workers are very seldom seen.

They are set incongruously in front of a photography car that so often saw through or around them.   The  car was labeled  "U.P.R.R. Photograph J.B. Silvis Stereoscopic & Landscape Views of Notable Points on line of Pacific R.R. Always on Hand", and I found it tempting to try to see in the photograph that it was made solely for the photographer's advertisement, but the central placement of the workers makes a good argument against this.  On the other hand, when you look at some of the other work of Silvis documenting his railway car (see here), there are a number of group images where he gathers cowboys or Indians  or makes a photo with his car in an unusual place, he is definitely using those people and locales to establish the idea of remoteness and wildness of the places in which he was working. It seems to me that in the end, he was using the Chinese laborers as a piece of his advertising ensemble more than documenting them. Again, this is very speculative.

It is a very unusual image which I think is knee-deep in irony. 

I should also like to point out that most of the workers have taken care to sew  large leather patches on their breeches--that to help their thighs when pulling that heavy metal lever across their bodies while setting and moving track. 

[All images via Denver Public Library, here.]

Vernacular Found-Polygonism 2: Walker Evans on the Roof

JF Ptak Science Books  Quick Post

How many polygons can you find? 

"Walker Evans climbed to the roof of the Fisk Building on Central Park South to  photograph the web of steel struts and electric signs that were rapidly filling the skies over Manhattan. The electric signs in this photograph alternately  flashed the company's name and the names of its two principal products. As there  were approximately a hundred million wheels rolling over America's roads in  1928, the sale of tires quickly overtook that of rubber galoshes. The image  expresses Evans' conviction that modern art could be timeless yet topical when  perfectly wrought of vernacular materials."--Metropolitan Museum of Art

This is one in a series of posts made on found geometries--here are a few others:

Found Alphabets and Geometry in Stone.(here)

Magritte-Like Disorienting Geometry in Found-Art Urban Design, 1925 (here)

Sierpinski Triangles & the Empire State Building (here)

 

Images of Shadows in Storytelling

JF Ptak Science Books   Post 1836

'There is seldom in shadow a mystery less hidden"--Ombra Nichts Schatten, The Non-Mystery of the Shadow, London, 1842

Shadows have long played havoc in the imagination, for good and for evil, for elucidation and of mystery--they have hidden nothing and everything, and displayed as little as possible and as much as can be imagined. A simple shadow in a hole had proved the circumference of the Earth twenty centuries ago, and before that the Earth's shadow on the face of the Moon showed us to be a sphere; the shadow allowed us to measure the heights of mountains on the Moon before we could do so (accurately) on Earth; we measure shadows in X-rays, and follow the trails of subatomic particles, and on and on.  Shadows are particularly interesting in story telling, whether they be suggested  aurally or in text, or of course in illustration: 

Chalres H. Bennet, Shadow and Substance, London 1860.

A superior example of shadow-art is seen in Indonesian shadow puppet theatre, "Wayang Kulit", where the shadows of Javanese-Indonesian characters are projected onto a cloth screen by a strong light from behind.

Audiences were bathed in direct and brilliant light while being swamped in shadow in the early 19th century as part of an early form of non-cinema cinema, as we see here in the frontispiece from Robertson’s Mémoires récréatifs, which depicts a phantasmagoria of lantern projections:

 

And more forthright illusions as seen in this engraving showing the spectre “Dr. Pepper’s Ghost,” from Theodor Eckardt, Die Physik in Bildern Eßlingen, 1881:

 

The shadow may have been invented in cinema by the German Expressionists, with  Friedrich Wilhelm Murnau's Nosferatu (1919) as a shining example:

And of course the shadow is used with great effect in the  very black-and-white and no-gray-tones Film Noir world, particularly in the hands of a master like Mr. Welles in films like The Third Man:

And in Fritz Lang's diabolically-bad M, earlier, in 1931 (featuring an impossible shadow in the movie still below):

 

Shadow has been used to given questionable dimensionality in addition to giving perspective to dimensions that we are familiar with:

 

 

And the artificial shadow made for the geographical clock dial to tell the story of passing time:

And also for shadow puzzle toys:

 

And on and on, deep into the night...

 

An Episode in the History of Anticipation: Death at Archimedes' Door

JF Ptak Science Books   Post 1665

Earlier in this blog there appeared an entry on the death of Archimedes--actually, it was a piece on an image depicting the killing of the great mathematician.  It is a pretty gruesome affair, even by the very early 18th century standards under which the engraving was made--gruesome still by today's standards, what with the man's head being cleaved laterally in two by the summoned Roman Centurion. I'm not an historian of these images of Archimedes, but I can say that for whatever I am, I have not seen anything quite so graphic dealing with the man's death.

The usual images of Archimedes coming to his end show him working a problem in his dust/sand/earth "chalkboard", absorbed to such an extent in his thinking that he doesn't hear the chaos outside his rooms, and doesn't sense the approach of the soldier who finds Archimedes unresponsive to his calls and therefore a threat, and so kills him.

[Image source:  Titus Livius, Romanae historiae principia, libri omnes.  Printed in Frankfurt by Feyerabend, 1578.]

Looking at this image (above) brought to mind another in the history of anticipation--not knock knock knocking on Heaven's door, but the opposite, and the opposite of that, the opposite of  knocking on Death's door, or at Death's door:  Death knocking at our door. 

The title of this emblem--Cunctos mors una manet/death is all that remains--is meant to remind us

of our common foe.  It is the work of  one of the great engravers of his time, Otto van Veen (teacher of Rubens),  and appears (along with next image and 100 others) in his Q. Horati Flacci emblemata.  Imaginibus in acs incisis notisque illustrata, printed in Amsterdam in 1607 by H. Verduss.

--All images and most translations courtesy of the splendid work at The Emblem Project/Utrecht, here.--

Part of the legend (which appeared in four languages) of the image leaves us with the following reminders, choice bits on the folly of forgetting our common end:

La terre embrasse tout comme mere commune --Mother Earth embraces us all

Moritur sutor eodem modo ac Rex.--The King died the same as the shoemaker

Death is the thing that sucks the rivers of lives, "Del rico al pobre, del soldado al Papa", From rich to poor, soldier of the Pope.

and so in image and word telling us that death will seek us out, whether king or shoemaker, rich or poor--and that in the coming end the Earth will take us all.  Archimedes didn't hear that one coming; nor did he care, I think. 

THis last image brings to mind Archimedes' work in the dust, though the intent of teh emblem ("Estote prudentes" //Be ye therefore wise // Be Cautious) wouold have been completely lost on him.

The legend translates (Thanks to the Emblem Project for this):

When the serpent sees that it is going to be attacked with, Lethal wound, it protects its head with artful care. Here lie the dwellings of the soul, the sanctuary of the truth. Hence comes life that is to be hoped for by every body.

Surely Archimedes could relate to his lines and the expressions of his thought as the dwellings of his soul (if he actually believed in a soul), though I guess you could say that the artful deception of the serpent's head finally wound up killing him via the Roman soldier.

Letali serpens cùm se videt esse petendum
Vulnere, sollicita contegit arte caput.
Hîc animæ sedes positæ, verique recessus: (here placed the seat of the soul, in artful covering...)
Hinc spiranda omni corpore vita venit

In any case I was drawn to the similarities of these two events, and the bit of anticipation that seems common between them. 

History of Lines: Clouds

 JF Ptak Science Books  Post 1629  (On Clouds and Not-Clouds, Part I)

"...and they drew all manner if things--everything that begins with an M---'

    'Why with an M?' said Alice

   'Why not?', said the March Hare." --Lewis Carroll,  from "A Mad Tea Party", in Alice's Adventures in   Wonderland.

Why not, indeed?  I've long had an interest in clouds, and since this blog is ostensibly on the surfacing or definition of Cloud Bones, I though to spend a little time on the origins of the depictions of printed clouds in art. Not being an expert by any means on the history of art, it just seems to me that after long exposure clouds are not well-represented in woodcuts, wood engravings and other early engravings, or at least not so well depicted as their landsmen in paintings.  There seems to be no shortage of effort to reveal gorgeous clouds  through the early Renaissance--but the doesn't seem to apply very often to their representation in prints.

And that of course is when the detail of the sky is depicted at all. It seems that more often than not, in woodcuts printed from say 1460 through 1550, that the sky is left blank, like this image from Ovid (Accipe Studiose Lector P. Ouidij Metamorphosin...printed in Venice in 1509:

"You could not see a cloud, because
No cloud was in the sky:
No birds were flying overhead --
There were no birds to fly".--Lewis Carroll, Through the Looking Glass. 

I could go on with many examples of the blank sky--the white, blank, settled nothingness--but exhibiting variations of nothing at this point isn't necessary.  But illustrating clouds is.

And for the most part, clouds don't look very much like themselves in prints, not really, not for more than a hundred years.  For example, Martin Schoengauer's spectacular  The Temptation of St. Anthony, which was printed in 1470/5, has a beautiful, fluid circularity to it, full of an earthy roundness even as the saint is pursued by demons.  But the sky in the background is populated with nothing but dashes to suggest clouds. 

Perhaps clouds would have taken away from the moment; but if that were the case, why bother with the dashes?

There are considerable exceptions to this practice, with Durer and Altdorfer coming quickly to mind--but in my experience, the oddly-formed cloud seems to be the majority rule in the woodcut.  

At this time there were of course many depictions of skies with no clouds in paintings, bare suggestions of themselves, even in some of the most famous works--Botticelli's Birth of Venus and Michelangelo's Fall of Man in the Sistine Chapel are fair examples.  But once you move away from the golden Sienese skies of the14th century¹, clouds are given full and beautiful shapes from early periods. (Giotto's Christ's Entering Jerusalem, 1305/6; Simone Martin The Road to Calvary, 1340; Duccio's Christ Entering Jerusalem, 1308-1311; Fra Angelico's The Dposition, 1436; Masaccio's The Tribute Money, 1424; Lippi's Annunciation, a perfect cloud treatise, 1442, and on and on. Other examples are found in continued reading below.)

Clouds in prints are a different matter--I'm not sure if it was just too technically difficult to create clouds in wood, or if there was some sort of languishing Byzantine sensibility inherent in woodblocks that was not so in oil. I'm really not so sure about this, and as much as anything else I'm thinking out loud about this lack of cloud definition.  I don't have an answer for it.  But I do want to share the beginning of a timeline for undefined clouds as they appeared (or not) over the course of about one hundred years,  from 1485 to about the end of the 16th century.   As I mentioned clouds appeared beautifully in paintings from earlier periods, and there doesn't really seem to be a substandard-cloud complement in the painting world as there was in the print world.  Of course, in western philosophy and science, clouds were pretty much left alone from inquiry, even by a series of the great natural history classifiers--they wouldn't really be given a fully taxonomic appreciation until 1803 by Luke Howard (which I wrote about in this blog earlier, here).

A Timeline of Clouds in Prints, 1485-1596

Franciscus de Retza, De Generatione Christi, sive Defensorium Castiatis Beatae Virginis Mariae, a beautiful work in Gothic type--a picture book, really, with two illustrations of magnets.  Printed in 1485, this image depicts Isidorus in a magnetic coffin which is floating in the air:

"The Adoration of the Magi", from Legenda Sanctorum Trium Regum, printed in Modena in 1490:

The Triumph of Love, 1492/3:

A Forty-Year Precursor to Modernism--Found Cubism in 1870

JF Ptak Science Books  Quick Post     [History of Lines #18]

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.]

History of Lines, #17: the Artist Painting the Negative, Camille Corot, 1874

JF Ptak Science Books   Post 1584   [Part of the History of Lines series]

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. 

Notes:

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.

The images:

History of Lines: Looking Straight Down from Straight Up, 1786

JF Ptak Science Books   Post 1581

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): 

History of Lines: the Desire Lines of William Blake

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 Series "For Children" of 1793:

History of Lines--a Note on the First Appearance of the Addition ("+") Sign

JF Ptak Science Books   Post 1575  [Part of the History of Lines series]

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's² Arithmetic³ 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. 

Notes:

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)

3.  In his introduction, Hodder says:

History of Lines--Measuring Things with People, 1522

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. 

History of Lines--Where is "there"? The Medieval T-O World Map

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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. 

History of Lines--the Heart, Arteries and the Circulation of the Blood, 1628 (1639)

JF Ptak Science Books     Post 1570

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 (or On 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. 

Notes:

The detail from the big image in Copernicus' De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres), 1543.