Ptak Science Books

Before "Cosmos" 2012 there was "Cosmos" 1845

JF Ptak Science Books  Post 1577    

Before the Neil deGrasse Tyson version and update of Carl Sagan's landmark tlevision series, Cosmos, there was Alexander von Humboldt, and his enormously influential book of the same title, printed in 1845-1862.  Well, von Humboldt's (1769-1859¹) book was actually Kosmos when published in German, which is where it started its life (and which von Humboldt suffered mightily for in it English translation).  Von Humboldt was enormously studied and educated and of a high scientific mind over many subjects, one of those 19th century figures who seemed as though they could know everything, a polymath of high order (along the lines of Goethe and von Helmholtz and Thomas Young and others).  He was a meteorologist and biogeographer before those sciences existed; a naturalist, geographer, archaeologist, and explorer, a natural philosopher of magnitudes.

Kosmos reflected his lifelong interest in order, and what he did was astonishing--he attempted to unifying the complexities of nature in one book (of five volumes), binding the various branches of science together in a cohesive whole, attempting to show how the laws of the universe acted here on Earth.  It was a very influential work, very progressive, a masterwork of scientific method.  Kosmos.

Sagan (and Tyson, soon) tried to explain what the universe was all about; 160+ years ago, so did von Humboldt, and for his time he came damned close to doing so, or as close as anyone could possibly come. 

Notes:

1.  von Humboldt died six months before the On the Origin of Species was born--an enormous pity. 

Map from the atlas to accompany  Kosmos, a masterpiece of physical geography and the display of quantitative data:

From the bibliography, Printing and the Mind of Man, which colelcted the epochal books in the history of science and medicine, we read this about Kosmos:

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

JF Ptak Science Books   Quick Post  

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--I AM a Man, 1968

JF Ptak Science Books   Quick Post for the History of Lines series

"I am an invisible man. No, I am not a spook like those who haunted Edgar Allan Poe; nor am I one of your Hollywood-movie ectoplasms. I am a man of substance, of flesh and bone, fiber and liquids—and I might even be said to possess a mind. I am invisible, understand, simply because people refuse to see me."
—Ralph Ellison, Invisible Man (1952)

There are many powerful images and messages from the American Civil Rights movement of the 1950's and 1960's.   To me, the sign held by the striking sanitation men in Memphis, Tennessee, during February/March/April 1968, is one of the most extraordinary.  The strike started in February after the limited response to requests for improved safety conditions for sanitation workers after two men were crushed to death by a truck failure several weeks earlier.   It grew quickly into something much larger. 

Martin Luther King had been in close contact with strike organizers, which had the help (by early March)  as well of James Bevel and Ralph Abernathy of the Southern Christian Leaderships Conference’s (SCLC).  King  returned to Memphis on 3 April, 1968, and gave what turned out to be his speech that evening.  It was purely magnificent; and if you watch it, after everything is said and done, you'll see how exhausted the man was, as he almost collapses at its end.

King ends the speech this way:

“Like anybody, I would like to live a long life--longevity has its place. But I'm not concerned about that now… I've seen the Promised Land. I may not get there with you. But I want you to know tonight that we, as a people, will get to the Promised Land”

Dr. King was shot and killed the next day, shot to death on the balcony of the Loraine Motel, as he was getting ready to go to dinner.

The mayor of Memphis was not moved enough by this event to settle the strike, and stood firm.  The strike was finally ended after the intercession of President Johnson.

I'm interested in the "I Am a Man" sign not only for the lines of resistance of the marchers who held these and other signs, but also for its sublime simplicity, and the insistence of the underlining of Am.  These are some of the strongest lines that have ever been made in this country. 

 

 

History of Lines (Note)--Getting There for the Common Reader. Sebastian Munster, 1551

JF Ptak Science Books   Quick Post for the History of Lines*series

Sebastian Munster (1488-1552) did not contribute a great or even an original work in the history of mathematics, or even in surveying, or map making.  What makes his Cosmographia  important, and what made it so very successful (entering 24 editions over a hundred years), was that he was among the first scholars of the time to put all of this disparate material together, and to give credit where credit was due, and to present an accumulation of important information in a scholarly, reasoned way.  He also made all of this accessible to the general reader, so that the information and methodology could be spread very wide.  It was in fact the first time that the stuff of the world in general was described in German--that of course is very important; but the fact of the matter is that the presentation and scholarship that resulted in this work was in itself ground-breaking.

I've chosen an image from another of Munster's works, his Rudimenta mathematica¹, which was a practical work on time reckoning, and another work of celebrated importance.

1. Rudimenta mathematica : haec in duos digeruntur libros, quorum prior geometriae tradit principia seu prima elementa, unà cum rerum et uariarum figuraru[m] dimensionibus, posterior uerò omnigenum horologiorum docet delineationes, 1551. 

And the full image, one of the woodcuts illustrating the section on the construction of sun dials:

 

Contents of the 16th century editions of the Cosmographia.

1. Book I - Astronomy, Mathematics, Physical Geography, Cartography
2. Book II - England, Scotland, Ireland, Spain, France, Belgium, The Netherlands, Luxembourg, Savoy, Trier, Italy
3. Book III - Germany, Alsace, Switzerland, Austria, Carniola, Istria, Bohemia, Moravia, Silesia, Pomerania, Prussia, Livland
4. Book IV - Denmark, Norway, Sweden, Finland, Iceland, Hungary, Poland, Lithuania, Russia, Walachia, Bosnia, Bulgaria, Greece, Turkey
5. Book V - Asia Minor, Cyprus, Armenia, Palestine, Arabia, Persia, Central Asia, Afghanistan, Scythia, Tartary, India, Ceylon, Burma, China, East Indies, Madagascar, Zanzibar, America
6. Book VI - Mauritania, Tunisia, Libya, Egypt, Senegal, Gambia, Mali, South Africa, East Africa

Note on introducing line fragments for the History of Lones series:

* 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.)

	[Source]

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.

History of Lines--Naive Rivers and Trees, 1670

JF Ptak Science Books   Quick Post in the History of LInes series.

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...

Barbed Wire, Trench Warfare, and the Next Lethal Step: Electric WIres

JF Ptak Science Books  Post 1555   [Part of the History of Lines series]

Barbed wire was one of the most successful and horrifying defensive weapons of World War I.  In 1915 it was made more effective yet by adding high-voltage electricity to the emplacements.  In general the electrical barbed wire fence was employed as only a tiny fraction of all wire fences during the war--as the non-electrified fence was already extremely effective, very cheap to produce and very easily installed--but the possibility of finding an electrified wire somewhere along the lengthy rat's nests of mile sand miles of this thing must've had some sort of weight in most soldiers' minds. 

The following image (and details) from The Illustrated London News for 9 October 1915:

And the places where the barbed wire was made and packaged, again from The Illustrated London News for 16 October 1915.

It looks as though the wire was stretched across 3.5 foot poles, with the barbed wire added diagonally, and then rolled up in long sections for easy transport and deployment.

History of Lines: Complicated Simplicity and Marconi's Lines of Communications

JF Ptak Science Books  Post 1547   [Part of the History of Lines series.]

This is an illustration of the approximate times and places that ships at sea could expect to be able to communication with each other by the relatively new invention of wireless telegraphy. (We're talking about Marconi here and just very briefly; this is not the place for the discussion of what he did or didn't "borrow" from his predecessors and contemporaries such as Heinrich Hertz, Oliver Lodge and Nikolai Tesla.  He at the very least however owed all of them at least an enormous helping of gratitude, and probably more.  Then there's Marconi's very conservative technical continuation in the field which is confusing and interesting.  And finally but not the least of all of the stuff about Marconi is his comfort and support of the Fascist regime in Italy, where Marconi became a member in 1923, escalating in his fame through the party ranks to have none other than Benito Mussolini serve as the best man in his second wedding.  But as I said that's all for another day.) It appeared in The Illustrated London News for 7 September 1907,surrounded by an article on Obelia in the "Science Jottings" section of the magazine.  This chart isn't

quite as complicated as it seems, really: all you need to do is follow one line from the top to the bottom.  Simply put, each diagonal line represents a specific ship (all of which are named) and their positions as they make their ways across the North Atlantic ocean; each intersection represents the time and place that two ships can communicate via wireless with one another.  So, for example, the Empress of Britain will on its six-day voyage be able to communicate at least 26 times with other ships for news and information.

What this seems to me to be is the supplemental efforts of the ocean-going ships

to the newly established trans-Atlantic radio-telegraphic company and installation opened by Marconi in October 1907.  Even though the first transatlantic communication is celebrated as having taken place in 1901, the performance, even in 1907, was still spotty.

Again, I'm just after this for the image 

The History of Lines: Lines Come and Gone.

JF Ptak Science Books  Post 1546    [Part of the History of Lines series.]

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. 

The History of Lines, an Introduction: Barbed Wire, Telegraphs, Treaties and Railroad Rails

JF Ptak Science Books   Post 1539

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.

NOTES

The full text of the "Millions of Acres" (seen above) broadside is as follows:

The Solids in Uccello

My ueber-brilliant wife, Patti Digh, has for decades been fascinated by the monstrous-great William Gaddis, and in particular, by his novel The Recognitions.  It is a difficult book to feel at home in—it took me four tries to feel comfortable in this complex wristbender, but once in, the water was fine, and I finished it during a boring and largely vacant astronomy meeting in Pittsburgh years ago.  It is perhaps one of the best books written by an American in the 20th century, and among the many threads that wind their way through the 950 pages, one involves
the gorgeous 15th century painter, Paolo Uccello.   Uccello, in short, was one of the first Renaissance painters to (re)discover and paint using perspective, and did so magnificently.  Gaddis refers cryptically, however, to the “solids in Uccello”. 

Books on perspective are some of the most beautifully illustrated works ever printed. They are full of insight and detail—a detail, the seeing of which, is a mystery (and to Uccello, mystical) beauty, a submerged, geological magnificence that is also an extraordinarily powerful tool.

I wrote two posts or so ago about the importance of Leonardo’s illustrations to Pacioli’s work on perspective, and how this was really about the first time that geometrical figures were illustrated , published, for the first time, in perspective.  And of course the images were drop-dead gorgeous. 

Vredeman de Vries (Perspectiva) was a 17th century Dutchman who is perhaps one of my favorites—shown here is his projection for an open loggia in which an illusionary ceiling could be painted (in the manner of Andrea Pozzo’s The Transmisson of the Divine Spirit (1688-1694) , an extraordinary painting of tremendous depth on the curved vault of S. Ignazzio in Rome).   (Another example of de Vries at bottom is a simple perspective of diverse architectural forms.) 

Wenzel Jamnitzer's Perspectiva corporum regularium (1568) is a somewhat earlier work of great depth and beauty—this image is again just a “simple” arrangement of geometrical objects, but there’s really nothing very “simple” about it.  The forms are difficult and arranged in a difficult presentation, and rendering them in perspective was a great achievement, and I think a wonder for the mid-16thc mind to see. 

Brook Taylor’s simple, clean lines and presentation of these architectural forms from his New Principles of Linear Perspective (2nd edition, London, 1719) is another perspective miracle of the 18th century.  To me the lines of perspective showing the view of the objections connected to the spare presentation of the objects themselves look completely modern to me rather than being a technical treatise from 289 years ago. ,

Uccello understood all of this, and painted using these techniques with enormous power.  The “solids’ recognized by Gaddis (and not really discussed) are incredible to me.  Looking at his painting Battle of San Romano  (1457) we see Perspective in her place; when we look at, say, the rumps of the horses, we see almost no detail, just a mass of color, a solid, with spectacular plainness. What in the world was he thinking?  He could certainly have painted the horse and the other solids with texture and detail, but he didn’t, and to me it seems antithetical to the painting.  What in the name of all motherly things was he thinking?  And who else on earth was using such huge amounts of plain solids in their paintings?  I’m not aware that anyone else was, and I am relatively clueless as to why he did it, abandoning as it were the potentials of the beauty of excruciating detail that we see in these other works. 

I would love to know what Uccello was thinking when he decided to create that mass of color, that solid, when there was no one else doing exactly that.  But my major thanks go to Patti Digh for loving that, and to Mr. Gaddis for creating the question.