Author: JF Ptak

The Paper Microscope: Cities in Stone

JF Ptak Science Books Post 2016

This is a Paper Microscope presentation of an 18th century image, presented in the form of an amalgamated 19th century microscope slide:

The presentation of the specimen is the detail as follows, from an engraving from 1788:

James Hutton explained this cross-section in iron-stone as a function of the internal heat of the Earth, “by means of fusion, or by congelation from a state of simple fluidity and expansion” as he wrote in 1788 (in the Transactions of the Royal Society of Edinburgh)–now he may be explaining why this rock looks the way it does and getting at the root of his uniformitarianism, but what I see is a city plan.

Seeing things in stone like this was not terribly unusual, though seeing maps may well have been. One of our favorite Jesuits, the problematic Athanasius Kircher, saw cities in stone–except Fr. Kircher saw profiles of buildings more so than maps. Let’s make no mistake about it: Hutton did not see city maps, though Kircher did see buildings in his stones…and more.

For example exhibited an image of St. Jerome (in no less a place than the cave of the Nativity in Bethlehem!) that he found in agate. His Mundus Subterraneus (1661) is a home to a wide range of these objects: quadrupeds of all shapes and descriptions, human full-length portraits, hands with jewels, and even the Virgin Mary and child. As spectacular as these are there is always more: the magnificent cityscape (reproduced here) and the sublime discoveries of a full set of the alphabet and a series of 15 geometrical drawings, all naturally impressed in stone.

Then down in Arizona, near Silver City, there is another city in stone, the City of Rocks, a real collection of rocks but not a real city, these being the remnants of an ancinet volcano, place-keepers for the stuff that wasn’t there any longer, a hint of a great hulking mass, a sort of plan in their own way:

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Absurdist, Unintentional — Information, Quantitative Display of
On Learned Ignorance

JF Ptak Science Books Post 2015

In keeping with a post earlier today on a Medieval jewel of scholarship (Sacrobosco’s Sphaera) is this short note on Nicolas of Cusa’s beautifully-named de docta ignorantia, or On Learned Ignorance. Nicolaus (1401-1464, Nicholas Cusanus/Kues) was a philosopher, mathematician, theologian, astronomer, cardinal, and mystic, a product of the University of Padua (1423) and then the University of Cologne, and “arguably the most important German thinker of fifteenth century” (Stanford Encyclopedia of Philosophy, here). He was deeply intuitive, a visionary, and in his Learned Ignorance he presented a way of the human mind to release itself to learn the mind of god (among many other things). [Image: detail in Meister des Marienlebens, located in the hospital at Kues (Germany), showing Nicolas of Cusa.]

In this work is something really amazing–here’s this wide thinker at the end of the Medieval period, writing on advanced theological issues, finding time to stop and smell the astronomical/cosmological roses long enough to think about the unending nature of the universe, about infinity, about the stars being suns for other planets, about the Earth spinning on an axis and circling the Sun. And all of this done without observations, and without calculation, and without a theory–its just a bunch of the big thoughts of modernity found in a small tract about knowing the Creator. Very curious.

The astronomical views of the cardinal are scattered through his philosophical treatises. They evince complete independence of traditional doctrines, though they are based on symbolism of numbers, on combinations of letters, and on abstract speculations rather than observation. The earth is a star like other stars, is not the centre of the universe, is not at rest, nor are its poles fixed. The celestial bodies are not strictly spherical, nor are their orbits circular. The difference between theory and appearance is explained by relative motion. Had Copernicus been aware of these assertions he would probably have been encouraged by them to publish his own monumental work.–Catholic Encyclopedia, 1913

Indeed! But I doubt that last sentence–Nicolas’ work was entirely theoretical, and Copernicus was very heavy and deeply laden with data. Even though Nicolas was never considered a heretic–though it must have been a close call here and there–an earlier confrontation by Copernicus with his De Revolutionibus on anything but his death bed would probably have been received with a closed fist.

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Astronomy — Books: Great & Lost in the Dust — Information, Quantitative Display of
A Long-Lived Medieval Astronomy Text

JF Ptak Science Books Post 2014

Sacro Busto, or Sacrobosco (also called John or Johannes Halifax, Holyfax, Holywalde, Sacroboscus, Sacrobuschus, de Sacro Bosco, or de Sacro Busto) was a member of the Order of St. Augustine and a professor of mathematics and atronomy/astrology at Paris ca. 1230. (There are many places attributed to be his birthplace, but it seems fairly certain that he at least was educated at Oxford.) He became a celebrated member of the intelligensia, with his fame in the later centuries coming via three of his surviving works, each an elementary textbook on mathematics and astronomy: De algorismo, the De computo, and De sphaera.

[Source for this image and the third, fourth and fifth, below, come from a 1531 edition of the Tractatus viewable in full via Google Books, here.]

I think it is accurate to say that the Sphaera was the most famous of his works–it is a very long-lived fundamental textobok on astronomy (and the second astronomical text everprinted, in 1472) and went through 24 editions to 1500, and then another 40 editions from 1500 to 1547. The book was still in use in the mid-17th century but far less so, until it finally was superceded and fell away into the aniquarian dust. It was a short work–basically about 35 pages–and concisely written, even elementary, but it did receive some close attention by some of the great early thinkers in astronomy and mathematics who contributed commetaries, including Michael Scot (between 1230 and 1235), John Pecham (prior to 1279), and by Campanus of Novara between (1265 to 1292).

It may seem a little trifling after this to concentrate on the interesting aspect of the images in his Sphaera, but that is what brought me to Sacrobusto today. For example, this is the beautiful title page, showing (via an early metal engraving process utilizing little punches making those fine small dots) the structure of our existence:

The work (29 cm tall and as I said 35 pages long) is called (in full) Textus de sphaera Ioannis de Sacrobosco. Introductoria additione (quantu necessarium est) commentario[que], ad vtilitatem studentiu philosophiae Parisiensis Academiae illustratus. Cum copositione Annuli astronomici Boneti Latensis: Et Geometria Euclidis Megarensis, which was printed in Paris (Parisiis) by Simonem Colinaeum in 1527, while Sacrobusto was a professor there.

[Source: Johannes de Sacrobosco – Editions of the Tractatusde Sphaera – home, Roberto de Andrade Martins http://www.ghtc.usp.br/server/Sacrobosco/Sacrobosco-ed1.htm.]

There are a number of beautiful and small woodcut illustrations throughout the book in its various editions, for example:

And:

And this:

And so:

Meanwhile in Sacro Busto’s Vberrimum sphere mundi comētū intersertis etiā questionibus dñi
Petri de aliaco …[Paris, Guy Marchand for Jean Petit, February, 1498-99.] we find this beautiful illustration of a solar eclipse–finding again those curious stick-figure humans under a very Martin-Luther-like Sun:

[Source: Lilly Library, Indiana University, here.]

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Astronomy — Beautiful books — Information, Quantitative Display of
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.

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Lines, History of — Maps, Cartography, History of Mapmaking — Maps/Diagrams of Imagination & Ideas
History of Holes: the Battle of the Bulge, 1944-5

JF Ptak Science Books Post 2013 History of Holes

This detail is from a pivotal moment in time in a crucial battle in the endgame of the European Theatre of WWII. It is Christmas, 1944, and the action takes place in the Ardennes. The German forces made a very unexpected assault through thick and very problematic wood, pushing Allied forces back along a long front, forcing a very perceptible bulge in the line–a bulge pointed the wrong way. The bulge was pretty much in the middle of the line and in the middle of the bulge was a famous circle, and inside this circle was the 101st Airborne division in the town of Bastogne, and it was surrounded for the time being by overpowering elements of the Wehrmacht, including three infantry divisions and a panzer division The boxes with the cross-hatches are all enemy forces, and for a time, the “AB101” stood quite by themselves.

The full map from which this detail is made is found at the Library of Congress site, here; the full suite of eleven maps showing the development of the battle from 16 December 1944 to 18 January 18, 1945 is also found here.

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History of Holes — Maps, Cartography, History of Mapmaking
Notes on the History of Lines: Sight Lines

JF Ptak Science Books Quick Post History of Lines

These are particularly fine and relatively early printed images depicting a specific kind of line of sight–this one, a positioning, rather than a line of sight in fire control, or radial velocity, EM radiation or acoustics wave propagation, or targeting…this instrument was used to establish an imaginary line in perceived objects.

This is a detail from Andrew Wakley’s The mariner’s compass rectified : containing tables, shewing the true hour of the day, the sun being upon any point of the compass ; with the true time of the rising and setting of the sun and stars, and the points of the compass upon which they rise and set … With the description and use of those instruments most in use in the art of navigation. Also a table of the latitudes and longitudes of places, published in 1763 and reprinted many times after that. (Full text is available from Google books and also from the Haithi Trust which offers a text version of the book as well.)

The full page from which the detail is drawn:

There is a certain continuum in developing sight lines that comes to mind, as with this famous image drawn by Leonardo in 1508, perhaps the first modern interpretation of how the eye functions, kept privately in manuscript, the result of theory and experimentation:

Which leads us to the sigh lines of Albrecht Durer, illustrating (some 17 years later) the use of a perspective tool, the vielo, in his work The Drawing Manual published in 1525:

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History of Lines — Perception — Perspective — Technology, History of
A Beautiful Timeline: the U.S. Civil War

JF Ptak Science Books Quick Post

This fantastic timeline of the U.S. Civil War (History of the Civil War in the United States, 1860-1865) was compiled by J. Kellick Bathurst, drawn by Edward Perrin, and printed by the Courier Lithographic Co. of Buffalo, N.Y. in 1897. It is a beautiful thing, and is actually pretty useful:

Source: the Library of Congress, here.

A detailed view reveals that the timeline includes major (and minor) battles weighted for their importance and distinction:

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Maps/Diagrams of Imagination & Ideas
Decimals, Holes & Dots in the History of Mathematics

JF Ptak Science Books Post 2011

There is an interesting side note to this blog’s series on the histories of holes and dots–a mathematical aspect involving decimal points, decimal notation and placeholders. This is exclusive of the number zero, however, which is an entirely different topic.

The book that this beautifully-illustrated counting board (below) is found is in Gregor Reisch’s (1467-1525) Margarita Philosophica (1503) and depicts (amidst much else in the greatly humanist volume) representations of the mathematicians Boethius and Pythagoras working math problems on the given tools of their day. The tools on the right seem to be circles, but they’re not–they’re counting stones, and for our intents and purposes here, they shall be dots, and in the history of dots in math and business reckoning they have had a strong and long life.

We can see in his expression that Boethius, on the left, is rather enjoying himself, knowing the superiority of his system of counting, which was the the Hindu-Arabic number notation–he definitely has a sly, self-appreciating smile on his face. Pythagoras, working with the old counting table, definitely looks worried, or at least unhappy, unsettled. Never mind that Pythagoras (570-495 b.c.e., none of whose works exist in the original, another sort of entry in our Blank History category) was at a definite disadvantage in the calculating department, being dead and all that for hundreds of years before the Arabic notation was more widely introduced in the West, probably being introduced by Pisano/Fibonnaci in the 12th century. But it does fall to Boethius, the smirker, to have introduced the digits into Europe for the very first time, deep into the history of the Roman Empire, in the 6th century.

The numerical stand-ins in the Reisch book with which Pythagoras worked were blank, coin-like slugs used as placeholders, and would be used in place of rocks or pebbles or whatever other material was at hand. It is interesting to note that the Latin expression, “calculos ponere”, which basically means “to calculate”or “to compute”, is more literally translated into “to set counters” or “to place pebbles” (upon a counting board) or to set an argument², which is exactly what some of the Roman daily reckoners would do at their work. And also used, in this case, by the unhappy Pythagoras.

The foundation for the .14159… that comes to the right of the integer 3 in pi is a relatively recent idea in the history of the maths–at least so far as the represrntation of the ideas in numbers and the decimal point is concerned.

Simon Stevin (1548-1620) introduced the idea of decimal numbers in his 36-page De Thiende (‘The Art of Tenths”¹) in 1585, an idea that replaced much more cumbersome earlier methods of representation. So, the number 3.14159 would be written in the Stevein notation as (where in this case numbers enclosed by brackets, i.e. “[9]” would have been represented in print as a 9 within a circle) 3[0]1[1]4[2]1[3]5[4]9[5]. It is also seen here:

[Source: math Words, here.]

[Full text available here.]

The importance of the introduction of this idea is difficult to underestimate, according to many and by example the The Princeton Companion to Mathematics by Timothy Gowers:

The Flemish mathematician and engineer Simon Stevin is remembered for
his study of decimal fractions. Although he was not the first to use
decimal fractions (they are found in the work of the tenth-century
Islamic mathematician al-Uqlidisi),it was his tract De Thiende (“The tenth”), published in 1585 and translated into English (as Disme: The Art of Tenths, or Decimall Arithmetike Teaching ) in 1608, that led to their widespread adoption in
Europe. Stevin, however, did not use the notation we use today. He drew
circles around the exponents of the powers of one tenth: thus he wrote
7.3486 as 7�3�4�8�6�4. In De Thiende Stevin not only demonstrated how
decimal fractions could be used but also advocated that a decimal system
should be used for weights and measures and for coinage.

This idea would be further developed by Bartholomeus Pitiscus (1561-1613) who was the first to introduce the decimal point in 1612³. It was a far more robust and simple was of dealing with decimal notation than anything that had come before.

Notes:

1. Decimal arithmetic: Teaching how to perform all computations whatsoever by whole numbers without fractions, by the four principles of common arithmetic: namely, addition, subtraction, multiplication, and division.

2. The Reisch book is remarkable: it is basically a Renaissance encyclopedia of general knowledge, divided into twelve books: grammar, dialectics, rhetoric, arithmetic, music, geometry, astronomy, physics, natural history, physiology, psychology, and ethics.

3. Pitiscus was also the first to introduce the term “trigonometry” earlier in 1595 in a highly important and influential work he produced in 1595.

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History of Dots — History of Holes — mathematics, logic
Shovel-Leaners of 1565

JF Ptak Science Books Post 2011 Paper Microscope series

There is a particular class of illustration in which, among the secondary figures of the image, there is a small happening, an everyday trifle, that has been captured by the artist and included in the overall communication for no necessary reason. (for example, see here ). I’ve written about this a little before on this blog in posts about finding images-within-images: the unecessaries among the unnecessaries, the bits and pieces of everyday human existence that in and of itself is not worth commentary but which nearly everyone experiences. Small bits, they are, of a tremendous human nature, the things that are done in private, or are so universal but inconsequential that they are shocking to see when illustrated in print. Another fine example of the unexpected story enclosed in great detail is found in this earlier post, On Antique Waves and Dropping Your Hat in Them, based in an engraving in Romische Historie…, published in Mainz by Johann Schoeffler 1450 years later in 1514, which was one of the most beautifully illustrated books ever produced in that city.

Today’s example under the paper microscpe is a magnificent and complex recording of the procession of the Doge of Venice by Jost Amman (1539-1591, Swiss, Procession of the Doge to the Bucintoro on Ascension Day, with a View of Venice), and printed ca. 1565, (the full version of which is found here).

Its the worker leaning on the spade (above) that attracted my attention–just a worker taking a moment out of his worday to watch the procession, caught in the act by Amman…and here we see him still, 447 years later, a wonder occupying 1% or less of the engraving.

There are many of these small vignettes laced throughout the engraving, like these upper-echelon folks having a few liberties with each other from the roof of one of the buildings:

And the full engraving:

A full, searchable version is available here from the Metropolitan Museum of Art

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Prints–looking HARD/deeply at
Outsider Thinking–Space Friction, 1944

JF Ptak Science Books Quick Post

“Ist der Weltraum absolut leer, oder nicht?” (“Is outer space absolutely empty, or not?”)

Carl Kutter challenged Isaac Newton on the 1st law of motion. Or at least that is what it looks like to me, the story presented in a slim but attractively designed pamphlet, published in Basel in 1944. Die Weltraumreibung presents the issue of “space friction”, and I frankly could not make my way through that much of it–not even to the point of understanding whay Halley’s Comet is illustrated on the front cover. But the design is interesting, and the issue was certainly very highly unexpected.

This site is interesting: http://tvtropes.org/pmwiki/pmwiki.php/Main/SpaceFriction

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Absurdist, Unintentional — Outsider Logic