Forget Da Vinci, Try Solving the Piero della Francesca Code
Fans of Dan Brown (and Tom Hanks) hoped to get an education in the Italian Renaissance along with their beach reading (and movie-going) of The Da Vinci Code. But they're missing out on a Renaissance master of art and mathematics just as captivating and mysterious as Da Vinci—Piero della Francesca.
Fans of Dan Brown (and Tom Hanks) hoped to get an education in the Italian Renaissance along with their beach reading (and movie-going) of The Da Vinci Code. But they and those who think that Leonardo, Michelangelo, Raphael, and Donatello are just Teenage Mutant Ninja Turtles are missing out on a Renaissance master of art and mathematics just as captivating and mysterious as Da Vinci—Piero della Francesca.
In Piero della Francesca: Artist and Man, James R. Banker relies on newly discovered documents and years of study of the Renaissance to crack the “Piero Code.” You won’t run across the Knights Templar or unearth the Holy Grail in Banker’s biographical study, but you will come away with a real-life detective tale compellingly told and a greater understanding and appreciation of an artist whose art may look otherworldly but, as Banker suggests, grew directly from Piero’s hometown roots.
Piero grew up in Sansepolcro in the Tuscany region of Italy, only 4,500 people strong at his birth around 1412. Literally “Holy Sepulchre,” Sansepolcro took that name when two founders brought a stone there from the Holy Land’s Church of the Holy Sepulchre, which itself was built on the spot where Jesus Christ reportedly died, was buried, and rose from the dead. “How, then,” Banker asks, “did this young man from a provincial town 79 miles west from Florence and 169 miles from Rome and without an extensive formal education become, along with Leonardo da Vinci, both an outstanding geometrician and the most intellectual painter of the Quattrocento?”
Like Shakespeare’s origin from the sleepy hamlet of Stratford-upon-Avon, Piero’s origin story sounds impossible, at least until you look beneath the surface and accept the resources a determined aspiring artist could find in even the unlikeliest of places. “Piero’s education in the mixed merchant-artisan culture of Sansepolcro remained a vital element in his painting and writings until his death,” Banker argues, “influencing the language he used in his vernacular treatises, and evident in the deep respect that he retained throughout his life for the beautiful products from the hands of artisans, whether clothing, leather book bindings, gems, or veils.” Piero came from a long line of leather workers (and broke his father’s heart pursuing painting rather than joining the family business), so whenever you see a leather good in one of his paintings rendered with sensitivity and reverence, it’s a homecoming of sorts.
Banker struggles mightily with the shoddy surviving documentation of Piero’s life, which begins with the mystery of the year of his birth and continues throughout much of his life. We glimpse Piero’s whereabouts throughout his career secondhand through documented commissions, appearances as a witness in Sansepolcro legal papers, and other fragments of history that Banker meticulously brings together. Banker stays hot on Piero’s half-century-cold trail as the artist travels through Florence, Modena, Ferrara, Rome, and other cities in Italy and absorbs the influences of Brunelleschi, Masaccio, Donatello, and other contemporaries, plus the lessons of classical sculpture from newly discovered Ancient Roman artifacts. Banker calls the 1440’s Piero’s “lost decade” during which he painted little, but learned much. Banker pieces together the known dates of Piero’s movements, the artists he would have seen or met in those places at those times, and Piero’s paintings reflecting those influences to give us the best available picture of Piero’s progress as a provincial pilgrim through the heart of the big-city Renaissance.
By the end of these adventures, Piero arrives at what Banker defines as his “classical style of fully sculpted monumental figures with more gravitas than emotion in meticulously constructed perspectival space.” Aside from his wonderful detective work, Banker digs deep into Piero’s greatest hits to show how that “classical style” plays out in the work. Anyone familiar with the strangely otherworldly Flagellation of Christ knows how Piero uses, in Banker’s phrase, “incredibly deep perspective… rational in its organization of a complex set of spaces and shapes” to pull you into a theater of the imagination past the trio of men conversing at the surface of the work into its innermost depths where Christ is suffering the first stages of his passion and death. The late Brera Madonna stands as “a virtuoso example of Piero’s command of all his earlier techniques” such as using light to define figures and mathematical perspective to give the heavenly an earthly reality. “Despite the monumentalizing epic within which Piero’s figures act,” Banker asserts, “they are within the world of human possibility.” They may not have the drama of a Michelangelo figure, but they do display the gravitas of real people facing extraordinary events.
Aside from Piero’s technical skill and innovations, he approached his art and his subject with a perspective unique to the time. “For Piero, the Divine had to be on the plane of the human, the natural, and the historical,” Banker writes. When Piero painted the Madonna della Misericordia for the local Sansepolcro confraternity of laypeople dedicated to charity, he placed a group of everyday people physically under the protection of an oversized Madonna, who spreads her cloak around them. Later, Piero painted The Resurrection of Christ (detail shown above) in the Sansepolcro communal meeting house. “[T]he Resurrection served a civic function,” Banker says, “confronting the legislators whenever they considered what laws would promote the well-being of the townspeople of the Holy Sepulcher.” Piero paints Christ rising from the tomb triumphant and as judge and lawgiver of the people. Thus, The Resurrection of Christ combines “the eternal verities” of medieval art and the specific moments of Renaissance art to arrive at a powerfully poetic and pivotal moment in the history of art as well as history itself, as Italians learned to assume some democratic rule after centuries of warlords and chaos. The mystery of Christ’s assertive stare isn’t spiritually separated from life on Earth but rather a connection strung between faith in God and faith in humanity. Banker’s ability to connect to this connective quality of Piero’s art cracks the true Piero code and resurrects the artist in a way that no trove of documentation can.
This past summer Americans literally saw “Art Everywhere” as that campaign plastered fine art across the country with works such as George Tooker’s 1950 painting The Subway. Tooker idolized Piero della Francesca in his updating of the master’s deep perspective and sculpted figures for a modern audience. Sadly, Piero fell out of critical favor after his death until the early 20th century, when the Cubists tried to incorporate the mathematical aspects of his art into their own. Allied bombing during World War II almost destroyed much of Piero’s art (and Sansepolcro itself) until British officer Tony Clarke halted fire after remembering a 1925 essay by Aldous Huxley mentioning that little town as the home of the greatest painting in the world, The Resurrection of Christ. James R. Banker’s Piero della Francesca: Artist and Man reminds us that, despite the centuries between us and Piero and the fact that we frequent subways more now than cathedrals, the human scale of his art—the ability to have his divine characters look us square in the eye as our eyes square up the mathematically intense realism of his worlds—never gets old. It might not be the Holy Grail, but the “Piero Code” is something we can all hold on to.
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Hungarian cartographer travels the world while mapping its treasures.
- Simple idea, stunning result: the world's watersheds in glorious colors.
- The maps are the work of Hungarian cartographer Robert Szucs.
- His job: to travel and map the world, one good cause at a time.
The world<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8xOTE0MjUyNS9vcmlnaW4ucG5nIiwiZXhwaXJlc19hdCI6MTYzMzU3Njk1M30.rRdZpcl0bfVi4oBsljHdZSbcX0New9rdLcx6fr2mD7Y/img.png?width=980" id="f982a" class="rm-shortcode" data-rm-shortcode-id="fa67421340f881d5ab91463514cf9a6d" data-rm-shortcode-name="rebelmouse-image" />
Can you spot the world's ten largest drainage basins? In order of magnitude: Amazon, Congo, Nile, Mississippi, Ob, Parana, Yenisei, Lena, Niger, Amur. Image source: Grasshopper Geography
Africa<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8xOTE0MjUyNi9vcmlnaW4ucG5nIiwiZXhwaXJlc19hdCI6MTYzOTI2MzI0MX0.OeTS-scZwBES4AlZAan7fBlaBkznkig5hPjgcd1j6hw/img.png?width=980" id="e987c" class="rm-shortcode" data-rm-shortcode-id="2d3a8999ed4071a123b30efc5652fee9" data-rm-shortcode-name="rebelmouse-image" />
Africa is home to the rivers with the world's second- and third-largest catchment areas: the Congo (in blue), with a basin of 1.44 million square miles (3.73 million km2), and the Nile (in red), with basin area of 1.26 million square miles (3.25 million km2). The Nile is the longest river in Africa, though (4,130 miles; 6,650 km), followed by the Congo: 2,900 miles (4,700 km). The Congo River's alternative name, Zaire, comes from the Kikongo nzadi o nzere ('river swallowing rivers'). Image source: Grasshopper Geography
Europe<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8xOTE0MjUyOS9vcmlnaW4ucG5nIiwiZXhwaXJlc19hdCI6MTY0NTkzOTMyMH0.tq5fjnq8wvLqXY0C9gzfoUd0ahOAQ7IZQxbpVnC1FdY/img.png?width=980" id="a8ec4" class="rm-shortcode" data-rm-shortcode-id="1ce5f59691501103343e080905ce74a3" data-rm-shortcode-name="rebelmouse-image" />
The Volga (in yellow) is the river with the biggest catchment area in Europe (just under 545,000 square miles; 1.41 million km2). It flows exclusively through Russia, and the catchment area is entirely within Russia as well. Europe's number two is the Danube (in orange), which flows through 10 countries — more than any other river in the world. Its drainage basin (just over 307,000 square miles; almost 796,000 km2) includes nine more countries. Image: Grasshopper Geography
Germany<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8xOTE0MjUzMC9vcmlnaW4ucG5nIiwiZXhwaXJlc19hdCI6MTY0Mzk4ODA3Nn0.qX1sOfJWAI7TUbTQCiIob-R5p4_wj299wEtrYAUREmg/img.png?width=980" id="d5efa" class="rm-shortcode" data-rm-shortcode-id="8e73c53d75840f21b4f2ca4b8a1e7f51" data-rm-shortcode-name="rebelmouse-image" />
The hydrographic map of Germany is dominated by just four major drainage systems: the Danube (in orange) in the south, the Rhine (in blue) in the west, the Elbe (in purple) in the east and the Weser (in green) between the latter two. In Antiquity, the Rhine was the border between the Roman Empire and the Germans. Rome once attempted to shift the border to the Elbe, which would have radically altered the course of history, but it suffered a massive defeat in 9 CE at the Teutoburger Wald (roughly between both rivers). Image: Grasshopper Geography
Great Britain and Ireland<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8xOTE0MjUzMS9vcmlnaW4ucG5nIiwiZXhwaXJlc19hdCI6MTY1OTk2MjM3MX0.nDy__OLIyC1arty4_2xd54fjTzmfsIZo-2pe5QRjjA4/img.png?width=980" id="31a6f" class="rm-shortcode" data-rm-shortcode-id="d089f66097f37a10ab854eaccdac3581" data-rm-shortcode-name="rebelmouse-image" />
Both Ireland and Great Britain are islands, as a result of which neither boasts a continental-class river. Twenty of the 30 longest British rivers are less than 100 miles (160 km) long. The longest river in Britain is the Severn (220 miles, 354 km), its catchment area shown in blue in the southwest. Ireland's longest river is the Shannon (224 miles, 360 km). Even combined they're not as long as France's Seine (483 miles, 777 km). Image: Grasshopper Geography
United States<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8xOTE0MjUzNC9vcmlnaW4ucG5nIiwiZXhwaXJlc19hdCI6MTY2MDYyMzEyM30.7S_83dA6bcLyID_7BhH1R_OTy61tpgDZrBMQ_iPwnjM/img.png?width=980" id="a879d" class="rm-shortcode" data-rm-shortcode-id="a7c74a7b5a7887fb2d13b40d5d96223c" data-rm-shortcode-name="rebelmouse-image" />
Spread-eagled across the central part of the United States, the Mississippi's drainage basin covers all or parts of 32 U.S. states (and two Canadian provinces). The easternmost point of Ol' Man River's catchment area is really far east: Cobb Hill in northern Pennsylvania. Here rises the Allegheny, tributary of the Ohio, which in turn flows into the Mississippi at Cairo, Illinois. Image: Grasshopper Geography
Washington State<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8xOTE0MjUzNS9vcmlnaW4ucG5nIiwiZXhwaXJlc19hdCI6MTY0MzU2MzM4OH0.mniqbkEQq84rNaWOQIl4fB4mOhNdJf5WactNyE_VsyM/img.png?width=980" id="adc4d" class="rm-shortcode" data-rm-shortcode-id="97eb5a5add49c06ef00ff0bca812b380" data-rm-shortcode-name="rebelmouse-image" />
Even leaving out the Mississippi, there's enough going on in the rest of North America to keep the eye occupied. Here's a drainage map of Washington State. The big fish in this much smaller pond is the Columbia River (drainage area in blue), the largest river in the Pacific Northwest. Only in the western third of the state is there a colourful counterpoint, in the multitude of smaller river basins that are draining into the Pacific or into Puget Sound. Image: Grasshopper Geography
Australia<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8xOTE0MjUzNi9vcmlnaW4ucG5nIiwiZXhwaXJlc19hdCI6MTYzOTM0ODM2NH0.U7vckwnoNoxf-bk8SuYO246hNMpR2zXILILsd4pas9o/img.png?width=980" id="38c2b" class="rm-shortcode" data-rm-shortcode-id="0c44d30d61c6cb94b8d5c7205cbabd58" data-rm-shortcode-name="rebelmouse-image" />
At 1,558 miles (2,508 km), the Murray is Australia's longest river. It is often considered in conjunction with the Darling (915 miles, 1,472 km), the country's third-longest river, which flows into the Murray. The Murray-Darling basin (in blue, in the southeast) covers just under 410,000 square miles (1.06 million km2), or 14 percent of Australia's total territory. Don't let that spidery network of river courses in the interior fool you: Australia is the world's driest inhabited continent (Antarctica, bizarrely, is drier). Image: Grasshopper Geography
Russia<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8xOTE0MjUzNy9vcmlnaW4ucG5nIiwiZXhwaXJlc19hdCI6MTYwNzg5MzIxOX0.WhShHLjjWdEh4FF_OZsY1oTN3Vc77X29TbMYbVHrHqA/img.png?width=980" id="f5cee" class="rm-shortcode" data-rm-shortcode-id="53acd93f1ab67be979e6ab128c144ce6" data-rm-shortcode-name="rebelmouse-image" />
Four of the world's largest drainage basins are in Russia: the Ob, Yenisei and Lena (origin of Vladimir I. Ulyanov's nom de guerre, Lenin) entirely and the Amur, shared with China. The Volga may be Europe's longest river, but 84 percent or Russia's surface water is east of the Urals, in Siberia. The sparsely-populated region is traversed by 40 rivers longer than 1,000 km. Combined, the Ob, Yenisey and Lena rivers cover a drainage area of about 8 million km2, discharging nearly 50,000 m3 of water per second in the Arctic. Image: Grasshopper Geography
The images and our best computer models don't agree.
A trio of intriguing galaxy clusters<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDQzNDA0OS9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYxNTkzNzUyOH0.0IRzkzvKsmPEHV-v1dqM1JIPhgE2W-UHx0COuB0qQnA/img.jpg?width=980" id="d69be" class="rm-shortcode" data-rm-shortcode-id="2d2664d9174369e0a06540cb3a3a9079" data-rm-shortcode-name="rebelmouse-image" />
The three galaxy clusters imaged for the study
Mapping dark matter<span style="display:block;position:relative;padding-top:56.25%;" class="rm-shortcode" data-rm-shortcode-id="d904b585c806752f261e1215014691a6"><iframe type="lazy-iframe" data-runner-src="https://www.youtube.com/embed/fO0jO_a9uLA?rel=0" width="100%" height="auto" frameborder="0" scrolling="no" style="position:absolute;top:0;left:0;width:100%;height:100%;"></iframe></span><p>The assumption has been that the greater the lensing effect, the higher the concentration of dark matter.</p><p>As scientists analyzed the clusters' large-scale lensing — the massive arc and elongation visual effects produced by dark matter — they noticed areas of smaller-scale lensing within that larger distortion. The scientists interpret these as concentrations of dark matter within individual galaxies inside the clusters.</p><p>The researchers used spectrographic data from the VLT to determine the mass of these smaller lenses. <a href="https://www.oas.inaf.it/en/user/pietro.bergamini/" target="_blank" rel="noopener noreferrer">Pietro Bergamini</a> of the INAF-Observatory of Astrophysics and Space Science in Bologna, Italy explains, "The speed of the stars gave us an estimate of each individual galaxy's mass, including the amount of dark matter." The leader of the spectrographic aspect of the study was <a href="http://docente.unife.it/docenti-en/piero.rosati1/curriculum?set_language=en" target="_blank">Piero Rosati</a> of the Università degli Studi di Ferrara, Italy who recalls, "the data from Hubble and the VLT provided excellent synergy. We were able to associate the galaxies with each cluster and estimate their distances." </p><p>This work allowed the team to develop a thoroughly calibrated, high-resolution map of dark matter concentrations throughout the three clusters.</p>
But the models say...<p>However, when the researchers compared their map to the concentrations of dark matter computer models predicted for galaxies bearing the same general characteristics, something was <em>way</em> off. Some small-scale areas of the map had 10 times the amount of lensing — and presumably 10 times the amount of dark matter — than the model predicted.</p><p>"The results of these analyses further demonstrate how observations and numerical simulations go hand in hand," notes one team member, <a href="https://nena12276.wixsite.com/elenarasia" target="_blank">Elena Rasia</a> of the INAF-Astronomical Observatory of Trieste, Italy. Another, <a href="http://adlibitum.oats.inaf.it/borgani/" target="_blank" rel="noopener noreferrer">Stefano Borgani</a> of the Università degli Studi di Trieste, Italy, adds that "with advanced cosmological simulations, we can match the quality of observations analyzed in our paper, permitting detailed comparisons like never before."</p><p>"We have done a lot of testing of the data in this study," Meneghetti says, "and we are sure that this mismatch indicates that some physical ingredient is missing either from the simulations or from our understanding of the nature of dark matter." <a href="https://physics.yale.edu/people/priyamvada-natarajan" target="_blank">Priyamvada Natarajan</a> of Yale University in Connecticut agrees: "There's a feature of the real Universe that we are simply not capturing in our current theoretical models."</p><p>Given that any theory in science lasts only until a better one comes along, Natarajan views the discrepancy as an opportunity, saying, "this could signal a gap in our current understanding of the nature of dark matter and its properties, as these exquisite data have permitted us to probe the detailed distribution of dark matter on the smallest scales."</p><p>At this point, it's unclear exactly what the conflict signifies. Do these smaller areas have unexpectedly high concentrations of dark matter? Or can dark matter, under certain currently unknown conditions, produce a tenfold increase in lensing beyond what we've been expecting, breaking the assumption that more lensing means more dark matter?</p><p>Obviously, the scientific community has barely begun to understand this mystery.</p>
Scientists have found evidence of hot springs near sites where ancient hominids settled, long before the control of fire.