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Do artists and scientists see the same thing in the shape of trees? As a scientist who studies branching patterns in living things, Im starting to think so. Piet Mondrian was an early 20th-century abstract artist and art theorist obsessed with simplicity and essence of form. Even people who have never heard of Mondrian will likely recognize his iconic irregular grids of rectangles. Tableau I by Piet Mondrian, 1921. [Image: Kunstmuseum Den Haag] When I saw Mondrians 1911 Gray Tree, I immediately recognized something about trees that I had struggled to describe. By removing all but the most essential elements in an abstract painting, Mondrian demonstrated something I was attempting to explain using physics and fractal geometry. My field of research is mathematical biology. My colleagues and I try to explain how treelike structures such as veins and arteries, lungs and leaves fine-tune their physical form to efficiently deliver blood, air, water and nutrients. Grey Tree by Piet Mondrian, 1911. [Image: Kunstmuseum Den Haag] Fundamental research in the biology of branching helps cure cardiovascular diseases and cancer, design materials that can heal themselves and predict how trees will respond to a changing climate. Branching also shows up in ant foraging patterns, slime molds and cities. The treeless tree From 1890 to 1912, Mondrian painted dozens of trees. He started with full-color, realistic trees in context: trees in a farmyard or a dappled lane. Gradually he removed leaves, depth, color and eventually even branching from his tree paintings. Gray Tree uses only curved lines of various thickness superimposed on top of one another at seemingly random angles. Yet the image is unmistakably a tree. Polder Landscape with Silhouetted Young Tree by Piet Mondrian, 1900-1901. [Image: Wikimedia Commons] How did Mondrian convey the sense of a tree with so little? The science of trees may offer some clues. The science of branching One goal of mathematical biology is to synthesize what scientists know about the vast diversity of living systems where there seems to be an exception to every rule into clear, general principles, ideally with few exceptions. One such general principle is that evolution fine-tunes treelike structures in living things to make metabolism and respiration as efficient as possible. The body carefully controls the thickness of vessels as they branch, because deviation from the most efficient diameter wastes energy and causes disease, such as atherosclerosis. In many cases, such as human blood vessels, the body exerts much tighter control over diameter than length. So while veins and arteries might take circuitous routes to accommodate the vagaries of organs and anatomy, their diameter usually stays within 10% of the optimum. The same principle appears in tree branches as well. The precise calibration of branch diameter leads to a hallmark of fractal shapes called scale invariance. A scale invariance is a property that holds true regardless of the size of an object or part of an object youre looking at. Scale invariance occurs in trees because trunks, limbs and twigs all branch in similar ways and for similar reasons. Trees with different values of the scaling parameter . [Image: Gao and Newberry/PNAS Nexus] The scale invariance in branch diameter dictates how much smaller a limb should be as it branches and how much investment a tree makes in a few thick branches versus many thin ones. Trees have evolved scale invariance to transport water, reach light and resist gravity and wind load as efficiently as possible given physical limits. This science of trees inspired my colleague and me to measure the scaling of tree branch diameter in art. The art of trees Among my favorite images is a carving of a tree from a late-medieval mosque in India. Its exaltation of trees reminds me of Tolkiens Tree of Gondor and the human capacity to appreciate the simple beauty of living things. Siddi Saiyyed Mosque in Ahmedabad, Gujarat, India, carved ca. 1572. [Photo: Snehrashmi/Wiki Commons] But I also find mathematical inspiration in the Islamic Golden Age, a time when art, architecture, math and physics thrived. Medieval Islamic architects even decorated buildings with infinitely nonrepeating tiling patterns that were not understood by Western mathematics until the 20th century. The stylized tree carvings of the Sidi Saiyyed mosque also follow the precise system of proportions dictated by the scale invariance of real trees. This level of precision of branch diameter takes an attentive eye and a careful plan much better than I could freehand. Cherry Blossoms by Matsumura Goshun (17521811). [Image: Metropolitan Museum of Art] Indeed, wherever our team looked at trees in great artwork, such as Klimts Tree of Life or Matsumura Goshuns Cherry Blossoms, we also found precise scale invariance in the diameter of branches. Grey Tree also realistically captures the natural variation in branch diameters, even when the painting gives the viewer little else to go on. Without realistic scaling, would this painting even be a tree? As if to prove the point, Mondrian made a subsequent painting the following year, also with a gray background, curved lines and the same overall composition and dimensions. Even the position of some of the lines are the same. But, in Blooming Apple Tree (1912), all the lines are the same thickness. The scaling is gone, and with it, the tree. Before reading the title, most viewers would not guess that this is a painting of a tree. Yet Mondrians sketches reveal that Blooming Apple Tree and Gray Tree are the very same tree. Blooming Apple Tree by Piet Mondrian, 1912. [Image: Kunstmuseum Den Haag] The two paintings contain few elements that might signal a tree a concentration of lines near the center, lines that could be branches or a central trunk and lines that could indicate the ground or a horizon. Yet only Gray Tree has scale-invariant branch diameters. When Mondrian removes the scale invariance in Blooming Apple Tree, viewers just as easily see fish, scales, dancers, water or simply nonrepresentational shapes, whereas the tree in Gray Tree is unmistakable. Photo synthesis Mondrians tree paintings and scientific theory highlight the importance of the thickness of tree branches. Consilience is when different lines of evidence and reasoning reach the same conclusions. Art and math both explore abstract descriptions of the world, and so seeing great art and science pick out the same essential features of trees is satisfying beyond what art or science could accomplish alone. Just as great literature such as The Overstory and The Botany of Desire show us how treesinfluence our lives in ways we often dont notice, the art and science of trees show how humans are finely attuned to whats important to trees. I think this resonance is one reason people find fractals and natural landscapes so pleasing and reassuring. All these lines of thinking give us new ways to appreciate trees. Mitchell Newberry is a research assistant professor of biology at the University of New Mexico. This article is republished from The Conversation under a Creative Commons license. Read the original article.
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The German antitrust authority has charged Apple with abusing its market power through its app tracking tool and giving itself preferential treatment in a move that could result in daily fines for the iPhone maker if it fails to change its business practices. The move follows a three-year investigation by the Federal Cartel Office into Apple’s App Tracking Transparency feature, which allows users to block advertisers from tracking them across different applications. The U.S. tech giant has said the feature allows users to control their privacy but has drawn criticism from Meta Platforms, app developers and startups whose business models rely on advertising tracking. “The ATTF (app tracking tool) makes it far more difficult for competing app publishers to access the user data relevant for advertising,” Andreas Mundt, cartel office president, said in a statement. Apple defended the feature in an emailed statement to Reuters, adding that it “holds itself to a higher standard than it requires of any third-party developer.” “We will continue to constructively engage with the Federal Cartel Office to ensure users continue to have transparency and control over their data,” it added. Apple will be required to address the concerns set out in the German charge sheet or risk further proceedings and daily fines if it fails to do so by the time of a final ruling which could come this year but is more likely to land next year. The case was triggered by complaints from associations representing publishers, broadcasters, advertisers, their agencies and ad tech firms. “Today’s charges are groundbreaking. Apple’s measures had created an artificial opacity in its ecosystem that led to less choice, higher costs for apps, and less protection against ad fraud, all while boosting Apple’s revenues from services,” said Thomas Höppner, partner at law firm Hausfeld, which represents the complainants. “For the first time it has been clarified that Apple may not rely on pretextual privacy arguments to massively restrict competition in its favor,” he said. Companies found guilty of breaching Germany’s antitrust rules risk fines as much as 10% of their annual turnover. Rachel More and Foo Yun Chee, Reuters
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President Donald Trump’s choice to run the Department of Education, Linda McMahon, faces a U.S. Senate confirmation hearing on Thursday where Democrats are likely to grill her on the president’s plans to shut the department outright. Trump on Wednesday reiterated his call to shutter the department, which employs about 4,200 people and had a $251 billion budget in the fiscal year that ended in September. “I’d like it to be closed immediately,” Trump said. “The Department of Education’s a big con job.” Shuttering the Cabinet-level department, created in 1979, would ultimately require the approval of Congress, where many Republicans have pushed for years to prioritize local control of the nation’s schools. Despite calling for the department’s closure, Trump and his fellow Republicans have also pushed for the federal government to scrutinize school districts’ sports programs and investigate cases of transgender athletes competing on women’s teams. Democrats on the Senate Health, Education, Labor and Pensions Committee are expected to press McMahon on the Trump administration’s moves to undo diversity, equity and inclusion initiatives, and her positions on school choice options, federal spending for high-poverty school districts and funding for the nationwide school lunch program. While they will have the power to grill McMahon, a former professional wrestling executive who headed the Small Business Administration during Trump’s first term, they do not have the votes to block her confirmation in a chamber that Republicans control 53-47. So far Senate Republicans have not blocked any of Trump’s Cabinet nominees, including controversial picks such as new Director of National Intelligence Tulsi Gabbard and Health and Human Services Secretary nominee Robert F. Kennedy Jr. Republicans at McMahon’s Senate confirmation hearing could question her approach towards the nation’s powerful teacher unions, her views of religion and prayer in the classroom, as well as on federal student aid relief, which was implemented by the Biden administration and rolled back by Trump last month. Bo Erickson, Reuters
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