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Art and science illuminate the same subtle proportions in tree branches

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theconversation.com – Mitchell Newberry, Research Assistant Professor of Biology, University of New Mexico – 2025-02-11 07:36:00

Art and science illuminate the same subtle proportions in tree branches

Tree branches in art throughout history follow geometric rules related to fractal geometry. ‘Almond blossom’ by Vincent van Gogh.
Van Gogh Museum, Amsterdam.

Mitchell Newberry, University of New Mexico

Do artists and scientists see the same thing in the shape of trees? As a scientist who studies branching patterns in living things, I’m 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.

When I saw Mondrian’s 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.

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.

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 you’re looking at. Scale invariance occurs in trees because trunks, limbs and twigs all branch in similar ways and for similar reasons.

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 Tolkien’s Tree of Gondor and the human capacity to appreciate the simple beauty of living things.

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.

Indeed, wherever our team looked at trees in great artwork, such as Klimt’s “Tree of Life” or Matsumura Goshun’s “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 Mondrian’s sketches reveal that “Blooming Apple Tree” and “Gray Tree” are the very same tree.

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

Mondrian’s 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 trees influence our lives in ways we often don’t notice, the art and science of trees show how humans are finely attuned to what’s 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.The Conversation

Mitchell Newberry, Research Assistant Professor of Biology, University of New Mexico

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3D printing will help space pioneers make homes, tools and other stuff they need to colonize the Moon and Mars

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theconversation.com – Sven Bilén, Professor of Engineering Design, Electrical Engineering and Aerospace Engineering, Penn State – 2025-03-13 07:51:00

3D printing could make many of the components for future structures on Mars.
3000ad/iStock via Getty Images Plus

Sven Bilén, Penn State

Throughout history, when pioneers set out across uncharted territory to settle in distant lands, they carried with them only the essentials: tools, seeds and clothing. Anything else would have to come from their new environment.

So they built shelter from local timber, rocks and sod; foraged for food and cultivated the soil beneath their feet; and fabricated tools from whatever they could scrounge up. It was difficult, but ultimately the successful ones made everything they needed to survive.

Something similar will take place when humanity leaves Earth for destinations such as the Moon and Mars – although astronauts will face even greater challenges than, for example, the Vikings did when they reached Greenland and Newfoundland. Not only will the astronauts have limited supplies and the need to live off the land; they won’t even be able to breathe the air.

Instead of axes and plows, however, today’s space pioneers will bring 3D printers. As an engineer and professor who is developing technologies to extend the human presence beyond Earth, I focus my work and research on these remarkable machines.

3D printers will make the tools, structures and habitats space pioneers need to survive in a hostile alien environment. They will enable long-term human presence on the Moon and Mars.

An astronaut holding a wrench poses for the camera.
NASA astronaut Barry Wilmore holds a 3D-printed wrench made aboard the International Space Station.
NASA

From hammers to habitats

On Earth, 3D printing can fabricate, layer by layer, thousands of things, from replacement hips to hammers to homes. These devices take raw materials, such as plastic, concrete or metal, and deposit it on a computerized programmed path to build a part. It’s often called “additive manufacturing,” because you keep adding material to make the part, rather than removing material, as is done in conventional machining.

Already, 3D printing in space is underway. On the International Space Station, astronauts use 3D printers to make tools and spare parts, such as ratchet wrenches, clamps and brackets. Depending on the part, printing time can take from around 30 minutes to several hours.

For now, the print materials are mostly hauled up from Earth. But NASA has also begun recycling some of those materials, such as waste plastic, to make new parts with the Refabricator, an advanced 3D printer installed in 2019.

Manufacturing in space

You may be wondering why space explorers can’t simply bring everything they need with them. After all, that’s how the International Space Station was built decades ago – by hauling tons of prefabricated components from Earth.

But that’s impractical for building habitats on other worlds. Launching materials into space is incredibly expensive. Right now, every pound launched aboard a rocket just to get to low Earth orbit costs thousands of dollars. To get materials to the Moon, NASA estimates the initial cost at around US$500,000 per pound.

Still, manufacturing things in space is a challenge. In the microgravity of space, or the reduced gravity of the Moon or Mars, materials behave differently than they do on Earth. Decrease or remove gravity, and materials cool and recrystallize differently. The Moon has one-sixth the gravity of Earth; Mars, about two-fifths. Engineers and scientists are working now to adapt 3D printers to function in these conditions.

An illustration of an astronaut looking at a base camp on Mars.
An artist’s impressions of what a Mars base camp might look like.
peepo/E+ via Getty Images

Using otherworldly soil

On alien worlds, rather than plastic or metal, 3D printers will use the natural resources found in these environments. But finding the right raw materials is not easy. Habitats on the Moon and Mars must protect astronauts from the lack of air, extreme temperatures, micrometeorite impacts and radiation.

Regolith, the fine, dusty, sandlike particles that cover both the lunar and Martian surfaces, could be a primary ingredient to make these dwellings. Think of the regolith on both worlds as alien dirt – unlike Earth soil, it contains few nutrients, and as far as we know, no living organisms. But it might be a good raw material for 3D printing.

My colleagues began researching this possibility by first examining how regular cement behaves in space. I am now joining them to develop techniques for turning regolith into a printable material and to eventually test these on the Moon.

But obtaining otherworldly regolith is a problem. The regolith samples returned from the Moon during the Apollo missions in the 1960s and 70s are precious, difficult if not impossible to access for research purposes. So scientists are using regolith simulants to test ideas. Actual regolith may react quite differently than our simulants. We just don’t know.

What’s more, the regolith on the Moon is very different from what’s found on Mars. Martian regolith contains iron oxide –that’s what gives it a reddish color – but Moon regolith is mostly silicates; it’s much finer and more angular. Researchers will need to learn how to use both types in a 3D printer.

YouTube video
See models of otherworldly habitats.

Applications on Earth

NASA’s Moon-to-Mars Planetary Autonomous Construction Technology program, also known as MMPACT, is advancing the technology needed to print these habitats on alien worlds.

Among the approaches scientists are now exploring: a regolith-based concrete made in part from surface ice; melting the regolith at high temperatures, and then using molds to form it while it’s a liquid; and sintering, which means heating the regolith with concentrated sunlight, lasers or microwaves to fuse particles together without the need for binders.

Along those lines, my colleagues and I developed a Martian concrete we call MarsCrete, a material we used to 3D-print a small test structure for NASA in 2017.

Then, in May 2019, using another type of special concrete, we 3D-printed a one-third scale prototype Mars habitat that could support everything astronauts would need for long-term survival, including living, sleeping, research and food-production modules.

That prototype showcased the potential, and the challenges, of building housing on the red planet. But many of these technologies will benefit people on Earth too.

In the same way astronauts will make sustainable products from natural resources, homebuilders could make concretes from binders and aggregates found locally, and maybe even from recycled construction debris. Engineers are already adapting the techniques that could print Martian habitats to address housing shortages here at home. Indeed, 3D-printed homes are already on the market.

Meanwhile, the move continues toward establishing a human presence outside the Earth. Artemis III, now scheduled for liftoff in 2027, will be the first human Moon landing since 1972. A NASA trip to Mars could happen as early as 2035.

But wherever people go, and whenever they get there, I’m certain that 3D printers will be one of the primary tools to let human beings live off alien land.The Conversation

Sven Bilén, Professor of Engineering Design, Electrical Engineering and Aerospace Engineering, Penn State

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George Washington, a real estate investor and successful entrepreneur, knew the difference between running a business and running the government

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theconversation.com – Eliga Gould, Professor of History, University of New Hampshire – 2025-03-10 07:50:00

President George Washington delivers his first inaugural address in April 1789 in New York City.
Painting by T.H. Matteson, engraving by H.S. Sadd, via Library of Congress

Eliga Gould, University of New Hampshire

During his three presidential campaigns, Donald Trump promised to run the federal government as though it were a business. True to his word, upon retaking office, Trump put tech billionaire Elon Musk at the head of a new group in the executive branch called the Department of Government Efficiency.

DOGE, as Musk’s initiative is known, has so far fired, laid off or received resignations from tens of thousands of federal workers and says it has discovered large sums of wasted or fraudulently spent tax dollars. But even its questionable claim of saving US$65 billion is less than 1% of the $6.75 trillion the U.S. spent in the 2024 fiscal year, and a tiny fraction of the nation’s cumulative debt of $36 trillion. Because Musk’s operation has not been formalized by Congress, DOGE’s indiscriminate cuts also raise troubling constitutional questions and may be illegal.

Before they go too far trying to run the government like a business, Trump and his advisors may want to consider the very different example of the nation’s first chief executive while he was in office.

A man stands while behind him a man sits at a desk.
Elon Musk, left, and Donald Trump have undertaken an effort both describe as seeking to run government more like a business.
Andrew Harnik/Getty Images

The first businessman to become president

Like Trump, George Washington was a businessman with a large real estate portfolio. Along with property in Virginia and six other states, he had extensive claims to Indigenous land in the Ohio River Valley.

Partly because of those far-flung investments, the first president supported big transportation projects, took an active interest in the invention of the steamboat, and founded the Patowmack Company, a precursor to the builders of the Chesapeake and Ohio Canal.

Above all, Washington was a farmer. On his Mount Vernon estate, in northern Virginia, he grew tobacco and wheat and operated a gristmill. After his second term as president, he built a profitable distillery. At the time of his death, he owned nearly 8,000 acres of productive farm and woodland, almost four times his original inheritance.

Much of Washington’s wealth was based on slave labor. In his will, he freed 123 of the 300 enslaved African Americans who had made his successful business possible, but while he lived, he expected his workers to do as he said.

President Washington and Congress

If Washington the businessman and plantation owner was accustomed to being obeyed, he knew that being president was another matter.

In early 1790, near the end of his first year in office, he reflected on the difference in a letter to the English historian Catharine Macaulay. Macaulay had visited Mount Vernon several years before. She was eager to hear the president’s thoughts about what, in his reply, he described as “the last great experiment for promoting human happiness by reasonable compact.”

The new government, Washington wrote, was “a government of accommodation as well as a government of laws.”

As head of the executive branch, his own powers were limited. In the months since the inauguration, he had learned that “much was to be done by prudence, much by conciliation, much by firmness. Few, who are not philosophical Spectators,” he told his friend, “can realise the difficult and delicate part which a man in my situation (has) to act.”

Although Washington did not say why his situation was delicate, he didn’t need to. Congress, as everyone knew, was the most powerful branch of government, not the president.

The previous spring, Congress had shown just how powerful it was when it debated whether the president, who needed Senate confirmation to appoint heads of executive departments, could remove such officers without the same body’s approval. In the so-called Decision of 1789, Congress determined that the president did have that power, but only after Vice President John Adams broke the deadlock in the upper house.

The meaning of Congress’ vote was clear. On matters where the Constitution is ambiguous, Congress would decide what powers the president can legally exercise and what powers he – or, someday, she – cannot.

When it created a “sinking fund” in 1790 to manage the national debt, Congress showed just how far it could constrain presidential power.

Although the fund was part of the Treasury Department, whose secretary served at the president’s pleasure, the commission that oversaw it served for fixed terms set by Congress. The president could neither remove them nor tell them what to do.

Inefficient efficiency

William Humphrey, a member of the Federal Trade Commission, was unconstitutionally fired by Franklin Roosevelt in 1933.
Library of Congress

By limiting Washington’s power over the Sinking Fund Commission, Congress set a precedent that still holds, notably in the 1935 Supreme Court case of Humphrey’s Executor v. U.S.

To the displeasure of those, including Trump, who promote the novel “unitary executive” theory of an all-powerful president, the court ruled that President Franklin D. Roosevelt could not dismiss a member of the Federal Trade Commission before his term was up – even if, as Roosevelt said, his administration’s goals would be “carried out most effectively with personnel of my own selection.”

Like the businessman who currently occupies the White House, Washington did not always like having to share power with Congress. Its members were headstrong and independent-minded. They rarely did what they were told.

But he realized working with Congress was the only way to create a federal government that really was efficient, with each branch carrying out its defined powers, as the founders intended. Because of the Constitution’s checks and balances, the United States was – and is – a government based on compromise between the three branches. No one, not even the president, is exempt.

To his credit, Washington was quick to learn that lesson.The Conversation

Eliga Gould, Professor of History, University of New Hampshire

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5 ways schools have shifted in 5 years since the COVID-19

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theconversation.com – Rachel Besharat Mann, Assistant Professor in Education Studies, Wesleyan University – 2025-03-10 07:48:00

Students sit in pop-up tents during wind ensemble class at Wenatchee High School on Feb. 26, 2021 in Wenatchee, Wash..
David Ryder/Getty Images

Rachel Besharat Mann, Wesleyan University and Gravity Goldberg, Wesleyan University

The U.S. educational landscape has been drastically transformed since the COVID-19 pandemic shuttered school campuses five years ago.

Access to high-quality teachers and curriculum developed by teachers is shrinking, for example. Likewise, there has been a loss of emotional support for students and a decline in the school use of technology and social media.

As education scholars focused on literacy practices in schools, here are five ways we believe the COVID-19 pandemic – and the rapid shift to remote learning and back – has transformed education:

1. Teachers are leaving, and those staying are stressed

At the start of the 2024-2025 school year, 82% of U.S. public schools had teaching vacancies.

Schools have tried to adapt by expanding class sizes and hiring substitute teachers. They have also increased use of video conferencing to Zoom teachers into classrooms.

A teacher sits at home in front of a computer monitor.
A teacher works from her home due to the COVID-19 outbreak on April 1, 2020, in Arlington, Va.
Olivier Doulier/AFP via Getty Images

Teacher retention has been a problem for at least a decade. But after the pandemic, there was an increase in the number of teachers who considered leaving the profession earlier than expected.

When teachers leave, often in the middle of the school year, it can require their colleagues to step in and cover extra classes. This means teachers who stay are overworked and possibly not teaching in their area of certification.

This, in turn, leads to burnout. It also increases the likelihood that students will not have highly qualified teachers in some hard-to-fill positions like physical science and English.

2. Increase in scripted curriculum

As of fall 2024, 40 states and Washington had passed science of reading laws, which mandate evidence-based reading instruction rooted in phonics and other foundational skills.

While the laws don’t necessarily lead to scripted curriculum, most states have chosen to mandate reading programs that require teachers to adhere to strict pacing. They also instruct teachers not to deviate from the teachers’ manual.

Many of these reading programs came under scrutiny by curricular evaluators from New York University in 2022. They found the most common elementary reading programs were culturally destructive or culturally insufficient – meaning they reinforce stereotypes and portray people of color in inferior and destructive ways that reinforce stereotypes.

This leaves teachers to try to navigate the mandated curriculum alongside the needs of their students, many of whom are culturally and linguistically diverse. They either have to ignore the mandated script or ignore their students. Neither method allows teachers to be effective.

When teachers are positioned as implementers of curriculum instead of professionals who can be trusted to make decisions, it can lead to student disengagement and a lack of student responsiveness.

This form of de-professionalization is a leading cause of teacher shortages. Teachers are most effective, research shows, when they feel a sense of agency, something that is undermined by scripted teaching.

3. Improvements in teen mental health, but there’s more to do

Many of the narratives surrounding adolescent mental health, particularly since the pandemic, paint a doomscape of mindless social media use and isolation.

However, data published in 2024 shows improvements in teen reports of persistent sadness and hopelessness. Though the trend is promising in terms of mental health, in-school incidences of violence and bullying rose in 2021-22, and many teens report feeling unsafe at school.

Other reports have shown an increase in feelings of loneliness and isolation among teens since the pandemic.

4. Crackdown on students’ technology use in schools

COVID-19 prompted schools to make an abrupt switch to educational technology, and many schools have kept many of these policies in place.

For example, Google Classroom and other learning management systems are commonly used in many schools, particularly in middle school and high school.

These platforms can help parents engage with their children’s coursework. That facilitates conversations and parental awareness.

But this reliance on screens has also come under fire for privacy issues – the sharing of personal information and sensitive photos – and increasing screen time.

And with academia’s use of technology on the rise, cellphone usage has also increased among U.S. teens, garnering support for school cellphone bans.

A child wearing a face mask looks at a laptop computer.
A student attends an online class at the Crenshaw Family YMCA on Feb. 17, 2021, in Los Angeles during the COVID-19 pandemic.
Patrick T. Fallon/AFP via Getty Images

But banning these devices in schools may not help teens, as smartphone use is nearly universal in the U.S. Teens need support from educators to support them as they learn to navigate the complex digital world safely, efficiently and with balance.

In light of data surrounding adolescent mental health and online isolation – and the potential for connection through digital spaces – it’s also important that teens are aware of positive support networks that are available online.

Though these spaces can provide social supports, it is important for teens to understand the strengths and limitations of technology and receive authentic guidance from adults that a technology ban may prohibit.

5. Students and adults need social emotional support

Students returned to in-person schooling with a mix of skill levels and with a variety of social and emotional needs.

Social and emotional learning includes self-awareness, self-management, social awareness, relational skills and decision-making.

These skills are vital for academic success and social relationships.

Teachers reported higher student needs for social and emotional learning after they returned to in-person instruction.

While some of this social and emotional teaching came under fire from lawmakers and parents, this was due to confusion about what it actually entailed. These skills do not constitute a set of values or beliefs that parents may not agree with. Rather, they allow students to self-regulate and navigate social situations by explicitly teaching students about feelings and behaviors.

A teacher and student are separated by plexiglass as they sit across from each other at a desk.
A teacher provides instruction to a student at Freedom Preparatory Academy on Feb. 10, 2021, in Provo, Utah.
George Frey/Getty Images

One area where students may need support is with cognitive flexibility, or the ability to adapt to current situations and keep an open mind. Classroom instruction that engages students in varied tasks and authentic teaching strategies rooted in real-life scenarios can strengthen this ability in students.

Besides allowing students to be engaged members of a school community, cognitive flexibility is important because it supports the skill development that is part of many state English language arts and social studies standards.

Social and emotional learning and cognitive flexibility are key components that allow students to learn.

Due to vague or confusing state policies, many schools have stopped teaching social and emotional learning skills, or minimized their use.

This, coupled with teacher stress and burnout, means that both adults and children in schools are often not getting their social and emotional needs met.

Message of mistrust

While we described five shifts since the start of the pandemic, the overall trend in K-12 schools is one of mistrust.

We feel that the message – from districts, state legislators and parents – is that teachers cannot be trusted to make choices.

This represents a massive shift. During the initial phase of the COVID-19 lockdown, teachers were revered and thanked for their service.

We believe in teacher autonomy and professionalism, and we hope this list can help Americans reflect on the direction of the past five years. If society wants a different outcome in the next five years, it starts with trust.The Conversation

Rachel Besharat Mann, Assistant Professor in Education Studies, Wesleyan University and Gravity Goldberg, Visiting Assistant Professor in Education Studies, Wesleyan University

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