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Will I ever need math? A mathematician explains how math is everywhere – from soap bubbles to Pixar movies

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Will I ever need math? A mathematician explains how math is everywhere – from soap bubbles to Pixar movies

In addition to explaining natural phenomena, math can strengthen your brain.
Liz Arnold, CC BY-ND

Hortensia Soto, Colorado State University

Curious Kids is a series for children of all ages. If you have a question you’d like an expert to answer, send it to curiouskidsus@theconversation.com.


Will I ever need math besides for school or work? – Hadassah G., age 9, New Jersey


It can be easy to think that you need math only to do your algebra or geometry homework or if you have a job as an engineer. But, in fact, math pops up everywhere – even in the soap bubbles in your kitchen sink.

While washing dishes when I was 13, I noticed that the soap bubbles formed tiny 3D polygons, packed together like a honeycomb, but not all of these shapes were perfectly round. Why did some of the bubbles look like hexagons? Why were others shaped like squares full of air? Why didn’t I see any star-shaped bubbles, or bubbles with spikes?

A tightly packed collection of hexagon-shaped, rainbow-colored bubbles against a dark background
Math helps explain the shapes of bubbles and the reason they naturally pack together without any gaps.
Adrienne Bresnahan/Moment via Getty Images

When I learned that math could help answer these questions, I thought that was so cool! Now, as a professor of mathematics who studies how people learn math through play, I understand why bubbles are naturally lazy. I even studied the math behind the reason I saw only some shapes in soapy dishwater.

Besides helping explain the behavior of bubbles and other curiosities of nature, math is likely part of many of your everyday activities, along with the technology you enjoy and even the inner workings of your brain. Doing math isn’t just about computing, memorizing, solving an equation or doing word problems by yourself. It’s really about creative problem-solving and logical thinking with other people.

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Math in everyday life

Many topics you learn in elementary school – like fractions, percentages and measurements – are useful in everyday life.

For example, if you want to build a fence around your house, paint your walls a new color or with a design, or sew yourself a new outfit or quilt, all of those activities require knowledge about measurement and scaling. More complicated construction projects, such as building a treehouse, require lots of mathematical problem-solving skills.

Once you’ve laid out the plans for one of these projects, you need to buy all the materials. Percentages – which are special kinds of fractions – are especially important to understand when managing money. Understanding percentages can help you budget your money and increase your net worth.

Beyond budgeting, you might find yourself using percentages when cooking a double batch of brownies, determining how much medicine to take when you’re sick or understanding the weather forecast.

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Your favorite technology needs math

Math is an essential tool that animators use to make movies.

Pixar artists use math to make movies like ‘Elemental.’

Studios like Pixar rely on ideas from geometry to bring characters like Ember from “Elemental” to life. With an understanding of geometric transformations like reflections, rotations and translations, you can use your computer to make your own animations.

Coordinate systems, which are fundamental to geometry, show up in games like Minecraft. The 2D Minecraft world uses a 2D coordinate system – with an x-axis and a y-axis – where you can move north, south, east or . In the 3D Minecraft world, there’s also a z-axis, allowing you to move up and down. Middle and high school teachers can even use Minecraft to help students learn math concepts.

Many high-paying jobs use math, especially probability – again, fractions. Understanding probability helps identify how effective medical treatments are, informs coaches about ways their teams can improve and aids cryptographers in keeping private information – like your email password or ATM PIN – secret. Cryptography combines probability with number theory to create secret codes that are difficult to crack.

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Math helps your brain

Math can have a big impact on your internal life, too. You can use math activities to train your brain the same way you would train your body for a sport. Doing math helps your brain become flexible so you can better handle new tasks and ideas of all kinds.

Even doing things that don’t look like your math homework, such as crossword puzzles, word searches and board games like Set and Blokus, are deeply mathematical activities that help your brain get stronger. This kind of mental training helps the brain pay attention and solve problems and improves memory. A strong working memory supports brain functions that lower the risk of Alzheimer’s disease and dementia.

a stronger, more flexible brain also aids quantitative literacy, which can help you make sense of graphs that appear in the , reflect critically about and understand health and financial information.

Math can even help you outsmart artificial intelligence. With the rise of AI, it’s important to be able to think creatively, reason logically and make connections between concepts – whether mathematical or not. Puzzling through a difficult math problem nurtures these skills, even if you don’t get the right answer right away.

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A woman leans across a table to help one of several young children building a cubical structure out of small colorful balls and sticks.
Hortensia Soto demonstrates the hidden math of soap bubbles as part of Cafecito con Matemáticas, organized by Liz Arnold and Jocelyn Rios at Colorado State .
Liz Arnold, CC BY-ND

It’s important to remember that doing math doesn’t require you to be fast or to get the correct answer right away. In fact, you can learn a lot by getting the wrong answer. Working with other people can also help you to make sure you really understand the problem and builds communication and teamwork skills.

Math is so much more than memorizing times tables and filling out homework problem sets. So next time you kick back to watch your favorite animated , or start saving up for a fancy new tech gadget, hopefully you’ll appreciate how math is woven into so many parts of life.


Hello, curious kids! Do you have a question you’d like an expert to answer? Ask an adult to send your question to CuriousKidsUS@theconversation.com. Please tell us your name, age and the city where you .

And since curiosity has no age limit – adults, let us know what you’re wondering, too. We won’t be able to answer every question, but we will do our best.The Conversation

Hortensia Soto, Professor of Mathematics, Colorado State University

This article is republished from The Conversation under a Creative Commons license. Read the original article.

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Sunflowers make small moves to maximize their Sun exposure − physicists can model them to predict how they grow

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theconversation.com – Chantal Nguyen, Postdoctoral Associate at the BioFrontiers Institute, of Colorado Boulder – 2024-09-13 07:31:40

Sunflowers use tiny movements to follow the Sun’s path throughout the day.

AP Photo/Charlie Riedel

Chantal Nguyen, University of Colorado Boulder

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Most of us aren’t spending our days watching our houseplants grow. We see their signs of only occasionally – a new leaf unfurled, a stem leaning toward the window.

But in the summer of 1863, Charles Darwin lay ill in bed, with nothing to do but watch his plants so closely that he could detect their small movements to and fro. The tendrils from his cucumber plants swept in circles until they encountered a stick, which they proceeded to twine around.

“I am getting very much amused by my tendrils,” he wrote.

This amusement blossomed into a decadeslong fascination with the little-noticed world of plant movements. He compiled his detailed observations and experiments in a 1880 book called “The Power of Movement in Plants.”

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A zig-zagging line showing the movement of a leaf.

A diagram tracking the circumnutation of a leaf over three days.

Charles Darwin

In one study, he traced the motion of a carnation leaf every few hours over the course of three days, revealing an irregular looping, jagged path. The swoops of cucumber tendrils and the zags of carnation leaves are examples of inherent, ubiquitous plant movements called circumnutations – from the Latin circum, meaning circle, and nutare, meaning to nod.

Circumnutations vary in size, regularity and timescale across plant species. But their exact function remains unclear.

I’m a physicist interested in understanding collective behavior in living . Like Darwin, I’m captivated by circumnutations, since they may underlie more complex phenomena in groups of plants.

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Sunflower patterns

A 2017 study revealed a fascinating observation that got my colleagues and me wondering about the role circumnutations could play in plant growth patterns. In this study, researchers found that sunflowers grown in a dense row naturally formed a near-perfect zigzag pattern, with each plant leaning away from the row in alternating directions.

This pattern the plants to avoid shade from their neighbors and maximize their exposure to sunlight. These sunflowers flourished.

Researchers then planted some plants at the same density but constrained them so that they could grow only upright without leaning. These constrained plants produced less oil than the plants that could lean and get the maximum amount of sun.

While farmers can’t grow their sunflowers quite this close together due to the potential for disease spread, in the future they may be able to use these patterns to up with new planting strategies.

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Self-organization and randomness

This spontaneous pattern formation is a neat example of self-organization in nature. Self-organization refers to when initially disordered systems, such as a jungle of plants or a swarm of bees, achieve order without anything controlling them. Order emerges from the interactions between individual members of the system and their interactions with the .

Somewhat counterintuitively, noise – also called randomness – facilitates self-organization. Consider a colony of ants.

Ants secrete pheromones behind them as they crawl toward a food source. Other ants find this food source by the pheromone trails, and they further reinforce the trail they took by secreting their own pheromones in turn. Over time, the ants converge on the best path to the food, and a single trail prevails.

But if a shorter path were to become possible, the ants would not necessarily find this path just by following the existing trail.

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If a few ants were to randomly deviate from the trail, though, they might stumble onto the shorter path and create a new trail. So this randomness injects a spontaneous change into the ants’ system that allows them to explore alternative scenarios.

Eventually, more ants would follow the new trail, and soon the shorter path would prevail. This randomness helps the ants adapt to changes in the environment, as a few ants spontaneously seek out more direct ways to their food source.

A group of honeybees spread out standing on honeycomb.

Beehives are an example of self-organization in nature.

Martin Ruegner/Stone via Getty Images

In biology, self-organized systems can be found at a range of scales, from the patterns of proteins inside cells to the socially complex colonies of honeybees that collectively build nests and forage for nectar.

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Randomness in sunflower self-organization

So, could random, irregular circumnutations underpin the sunflowers’ self-organization?

My colleagues and I set out to explore this question by following the growth of young sunflowers we planted in the lab. Using cameras that imaged the plants every five minutes, we tracked the movement of the plants to see their circumnutatory paths.

We saw some loops and spirals, and lots of jagged movements. These ultimately appeared largely random, much like Darwin’s carnation. But when we placed the plants together in rows, they began to move away from one another, forming the same zigzag configurations that we’d seen in the previous study.

Five plants and a diagram showing loops and jagged lines that represent small movements made by the plants.

Tracking the circumnutations made by young sunflower plants.

Chantal Nguyen

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We analyzed the plants’ circumnutations and found that at any given time, the direction of the plant’s motion appeared completely independent of how it was moving about half an hour earlier. If you measured a plant’s motion once every 30 minutes, it would appear to be moving in a completely random way.

We also measured how much the plant’s leaves grew over the course of two weeks. By putting all of these results together, we sketched a picture of how a plant moved and grew on its own. This information allowed us to computationally model a sunflower and simulate how it behaves over the course of its growth.

A sunflower model

We modeled each plant simply as a circular crown on a stem, with the crown expanding according to the growth rate we measured experimentally. The simulated plant moved in a completely random way, taking a “step” every half hour.

We created the model sunflowers with circumnutations of lower or higher intensity by tweaking the step sizes. At one end of the spectrum, sunflowers were much more likely to take tiny steps than big ones, leading to slow, minimal movement on average. At the other end were sunflowers that are equally as likely to take large steps as small steps, resulting in highly irregular movement. The real sunflowers we observed in our experiment were somewhere in the middle.

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Plants require light to grow and have evolved the ability to detect shade and alter the direction of their growth in response.

We wanted our model sunflowers to do the same thing. So, we made it so that two plants that get too close to each other’s shade begin to lean away in opposite directions.

Finally, we wanted to see whether we could replicate the zigzag pattern we’d observed with the real sunflowers in our model.

First, we set the model sunflowers to make small circumnutations. Their shade avoidance responses pushed them away from each other, but that wasn’t enough to produce the zigzag – the model plants stayed stuck in a line. In physics, we would call this a “frustrated” system.

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Then, we set the plants to make large circumnutations. The plants started moving in random patterns that often brought the plants closer together rather than farther apart. Again, no zigzag pattern like we’d seen in the field.

But when we set the model plants to make moderately large movements, similar to our experimental measurements, the plants could self-organize into a zigzag pattern that gave each sunflower optimal exposure to light.

So, we showed that these random, irregular movements helped the plants explore their surroundings to find desirable arrangements that benefited their growth.

Plants are much more dynamic than people give them credit for. By taking the time to follow them, scientists and farmers can unlock their secrets and use plants’ movement to their advantage.The Conversation

Chantal Nguyen, Postdoctoral Associate at the BioFrontiers Institute, University of Colorado Boulder

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This article is republished from The Conversation under a Creative Commons license. Read the original article.

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Endometriosis pain leads to missed school and work in two-thirds of women with the condition, new study finds

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theconversation.com – Rasha Al-Lami, Researcher in Women’s , Yale – 2024-09-13 07:30:43

Endometriosis affects about 10% of reproductive-age women worldwide.

Xavier Lorenzo/Moment via Getty Images

Rasha Al-Lami, Yale University

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More than two-thirds of women with endometriosis missed school or work due to pain from the , in a study of more than 17,000 women between the ages of 15 and 44 in the U.S. That is a key finding of new research published in the Journal of Endometriosis and Uterine Disorders.

Our study also found that Black and Hispanic women were less likely to be diagnosed with endometriosis with white women. Interestingly, women who identified as part of the LGBTQ community had a higher likelihood of receiving an endometriosis diagnosis than heterosexual women.

We used data from the National Health and Nutrition Examination Survey, which is administered by the Centers for Disease Control and Prevention, for the period 2011 to 2019. The survey data use adjusted weights to account for the racial composition of U.S. society, meaning our sample of 17,619 women represents 51,981,323 women of the U.S. population.

We specifically examined factors related to quality of , such as poverty, education and functional impairment, as well as race and sexual orientation.

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I am a physician-scientist and a researcher in women’s health, working together with specialists in OB-GYN from Yale and the University of .

Why it matters

Endometriosis is a chronic, often painful condition that affects approximately 10% of reproductive-age women worldwide. It occurs when tissues that would normally line the inner surface of the uterus instead occur outside the uterus, such as on the ovaries or even in distant organs such as the lungs or brain. These abnormally located lesions respond to hormonal changes during the menstrual cycle, causing pain when stimulated by the hormones that regulate the menstrual cycle.

Our study sheds light on how endometriosis, despite its prevalence, remains underdiagnosed and underresearched. We found that 6.4% of reproductive-age women in the U.S. had an endometriosis diagnosis. More than 67% reported missed work or school, or been unable to perform daily activities, due to pain associated with endometriosis.

Our study highlights disparities in the diagnosis and management of endometriosis among different racial groups. Black women had 63% lower odds of getting an endometriosis diagnosis, and Hispanic women had 55% lower odds compared with non-Hispanic white women. This disparity may reflect historical biases in health care, pointing to the need for more equitable practices.

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In addition, our study underscores the importance of considering women’s health across diverse population subgroups, with particular attention to sexual orientation. We found that non-heterosexual lesbian, gay, bisexual, transgender and queer women had 54% higher odds of receiving an endometriosis diagnosis compared with straight women. Our study was the first to examine endometriosis likelihood among non-heterosexual women at the national level in the U.S.

We found no significant association between endometriosis and other quality-of-life indicators such as poverty, education or employment status, which suggests that the condition affects women across various socioeconomic backgrounds.

A common theory about the cause of endometriosis is that women have menstrual blood that seeds outside of the uterus, but recent research supports inflammatory causes.

What other research is being done

Our work adds to the growing body of evidence that Black women are less likely to be diagnosed with endometriosis and that their reported pain symptoms are often overlooked.

Explanations for this inequity include health care bias against minority women and limited access to medical care among Black women. Research also shows that many medical professionals as well as medical students and believe that Black women have a lower pain threshold compared with the white population.

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This is another possible reason that pain symptoms among Black women with endometriosis get neglected. Researchers from the U.K reported the same findings, attributing these disparities to systemic bias and inequitable medical care.

Another study estimates that the lifetime costs associated with having endometriosis are about US$27,855 per year per patient in the U.S., costing the country about $22 annually on health care expenditures.The Conversation

Rasha Al-Lami, Researcher in Women’s Health, Yale University

This article is republished from The Conversation under a Creative Commons license. Read the original article.

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Biobots arise from the cells of dead organisms − pushing the boundaries of life, death and medicine

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theconversation.com – Peter A Noble, Affiliate Professor of Microbiology, of Washington – 2024-09-12 07:31:37

Biobots could one day be engineered to deliver and clear up arterial plaque.
Kriegman et al. 2020/PNAS, CC BY-SA

Peter A Noble, University of Washington and Alex Pozhitkov, Irell & Manella Graduate School of Biological Sciences at City of Hope

Life and are traditionally viewed as opposites. But the emergence of new multicellular life-forms from the cells of a dead organism introduces a “third state” that lies beyond the traditional boundaries of life and death.

Usually, scientists consider death to be the irreversible halt of functioning of an organism as a whole. However, practices such as organ donation highlight how organs, tissues and cells can continue to function even after an organism’s demise. This resilience raises the question: What mechanisms allow certain cells to keep working after an organism has died?

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We are researchers who investigate what happens within organisms after they die. In our recently published review, we describe how certain cells – when provided with nutrients, oxygen, bioelectricity or biochemical cues – have the capacity to transform into multicellular organisms with new functions after death.

Life, death and emergence of something new

The third state challenges how scientists typically understand cell behavior. While caterpillars metamorphosing into butterflies, or tadpoles evolving into frogs, may be familiar developmental transformations, there are few instances where organisms change in ways that are not predetermined. Tumors, organoids and cell lines that can indefinitely divide in a petri dish, like HeLa cells, are not considered part of the third state because they do not develop new functions.

However, researchers found that skin cells extracted from deceased frog embryos were able to adapt to the new conditions of a petri dish in a lab, spontaneously reorganizing into multicellular organisms called xenobots. These organisms exhibited behaviors that extend far beyond their original biological roles. Specifically, these xenobots use their cilia – small, hair-like structures – to navigate and move through their surroundings, whereas in a living frog embryo, cilia are typically used to move mucus.

Xenobots can move, heal and interact with their environment on their own.

Xenobots are also able to perform kinematic self-replication, meaning they can physically replicate their structure and function without growing. This differs from more common replication processes that involve growth within or on the organism’s body.

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Researchers have also found that solitary human lung cells can self-assemble into miniature multicellular organisms that can move around. These anthrobots behave and are structured in new ways. They are not only able to navigate their surroundings but also repair both themselves and neuron cells placed nearby.

Taken together, these findings demonstrate the inherent plasticity of cellular and the idea that cells and organisms can evolve only in predetermined ways. The third state suggests that organismal death may play a significant role in how life transforms over time.

Microscopy images of a black blob fusing together two groundglass walls in three panels, and a green web plugging a gap in a web of pink
Diagram A shows an anthrobot building a bridge across a scratched neuron over the course of three days. Diagram B highlights the ‘stitch’ in green at the end of Day 3.
Gumuskaya et al. 2023/Advanced Science, CC BY-SA

Postmortem conditions

Several factors influence whether certain cells and tissues can survive and function after an organism dies. These include environmental conditions, metabolic activity and preservation techniques.

Different cell types have varying survival times. For example, in humans, white blood cells die between 60 and 86 hours after organismal death. In mice, skeletal muscle cells can be regrown after 14 days postmortem, while fibroblast cells from sheep and goats can be cultured up to a month or so postmortem.

Metabolic activity plays an important role in whether cells can continue to survive and function. Active cells that require a continuous and substantial supply of energy to maintain their function are more difficult to culture than cells with lower energy requirements. Preservation techniques such as cryopreservation can allow tissue samples such as bone marrow to function similarly to that of living donor sources.

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Inherent survival mechanisms also play a key role in whether cells and tissues live on. For example, researchers have observed a significant increase in the activity of stress-related genes and immune-related genes after organismal death, likely to compensate for the loss of homeostasis. Moreover, factors such as trauma, infection and the time elapsed since death significantly affect tissue and cell viability.

Microscopy image of developing white and red blood cells
Different cell types have different capacities for survival, white blood cells.
Ed Reschke/Stone via Getty Images

Factors such as age, , sex and type of species further shape the postmortem landscape. This is seen in the challenge of culturing and transplanting metabolically active islet cells, which produce insulin in the pancreas, from donors to recipients. Researchers believe that autoimmune processes, high energy costs and the degradation of protective mechanisms could be the reason behind many islet transplant failures.

How the interplay of these variables allows certain cells to continue functioning after an organism dies remains unclear. One hypothesis is that specialized channels and pumps embedded in the outer membranes of cells serve as intricate electrical circuits. These channels and pumps generate electrical that allow cells to communicate with each other and execute specific functions such as growth and movement, shaping the structure of the organism they form.

The extent to which different types of cells can undergo transformation after death is also uncertain. Previous research has found that specific genes involved in stress, immunity and epigenetic regulation are activated after death in mice, zebrafish and people, suggesting widespread potential for transformation among diverse cell types.

Implications for biology and medicine

The third state not only offers new insights into the adaptability of cells. It also offers prospects for new treatments.

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For example, anthrobots could be sourced from an individual’s living tissue to deliver drugs without triggering an unwanted immune response. Engineered anthrobots injected into the body could potentially dissolve arterial plaque in atherosclerosis patients and remove excess mucus in cystic fibrosis patients.

Importantly, these multicellular organisms have a finite life span, naturally degrading after four to six weeks. This “kill switch” prevents the growth of potentially invasive cells.

A better understanding of how some cells continue to function and metamorphose into multicellular entities some time after an organism’s demise holds promise for advancing personalized and preventive medicine.The Conversation

Peter A Noble, Affiliate Professor of Microbiology, University of Washington and Alex Pozhitkov, Senior Technical Lead of Bioinformatics, Irell & Manella Graduate School of Biological Sciences at City of Hope

This article is republished from The Conversation under a Creative Commons license. Read the original article.

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