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Anyone can play Tetris, but architects, engineers and animators alike use the math concepts underlying the game

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Anyone can play Tetris, but architects, engineers and animators alike use the math concepts underlying the game

Tetris has hooked people for decades.
AP Photo/Richard Drew

Leah McCoy, Wake Forest University

With its bright colors, easy-to-learn rules and familiar music, the Tetris has endured as a pop culture icon over the last 40 years. Many people, like me, have been playing the game for decades, and it has evolved to adapt to new technologies like game systems, phones and tablets. But until January 2024, nobody had ever been able to beat it.

A teen from Oklahoma the Tetris title after he crashed the game on Level 157 and beat the game. Beating it means the player moved the tiles too fast for the game to keep up with the score, causing the game to crash. Artificial intelligence can suggest strategies that allow players to more effectively control the game tiles and slot them into place faster – these strategies helped crown the game’s first winner.

The Las Vegas sphere lit up with a massive game of Tetris in January 2024. The game’s appeal spans generations.

But there’s far more to Tetris than the elusive promise of winning. As a mathematician and mathematics educator, I recognize that the game is based on a fundamental element of geometry, called dynamic spatial reasoning. The player uses these geometric skills to manipulate the game pieces, and playing can both test and improve a player’s dynamic spatial reasoning.

Playing the game

A Russian computer scientist named Alexey Pajitnov invented Tetris in 1984. The game itself is very simple: The Tetris screen is composed of a rectangular game board with dropping geometric figures. These figures are called tetrominoes, made up of four squares connected on their sides in seven different configurations.

The game pieces drop from the top, one at a time, stacking up from the bottom. The player can manipulate each one as it falls by turning or sliding it and then dropping it to the bottom. When a row completely fills up, it disappears and the player earns points.

As the game progresses, the pieces appear at the top more quickly, and the game ends when the stack reaches the top of the board.

Dynamic spatial reasoning

A Tetris board, which has blocks made up of four squares arranged in different formations, stacked atop each other.
A Tetris board.
Brandenads/Wikimedia Commons

Manipulating the game pieces gives the player an exercise in dynamic spatial reasoning. Spatial reasoning is the ability to visualize geometric figures and how they will move in . So, dynamic spatial reasoning is the ability to visualize actively moving figures.

The Tetris player must quickly decide where the currently dropping game piece will best fit and then move it there. This movement involves both translation, or moving a shape right and left, and rotation, or twirling the shape in increments of 90 degrees on its axis.

Spatial visualization is partly inherent ability, but partly learned expertise. Some researchers identify spatial skill as necessary for successful problem solving, and it’s often used alongside mathematics skills and verbal skills.

Spatial visualization is a key component of a mathematics discipline called transformational geometry, which is usually first taught in middle school. In a typical transformational geometry exercise, might be asked to represent a figure by its x and y coordinates on a coordinate graph and then identify the transformations, like translation and rotation, necessary to move it from one position to another while keeping the piece the same shape and size.

Reflection and dilation are the two other basic mathematical transformations, though they’re not used in Tetris. Reflection flips the image across any line while maintaining the same size and shape, and dilation changes the size of the shape, producing a similar figure.

Transformations may seem simple, but they underlie lots of more complex math concepts.

For many students, these exercises are tedious, as they involve plotting many points on graphs to move a figure’s position. But like Tetris can students grasp these concepts in a dynamic and engaging way.

Transformational geometry beyond Tetris

While it may seem simple, transformational geometry is the foundation for several advanced topics in mathematics. Architects and engineers both use transformations to draw up blueprints, which represent the real world in scale drawings.

Animators and computer graphic designers use concepts of transformations as well. Animation involves representing a figure’s coordinates in a matrix array and then creating a sequence to change its position, which moves it across the screen. While animators use computer programs that automatically move figures around, they are all based on translation.

Calculus and differential geometry also use transformation. The concept of optimization involves representing a situation as a function and then finding the maximum or minimum value of that function. Optimization problems often involve graphic representations where the student uses transformations to manipulate one or more of the variables.

Lots of real-world applications use optimization – for example, businesses might want to find out the minimum cost of distributing a product. Another example is figuring out the size of a theoretical box with the largest possible volume.

All of these advanced topics use the same concepts as the simple moves of Tetris.

Tetris is an engaging and entertaining video game, and players with transformational geometry skills might find playing it. Research has found that manipulating rotations and translations within the game can a solid conceptual foundation for advanced mathematics in numerous science fields.

Playing Tetris may lead students to a future aptitude in business analytics, engineering or computer science – and it’s fun. As a mathematics educator, I encourage students and friends to play on.The Conversation

Leah McCoy, Professor of Education, Wake Forest University

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

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The Conversation

Election anxiety doesn’t need to win − here are 3 science-backed strategies from a clinical psychologist to rein in the stress

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theconversation.com – Shannon Sauer-Zavala, Associate Professor of Psychology & Licensed Clinical Psychologist, University of Kentucky – 2024-11-01 15:46:00

The world won’t end if you stop scrolling.
georgeclerk/E+ via Getty Images

Shannon Sauer-Zavala, University of Kentucky

Uncertainty about the election getting to you? Is anxiety the dominant feature of your emotional landscape, maybe with a small sprinkling of impending doom?

You are not alone. A recent survey found 69% of American adults are seriously stressed about the 2024 presidential election.

It’s difficult not to be worked up about in ‘s polarized climate. Regardless of which side of the political aisle you sit on, you may find yourself glued to your browser or TV, gobbling up every tiny tidbit of news and feeling your stress levels skyrocket.

I’m a psychologist who develops and tests strategies for combating anxiety. As I constantly tell my stressed-out clients, when it comes to election news, there’s a fine line between being well informed and being oversaturated with information.

If you’re ready to short-circuit your stress spiral, here are three science-backed strategies for coping with anxiety in times of uncertainty.

Approach your emotions with mindfulness

Being mindful refers to the quality of awareness you bring to your experiences – specifically, nonjudgmental attention focused on what’s right now.

Mindfulness practices originated in Eastern spiritual traditions, including Buddhism. Over the past several decades, mindfulness has gained popularity as a powerful tool for managing anxiety. For instance, meditation apps such as Headspace and Calm incorporate it. Even if meditation isn’t your thing, though, you can still apply nonjudgmental awareness, focused on the present, to election-related anxiety.

Be present. Anxiety can draw you into an uncomfortable spiral of “what-ifs” about the future. When you make a point to be present, you remind yourself what is actually happening right now, rather than letting hypothetical fears take over.

Although you may have serious concerns about the fate of the nation, those outcomes have not yet to bear. As I tell my , “We’ll cross that bridge if we come to it. For now, focus on the step right in front of you.”

If you notice yourself getting carried away by thoughts of the future, you can pull yourself back to the present by bringing awareness to simple sensations – the feel of your feet on the floor, the rhythm of your breath, or the sounds around you – and remind yourself that you are safe in the current moment.

Pay nonjudgmental attention. Many people are hard on themselves for feeling strong emotions. This critical mindset might look like telling yourself that you’re overreacting, or that it’s weak to let others see that you’re upset. You might even view that uncomfortable feeling in the pit of your stomach as evidence that negative outcomes are right around the corner.

Making judgments about your emotions only serves to make you feel worse. In fact, researchers find that pushing away emotions or beating yourself up for them leads to more frequent and stronger anxiety.

Instead, try giving yourself a break. Tell yourself, “This election is high stakes, so it makes sense I’m anxious.” Then, notice if your anxiety is driven by a fear about the future, and bring yourself back to the present.

older woman comforts a younger woman who is looking off into distance
Pull your thoughts back to the here and now.
supersizer/E+ via Getty Images

Get flexible with your thinking

Cognitive flexibility is the ability to shift away from rigid, all-or-nothing thinking about the future.

When people are anxious, they tend to focus on the worst-case scenario. For example, you might be telling yourself, “With this candidate in office, things will be terrible and I won’t be able to cope.”

In this scenario, I encourage my patients to move past that initial thought of how awful it will be and instead consider exactly how they will respond to the inauguration, the next day, , month and so on.

Cognitive flexibility allows you to explore how you will cope, even in the face of a negative outcome, helping you feel a bit less out of control. If you’re experiencing a lot of anxiety about the election, try thinking through what you’d do if the undesirable candidate takes office – thoughts like “I’ll to causes that are important to me” and “I’ll attend protests.”

Choose your actions with intention

Another tool for managing your anxiety is to consider whether your behaviors are affecting how you feel.

Remember, for instance, the goal of 24-hour news networks is to increase ratings. It’s in their interest to keep you riveted to your screens by making it seem like important announcements are imminent. As a result, it may feel difficult to disconnect and take part in your usual self-care behavior.

Try telling yourself, “If something happens, someone will text me,” and go for a walk or, better yet, to bed. Keeping up with healthy habits can reduce your vulnerability to uncontrolled anxiety.

woman faces away from camera, wearing a 'VOTE' t shirt
It’s not on your shoulders to solve every single problem in the world.
AP Photo/John Hanna

Post-Election Day, you may continue to feel drawn to the news and motivated to show up – whether that means donating, volunteering or protesting – for a variety of causes you think will be affected by the election results. Many people describe feeling guilty if they say no or disengage, leading them to overcommit and wind up overwhelmed.

If this sounds like you, try reminding yourself that taking a break from politics to cook, engage with your family or friends, get some work done or go to the gym does not mean you don’t care. In fact, keeping up with the activities that fuel you will give you the energy to contribute to important causes more meaningfully.The Conversation

Shannon Sauer-ZavalaUniversity of Kentucky

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

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The Conversation

How to overcome your device dependency and manage a successful digital detox

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theconversation.com – Kelley Cours Anderson, Assistant Professor of Marketing, College of Charleston – 2024-11-01 07:39:00

Getting outside – without your phone – is one way to disconnect.
We Are/DigitalVision via Getty Images

Kelley Cours Anderson, College of Charleston and Karen Anne Wallach, University of Alabama in Huntsville

Life in the digital world can be rewarding. It’s convenient to order groceries for pickup, share photographs or music, and keep in touch with and friends, no matter the distance. However, it can also be draining. The feeling of being constantly “on” and productive has driven people to reconsider their balance in the saturated digital world.

More than 70% of American adults are concerned about how technology affects their mental health and personal relationships. This worry is reinforced through media that point to people’s unhealthy habits with social media and phones.

What to do? There is a fuzzy line between healthy and unhealthy digital consumption. Some folks feel the need to fully disconnect from the digital world to understand this boundary. The idea of digital detoxing is gaining popularity. This practice involves intentionally unplugging from digital technologies in the pursuit of balance and digital well-being. Nearly half of Americans that they are making a conscious effort to regularly step away from their screens.

But is this attempt enough? It’s no surprise that 62% of Americans confess to feeling addicted to their devices and the internet. Despite people’s best efforts to unplug and strike a balance, research indicates that digital detoxes often fall short.

two men in a park grin as one tosses a bean bag
Getting outside, being with someone else and fun are all good approaches to disconnecting from the digital world.
kali9/E+ via Getty Images

Digital well-being is subjective. We research technology and consumer behavior. Our recent research studied the digital detox journey, where people take a much-needed break from digital consumption, aiming to uncover what supports or sabotages those seeking digital well-being. Our findings highlighted four key strategies to improve the outcome of this journey toward achieving a healthier digital balance: replacement practices, social bonds, mindfulness and digital well-being as a journey.

1. Finding replacement practices

We found that feelings of withdrawal during a digital detox are quite common. For many, reaching for their phones and scrolling has become such a ritual that they often don’t realize they are doing it. Many turn to their devices when bored or stressed, much like an adult pacifier. As a result, finding an alternative to distract your mind and occupy your hands can be crucial during a digital detox.

These replacement practices often involve hobbies or activities that result in play. As adults, people sometimes forget what it feels like to have fun. By separating fun from your task list and engaging in play for its own sake, you can significantly reduce stress levels and boost your digital well-being.

2. Shoring up social bonds

Humans are inherently social creatures. Indeed, tools such as email, text messages and social media offer ways to enhance social connections. This innate desire for connection, however, combined with people’s reliance on technology, can to feelings of FOMO – fear of missing out – and anxiety during a digital detox.

The average adult now spends 70% less time with friends than they did two decades ago. Digital devices offer connection, but pieces of the experience are missing, such as the joy of in-person contact and trust in others that can be difficult to get online. So while we’re a more connected society, relationships suffer and people are more lonely than ever.

Therefore, during a digital detox it is vital to fill your cup with community, whether through existing friendships or by creating new ones. We recommend engaging in a digital detox alongside others, because FOMO may rear its ugly head if your friend pulls out their phone during a night out.

Taking a short digital detox with the Offline Club.

3. Emphasizing mindfulness

In ‘s fast-paced environment, finding a moment to pause can feel nearly impossible. Many experience solitude deprivation, meaning people often don’t have moments to be alone with their own thoughts. Yet, the ability to just be can allow time for reflection, helping you consider what makes you happy and healthy. Finding moments where you can step away – to be still and silent – can provide a much-needed recharge.

With adults spending about 90% of their time indoors, breaking the routine and outside can offer a more holistic perspective on both personal and global well-being. In our study, yoga and meditation were common ways that detoxers found moments to become more aware of their own thoughts, which helped foster more intentional behaviors.

4. Viewing digital well-being as an ongoing journey

Ultimately, digital well-being is a journey. It is not a checklist that, once completed, means you are fulfilled.

Unfortunately, a single detox isn’t enough to cure digital imbalance. Instead, a successful detox often leaves people feeling introspective and curious. Our research participants shared that relapses are common, especially if they don’t set and monitor ongoing goals. Importantly, your needs change and evolve over time. In other words, what works now might not be what you need in the future.

Willpower just isn’t enough. We recommend identifying specific goals for yourself related to your own digital well-being. These aren’t productivity goals but goals to be unproductive. The aim is to unplug in more fulfilling ways. Whether planning a weekly night with friends or taking a 10-minute walk without your phone, making time to unplug is worth it in the long .

Researchers still have more to learn to digital wellness. We should remember, though, that individual differences play a crucial role in this equation, meaning that the journey to achieving digital harmony is uniquely personal. Thus, as people navigate their tech-saturated lives, it’s clear that finding the right balance is a complex, highly individualized process.

The digital detox journey can be challenging, but many people discover it to be rewarding in the end. People are not machines, however, so recognizing your limits and finding ways to reconnect with yourself and others during a detox can significantly enhance your sense of humanity and digital well-being.The Conversation

Kelley Cours Anderson, Assistant Professor of Marketing, College of Charleston and Karen Anne Wallach, Assistant Professor of Marketing, University of Alabama in Huntsville

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

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The Conversation

‘Safe route’ or ‘sushi route’ − 2 strategies to turn yuck to yum and convince people to eat unusual foods

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theconversation.com – Alexandra Plakias, Associate Professor of Philosophy, Hamilton College – 2024-11-01 07:39:00

By the 1980s, many New Yorkers were all in on sushi, a food that seemed weird just decades before.
Allan Tannenbaum/Getty Images

Alexandra Plakias, Hamilton College

What will the diets of the future look like? The answer depends in part on what foods Westerners can be persuaded to eat.

These consumers are increasingly being told their diets need to change. Current eating habits are unsustainable, and the global demand for meat is growing.

Recent years have seen increased interest and investment in what are called alternative proteins – products that can replace typical meats with more sustainable alternatives. One option is cultivated, or cultured, meat and seafood: muscle tissue grown in labs in bioreactors, using animal stem cells. Another approach involves replacing standard meat with such options as insects or plant-based imitation meats. All of these products promise a more sustainable alternative to factory-farmed meat. The question is, will consumers accept them?

I’m a philosopher who studies food and disgust, and I’m interested in how people react to new foods such as lab-grown meat, bugs and other so-called alternative proteins. Disgust and food neophobia – a fear of new foods – are often cited as obstacles to adopting new, more sustainable food choices, but I believe that recent history offers a more complicated picture. Past shifts in food habits suggest there are two paths to the adoption of new foods: One relies on familiarity and safety, the other on novelty and excitement.

Disgust and the yuck factor

Disgust is a strong feeling of revulsion in response to objects perceived to be contaminating, polluting or unclean. Scientists believe that it evolved to protect human beings from invisible contaminants such as pathogens and parasites. Some causes of disgust are widely shared, such as feces or vomit. Others, including foods, are more culturally variable.

So it’s not surprising that self-reported willingness to eat insects varies across nationalities. Insects have been an important part of traditional diets of cultures around the world for thousands of years, the ancient Greeks.

Many articles about the possibility of introducing insects to Western or American diners have emphasized the challenges posed by neophobia and “the yuck factor.” People won’t accept these new foods, the thinking goes, because they’re too different or even downright disgusting.

If that’s right, then the best approach to win on the plate for new foods might be to try to make them seem similar to familiar menu items.

The safe route to food acceptance

Poster from 1940s with photo of soldier and civilians saluting with heading 'Sure – We'll 'Share the Meat''
During World War II, the worked to make it seem patriotic to not pig out on the usual meat.
U.S. National Archives/Flickr, CC BY

During World War II, the United States government wanted to redirect its limited meat supply to troops on the front lines. So it needed to convince home cooks to give up their steaks, chops and roasts in favor of what it called variety meats: kidneys, liver, tongue and so on.

To figure out how to shift consumer habits, a team of psychologists and anthropologists was charged with studying how food habits and preferences were formed – and how they could be changed.

The Committee on Food Habits recommended stressing these organ meats’ similarity to available, familiar, existing foods. This approach – call it the “safe route” – focuses on individual attitudes and choices. It tries to psychological and practical barriers to individual choice and counteracts beliefs or values that might dissuade people from adopting new foods.

As the name suggests, the safe route tries to downplay novelty, using familiar forms and tastes. For example, it would incorporate unfamiliar cuts of meats into meatloaf or meatballs or grind crickets into flour for cookies or protein bars.

The sushi route

But more recent history suggests something different: Foods such as sushi, offal and even lobster became desirable not despite but because of their novelty and difference.

Sushi’s arrival in the postwar U.S. coincided with the rise of consumer culture. Dining out was gaining traction as a leisure activity, and people were increasingly open to new experiences as a sign of status and sophistication. Rather than appealing to the housewife preparing comfort foods, sushi gained popularity by appealing to the desire for new and exciting experiences.

By 1966, The New York Times reported that New Yorkers were dining on “raw fish dishes, sushi and sashimi, with a gusto once reserved for corn flakes.” Now, of course, sushi is widely consumed, available even in grocery stores nationwide. In fact, the grocery chain Kroger sells more than 40 million pieces of sushi a year. Whereas the safe route suggests sneaking new foods into our diets, the sushi route suggests embracing their novelty and using that as a selling point.

Sushi is just one example of a food adopted via this route. After the turn of the millennium, a new generation of diners rediscovered offal as high-end restaurants and chefs offered “nose to tail” dining. Rather than positioning foods like tongue and pigs’ ears as familiar and comforting, a willingness to embrace the yuck factor became a sign of adventurousness, even masculinity. This framing is the exact opposite of the safe route recommended by the Committee on Food Habits.

Chef displaying a plate of fried bugs with guacamole
Mexico is one place that has a centuries-old tradition of eating some insects.
AP Photo/Dario Lopez-Mills

The future of alternative proteins

What lessons can be drawn from these examples? For dietary shifts to last, they should be framed positively. Persuading customers that variety meats were a necessary wartime substitution worked temporarily but ultimately led to the perception that they were subpar choices. If cultivated meat and insects are pitched as necessary sacrifices, any gains they make may be temporary at best.

Instead, producers could appeal to consumers’ desire for healthier, more sustainable and more exciting foods.

Cultivated meat may be “safe-ly” marketed as nuggets and burgers, but, in principle, the options are endless: Curious consumers could sample lab-grown whale or turtle meat guilt-, or even find out what woolly mammoth tasted like.

Ultimately, the chefs, consumers and entrepreneurs seeking to remake our food don’t need to choose just one route. While we can grind insects into protein powders, we can also look to chefs cooking traditional cuisines that use insects to broaden our culinary horizons.The Conversation

Alexandra Plakias, Associate Professor of Philosophy, Hamilton College

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

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