fbpx
Connect with us

The Conversation

From thousands to millions to billions to trillions to quadrillions and beyond: Do numbers ever end?

Published

on

theconversation.com – Manil Suri, Professor of Mathematics and Statistics, of Maryland, Baltimore County – 2024-04-15 07:27:50
The number zero was a relatively recent and crucial addition − it allows numbers to extend in both directions forever.
pixel_dreams/iStock via Getty Images Plus

Manil Suri, University of Maryland, Baltimore County

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


Why don't numbers end? – Reyhane, age 7, Tehran, Iran


Here's a game: Ask a friend to give you any number and you'll return one that's bigger. Just add “1” to whatever number they up with and you're sure to win.

The reason is that numbers go on forever. There is no highest number. But why? As a professor of mathematics, I can you find an answer.

Advertisement

First, you need to understand what numbers are and where they come from. You learned about numbers because they enabled you to count. Early humans had similar needs – whether to count animals killed in a hunt or keep track of how many days had passed. That's why they invented numbers.

But back then, numbers were quite limited and had a very simple form. Often, the “numbers” were just notches on a bone, going up to a couple hundred at most.

How numbers evolved throughout the centuries.

When numbers got bigger

As time went on, people's needs grew. Herds of livestock had to be counted, goods and services traded, and measurements made for buildings and navigation. This led to the invention of larger numbers and better ways of representing them.

About 5,000 years ago, the Egyptians began using symbols for various numbers, with a final symbol for one million. Since they didn't usually encounter bigger quantities, they also used this same final symbol to depict “many.”

Advertisement

The Greeks, starting with Pythagoras, were the first to study numbers for their own sake, rather than viewing them as just counting tools. As someone who's written a book on the importance of numbers, I can't emphasize enough how crucial this step was for humanity.

By 500 BCE, Pythagoras and his disciples had not only realized that the counting numbers – 1, 2, 3 and so on – were endless, but also that they could be used to explain cool stuff like the sounds made when you pluck a taut string.

Zero is a critical number

But there was a problem. Although the Greeks could mentally think of very large numbers, they had difficulty writing them down. This was because they did not know about the number 0.

Think of how important zero is in expressing big numbers. You can start with 1, then add more and more zeroes at the end to quickly get numbers like a million – 1,000,000, or 1 followed by six zeros – or a , with nine zeros, or a trillion, 12 zeros.

Advertisement

It was only around 1200 CE that zero, invented centuries earlier in India, came to Europe. This led to the way we write numbers .

This brief history makes clear that numbers were developed over thousands of years. And though the Egyptians didn't have much use for a million, we certainly do. Economists will tell you that expenditures are commonly measured in millions of dollars.

Also, science has taken us to a point where we need even larger numbers. For instance, there are about 100 billion stars in our galaxy – or 100,000,000,000 – and the number of atoms in our universe may be as high as 1 followed by 82 zeros.

Don't worry if you find it hard to picture such big numbers. It's fine to just think of them as “many,” much like the Egyptians treated numbers over a million. These examples point to one reason why numbers must continue endlessly. If we had a maximum, some new use or discovery would surely make us exceed it.

Advertisement
The symbols of math include +, -, x and =.

Exceptions to the rule

But under certain circumstances, sometimes numbers do have a maximum because people design them that way for a practical purpose.

A good example is a clock – or clock arithmetic, where we use only the numbers 1 through 12. There is no 13 o'clock, because after 12 o'clock we just go back to 1 o'clock again. If you played the “bigger number” game with a friend in clock arithmetic, you'd lose if they chose the number 12.

Since numbers are a human invention, how do we construct them so they continue without end? Mathematicians started looking at this question starting in the early 1900s. What they came up with was based on two assumptions: that 0 is the starting number, and when you add 1 to any number you always get a new number.

These assumptions immediately give us the list of counting numbers: 0 + 1 = 1, 1 + 1 = 2, 2 + 1 = 3, and so on, a progression that continues without end.

Advertisement

You might wonder why these two rules are assumptions. The reason for the first one is that we don't really know how to define the number 0. For example: Is “0” the same as “nothing,” and if so, what exactly is meant by “nothing”?

The second might seem even more strange. After all, we can easily show that adding 1 to 2 gives us the new number 3, just like adding 1 to 2002 gives us the new number 2003.

But notice that we're saying this has to hold for any number. We can't very well verify this for every single case, since there are going to be an endless number of cases. As humans who can perform only a limited number of steps, we have to be careful anytime we make claims about an endless process. And mathematicians, in particular, refuse to take anything for granted.

Here, then, is the answer to why numbers don't end: It's because of the way in which we define them.

Advertisement

Now, the negative numbers

How do the negative numbers -1, -2, -3 and more fit into all this? Historically, people were very suspicious about such numbers, since it's hard to picture a “minus one” apple or orange. As late as 1796, math textbooks warned against using negatives.

The negatives were created to address a calculation issue. The positive numbers are fine when you're adding them together. But when you get to subtraction, they can't handle differences like 1 minus 2, or 2 minus 4. If you want to be able to subtract numbers at will, you need negative numbers too.

A simple way to create negatives is to imagine all the numbers – 0, 1, 2, 3 and the rest – drawn equally spaced on a straight line. Now imagine a mirror placed at 0. Then define -1 to be the reflection of +1 on the line, -2 to be the reflection of +2, and so on. You'll end up with all the negative numbers this way.

As a bonus, you'll also know that since there are just as many negatives as there are positives, the negative numbers must also go on without end!

Advertisement

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 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

Manil Suri, Professor of Mathematics and Statistics, University of Maryland, Baltimore County

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

Advertisement

The Conversation

Teens see social media algorithms as accurate reflections of themselves, study finds

Published

on

theconversation.com – Nora McDonald, Assistant Professor of Information Technology, George Mason – 2024-04-29 07:26:15

Teens say ‘for you' algorithms get them right.

Photo illustration by Spencer Platt/Getty Images

Nora McDonald, George Mason University

Social apps regularly present teens with algorithmically selected content often described as “for you,” suggesting, by implication, that the curated content is not just “for you” but also “about you” – a mirror reflecting important about the person you are.

Advertisement

All users of social media are exposed to these signals, but researchers understand that teens are at an especially malleable stage in the formation of personal identity. Scholars have begun to demonstrate that technology is having generation-shaping effects, not merely in the way it influences cultural outlook, behavior and privacy, but also in the way it can shape personality among those brought up on social media.

The prevalence of the “for you” message raises important questions about the impact of these algorithms on how teens perceive themselves and see the world, and the subtle erosion of their privacy, which they accept in exchange for this view.

Teens like their algorithmic reflection

Inspired by these questions, my colleagues John Seberger and Afsaneh Razi of Drexel University and I asked: How are teens navigating this algorithmically generated milieu, and how do they recognize themselves in the mirror it presents?

In our qualitative interview study of teens 13-17, we found that personalized algorithmic content does seem to present what teens interpret as a reliable mirror image of themselves, and that they very much like the experience of seeing that social media reflection.

Advertisement

Teens we spoke with say they prefer a social media completely customized for them, depicting what they agree with, what they want to see and, thus, who they are.

If I look up something that is important to me that will show up as one of the top posts [and] it'll show, like, people [like me] that are having a nice discussion.

It turns out that the teens we interviewed believe social media algorithms like TikTok's have gotten so good that they see the reflections of themselves in social media as quite accurate. So much so that teens are quick to attribute content inconsistencies with their self-image as anomalies – for instance, the result of inadvertent engagement with past content, or just a glitch.

At some point I saw something about that show, maybe on TikTok, and I interacted with it without actually realizing.

When personalized content is not agreeable or consistent with their self-image, the teens we interviewed say they scroll past it, hoping never to see it again. Even when these perceived anomalies take the form of extreme hypermasculine or “nasty” content, teens do not attribute this to anything about themselves specifically, nor do they claim to look for an explanation in their own behaviors. According to teens in our interviews, the social media mirror does not make them more self-reflective or their sense of self.

One thing that surprised us was that while teens were aware that what they see in their “for you” feed is the product of their scrolling habits on social media platforms, they are largely unaware or unconcerned that that data captured across apps contributes to this self-image. Regardless, they don't see their “for you” feed as a challenge to their sense of self, much less a risk to their self-identity – nor, for that matter, any basis for concern at all.

Advertisement

The human brain continues to develop during adolescence.

Shaping identity

Research on identity has a long way since sociologist Erving Goffman proposed the “presentation of self” in 1959. He posited that people manage their identities through social performance to maintain equilibrium between who they think they are and how others perceive them.

When Goffman first proposed his theory, there was no social media interface available to hold up a handy mirror of the self as experienced by others. People were obligated to create their own mosaic image, derived from multiple sources, encounters and impressions. In recent years, social media recommender algorithms have inserted themselves into what is now a three-way negotiation among self, public and social media algorithm.

“For you” offerings create a private-public through which teens can access what they feel is a largely accurate test of their self-image. At the same time, they say they can easily ignore it if it seems to disagree with that self-image.

The pact teens make with social media, exchanging personal data and relinquishing privacy to secure access to that algorithmic mirror, feels to them like a good bargain. They represent themselves as confidently able to tune out or scroll past recommended content that seems to contradict their sense of self, but research shows otherwise.

Advertisement

They have, in fact, proven themselves highly vulnerable to self-image distortion and other mental health problems based on social media algorithms explicitly designed to create and reward hypersensitivities, fixations and dysmorphia – a mental disorder where people fixate on their appearance.

Given what researchers know about the teen brain and that stage of social – and given what can reasonably be surmised about the malleability of self-image based on social feedback – teens are wrong to believe that they can scroll past the self-identity risks of algorithms.

U.S. Surgeon General Vivek Murthy discusses the harms teens face from social media.

Interventions

Part of the remedy could be to build new tools using artificial intelligence to detect unsafe interactions while also protecting privacy. Another approach is to teens reflect on these “data doubles” that they have constructed.

My colleagues and I are now exploring more deeply how teens experience algorithmic content and what types of interventions can help them reflect on it. We encourage researchers in our field to design ways to challenge the accuracy of algorithms and expose them as reflecting behavior and not being. Another part of the remedy may involve arming teens with tools to restrict access to their data, including limiting cookies, having different search profiles and turning off location when using certain apps.

Advertisement

We believe that these are all steps that are likely to reduce the accuracy of algorithms, creating much-needed friction between algorithm and self, even if teens are not necessarily happy with the results.

Getting the kids involved

Recently, my colleagues and I conducted a Gen Z workshop with young people from Encode Justice, a global organization of high school and college students advocating for safe and equitable AI. The aim was to better understand how they are thinking about their lives under algorithms and AI. Gen Zers say they are concerned but also eager to be involved in shaping their future, including mitigating algorithm harms. Part of our workshop goal was to call attention to and foster the need for teen-driven investigations of algorithms and their effects.

What researchers are also confronting is that we don't actually know what it means to constantly negotiate identity with an algorithm. Many of us who study teens are too old to have grown up in an algorithmically moderated world. For the teens we study, there is no “before AI.”

I believe that it's perilous to ignore what algorithms are doing. The future for teens can be one in which society acknowledges the unique relationship between teens and social media. This means involving them in the , while still providing guidance.The Conversation

Nora McDonald, Assistant Professor of Information Technology, George Mason University

Advertisement

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

Continue Reading

The Conversation

Why are some people faster than others? 2 exercise scientists explain the secrets of running speed

Published

on

theconversation.com – Dawn P. Coe, Associate Professor of Exercise Science, University of Tennessee – 2024-04-29 07:23:48

Jamaican sprinter Usain Bolt, in yellow, holds the world's speed record for humans.

AP Photo/David J. Phillip

Dawn P. Coe, University of Tennessee and Elizabeth (Kip) Webster, University of Tennessee

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

Advertisement

Why are some people faster than others? – Jon, age 14, Macon, Georgia


Usain Bolt, the world's fastest human, ran a 100-meter sprint at a speed of 23.35 miles per hour (37.57 kilometers per hour).

That's mind-blowingly fast for a human. It's about the same speed as cruising in a car through your neighborhood or in a school zone. It might not seem that fast when you're in the car, but for a person? Few runners in the world can even close.

There are several reasons why some people can run very fast while others tend to run more slowly. Genetics – the traits you inherit from your play a role, but so do your choices and experiences.

As pediatric exercise scientists, we create and evaluate programs that help children be healthy. The exciting news is that while you have no control over your genetics, you can train to improve your speed.

Advertisement

Fast twitch, slow twitch

One major factor that influences your ability to run fast is the structure of your body, including how your muscles work.

The human body has more than 600 muscles that work together, allowing you to move in different directions and at various speeds. These muscles are made up of groups of fibers. There are two main types: fast twitch and slow twitch.

Muscles have different mixes of these fiber types. For example, two muscles make up the calf: One is predominantly fast twitch – that's the gastrocnemius, used for sprinting and jumping. The other is mostly slow twitch – that's the soleus, used for walking and jogging.

Two women play soccer, one is in motion, clearly sprinting to kick the ball.

Speed and endurance are both important when you're playing soccer.

AP Photo/John Cowpland

Advertisement

Fast-twitch muscle fibers are larger and help your body move quickly and generate significant force. Sprinters tend to have an abundance of fast-twitch muscle fibers. However, this muscle fiber type also tires quickly, which limits how long you can run at top speed to relatively short distances.

Slow-twitch muscle fibers are smaller and help you run at slower speeds, but with greater endurance. Long-distance runners and competitive cyclists tend to have a lot of these muscles.

How much you have of each type of muscle fiber – fast twitch and slow twitch – is mostly determined by your genes, so you'll have to work with what you're born with when it to muscle types. But exercises can help train those muscles.

Your brain plays a big role

Physical ability isn't just about muscle. Your brain plays an important role, too.

Advertisement

Your skeletal muscles are controlled by your brain – you think about your actions and then execute the movements. For example, you can control how long your stride is, how your arms move, how your feet hit the ground and even the techniques you use to breathe.

You can teach your body to use the best running techniques. That includes proper posture, so your body is standing tall, and an economical stride, so your feet below you rather than too far out in front, where they can slow you down.

Five tips for running faster, from an Olympic sprinting coach.

You can also improve your running form by using your whole body, with your arms pumping in opposition to the legs, running on your toes and maximizing the time spent in flight phase with both feet off the ground. Using proper running techniques helps the muscles create more force and work together, which helps you run faster.

The more you practice an activity, the better you will get. As your ability to run fast increases, yourself to run even faster.

Advertisement

How to train to run faster – myth-busting!

You may have heard your friends chatting about ways to boost your speed or searched the internet for tips on getting faster. Time to bust some of those myths.

Myth 1: You have to run as fast as you can to train to be faster. That's false!

You don't have to run as fast as you can to get faster, and it actually helps to take short breaks to recover in between activities where you are sprinting.

Myth 2: You need to lift heavy weights to get faster. False!

Advertisement

Functional strength training involves performing exercises that help you get better at specific movements. They involve using either medium weights or just the resistance of your own body weight. Doing planks, lunges, step-ups or jump squats are great examples. These activities focus on the muscles that are instrumental during running.

Myth 3: You need to specialize in running early in to become a fast runner. False!

Picking one activity to focus on early in life may actually limit your ability to develop into a fast runner. Doing a variety of physical activities can help you develop new skills that improve your running. For example, the movements and endurance used in soccer may translate into the ability to run faster.

Myth 4: isn't fun. False!

Advertisement

Training programs can take many shapes and forms. You can play running with your friends, work on fast footwork using an agility ladder or create obstacle courses. There's nothing like a little healthy competition to motivate your training.

What's important is fun while training and participating in

activities that promote running speed on a regular basis.

So, whether you want to be the next Usain Bolt or you just want to win a race against your friend, remember that with a little bit of genetic luck and hard work, it may just be possible.The Conversation

Dawn P. Coe, Associate Professor of Exercise Science, University of Tennessee and Elizabeth (Kip) Webster, Associate Professor of Exercise Science, University of Tennessee

Advertisement

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

Continue Reading

The Conversation

Ghosted, orbited, breadcrumbed? A psychotherapist breaks down some perils of digital dating and how to cope

Published

on

theconversation.com – Danielle Sukenik, Instructor of Psychiatry, of Colorado Anschutz Medical Campus – 2024-04-29 07:22:52

About a third of U.S. adults have looked for love online.

Maria Korneeva/Moment via Getty Images

Danielle Sukenik, University of Colorado Anschutz Medical Campus

Buzzwords describing the digital dating scene are all over social . Have you been ghosted? Is someone orbiting you? Are you being breadcrumbed? While these dating patterns may not be new, the words to describe them continue to evolve.

Advertisement

As a psychotherapist, I see firsthand the impact these experiences can have on mental . Given the sheer number of people using dating apps – 53% of American 18-to-29-year-olds and 37% of 30-to-49-year-olds – it's likely you have some first- or secondhand exposure to this world.

If you're curious about the latest psychological research on digital dating – and are looking for evidence-based strategies to cope – read on.

Ghosting and orbiting

Ghosting is a sudden disruption in a relationship without any explanation. The “ghoster” vanishes suddenly, often leaving the other person with questions. And orbiting? That's when someone ghosts but continues to follow the other person on social media by watching stories or occasionally engaging in their content. These behaviors are pretty common, and you might wonder about their impact.

A 2022 study the psychological consequences of being ghosted, orbited or rejected by asking 176 participants about one randomly assigned breakup strategy they had experienced out of these three. Then, participants completed a questionnaire rating various feelings about their breakup.

Advertisement

While feelings of rejection did not differ between the three breakup strategies – the end of a relationship hurts regardless – the results showed that ghosting led to stronger feelings of exclusion than being rejected outright. People in the ghosting category were also more likely to feel that their basic needs of belonging, self-esteem and control were threatened.

Being orbited, on the other hand, seemed to buffer victims partially from the emotional consequences of a breakup. Victims of orbiting, too, reported feeling higher levels of exclusion and threat to their basic needs than those who were rejected outright, but less than victims of ghosting did. Perhaps sporadic attention softens feelings of exclusion.

These findings are in line with other research. Understanding a breakup is important and helps individuals recover from the . With no explanation, the rejected individual may be left feeling confused and uncertain, sometimes with unhealed psychological wounds.

Orbiting may cause further ambiguity, as the orbiter's behavior suggests a mild residual interest in the other person. An individual might wonder if the other person is still attracted or might want to return to the relationship. For some people, this uncertainty can be harmful, while others find it easier to let go of a relationship if they're still receiving some level of digital attention.

Advertisement

A pair of studies in 2004 and 2005 showed people prefer receiving negative attention over being ignored entirely. In these role-playing experiments, those who experienced ostracism reported lower levels of belonging, control, meaningful existence and superiority than those who experienced an argument.

Sad woman reading her smart phone.

Being toyed with by a potential partner is especially damaging.

MementoJpeg/Moment/via Getty Images

Breadcrumbing

Breadcrumbing is when someone drops morsels of flirtatious attention to keep the other person interested, even though they have no intention of participating in a relationship. Some classic signs of breadcrumbing are not responding to messages for long periods of time, vague communication, and avoidance of discussions related to feelings. These patterns tend to boost the breadcrumber's ego, self-worth and sense of power.

For the person being breadcrumbed, it's a different story. A 2020 study of 626 adults found victims of breadcrumbing were significantly more likely to have feelings of loneliness, helplessness and less life satisfaction than victims of ghosting. Because people on the receiving end of breadcrumbing remain in limbo longer, they experience repeated feelings of exclusion and ostracism. The ongoing nature of breadcrumbing explains why it can have more negative effects on mental health.

Advertisement

Taking care of yourself

Given the prevalence of these behaviors, it's likely you've employed some of these dating tactics yourself. If so, I invite you to be mindful and think about how these patterns are serving you and consider your impact on others.

If you're also on the receiving end, here are some evidence-based strategies you can use to yourself and maintain a positive outlook about the dating scene.

Any time you have an experience, your mind is quick to create a narrative around what happened in order to make sense of it and create an illusion of control or safety. If you're not aware of the stories you tell yourself, you may find yourself incorrectly assigning blame or fault, which can to negative self-talk, anxiety and depression.

For example, rather than think, “I did something wrong to cause them to ghost me,” you could think, “Their to disengage from the relationship is more about them and how they relate to others than it is about me.” Being mindful of your cognitive patterns and practicing changing your narratives can keep online dating from wreaking havoc on your psyche.

Advertisement

Group of young people planting trees.

Living your values can have many .

miodrag ignjatovic/E+/via Getty Images

It's also crucial to take inventory of what's most important to you. Identifying your values will not only allow you to better match with like-minded people, but it will also improve your relationship with yourself. When your life aligns with what's important to you, you increase its meaning, purpose and overall well-being. In living this way, you might find looking for a relationship is less urgent, which could help you to better spot red flags or mismatches.

I also recommend varying the ways you connect to others to mitigate burnout. A healthy mix of apps and meeting people “in the wild” will often yield the best outcome and allow the dating adventure to remain exciting.The Conversation

Danielle Sukenik, Instructor of Psychiatry, University of Colorado Anschutz Medical Campus

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

Advertisement
Continue Reading

News from the South

Trending