Picture Parade Four Hundred and Thirty

Again, back to Unsplash.

Photo by Henos Solomon on Unsplash

Photo by Dineshkumar M on Unsplash

Not the usual friendly face but still a terrific photograph.

Photo by Jelena Kostic on Unsplash

Photo by Nam-Huong Nguyen on Unsplash

Photo by Photographer Frederik Trovatten on Unsplash

Photo by Erin Minuskin on Unsplash

That is all for this Sunday. You all have a good week ahead (that’s an order 😉 )

A new dog!

Another compelling story.

Yet another fantastic story of a dog being transformed, courtesy of The Dodo.

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Dog Is Completely Transformed After Groomers Give Her An Emergency Makeover

She’s unrecognizable.

By Stephen Messenger, Published on April 5, 2024

Recently, staff at the Wyandotte Animal Shelter in Michigan took in a dog whose condition was described as among the worst they’d ever seen. Pixie, as the dog is named, had fur so overgrown and matted that she could hardly move.

Gazing upon Pixie, one might never guess that an adorable dog existed beneath it.

Wyandotte Animal Shelter

According to staff at the shelter, Pixie was surrendered by her owner, who, regrettably, had neglected to give her the care and attention she needed — leading to her severely unkempt condition. Ultimately, though, his decision to surrender her is what Pixie needed most.

“He had a hard time letting her go but surrendered her to us so we could ensure she would go to someone who could give her the life she deserved,” the shelter wrote.

With that, Pixie’s world was about to change forever — and it would have to start with a much-needed haircut.

Wyandotte Animal Shelter

Staff at the shelter reached out to The Downriver Grooming Co. for what would be an emergency grooming session to help Pixie escape from her matted prison.

“[They got] her in within minutes of our call, and for [three] hours they spent freeing her from that matted fur,” the shelter wrote.

Wyandotte Animal Shelter

After all was said and done, the real Pixie had emerged.

She was totally unrecognizable from her former self.

Wyandotte Animal Shelter

“This little girl was only 5.5 pounds, but she seemed twice her size due to the matted fur,” the shelter wrote, adding that she was in remarkably good health, despite her ordeal beneath that overgrown coat.

Pixie’s world had changed for the better — but it wouldn’t be long until it improved even more.

Wyandotte Animal Shelter

Within days of Pixie’s transformation, thanks to the kindness of those who’d helped her, the little dog got the second chance she so desperately needed.

“Pixie was adopted,” a spokesperson for the Wyandotte Animal Shelter told The Dodo. “Her new family reports that she is doing very well in her new home.”

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We all need second chances from time to time, humans and dogs.

Stonehenge

A fascinating account of this English site.

Although I was born in London in 1944, as a result of an affair between my father and mother, my father had two daughters with his wife, Maud, and Rhona and Corinne, for they were their names, took me under their wing. In the 50s Maud, Rhona and Corinne all moved to Devon and I started going regularly to Totnes. When I started driving I usually stopped for a break close by Stonehenge so the site has a special interest to me.

So when I saw this article in The Conversation it had to be shared.

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Stonehenge may have aligned with the Moon as well as the Sun

Stonehenge during winter solstice sunset Chuta Kooanantkul/Shutterstock

Fabio Silva, Bournemouth University; Amanda Chadburn, Bournemouth University, and Erica Ellingson, University of Colorado Boulder

When it comes to its connection to the sky, Stonehenge is best known for its solar alignments. Every midsummer’s night tens of thousands of people gather at Stonehenge to celebrate and witness the rising Sun in alignment with the Heel stone standing outside of the circle. Six months later a smaller crowd congregates around the Heel stone to witness the midwinter Sun setting within the stone circle.

But a hypothesis has been around for 60 years that part of Stonehenge also aligns with moonrise and moonset at what is called a major lunar standstill. Although a correlation between the layout of certain stones and the major lunar standstill has been known about for several decades, no one has systematically observed and recorded the phenomenon at Stonehenge.

This is what we are aiming to do in a project bringing together archaeologists, astronomers and photographers from English Heritage, Oxford, Leicester and Bournemouth universities as well as the Royal Astronomical Society.

There is now an abundance of archaeological evidence that indicates the solar alignment was part of the architectural design of Stonehenge. Around 2500 BC, the people who put up the large stones and dug an avenue into the chalk seemed to want to cement the solstice axis into the architecture of Stonehenge.

Archaeological evidence from nearby Durrington Walls, the place where scientists believe the ancient people who visited Stonehenge stayed, indicates that of the two solstices it was the midwinter one that drew the largest crowd.

But Stonehenge includes other elements, such as 56 pits arranged in a circle, an earthwork bank and ditch, and other smaller features such as the four station stones. These are four sarsen stones, a form of silicified sandstone common in Wiltshire, that were carefully placed to form an almost exact rectangle encompassing the stone circle.

Only two of these stones are still there, and they pale in comparison to their larger counterparts as they are only a few feet high. So what could their purpose be?

Aerial view of Stonehenge
Only two of the station stones are still there. Drone Explorer/Shutterstock

Lunar standstill

The rectangle that they form is not just any rectangle. The shorter sides are parallel to the main axis of the stone circle and this may be a clue as to their purpose. The longer sides of the rectangle skirt the outside of the stone circle.

It is these longer sides that are thought to align with the major lunar standstill. If you marked the position of moonrise (or set) over the course of a month you would see that it moves between two points on the horizon. These southern and northern limits of moonrise (or set) change on a cycle of 18.6 years between a minimum and a maximum range – the so-called minor and major lunar standstills, respectively.

The major lunar standstill is a period of about one and a half to two years when the northernmost and southernmost moonrises (or sets) are furthest apart. When this happens the Moon rises (and sets) outside the range of sunrises and sets, which may have imbued this celestial phenomenon with meaning and significance.

Diagram showing Moonrise positions on a horizon.
The range of Moonrise positions on the horizon during minor and major lunar standstills. Fabio Silva, CC BY-NC

The strongest evidence we have for people marking the major lunar standstill comes from the US southwest. The Great House of Chimney Rock, a multi-level complex built by the ancestral Pueblo people in the San Juan National Forest, Colorado, more than 1,000 years ago.

It lies on a ridge that ends at a natural formation of twin rock pillars – an area that has cultural significance to more than 26 native American tribal nations. From the vantage point of the Great House, the Sun will never rise in the gap between the pillars.

However, during a major standstill the Moon does rise between them in awe-inspiring fashion. Excavations unearthed preserved wood that meant researchers could date to the year episodes of construction of the Great House.

Of six cutting dates, four correspond to major lunar standstill years between the years AD1018 and AD1093, indicating that the site was renewed, maintained or expanded on consecutive major standstills.

Returning to southern England, archaeologists think there is a connection between the major lunar standstill and the earliest construction phase of Stonehenge (3000-2500 BC), before the sarsen stones were brought in.

Several sets of cremated human remains from this phase of construction were found in the southeastern part of the monument in the general direction of the southernmost major standstill moonrise, where three timber posts were also set into the bank. It is possible that there was an early connection between the site of Stonehenge and the Moon, which was later emphasised when the station stone rectangle was built.

The major lunar standstill hypothesis, however, raises more questions than it answers. We don’t know if the lunar alignments of the station stones were symbolic or whether people were meant to observe the Moon through them. Neither do we know which phases of the Moon would be more dramatic to witness.

A search for answers

In our upcoming work, we will be trying to answer the questions the major lunar standstill hypothesis raises. It’s unclear whether the Moon would have been strong enough to cast shadows and how they would have interacted with the other stones. We will also need to check whether the alignments can still be seen today or if they are blocked by woods, traffic and other features.

The Moon will align with the station stone rectangle twice a month from about February 2024 to November 2025, giving us plenty of opportunities to observe this phenomenon in different seasons and phases of the Moon.

To bring our research to life, English Heritage will livestream the southernmost Moonrise in June 2024, and host a series of events throughout the year, including talks, a pop-up planetarium, stargazing and storytelling sessions.

Across the Atlantic, our partners at the US Forest Service are developing educational materials about the major lunar standstill at Chimney Rock National Monument. This collaboration will result in events showcasing and debating the lunar alignments at both Stonehenge and at Chimney Rock.

Fabio Silva, Senior Lecturer in Archaeological Modelling, Bournemouth University; Amanda Chadburn, Member of Kellogg College, University of Oxford and Visiting Fellow in Archaeology, Bournemouth University, and Erica Ellingson, Professor in Astrophysics, Emeritus, University of Colorado Boulder

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

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Well I learnt something from this, which just goes to show that we are never too old to learn.

To come back to the article, the skills of those ancient peoples were just awe-inspiring.

Picture Parade Four Hundred and Twenty-Nine, not!

It is about Whale songs and is just a fabulous sound!

Last Friday there was an item on the BBC about whale song. It appears I can publish the article for you all. It is my choice over my regular Sunday Picture Parade. I hope you agree! Update: The track just 26 seconds long cannot be reproduced in this post.

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Whale song mystery solved by scientists

21 February 2024, By Helen Briggs and Victoria Gill,Science correspondents, BBC News

Humpback whale breaching near Bering Island, Kamchatka, Russia – Olga Filatova, University of Southern Denmark

Scientists have worked out how some of the largest whales in the ocean produce their haunting and complex songs.

Humpbacks and other baleen whales have evolved a specialised “voice box” that enables them to sing underwater. 

The discovery, published in the journal Nature, has also revealed why the noise we make in the ocean is so disruptive for these ocean giants. 

Whale song is restricted to a narrow frequency that overlaps with the noise produced by ships. 
“Sound is absolutely crucial for their survival, because it’s the only way they can find each other to mate in the ocean,” explained Prof Coen Elemans, of the University of Southern Denmark, who led the study. 

Blue whales return to ‘safe’ tropical haven
Orcas ‘learning from adults’ to target boats
Study to measure the oceans’ ‘year of quiet’

“[These are some] of the most enigmatic animals that ever lived on the planet,” he told BBC News. “They are amongst the biggest animals, they’re smart and they’re highly social.”

Humpback whale song (For whatever reason the track cannot be listened to on this blog. That is a great shame as the song is magnificent. So please go to the BBC website for this; the link is https://www.bbc.com/news/science-environment-68358414 )

Baleen whales are a group of 14 species, including the blue, humpback, right, minke and gray whale. Instead of teeth, the animals have plates of what is called baleen, through which they sieve huge mouthfuls of tiny creatures from the water.

Exactly how they produce complex, often haunting songs has been a mystery until now. Prof Elemans said it was “super-exciting” to have figured it out.

A diver descends between three juvenile humpback whales the size of buses – Karim Iliya

He and his colleagues carried out experiments using larynxes, or “voice boxes”, that had been carefully removed from three carcasses of stranded whales – a minke, a humpback and a sei whale. They then blew air through the massive structures to produce the sound. 

In humans, our voices come from vibrations when air passes over structures called vocal folds in our throat. Baleen whales, instead, have a large U-shaped structure with a cushion of fat at the top of the larynx.

This vocal anatomy allows the animals to sing by recycling air, and it prevents water from being inhaled.

Artwork indicating the cartilages of the larynx in a humpback whale – Patricia Jaqueline Matic, Vienna

The researchers produced computer models of the sounds and showed that baleen whale song is restricted to a narrow frequency which overlaps with noise produced by shipping vessels. 

“They cannot simply choose to, for example, sing higher to avoid the noise we make in the ocean,” explained Prof Elemans. 

His study demonstrated how our ocean noise could prevent whales from communicating over long distances. That knowledge could be vital for the conservation of humpbacks, blue whales and other endangered giants of the sea.

It also provides insight into questions that researchers have been asking for decades about these eerie songs, which some sailors used to attribute to ghosts or mythical sea creatures.

Whale communication expert Dr Kate Stafford, from Oregon State University, called the study “groundbreaking”. 

“The production and reception of sound is the most important sense for marine mammals, so any studies that elucidate how they make sounds has the potential to move the field forward,” she told BBC News.

Researchers say evidence of the harm ocean noise pollution can do has been building for decades –
Alamy

The research also paints an evolutionary picture – of how the ancestors of whales returned to the oceans from the land, and the adaptations that made it possible to communicate underwater.

The way so-called toothed whales produce sound is better understood, because the animals are easier to study. These marine mammals, which include dolphins, orcas, sperm whales and porpoises, blow air through a special structure in their nasal passages.

Dr Ellen Garland, from the Sea Mammal Research Unit at the University of St Andrews, said: “I’ve always wondered exactly how baleen whales – especially humpbacks, which my research is focused on – actually produce the variety of sounds they do.

“Studying large whales is extremely challenging at the best of times, but trying to uncover how they produce sound when you may not even be able to see them underwater while vocalising is an added level of difficulty, so these researchers have been very creative.”

Dr Stafford added that the mammals’ ability to make such complex vocal signals was “remarkable” and highlighted “how special these animals are”.

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There! I do hope you all agree that this was very worthwhile. Plus, you all got to listen to those twenty-six seconds of the very beautiful sound.

We humans!

No clear reaction comes to mind.

I came across this post yesterday and thought that it would make a good article for today. But the truth is that I, and I expect many other readers, do not understand the article.

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Employees Heartbroken When They See Someone Tied To ‘Do Not Abandon Animals’ Sign

She waited there 11 hours 💔

By Caitlin Jill Anders, Published on the 11th April, 2024.

Outside the front door of the Harbor Humane Society sits a sign. “Do not abandon an animal here,” the sign reads. “Wait until business hours. No fee for bringing an animal to HHS. For the sake of the animal, please be humane.” An older, outdated version of the same sign sits at the back of the shelter, too, near some picnic tables where employees can take a break. When they arrived at work one morning recently, there were no animals waiting for them out front.

Harbor Humane Society

Sadly, the same could not be said for the sign in the back.

Tied to the base of the “do not abandon animals” sign was a tiny dog who had been abandoned there the night before. Security footage showed the dog, later named Trixie, had been tied to the sign around 9 p.m. and wasn’t found until 7:30 a.m. the next morning, meaning she’d waited there for 11 hours.

Harbor Humane Society

“Our team member was just about to unarm the building (had just arrived to start their morning shift) when she noticed the dog tied to the signpost near our intake door located toward the back side of the shelter,” Jen Nuernberg, director of marketing and strategic initiatives at Harbor Humane Society, told The Dodo. “Initially, she was nervous and scared, barking at her. But once she crouched down and gave her some time, she quickly warmed up and crawled right into her lap. She has been very friendly ever since!”

Harbor Humane Society

Trixie was terrified out there all alone, wondering why she’d ended up there. As soon as she met her rescuer, though, all was well. She was rushed inside and eventually met the rest of the staff members, who were just as heartbroken by the situation. Thankfully, Trixie seemed to be pretty healthy, just a little confused — as was everyone at the shelter.

“When someone abandons an animal without any information, we are just left to guess,” Jen Self Aulgur, executive director at Harbor Humane Society, told The Dodo. “So we can assume she is about 3 to 4 years old, but we don’t know her story, her name, her likes, her favorite treats or toys. This is all information we try to get on animals when they are surrendered to the shelter.”

Harbor Humane Society

The shelter employees are still hoping someone might come forward to give them some information about Trixie before she’s adopted, just to make sure she’s getting the best care possible.

“This pup deserves to have her story and history known,” Self Aulgur said. “We do not want to shame or get you in trouble — we just want to help this poor pup.”

Harbor Humane Society

Trixie is safe now and will be available for adoption in about a week or so. Until then, she’s getting as many kisses and cuddles as the staff can give her while she dreams of her loving forever family.

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Let me add my wishes to the Harbor Humane Society in hoping that very soon Trixie will be adopted by that loving family.

A tribute to Julie Christie

Just a fabulous video!

There were so many things that I could have written about for today but they were all swept aside by an email that came in from an old friend of mine, Chris Snuggs.

Chris and I go back many years to the time when I was a visiting teacher at Isuga in France.

But the point of this post is to share the video that Chris provided about Julie Christie. Here is the first part of a WikiPedia article:

Julie Frances Christie (born 14 April 1940)[1] is a British actress. An icon of the Swinging Sixties, Christie is the recipient of numerous accolades including an Academy Award, a BAFTA Award, a Golden Globe, and a Screen Actors Guild Award. She has appeared in six films ranked in the British Film Institute‘s BFI Top 100 British films of the 20th century, and in 1997, she received the BAFTA Fellowship for lifetime achievement.

Now to the video:

Fantastic!

Picture Parade Four Hundred and Twenty-Eight

Back to Unsplash!

Photo by Laula Co on Unsplash

Photo by Vincent van Zalinge on Unsplash

Photo by Karsten Winegeart on Unsplash

Photo by Shayna Douglas on Unsplash

Photo by sippakorn yamkasikorn on Unsplash

Photo by Kinshuk Bose on Unsplash

Until next week!

A good night’s sleep?

This article has some deeper implications.

As 99% of you know, Jean, my wife, has Parkinson’s Disease. One of the characteristics of the disease is the effect it has on sleeping; Jean frequently has a bad night. Plus, our two dogs, Cleopatra and Oliver sleep in the bedroom on dog beds.

But if I was on my own I would find it difficult not to encourage our dogs to sleep on our double bed. That’s my assessment, at least! Over to The Conversation on the topic.

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Could sharing a bedroom with your pets be keeping you from getting a good night’s sleep?

Your dog may not be the best sleep partner. gollykim/E+ via Getty Images

Brian N. Chin, Trinity College

Sleeping with your dog in the same room could be negatively affecting your sleep quality, according to my team’s recently published research in Scientific Reports.

We recruited a nationally representative sample of more than 1,500 American adults who completed questionnaires assessing their sleep habits. Overall, about half of the participants reported co-sleeping with pets – defined in our study as sleeping in the same room with your pet for at least part of the night.

Next, our research team compared the sleep habits of people who did and didn’t co-sleep with pets. Our analyses revealed that participants who co-slept with pets had poorer sleep quality and more insomnia symptoms than those who did not. These findings persisted even after accounting for demographic differences between these groups. When considering pet type, we found evidence for a negative effect on sleep when co-sleeping with dogs but no evidence for a negative effect on sleep when co-sleeping with cats.

Orange and white cat sleeping against the covered legs of their owner sleeping in bed
Cats may have less of a negative effect on sleep than dogs when sharing the same room with their owners. Lewis Tse Pui Lung/iStock via Getty Images Plus

Surprisingly, 93% of people in our study who co-slept with their pets believed that their pets had either a positive or neutral overall effect on their sleep. Although more research is needed, these findings could suggest that most people are unaware of the potential negative effects their pets may have on their sleep.

Why it matters

Most pet owners report that their pets have a generally positive effect on their mental health. Pets can improve their owners’ health in numerous ways during the day, such as by encouraging physical activity, promoting a daily routine and providing love and companionship.

However, our study fills an important knowledge gap by indicating that co-sleeping with pets can affect sleep quality. Good sleep is a pillar of health and wellness. Even though pets may have an overall positive effect on mental health, it is possible that some of this benefit may be undermined if they are also causing you to lose sleep at night.

Although some people report that co-sleeping with their pets can provide them with a sense of comfort or intimacy, it is important for people sharing a bedroom with their pets to be aware of their potential to serve as a source of nighttime noise, heat or movement that can disrupt your ability to fall or stay asleep.

What still isn’t known

Survey-based studies like ours are unable to prove that co-sleeping with pets causes disrupted sleep, although there is some evidence suggesting that this could be the case.

One important factor that our study did not assess was whether participants were also co-sleeping with other people like a spouse or child. Previous research suggests that sharing a bed with other people can also affect our sleep and that the mental health benefits of pet ownership could be stronger for people with a romantic partner.

Chocolate Labrador dog sleeping on owner's bed, sunlight streaming in through window
Pets provide many health benefits during the day, but consider keeping them out of your bed at night. Justin Paget/DigitalVision via Getty Images

What’s next

It probably isn’t realistic for most people to just stop co-sleeping with their pets. So, what should someone do to improve their sleep if they already share a bed with their pets?

Some expert tips include choosing a mattress that is large enough for you and your pets, washing and changing your bedding regularly, and establishing and maintaining a consistent bedtime routine with your pets. Further research is needed to identify more specific habits and routines that pet owners can adopt to ensure a good night’s sleep when sharing the bedroom with their pets.

The Research Brief is a short take about interesting academic work.

Brian N. Chin, Assistant Professor of Psychology, Trinity College

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

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Coming back to Jean and me at least we have a pretty regular routine with us going to our bedroom around 7pm to 8pm. In the morning over our daily coffees I always ask Jean what sort of night she had. Yesterday morning Jean replied that she had had a poor night. My judgement is that Jean has roughly one in two poor nights.

To state the obvious, it’s in the numbers!

A wonderful, and educational, item on The Conversation.

I was listening to an item on the BBC yesterday morning and counting came up. The need for counting was incredibly early on in our history. Here is a copy of the part of the introduction to The Universal History of Numbers: From Prehistory to the Invention of the Computer.

A riveting history of counting and calculating from the time of the cave dwellers to the late twentieth century, The Universal History of Numbers is the first complete account of the invention and evolution of numbers the world over. As different cultures around the globe struggled with problems of harvests, constructing buildings, educating their citizens, and exploring the wonders of science, each civilization created its own unique and wonderful mathematical system. 

Dubbed the “Indiana Jones of numbers,” Georges Ifrah traveled all over the world for ten years to uncover the little-known details of this amazing story. From India to China, and from Egypt to Chile, Ifrah talked to mathematicians, historians, archaeologists, and philosophers. He deciphered ancient writing on crumbling walls; scrutinized stones, tools, cylinders, and cones; and examined carved bones, elaborately knotted counting strings, and X-rays of the contents of never-opened ancient clay accounting balls. Conveying all the excitement and joy of the process of discovery, Ifrah writes in a delightful storytelling style, recounting a plethora of intriguing and amusing anecdotes along the way.

Now to that article on The Conversation.

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

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 series for children 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 come 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 help you find an answer.

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.”

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 billion, with nine zeros, or a trillion, 12 zeros.

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

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 government 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.

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.

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.

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!


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 live.

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.

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.

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This article was written for those a great deal younger than I am. But, to be honest, it is a fascinating account of something so utterly basic to humans and human cognition.

Enjoy!

Picture Parade Four Hundred and Twenty-Seven

And it has to be the 2024 Eclipse.

(With thanks to Unsplash.)

April 8th, 2024

Photo by Jeni Holland on Unsplash

Photo by Luis Olmos on Unsplash

Photo by Nikhil Mitra on Unsplash

Photo by Stephen Walker on Unsplash

Photo by Nikhil Mitra on Unsplash

These are just a few of the photographs available on Unsplash. These and the others are just wonderful.