A terrific set of videos!
John Zande sent me an email yesterday. It contained a link that when clicked on took me to a series of videos.
Here is the first one I looked at:
That link sent by John is here: https://www.youtube.com/@BarkBondOfc
Category: Technology
Technology, and Scamming
The title says it all!
We live in a world that is rapidly becoming more and more digital. But we also live in a world where the criminals are becoming better at carrying out their crimes. So a recent article in The Conversation seemed appropriate to republish.
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Scams and frauds: Here are the tactics criminals use on you in the age of AI and cryptocurrencies
Rahul Telang, Carnegie Mellon University
Scams are nothing new – fraud has existed as long as human greed. What changes are the tools.
Scammers thrive on exploiting vulnerable, uninformed users, and they adapt to whatever technologies or trends dominate the moment. In 2025, that means AI, cryptocurrencies and stolen personal data are their weapons of choice.
And, as always, the duty, fear and hope of their targets provide openings. Today, duty often means following instructions from bosses or co-workers, who scammers can impersonate. Fear is that a loved one, who scammers also can impersonate, is in danger. And hope is often for an investment scheme or job opportunity to pay off.
AI-powered scams and deepfakes
Artificial intelligence is no longer niche – it’s cheap, accessible and effective. While businesses use AI for advertising and customer support, scammers exploit the same tools to mimic reality, with disturbing precision.
Deepfake scams use high-tech tools and old-fashioned emotional manipulation.
Criminals are using AI-generated audio or video to impersonate CEOs, managers or even family members in distress. Employees have been tricked into transferring money or leaking sensitive data. Over 105,000 such deepfake attacks were recorded in the U.S. in 2024, costing more than US$200 million in the first quarter of 2025 alone. Victims often cannot distinguish synthetic voices or faces from real ones.
Fraudsters are also using emotional manipulation. The scammers make phone calls or send convincing AI-written texts posing as relatives or friends in distress. Elderly victims in particular fall prey when they believe a grandchild or other family member is in urgent trouble. The Federal Trade Commission has outlined how scammers use fake emergencies to pose as relatives.
Cryptocurrency scams
Crypto remains the Wild West of finance — fast, unregulated and ripe for exploitation.
Pump-and-dump scammers artificially inflate the price of a cryptocurrency through hype on social media to lure investors with promises of huge returns – the pump – and then sell off their holdings – the dump – leaving victims with worthless tokens.
Pig butchering is a hybrid of romance scams and crypto fraud. Scammers build trust over weeks or months before persuading victims to invest in fake crypto platforms. Once the scammers have extracted enough money from the victim, they vanish.
Pig-butchering scams lure people into fake online relationships, often with devastating consequences.
Scammers also use cryptocurrencies as a means of extracting money from people in impersonation scams and other forms of fraud. For example, scammers direct victims to bitcoin ATMs to deposit large sums of cash and convert it to the untraceable cryptocurrency as payment for fictitious fines.
Phishing, smishing, tech support and jobs
Old scams don’t die; they evolve.
Phishing and smishing have been around for years. Victims are tricked into clicking links in emails or text messages, leading to malware downloads, credential theft or ransomware attacks. AI has made these lures eerily realistic, mimicking corporate tone, grammar and even video content.
Tech support scams often start with pop-ups on computer screens that warn of viruses or identity theft, urging users to call a number. Sometimes they begin with a direct cold call to the victim. Once the victim is on a call with the fake tech support, the scammers convince victims to grant remote access to their supposedly compromised computers. Once inside, scammers install malware, steal data, demand payment or all three.
Fake websites and listings are another current type of scam. Fraudulent sites impersonating universities or ticket sellers trick victims into paying for fake admissions, concerts or goods.
One example is when a website for “Southeastern Michigan University” came online and started offering details about admission. There is no such university. Eastern Michigan University filed a complaint that Southeastern Michigan University was copying its website and defrauding unsuspecting victims.
The rise of remote and gig work has opened new fraud avenues.
Victims are offered fake jobs with promises of high pay and flexible hours. In reality, scammers extract “placement fees” or harvest sensitive personal data such as Social Security numbers and bank details, which are later used for identity theft.
How you can protect yourself
Technology has changed, but the basic principles remain the same: Never click on suspicious links or download attachments from unknown senders, and enter personal information only if you are sure that the website is legitimate. Avoid using third-party apps or links. Legitimate businesses have apps or real websites of their own.
Enable two-factor authentication wherever possible. It provides security against stolen passwords. Keep software updated to patch security holes. Most software allows for automatic update or warns about applying a patch.
Remember that a legitimate business will never ask for personal information or a money transfer. Such requests are a red flag.
Relationships are a trickier matter. The state of California provides details on how people can avoid being victims of pig butchering.
Technology has supercharged age-old fraud. AI makes deception virtually indistinguishable from reality, crypto enables anonymous theft, and the remote-work era expands opportunities to trick people. The constant: Scammers prey on trust, urgency and ignorance. Awareness and skepticism remain your best defense.
Rahul Telang, Professor of Information Systems, Carnegie Mellon University
This article is republished from The Conversation under a Creative Commons license. Read the original article.
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That last paragraph really spells out how it is in the modern world. I repeat that last sentence: “Awareness and skepticism remain your best defense.“
Life on other planets
A fascinating article from The Conversation.
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Earth-size stars and alien oceans – an astronomer explains the case for life around white dwarfs
Juliette Becker, University of Wisconsin-Madison
The Sun will someday die. This will happen when it runs out of hydrogen fuel in its core and can no longer produce energy through nuclear fusion as it does now. The death of the Sun is often thought of as the end of the solar system. But in reality, it may be the beginning of a new phase of life for all the objects living in the solar system.
When stars like the Sun die, they go through a phase of rapid expansion called the Red Giant phase: The radius of the star gets bigger, and its color gets redder. Once the gravity on the star’s surface is no longer strong enough for it to hold on to its outer layers, a large fraction – up to about half – of its mass escapes into space, leaving behind a remnant called a white dwarf.
I am a professor of astronomy at the University of Wisconsin-Madison. In 2020, my colleagues and I discovered the first intact planet orbiting around a white dwarf. Since then, I’ve been fascinated by the prospect of life on planets around these, tiny, dense white dwarfs.
Researchers search for signs of life in the universe by waiting until a planet passes between a star and their telescope’s line of sight. With light from the star illuminating the planet from behind, they can use some simple physics principles to determine the types of molecules present in the planet’s atmosphere.
In 2020, researchers realized they could use this technique for planets orbiting white dwarfs. If such a planet had molecules created by living organisms in its atmosphere, the James Webb Space Telescope would probably be able to spot them when the planet passed in front of its star.
In June 2025, I published a paper answering a question that first started bothering me in 2021: Could an ocean – likely needed to sustain life – even survive on a planet orbiting close to a dead star?
A universe full of white dwarfs
A white dwarf has about half the mass of the Sun, but that mass is compressed into a volume roughly the size of Earth, with its electrons pressed as close together as the laws of physics will allow. The Sun has a radius 109 times the size of Earth’s – this size difference means that an Earth-like planet orbiting a white dwarf could be about the same size as the star itself.
White dwarfs are extremely common: An estimated 10 billion of them exist in our galaxy. And since every low-mass star is destined to eventually become a white dwarf, countless more have yet to form. If it turns out that life can exist on planets orbiting white dwarfs, these stellar remnants could become promising and plentiful targets in the search for life beyond Earth.
But can life even exist on a planet orbiting a white dwarf? Astronomers have known since 2011 that the habitable zone is extremely close to the white dwarf. This zone is the location in a planetary system where liquid water could exist on a planet’s surface. It can’t be too close to the star that the water would boil, nor so far away that it would freeze.
The habitable zone around a white dwarf would be 10 to 100 times closer to the white dwarf than our own habitable zone is to our Sun, since white dwarfs are so much fainter.
The challenge of tidal heating
Being so close to the surface of the white dwarf would bring new challenges to emerging life that more distant planets, like Earth, do not face. One of these is tidal heating.
Tidal forces – the differences in gravitational forces that objects in space exert on different parts of a nearby second object – deform a planet, and the friction causes the material being deformed to heat up. An example of this can be seen on Jupiter’s moon Io.
The forces of gravity exerted by Jupiter’s other moons tug on Io’s orbit, deforming its interior and heating it up, resulting in hundreds of volcanoes erupting constantly across its surface. As a result, no surface water can exist on Io because its surface is too hot.
In contrast, the adjacent moon Europa is also subject to tidal heating, but to a lesser degree, since it’s farther from Jupiter. The heat generated from tidal forces has caused Europa’s ice shell to partially melt, resulting in a subsurface ocean.
Planets in the habitable zone of a white dwarf would have orbits close enough to the star to experience tidal heating, similar to how Io and Europa are heated from their proximity to Jupiter.
This proximity itself can pose a challenge to habitability. If a system has more than one planet, tidal forces from nearby planets could cause the planet’s atmosphere to trap heat until it becomes hotter and hotter, making the planet too hot to have liquid water.
Enduring the red giant phase
Even if there is only one planet in the system, it may not retain its water.
In the process of becoming a white dwarf, a star will expand to 10 to 100 times its original radius during the red giant phase. During that time, anything within that expanded radius will be engulfed and destroyed. In our own solar system, Mercury, Venus and Earth will be destroyed when the Sun eventually becomes a red giant before transitioning into a white dwarf.
For a planet to survive this process, it would have to start out much farther from the star — perhaps at the distance of Jupiter or even beyond.
If a planet starts out that far away, it would need to migrate inward after the white dwarf has formed in order to become habitable. Computer simulations show that this kind of migration is possible, but the process could cause extreme tidal heating that may boil off surface water – similar to how tidal heating causes Io’s volcanism. If the migration generates enough heat, then the planet could lose all its surface water by the time it finally reaches a habitable orbit.
However, if the migration occurs late enough in the white dwarf’s lifetime – after it has cooled and is no longer a hot, bright, newly formed white dwarf – then surface water may not evaporate away.
Under the right conditions, planets orbiting white dwarfs could sustain liquid water and potentially support life.
Search for life on planets orbiting white dwarfs
Astronomers haven’t yet found any Earth-like, habitable exoplanets around white dwarfs. But these planets are difficult to detect.
Traditional detection methods like the transit technique are less effective because white dwarfs are much smaller than typical planet-hosting stars. In the transit technique, astronomers watch for the dips in light that occur when a planet passes in front of its host star from our line of sight. Because white dwarfs are so small, you would have to be very lucky to see a planet passing in front of one.
The transit technique for detecting exoplanets requires watching for the dip in brightness when a planet passes in front of its host star.
Nevertheless, researchers are exploring new strategies to detect and characterize these elusive worlds using advanced telescopes such as the Webb telescope.
If habitable planets are found to exist around white dwarfs, it would significantly broaden the range of environments where life might persist, demonstrating that planetary systems may remain viable hosts for life even long after the death of their host star.
Juliette Becker, Assistant Professor of Astronomy, University of Wisconsin-Madison
This article is republished from The Conversation under a Creative Commons license. Read the original article.
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I take my hats off to the researchers that are looking for life elsewhere.
Black holes
How black holes challenge our technological world.
I had no idea until reading this recent article that distant black holes are essential for measuring accurately where we are. Have a read.
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Scientists look to black holes to know exactly where we are in the Universe. But phones and wifi are blocking the view
Lucia McCallum, University of Tasmania
The scientists who precisely measure the position of Earth are in a bit of trouble. Their measurements are essential for the satellites we use for navigation, communication and Earth observation every day.
But you might be surprised to learn that making these measurements – using the science of geodesy – depends on tracking the locations of black holes in distant galaxies.
The problem is, the scientists need to use specific frequency lanes on the radio spectrum highway to track those black holes.
And with the rise of wifi, mobile phones and satellite internet, travel on that highway is starting to look like a traffic jam.
Why we need black holes
Satellites and the services they provide have become essential for modern life. From precision navigation in our pockets to measuring climate change, running global supply chains and making power grids and online banking possible, our civilisation cannot function without its orbiting companions.
To use satellites, we need to know exactly where they are at any given time. Precise satellite positioning relies on the so-called “global geodesy supply chain”.
This supply chain starts by establishing a reliable reference frame as a basis for all other measurements. Because satellites are constantly moving around Earth, Earth is constantly moving around the Sun, and the Sun is constantly moving through the galaxy, this reference frame needs to be carefully calibrated via some relatively fixed external objects.
As it turns out, the best anchor points for the system are the black holes at the hearts of distant galaxies, which spew out streams of radiation as they devour stars and gas.
These black holes are the most distant and stable objects we know. Using a technique called very long baseline interferometry, we can use a network of radio telescopes to lock onto the black hole signals and disentangle Earth’s own rotation and wobble in space from the satellites’ movement.
Different lanes on the radio highway
We use radio telescopes because we want to detect the radio waves coming from the black holes. Radio waves pass cleanly through the atmosphere and we can receive them during day and night and in all weather conditions.
Radio waves are also used for communication on Earth – including things such as wifi and mobile phones. The use of different radio frequencies – different lanes on the radio highway – is closely regulated, and a few narrow lanes are reserved for radio astronomy.
However, in previous decades the radio highway had relatively little traffic. Scientists commonly strayed from the radio astronomy lanes to receive the black hole signals.
To reach the very high precision needed for modern technology, geodesy today relies on more than just the lanes exclusively reserved for astronomy.
Radio traffic on the rise
In recent years, human-made electromagnetic pollution has vastly increased. When wifi and mobile phone services emerged, scientists reacted by moving to higher frequencies.
However, they are running out of lanes. Six generations of mobile phone services (each occupying a new lane) are crowding the spectrum, not to mention internet connections directly sent by a fleet of thousands of satellites.
Today, the multitude of signals are often too strong for geodetic observatories to see through them to the very weak signals emitted by black holes. This puts many satellite services at risk.
What can be done?
To keep working into the future – to maintain the services on which we all depend – geodesy needs some more lanes on the radio highway. When the spectrum is divided up via international treaties at world radio conferences, geodesists need a seat at the table.
Other potential fixes might include radio quiet zones around our essential radio telescopes. Work is also underway with satellite providers to avoid pointing radio emissions directly at radio telescopes.
Any solution has to be global. For our geodetic measurements, we link radio telescopes together from all over the world, allowing us to mimic a telescope the size of Earth. The radio spectrum is primarily regulated by each nation individually, making this a huge challenge.
But perhaps the first step is increasing awareness. If we want satellite navigation to work, our supermarkets to be stocked and our online money transfers arriving safely, we need to make sure we have a clear view of those black holes in distant galaxies – and that means clearing up the radio highway.
Lucia McCallum, Senior Scientist in Geodesy, University of Tasmania
This article is republished from The Conversation under a Creative Commons license. Read the original article.
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The last paragraph of Lucia’s article is key, in my opinion. Hopefully me posting this article will assist in the task of increasing awareness,
The mystery of Dark Matter
This very interesting article is worth a read.
Patrice Ayme published a post on Wednesday, 25th June, 2025 that is deeply conected to the following post from The Conversation.
His post was called: ‘How Does The Universe Expand? The Way Cosmologists Decided That It Does, FLRW Metric! A Causal Loop Is At The Heart Of Modern ΛCDM Cosmology!’
Thus I recommend that you read that article and then the one that is republished by me, with permission, from The Conversation.
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The Vera C. Rubin Observatory will help astronomers investigate dark matter, continuing the legacy of its pioneering namesake
Samantha Thompson, Smithsonian Institution
Everything in space – from the Earth and Sun to black holes – accounts for just 15% of all matter in the universe. The rest of the cosmos seems to be made of an invisible material astronomers call dark matter.
Astronomers know dark matter exists because its gravity affects other things, such as light. But understanding what dark matter is remains an active area of research.
With the release of its first images this month, the Vera C. Rubin Observatory has begun a 10-year mission to help unravel the mystery of dark matter. The observatory will continue the legacy of its namesake, a trailblazing astronomer who advanced our understanding of the other 85% of the universe.
As a historian of astronomy, I’ve studied how Vera Rubin’s contributions have shaped astrophysics. The observatory’s name is fitting, given that its data will soon provide scientists with a way to build on her work and shed more light on dark matter.
Wide view of the universe
From its vantage point in the Chilean Andes mountains, the Rubin Observatory will document everything visible in the southern sky. Every three nights, the observatory and its 3,200 megapixel camera will make a record of the sky.
This camera, about the size of a small car, is the largest digital camera ever built. Images will capture an area of the sky roughly 45 times the size of the full Moon. With a big camera with a wide field of view, Rubin will produce about five petabytes of data every year. That’s roughly 5,000 years’ worth of MP3 songs.
After weeks, months and years of observations, astronomers will have a time-lapse record revealing anything that explodes, flashes or moves – such as supernovas, variable stars or asteroids. They’ll also have the largest survey of galaxies ever made. These galactic views are key to investigating dark matter.
Galaxies are the key
Deep field images from the Hubble Space Telescope, the James Webb Space Telescope and others have visually revealed the abundance of galaxies in the universe. These images are taken with a long exposure time to collect the most light, so that even very faint objects show up.
Researchers now know that those galaxies aren’t randomly distributed. Gravity and dark matter pull and guide them into a structure that resembles a spider’s web or a tub of bubbles. The Rubin Observatory will expand upon these previous galactic surveys, increasing the precision of the data and capturing billions more galaxies.
In addition to helping structure galaxies throughout the universe, dark matter also distorts the appearance of galaxies through an effect referred to as gravitational lensing.
Light travels through space in a straight line − unless it gets close to something massive. Gravity bends light’s path, which distorts the way we see it. This gravitational lensing effect provides clues that could help astronomers locate dark matter. The stronger the gravity, the bigger the bend in light’s path.
Discovering dark matter
For centuries, astronomers tracked and measured the motion of planets in the solar system. They found that all the planets followed the path predicted by Newton’s laws of motion, except for Uranus. Astronomers and mathematicians reasoned that if Newton’s laws are true, there must be some missing matter – another massive object – out there tugging on Uranus. From this hypothesis, they discovered Neptune, confirming Newton’s laws.
With the ability to see fainter objects in the 1930s, astronomers began tracking the motions of galaxies.
California Institute of Technology astronomer Fritz Zwicky coined the term dark matter in 1933, after observing galaxies in the Coma Cluster. He calculated the mass of the galaxies based on their speeds, which did not match their mass based on the number of stars he observed.
He suspected that the cluster could contain an invisible, missing matter that kept the galaxies from flying apart. But for several decades he lacked enough observational evidence to support his theory.
Enter Vera Rubin
In 1965, Vera Rubin became the first women hired onto the scientific staff at the Carnegie Institution’s Department of Terrestrial Magnetism in Washington, D.C.
She worked with Kent Ford, who had built an extremely sensitive spectrograph and was looking to apply it to a scientific research project. Rubin and Ford used the spectrograph to measure how fast stars orbit around the center of their galaxies.
In the solar system, where most of the mass is within the Sun at the center, the closest planet, Mercury, moves faster than the farthest planet, Neptune.
“We had expected that as stars got farther and farther from the center of their galaxy, they would orbit slower and slower,” Rubin said in 1992.
What they found in galaxies surprised them. Stars far from the galaxy’s center were moving just as fast as stars closer in.
“And that really leads to only two possibilities,” Rubin explained. “Either Newton’s laws don’t hold, and physicists and astronomers are woefully afraid of that … (or) stars are responding to the gravitational field of matter which we don’t see.”
Data piled up as Rubin created plot after plot. Her colleagues didn’t doubt her observations, but the interpretation remained a debate. Many people were reluctant to accept that dark matter was necessary to account for the findings in Rubin’s data.
Rubin continued studying galaxies, measuring how fast stars moved within them. She wasn’t interested in investigating dark matter itself, but she carried on with documenting its effects on the motion of galaxies.
Vera Rubin’s legacy
Today, more people are aware of Rubin’s observations and contributions to our understanding of dark matter. In 2019, a congressional bill was introduced to rename the former Large Synoptic Survey Telescope to the Vera C. Rubin Observatory. In June 2025, the U.S. Mint released a quarter featuring Vera Rubin.
Rubin continued to accumulate data about the motions of galaxies throughout her career. Others picked up where she left off and have helped advance dark matter research over the past 50 years.
In the 1970s, physicist James Peebles and astronomers Jeremiah Ostriker and Amos Yahil created computer simulations of individual galaxies. They concluded, similarly to Zwicky, that there was not enough visible matter in galaxies to keep them from flying apart.
They suggested that whatever dark matter is − be it cold stars, black holes or some unknown particle − there could be as much as 10 times the amount of dark matter than ordinary matter in galaxies.
Throughout its 10-year run, the Rubin Observatory should give even more researchers the opportunity to add to our understanding of dark matter.
Samantha Thompson, Astronomy Curator, National Air and Space Museum, Smithsonian Institution
This article is republished from The Conversation under a Creative Commons license. Read the original article.
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It is difficult to say anything more as my comment will mean practically nothing compared to Patrice Ayme and Samantha Thompson.
I am just grateful that these fine people publish their research with permission for it to be republished elsewhere. Thank you!
The building blocks of numbers
We are talking of prime numbers.
Science and mathematics have been a long interest of mine and I regret that I did not go to university to study science. But that was a long time ago!
However, thanks to The Conversation I can write about mathematics, in this case Prime Numbers.
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Prime numbers, the building blocks of mathematics, have fascinated for centuries − now technology is revolutionizing the search for them
Jeremiah Bartz, University of North Dakota
A shard of smooth bone etched with irregular marks dating back 20,000 years puzzled archaeologists until they noticed something unique – the etchings, lines like tally marks, may have represented prime numbers. Similarly, a clay tablet from 1800 B.C.E. inscribed with Babylonian numbers describes a number system built on prime numbers.
As the Ishango bone, the Plimpton 322 tablet and other artifacts throughout history display, prime numbers have fascinated and captivated people throughout history. Today, prime numbers and their properties are studied in number theory, a branch of mathematics and active area of research today.
A history of prime numbers
Informally, a positive counting number larger than one is prime if that number of dots can be arranged only into a rectangular array with one column or one row. For example, 11 is a prime number since 11 dots form only rectangular arrays of sizes 1 by 11 and 11 by 1. Conversely, 12 is not prime since you can use 12 dots to make an array of 3 by 4 dots, with multiple rows and multiple columns. Math textbooks define a prime number as a whole number greater than one whose only positive divisors are only 1 and itself.
Math historian Peter S. Rudman suggests that Greek mathematicians were likely the first to understand the concept of prime numbers, around 500 B.C.E.
Around 300 B.C.E., the Greek mathematician and logician Euler proved that there are infinitely many prime numbers. Euler began by assuming that there is a finite number of primes. Then he came up with a prime that was not on the original list to create a contradiction. Since a fundamental principle of mathematics is being logically consistent with no contradictions, Euler then concluded that his original assumption must be false. So, there are infinitely many primes.
The argument established the existence of infinitely many primes, however it was not particularly constructive. Euler had no efficient method to list all the primes in an ascending list.
In the middle ages, Arab mathematicians advanced the Greeks’ theory of prime numbers, referred to as hasam numbers during this time. The Persian mathematician Kamal al-Din al-Farisi formulated the fundamental theorem of arithmetic, which states that any positive integer larger than one can be expressed uniquely as a product of primes.
From this view, prime numbers are the basic building blocks for constructing any positive whole number using multiplication – akin to atoms combining to make molecules in chemistry.
Prime numbers can be sorted into different types. In 1202, Leonardo Fibonacci introduced in his book “Liber Abaci: Book of Calculation” prime numbers of the form (2p – 1) where p is also prime.
Today, primes in this form are called Mersenne primes after the French monk Marin Mersenne. Many of the largest known primes follow this format.
Several early mathematicians believed that a number of the form (2p – 1) is prime whenever p is prime. But in 1536, mathematician Hudalricus Regius noticed that 11 is prime but not (211 – 1), which equals 2047. The number 2047 can be expressed as 11 times 89, disproving the conjecture.
While not always true, number theorists realized that the (2p – 1) shortcut often produces primes and gives a systematic way to search for large primes.
The search for large primes
The number (2p – 1) is much larger relative to the value of p and provides opportunities to identify large primes.
When the number (2p – 1) becomes sufficiently large, it is much harder to check whether (2p – 1) is prime – that is, if (2p – 1) dots can be arranged only into a rectangular array with one column or one row.
Fortunately, Édouard Lucas developed a prime number test in 1878, later proved by Derrick Henry Lehmer in 1930. Their work resulted in an efficient algorithm for evaluating potential Mersenne primes. Using this algorithm with hand computations on paper, Lucas showed in 1876 that the 39-digit number (2127 – 1) equals 170,141,183,460,469,231,731,687,303,715,884,105,727, and that value is prime.
Also known as M127, this number remains the largest prime verified by hand computations. It held the record for largest known prime for 75 years.
Researchers began using computers in the 1950s, and the pace of discovering new large primes increased. In 1952, Raphael M. Robinson identified five new Mersenne primes using a Standard Western Automatic Computer to carry out the Lucas-Lehmer prime number tests.
As computers improved, the list of Mersenne primes grew, especially with the Cray supercomputer’s arrival in 1964. Although there are infinitely many primes, researchers are unsure how many fit the type (2p – 1) and are Mersenne primes.
By the early 1980s, researchers had accumulated enough data to confidently believe that infinitely many Mersenne primes exist. They could even guess how often these prime numbers appear, on average. Mathematicians have not found proof so far, but new data continues to support these guesses.
George Woltman, a computer scientist, founded the Great Internet Mersenne Prime Search, or GIMPS, in 1996. Through this collaborative program, anyone can download freely available software from the GIMPS website to search for Mersenne prime numbers on their personal computers. The website contains specific instructions on how to participate.
GIMPS has now identified 18 Mersenne primes, primarily on personal computers using Intel chips. The program averages a new discovery about every one to two years.
The largest known prime
Luke Durant, a retired programmer, discovered the current record for the largest known prime, (2136,279,841 – 1), in October 2024.
Referred to as M136279841, this 41,024,320-digit number was the 52nd Mersenne prime identified and was found by running GIMPS on a publicly available cloud-based computing network.
This network used Nvidia chips and ran across 17 countries and 24 data centers. These advanced chips provide faster computing by handling thousands of calculations simultaneously. The result is shorter run times for algorithms such as prime number testing.
The Electronic Frontier Foundation is a civil liberty group that offers cash prizes for identifying large primes. It awarded prizes in 2000 and 2009 for the first verified 1 million-digit and 10 million-digit prime numbers.
Large prime number enthusiasts’ next two challenges are to identify the first 100 million-digit and 1 billion-digit primes. EFF prizes of US$150,000 and $250,000, respectively, await the first successful individual or group.
Eight of the 10 largest known prime numbers are Mersenne primes, so GIMPS and cloud computing are poised to play a prominent role in the search for record-breaking large prime numbers.
Large prime numbers have a vital role in many encryption methods in cybersecurity, so every internet user stands to benefit from the search for large prime numbers. These searches help keep digital communications and sensitive information safe.
Jeremiah Bartz, Associate Professor of Mathematics, University of North Dakota
This article is republished from The Conversation under a Creative Commons license. Read the original article.
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I find it unbelievable that there are prizes for the first 100 million-digit prime number and also the first 1 billion-digit prime number. It is so far away from my understanding of these numbers that all I can say is: I find it unbelievable!
Artificial Intelligence and Mars
NASA hasn’t landed humans on Mars yet. But thanks to robotic missions, scientists now know more about the planet’s surface than they did when the movie, The Martian, was released.
Our human knowledge is constantly growing. In many, many directions. Here is a fascinating (well it is to me!) article from The Conversation.
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A decade after the release of ‘The Martian’ and a decade out from the world it envisions, a planetary scientist checks in on real-life Mars exploration
Ari Koeppel, Dartmouth College
Andy Weir’s bestselling story “The Martian” predicts that by 2035 NASA will have landed humans on Mars three times, perfected return-to-Earth flight systems and collaborated with the China National Space Administration. We are now 10 years past the Hollywood adaptation’s 2015 release and 10 years shy of its fictional timeline. At this midpoint, Mars exploration looks a bit different than how it was portrayed in “The Martian,” with both more discoveries and more controversy.
As a planetary geologist who works with NASA missions to study Mars, I follow exploration science and policy closely. In 2010, the U.S. National Space Policy set goals for human missions to Mars in the 2030s. But in 2017, the White House Space Policy Directive 1 shifted NASA’s focus toward returning first to the Moon under what would become the Artemis program.
Although concepts for crewed missions to Mars have gained popularity, NASA’s actual plans for landing humans on Mars remain fragile. Notably, over the last 10 years, it has been robotic, rather than crewed, missions that have propelled discovery and the human imagination forward.
Robotic discoveries
Since 2015, satellites and rovers have reshaped scientists’ understanding of Mars. They have revealed countless insights into how its climate has changed over time.
As Earth’s neighbor, climate shifts on Mars also reflect solar system processes affecting Earth at a time when life was first taking hold. Thus, Mars has become a focal point for investigating the age old questions of “where do we come from?” and “are we alone?”
The Opportunity, Curiosity and Perseverance rovers have driven dozens of miles studying layered rock formations that serve as a record of Mars’ past. By studying sedimentary layers – rock formations stacked like layers of a cake – planetary geologists have pieced together a vivid tale of environmental change that dwarfs what Earth is currently experiencing.
Mars was once a world of erupting volcanoes, glaciers, lakes and flowing rivers – an environment not unlike early Earth. Then its core cooled, its magnetic field faltered and its atmosphere drifted away. The planet’s exposed surface has retained signs of those processes ever since in the form of landscape patterns, sequences of layered sediment and mineral mixtures.
Arabia Terra
One focus of scientific investigation over the last 10 years is particularly relevant to the setting of “The Martian” but fails to receive mention in the story. To reach his best chance of survival, protagonist Mark Watney, played by Matt Damon, must cross a vast, dusty and crater-pocked region of Mars known as Arabia Terra.
In 2022 and 2023, I, along with colleagues at Northern Arizona University and Johns Hopkins University, published detailed analyses of the layered materials there using imagery from the Mars Reconnaissance Orbiter and Mars Odyssey satellites.
By using infrared imagery and measuring the dimensions of surface features, we linked multiple layered deposits to the same episodes of formation and learned more about the widespread crumbling nature of the terrain seen there today. Because water tends to cement rock tightly together, that loose material indicates that around 3.5 billion years ago, that area had a drying climate.
To make the discussions about this area easier, we even worked with the International Astronomical Union to name a few previously unnamed craters that were mentioned in the story. For example, one that Watney would have driven right by is now named Kozova Crater, after a town in Ukraine.
More to explore
Despite rapid advances in Mars science, many unknowns remain. Scientists still aren’t sure of the precise ages, atmospheric conditions and possible signatures of life associated with each of the different rock types observed on the surface.
For instance, the Perseverance rover recently drilled into and analyzed a unique set of rocks hosting organic – that is, carbon-based – compounds. Organic compounds serve as the building blocks of life, but more detailed analysis is required to determine whether these specific rocks once hosted microbial life.
The in-development Mars Sample Return mission aims to address these basic outstanding questions by delivering the first-ever unaltered fragments of another world to Earth. The Perseverance rover is already caching rock and soil samples, including ones hosting organic compounds, in sealed tubes. A future lander will then need to pick up and launch the caches back to Earth.
Sampling Mars rocks could tell scientists more about the red planet’s past, and whether it could have hosted life.
Once home, researchers can examine these materials with instruments orders of magnitude more sensitive than anything that could be flown on a spacecraft. Scientists stand to learn far more about the habitability, geologic history and presence of any signs of life on Mars through the sample return campaign than by sending humans to the surface.
This perspective is why NASA, the European Space Agency and others have invested some US$30 billion in robotic Mars exploration since the 1960s. The payoff has been staggering: That work has triggered rapid technological advances in robotics, telecommunications and materials science. For example, Mars mission technology has led to better sutures for heart surgery and cars that can drive themselves.
It has also bolstered the status of NASA and the U.S. as bastions of modern exploration and technology; and it has inspired millions of students to take an interest in scientific fields.
Calling the red planet home?
Colonizing Mars has a seductive appeal. It’s hard not to cheer for the indomitable human spirit while watching Watney battle dust storms, oxygen shortages and food scarcity over 140 million miles from rescue.
Much of the momentum toward colonizing Mars is now tied to SpaceX and its CEO Elon Musk, whose stated mission to make humanity a “multi-planetary species” has become a sort of rallying cry. But while Mars colonization is romantic on paper, it is extremely difficult to actually carry out, and many critics have questioned the viability of a Mars habitation as a refuge far from Earth.
Now, with NASA potentially facing a nearly 50% reduction to its science budget, the U.S. risks dissolving its planetary science and robotic operations portfolio altogether, including sample return.
Nonetheless, President Donald Trump and Musk have pushed for human space exploration to somehow continue to progress, despite those proposed cuts – effectively sidelining the robotic, science-driven programs that have underpinned all of Mars exploration to date.
Yet, it is these programs that have yielded humanity’s richest insights into the red planet and given both scientists and storytellers like Andy Weir the foundation to imagine what it must be like to stand on Mars’ surface at all.
Ari Koeppel, Postdoctoral Scientist in Earth and Planetary Science, Dartmouth College
This article is republished from The Conversation under a Creative Commons license. Read the original article.
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Nothing to add from yours truly except to say that this quote is highly relevant: “Challenges are what make life interesting and overcoming them is what makes life meaningful.” – Joshua J. Marine
(And this was the result of me looking online for quotes and coming across 50 quotes from USA Today.)
Light speed
There is more to this topic that many of us do not know.
Photons are massless. They travel at a speed that 99% of us do not really comprehend. But over to Prof. Jarred Roberts who does comprehend the subject.
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Do photons wear out? An astrophysicist explains light’s ability to travel vast cosmic distances without losing energy
Jarred Roberts, University of California, San Diego
My telescope, set up for astrophotography in my light-polluted San Diego backyard, was pointed at a galaxy unfathomably far from Earth. My wife, Cristina, walked up just as the first space photo streamed to my tablet. It sparkled on the screen in front of us.
“That’s the Pinwheel galaxy,” I said. The name is derived from its shape – albeit this pinwheel contains about a trillion stars.
The light from the Pinwheel traveled for 25 million years across the universe – about 150 quintillion miles – to get to my telescope.
My wife wondered: “Doesn’t light get tired during such a long journey?”
Her curiosity triggered a thought-provoking conversation about light. Ultimately, why doesn’t light wear out and lose energy over time?
Let’s talk about light
I am an astrophysicist, and one of the first things I learned in my studies is how light often behaves in ways that defy our intuitions.
Light is electromagnetic radiation: basically, an electric wave and a magnetic wave coupled together and traveling through space-time. It has no mass. That point is critical because the mass of an object, whether a speck of dust or a spaceship, limits the top speed it can travel through space.
But because light is massless, it’s able to reach the maximum speed limit in a vacuum – about 186,000 miles (300,000 kilometers) per second, or almost 6 trillion miles per year (9.6 trillion kilometers). Nothing traveling through space is faster. To put that into perspective: In the time it takes you to blink your eyes, a particle of light travels around the circumference of the Earth more than twice.
As incredibly fast as that is, space is incredibly spread out. Light from the Sun, which is 93 million miles (about 150 million kilometers) from Earth, takes just over eight minutes to reach us. In other words, the sunlight you see is eight minutes old.
Alpha Centauri, the nearest star to us after the Sun, is 26 trillion miles away (about 41 trillion kilometers). So by the time you see it in the night sky, its light is just over four years old. Or, as astronomers say, it’s four light years away. Imagine – a trip around the world at the speed of light.
With those enormous distances in mind, consider Cristina’s question: How can light travel across the universe and not slowly lose energy?
Actually, some light does lose energy. This happens when it bounces off something, such as interstellar dust, and is scattered about.
But most light just goes and goes, without colliding with anything. This is almost always the case because space is mostly empty – nothingness. So there’s nothing in the way.
When light travels unimpeded, it loses no energy. It can maintain that 186,000-mile-per-second speed forever.
It’s about time
Here’s another concept: Picture yourself as an astronaut on board the International Space Station. You’re orbiting at 17,000 miles (about 27,000 kilometers) per hour. Compared with someone on Earth, your wristwatch will tick 0.01 seconds slower over one year.
That’s an example of time dilation – time moving at different speeds under different conditions. If you’re moving really fast, or close to a large gravitational field, your clock will tick more slowly than someone moving slower than you, or who is further from a large gravitational field. To say it succinctly, time is relative.
Now consider that light is inextricably connected to time. Picture sitting on a photon, a fundamental particle of light; here, you’d experience maximum time dilation. Everyone on Earth would clock you at the speed of light, but from your reference frame, time would completely stop.
That’s because the “clocks” measuring time are in two different places going vastly different speeds: the photon moving at the speed of light, and the comparatively slowpoke speed of Earth going around the Sun.
What’s more, when you’re traveling at or close to the speed of light, the distance between where you are and where you’re going gets shorter. That is, space itself becomes more compact in the direction of motion – so the faster you can go, the shorter your journey has to be. In other words, for the photon, space gets squished.
Which brings us back to my picture of the Pinwheel galaxy. From the photon’s perspective, a star within the galaxy emitted it, and then a single pixel in my backyard camera absorbed it, at exactly the same time. Because space is squished, to the photon the journey was infinitely fast and infinitely short, a tiny fraction of a second.
But from our perspective on Earth, the photon left the galaxy 25 million years ago and traveled 25 million light years across space until it landed on my tablet in my backyard.
And there, on a cool spring night, its stunning image inspired a delightful conversation between a nerdy scientist and his curious wife.
Jarred Roberts, Project Scientist, University of California, San Diego
This article is republished from The Conversation under a Creative Commons license. Read the original article.
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This remark jumped out at me when I first read the article: ‘In the time it takes you to blink your eyes, a particle of light travels around the circumference of the Earth more than twice.’
The following photograph is the Milky Way.
The image is from Geography Realm.
Despite the fact that the article is far from me understanding it, it doesn’t reduce the wonder and the awe for me of outer space.
The Edwin Hubble Great Debate
The following is more than fascinating; it is an example of how far science has reached; both figuratively and literally.
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One large Milky Way galaxy or many galaxies? 100 years ago, a young Edwin Hubble settled astronomy’s ‘Great Debate’
Chris Impey, University of Arizona
A hundred years ago, astronomer Edwin Hubble dramatically expanded the size of the known universe. At a meeting of the American Astronomical Society in January 1925, a paper read by one of his colleagues on his behalf reported that the Andromeda nebula, also called M31, was nearly a million light years away – too remote to be a part of the Milky Way.
Hubble’s work opened the door to the study of the universe beyond our galaxy. In the century since Hubble’s pioneering work, astronomers like me have learned that the universe is vast and contains trillions of galaxies.
Nature of the nebulae
In 1610, astronomer Galileo Galilei used the newly invented telescope to show that the Milky Way was composed of a huge number of faint stars. For the next 300 years, astronomers assumed that the Milky Way was the entire universe.
As astronomers scanned the night sky with larger telescopes, they were intrigued by fuzzy patches of light called nebulae. Toward the end of the 18th century, astronomer William Herschel used star counts to map out the Milky Way. He cataloged a thousand new nebulae and clusters of stars. He believed that the nebulae were objects within the Milky Way.
Charles Messier also produced a catalog of over 100 prominent nebulae in 1781. Messier was interested in comets, so his list was a set of fuzzy objects that might be mistaken for comets. He intended for comet hunters to avoid them since they did not move across the sky.
As more data piled up, 19th century astronomers started to see that the nebulae were a mixed bag. Some were gaseous, star-forming regions, such as the Orion nebula, or M42 – the 42nd object in Messier’s catalog – while others were star clusters such as the Pleiades, or M45.
A third category – nebulae with spiral structure – particularly intrigued astronomers. The Andromeda nebula, M31, was a prominent example. It’s visible to the naked eye from a dark site.
The Andromeda galaxy, then known as the Andromeda nebula, is a bright spot in the sky that intrigued early astronomers.
Astronomers as far back as the mid-18th century had speculated that some nebulae might be remote systems of stars or “island universes,” but there was no data to support this hypothesis. Island universes referred to the idea that there could be enormous stellar systems outside the Milky Way – but astronomers now just call these systems galaxies.
In 1920, astronomers Harlow Shapley and Heber Curtis held a Great Debate. Shapley argued that the spiral nebulae were small and in the Milky Way, while Curtis took a more radical position that they were independent galaxies, extremely large and distant.
At the time, the debate was inconclusive. Astronomers now know that galaxies are isolated systems of stars, much smaller than the space between them.
Hubble makes his mark
Edwin Hubble was young and ambitious. At the of age 30, he arrived at Mount Wilson Observatory in Southern California just in time to use the new Hooker 100-inch telescope, at the time the largest in the world.
He began taking photographic plates of the spiral nebulae. These glass plates recorded images of the night sky using a light-sensitive emulsion covering their surface. The telescope’s size let it make images of very faint objects, and its high-quality mirror allowed it to distinguish individual stars in some of the nebulae.
Estimating distances in astronomy is challenging. Think of how hard it is to estimate the distance of someone pointing a flashlight at you on a dark night. Galaxies come in a very wide range of sizes and masses. Measuring a galaxy’s brightness or apparent size is not a good guide to its distance.
Hubble leveraged a discovery made by Henrietta Swan Leavitt 10 years earlier. She worked at the Harvard College Observatory as a “human computer,” laboriously measuring the positions and brightness of thousands of stars on photographic plates.
She was particularly interested in Cepheid variables, which are stars whose brightness pulses regularly, so they get brighter and dimmer with a particular period. She found a relationship between their variation period, or pulse, and their intrinsic brightness or luminosity.
Once you measure a Cepheid’s period, you can calculate its distance from how bright it appears using the inverse square law. The more distant the star is, the fainter it appears.
Hubble worked hard, taking images of spiral nebulae every clear night and looking for the telltale variations of Cepheid variables. By the end of 1924, he had found 12 Cepheids in M31. He calculated M31’s distance as a prodigious 900,000 light years away, though he underestimated its true distance – about 2.5 million light years – by not realizing there were two different types of Cepheid variables.
His measurements marked the end of the Great Debate about the Milky Way’s size and the nature of the nebulae. Hubble wrote about his discovery to Harlow Shapley, who had argued that the Milky Way encompassed the entire universe.
“Here is the letter that destroyed my universe,” Shapley remarked.
Always eager for publicity, Hubble leaked his discovery to The New York Times five weeks before a colleague presented his paper at the astronomers’ annual meeting in Washington, D.C.
An expanding universe of galaxies
But Hubble wasn’t done. His second major discovery also transformed astronomers’ understanding of the universe. As he dispersed the light from dozens of galaxies into a spectrum, which recorded the amount of light at each wavelength, he noticed that the light was always shifted to longer or redder wavelengths.
Light from the galaxy passes through a prism or reflects off a diffraction grating in a telescope, which captures the intensity of light from blue to red.
Astronomers call a shift to longer wavelengths a redshift.
It seemed that these redshifted galaxies were all moving away from the Milky Way.
Hubble’s results suggested the farther away a galaxy was, the faster it was moving away from Earth. Hubble got the lion’s share of the credit for this discovery, but Lowell Observatory astronomer Vesto Slipher, who noticed the same phenomenon but didn’t publish his data, also anticipated that result.
Hubble referred to galaxies having recession velocities, or speeds of moving away from the Earth, but he never figured out that they were moving away from Earth because the universe is getting bigger.
Belgian cosmologist and Catholic priest Georges Lemaitre made that connection by realizing that the theory of general relativity described an expanding universe. He recognized that space expanding in between the galaxies could cause the redshifts, making it seem like they were moving farther away from each other and from Earth.
Lemaitre was the first to argue that the expansion must have begun during the big bang.
NASA named its flagship space observatory after Hubble, and it has been used to study galaxies for 35 years. Astronomers routinely observe galaxies that are thousands of times fainter and more distant than galaxies observed in the 1920s. The James Webb Space Telescope has pushed the envelope even farther.
The current record holder is a galaxy a staggering 34 billion light years away, seen just 200 million years after the big bang, when the universe was 20 times smaller than it is now. Edwin Hubble would be amazed to see such progress.
Chris Impey, University Distinguished Professor of Astronomy, University of Arizona
This article is republished from The Conversation under a Creative Commons license. Read the original article.
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So wonderful that in this modern era we can read articles from distinguished scientists in the comfort of our own homes.
Essentially, life is about play
We take our decision from watching the animal kingdom.
A recent post in The Conversation provides the article for today’s blog post.
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At its core, life is all about play − just look at the animal kingdom
At Cambridge University Library, along with all the books, maps and manuscripts, there’s a child’s drawing that curators have titled “The Battle of the Fruit and Vegetable Soldiers.”
The drawing depicts a turbaned cavalry soldier facing off against an English dragoon. It’s a bit trippy: The British soldier sits astride a carrot, and the turbaned soldier rides a grape. Both carrot and grape are fitted with horses’ heads and stick appendages.
It’s thought to be the work of Francis Darwin, the seventh child of British naturalist Charles Darwin and his wife, Emma, and appears to have been made in 1857, when Frank would have been 10 or 11. And it’s drawn on the back of a page of a draft of “On the Origin of Species,” Darwin’s masterwork and the foundational text of evolutionary biology. The few sheets of the draft that survive are pages Darwin gave to his children to use for drawing paper.
Darwin’s biographers have long recognized that play was important in his personal and familial life. The Georgian manor in which he and Emma raised their 10 children was furnished with a rope swing hung over the first-floor landing and a portable wooden slide that could be laid over the main stairway. The gardens and surrounding countryside served as an open-air laboratory and playground.
Play also has a role in Darwin’s theory of natural selection. As I explain in my new book, “Kingdom of Play: What Ball-bouncing Octopuses, Belly-flopping Monkeys, and Mud-sliding Elephants Reveal about Life Itself,” there are many similarities – so many that if you could distill the processes of natural selection into a single behavior, that behavior would be play.
No goal, no direction
Natural selection is the process by which organisms that are best adapted to their environments are more likely to survive, and so able to pass on the characteristics that helped them thrive to their offspring. It is undirected: In Darwin’s words, it “includes no necessary and universal law of advancement or development.”
Through natural selection, the rock pocket mouse has evolved a coat color that hides it from predators in the desert Southwest.
In contrast to foraging and hunting – behaviors with clearly defined goals – play is likewise undirected. When a pony frolics in a field, a dog wrestles with a stick or chimpanzees chase each other, they act with no goal in mind.
Natural selection is utterly provisional: The evolution of any organism responds to whatever conditions are present at a given place and time. Likewise, animals at play are acting provisionally. They constantly adjust their movements in response to changes in circumstances. Playing squirrels, faced with obstacles such as falling branches or other squirrels, nimbly alter their tactics and routes.
Natural selection is open-ended. The forms of life are not fixed, but continually evolving. Play, too, is open-ended. Animals begin a play session with no plan of when to end it. Two dogs play-fighting, for instance, cease playing only when one is injured, exhausted or simply loses interest.
Natural selection also is wasteful, as Darwin acknowledged. “Many more individuals of each species are born than can possibly survive,” he wrote. But in the long term, he allowed, such profligacy could produce adaptations that enable an evolutionary line to become “more fit.”
Keepers noticed that Shanthi, a 36-year-old elephant at the Smithsonian national zoo, liked to make noise with objects, so they gave her horns, harmonicas and other noisemakers.
Play is likewise profligate. It requires an animal to expend time and energy that perhaps would be better devoted to behaviors such as foraging and hunting that could aid survival.
And that profligacy is also advantageous. Animals forage and hunt in specific ways that don’t typically change. But an animal at play is far more likely to innovate – and some of its innovations may in time be adapted into new ways to forage and hunt.
Competing and cooperating
As Darwin first framed it, the “struggle for existence” was by and large a competition. But in the 1860s, Russian naturalist Pyotr Kropotkin’s observations of birds and fallow deer led him to conclude that many species were “the most numerous and the most prosperous” because natural selection also selects for cooperation.
Scientists confirmed Kroptokin’s hypothesis in the 20th century, discovering all manner of cooperation, not only between members of the same species but between members of different species. For example, clown fish are immune to anemone stings; they nestle in anemone tentacles for protection and, in return, keep the anemones free of parasites, provide nutrients and drive away predators.
Play likewise utilizes both competition and cooperation. Two dogs play-fighting are certainly competing, yet to sustain their play, they must cooperate. They often reverse roles: A dog with the advantage of position might suddenly surrender that advantage and roll over on its back. If one bites harder than intended, it is likely to retreat and perform a play bow – saying, in effect, “My bad. I hope we can keep playing.”
River otters at the Oregon Zoo repeatedly separate and reunite while playing in a tub of ice.
Natural selection and play also may both employ deception. From butterflies colored to resemble toxic species to wild cats that squeal like distressed baby monkeys, many organisms use mimicry to deceive their prey, predators and rivals. Play – specifically, play-fighting – similarly offers animals opportunities to learn about and practice deception.
To live is to play
Darwin wrote that natural selection creates “endless forms most beautiful and most wonderful.” Play also creates beauty in countless ways, from the aerial acrobatics of birds of prey to the arcing, twisting leaps of dolphins.
In 1973, Ukrainian-American geneticist Theodosius Dobzhansky published an essay with the take-no-prisoners title “Nothing in Biology Makes Sense Except in the Light of Evolution.” Many biologists would agree. Perhaps the most satisfying definition of life attends not to what it is but to what it does – which is to say, life is what evolves by natural selection.
And since natural selection shares so many features with play, we may with some justification maintain that life, in a most fundamental sense, is playful.
David Toomey, Professor of English, UMass Amherst
This article is republished from The Conversation under a Creative Commons license. Read the original article.
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Prof. Toomey’s analysis is spot-on.
All of life involves some form of play.
Learning from Dogs 
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