The decimal expansion of 1/7 is

0.142857142857 …

Interestingly, if you split the repeating decimal period in half and add the two complements, you get a string of 9s:

142 + 857 = 999

It turns out this is true for every fraction with a prime denominator and a repeating decimal period of even length:

1/11 = 0.090909 …
0 + 9 = 9

1/13 = 076923 …
076 + 923 = 999

1/17 = 0.0588235294117647 …
05882352 + 94117647 = 99999999

1/19 = 0.052631578947368421 …
052631578 + 947368421 = 999999999

It was discovered by French mathematician E. Midy in 1836.

Today’s guest issue is from Vedad Siljak, a type designer running Chill Type from Salzburg, Austria, as well as a fellow archive enthusiast who discovered a treasure trove of toy catalogs.

I first learned about Tyco Toys from a YouTube video on the history of Lego. Tyco Super Blocks were one of their competitors in the ’80s and the ads featured in the video boasted about their superiority. The ads didn't necessarily catch my eye, but the logotype did: An ultra bold geometric 4-letter word with 2 ligatures in it, one of them (the CO) a tiny gap shy of becoming an infinity symbol. My excitement was immeasurable.

As I was looking for the logo online, a whole new world started unraveling itself. The Internet Archive has a big collection of Tyco catalogs ranging from the '60s to the '80s. They often feature the logo very prominently on the cover as it adapts itself to the art style around it. On one cover it gets a hand drawn outline, on the next one it serves as a divider between two worlds of toys and on yet another one it becomes part of the backdrop as a physical prop for the photo shoot. (On the 1978 cover it serves as a bridge AND as a divider.)

A look inside the catalogs reveals more type love from Tyco. The Chattanooga Choo- Choo, Curve Huggers and Nite-Glow each have their own distinct logotype. There's also whole spreads were the headlines become intertwined with the toys shown on the pages. Not only does it look really cool, it also helps establish more depth to the images, as the letters align with the vanishing points of the different compositions. It's always exciting to see type treated with this much care, as it helps paint a more nuanced picture and adds to the immersion of the world being built in front of you.

Vedad’s featured archive is Fonts In Use. It's one of the best places to explore how fonts are used in the real world and has entries dating back to the 1500s. It's also one of the most promising starting points when trying to identify unknown fonts.

Sources: Author’s scans

The University of California, San Diego has documented a steep decline in the academic preparation of its entering freshmen over the past five years, according to a report [PDF] released this month by the campus's Senate-Administration Working Group on Admissions. Between 2020 and 2025, the number of students whose math skills fall below middle-school level increased nearly thirtyfold, from roughly 30 to 921 students. These students now represent one in eight members of the entering cohort. The Mathematics Department redesigned its remedial program this year to focus entirely on elementary and middle school content after discovering students struggled with basic fractions and could not perform arithmetic operations taught in grades one through eight. The deterioration extends beyond mathematics. Nearly one in five domestic freshmen required remedial writing instruction in 2024, returning to pre-pandemic levels after a brief decline. Faculty across disciplines report students increasingly struggle to engage with longer and complex texts. The decline coincided with multiple disrupting factors. The COVID-19 pandemic forced remote learning starting in spring 2020. The UC system eliminated SAT and ACT requirements in 2021. High school grade inflation accelerated during this period, leaving transcripts unreliable as indicators of actual preparation. UC San Diego simultaneously doubled its enrollment from under-resourced high schools designated LCFF+, admitting more such students than any other UC campus between 2022 and 2024. The working group concluded that admitting large numbers of underprepared students risks harming those students while straining limited instructional resources. The report recommends developing predictive models to identify at-risk applicants and calls for the UC system to reconsider standardized testing requirements.

Read more of this story at Slashdot.

It likely isn’t news to you that Dungeons & Dragons became the world’s most popular tabletop role-playing game while also trafficking in outmoded and problematic concepts around race and gender. It also likely isn’t news to you that Dungeons & Dragons managed to expand and evolve, welcoming a wider audience and becoming more popular than it had ever been. But maybe it is news to you that some people who own the platform formerly known as Twitter seem to have feelings about this. (It was news to me! Don’t forget, though, that news doesn’t have to be surprising to be news.) Anyway, Atlantic writer and unabashed D&D devotee Adam Serwer digs into how fantasy tropes became what they are were, and why a certain breed of gamer seems to cling to them so fiercely.

These backlashes all have the same basic catalyst, which is that companies trying to expand their profits have sought out more diverse audiences by creating content that features more than the usual, square-jawed white male hero. When the damsels who were supposed to be in distress and the members of the races that were supposed to be disposable began to be the protagonists, some fans experienced that as a kind of loss. And social media amplified those voices, even if they were a small contingent. Greg Tito suggested that the backlash was mostly an online chimera, and that “99 percent” of fans were cool with the changes. The 1 percent who weren’t just happened to include, well, the “one percent.”

Measurement standards are needed for knowing “how much” exists.

A teacher giving rulers to children of the second grade (8 years old) in a primary school in Vaasa, on their second day of school in Finland. The ability to measure, quantitatively, “how much” of something you have is a key aspect at the foundation of all quantitative endeavors.

Early distance standards, like “cubits” or “feet,” were based on body parts.

This Ancient Egyptian artifact shows a fragment of a cubit measuring rod. Note the markings at the bottom of the rod showing various fractions of a cubit: forerunners of divisions like inches, centimeters, and millimeters.

A single “pace” was often used: around one yard/meter.

A pace, either defined by a single stride as shown or a “return to the same foot” stride, was used as the original definition of a mile, where 1000 or 2000 paces defined that mile. Before a meter was defined by a pendulum’s length, this non-consistent standard was frequently used for similar distances.

The idea of a “standard meter” came from pendulum observations.

A pendulum, so long as the weight is all in the bob at the bottom while air resistance, temperature changes, and large angle effects can be neglected, will always have the same period when subject to the same gravitational acceleration. The fact that the same pendulum swung at different rates between different locations in Europe and the Americas was a hint toward Newton’s gravitation, and the variation of surface gravity in a latitude-dependent fashion.

A swinging pendulum’s period is determined by two factors: length and gravity.

The front view (left) and side/schematic view (right) of the first pendulum clock ever built, in 1656/7, which was designed by Christiaan Huygens and built by Salomon Coster. The drawings come from Huygens’ 1658 treatise, Horologium. Many subsequent refinements, even prior to Newton’s gravity, were made to this original design; Huygens’ second pendulum clock, built in 1673, was designed to have each half-swing last for precisely one second.

A seconds pendulum, where each half-swing lasts one second, requires a pendulum one meter long.

In general, there are only two factors that determine the period of a pendulum: its length, where longer pendulums take longer to complete one oscillation, and the acceleration due to gravity, where larger amounts of gravity results in faster pendulum swings. This is why a pendulum clock is not universal, but must be calibrated to the specific gravitational acceleration at its location.

Because gravity varies by ~0.2% across Earth, any pendulum-based “length” isn’t universal.

The gravitational field on Earth varies not only with latitude, but also with altitude and in other ways, particularly due to crustal thickness and the fact that the Earth’s crust effectively floats atop the mantle. As a result, the gravitational acceleration varies by a few tenths of a percent across Earth’s surface.

In 1790, the meter was defined as 1/10,000,000th the distance from the North Pole to the equator.

This map shows the entire globe of the Earth projected onto a Mollweide projection, where areas are accurate and well-preserved and the map is fully connected, with no gaps. However, the perpendicularity of latitude and longitude is sacrificed at high latitudes and far away from the centrally projected longitude, while preserving the areas of the land masses and oceans. A meter was once defined as 1/10,000,000th the distance from the North Pole to the equator, along the meridian passing through Paris, France.

That distance was then cast into a platinum bar.

These two images show two bars that defined the meter: the top 100% platinum bar brought to the United States in 1799 at top, and the second meter bar following 1875’s Treaty of the Meter, received by President Benjamin Harrison in 1890, where this meter bar (No. 27) became the reference standard for all length measurements until 1960.

After correcting an early error of 0.2 millimeters, these bars became distance standards for decades.

Even though advances in quantum physics enabled superior definitions of the meter starting in 1927, the platinum-iridium bar, with an X-shape and with a meter determined by markings along it rather than by the cut ends of the bar itself, remained the global standard until 1960.

Platinum-iridium alloys, with X-shapes to better resist distortions, replaced those originals.

The idea behind a Michelson interferometer is that a source of light can be split into two by passing it through a device like a beam splitter, which sends half of the original light down each of two perpendicular paths. At the end of the path, a mirror bounces the light back toward the way it came from, and then those two beams are recombined, producing an interference pattern (or a null pattern, if the interference is 100% destructive) on the screen. If the speed of light is different down each path, or if the path length is different, then the interference pattern will change in response.

In the 1920s, atomic interferometry — based on light’s wavelength — superseded the “bar” standard.

This illustration shows how destructive interference (left) and constructive interference (right) determine what sort of interference pattern arises on the screen (at bottom, both panels) in an interferometer setup. By tuning the interferometer’s distance to a specific number of wavelengths of light, a quantity such as a “meter” can be either measured or even defined.

The right number of wavelengths of light defined the 20th century’s meter.

NIST’s William Meggers, shown here in March 1951, demonstrates a measurement of the wavelength of mercury-198, which he proposed could be used to define the meter. By defining the meter as a precise number of wavelengths emitted by a well-known atomic transition, a superior precision could be achieved compared to any “standardized” physical object, such as the classic meter bar.

First cadmium, then mercury, and next krypton atoms defined the meter.

In 1960, after years of experiments with cadmium, krypton, and mercury, the 11th Conférence Général des Poids et Mésures redefined the meter as the “length equal to 1,650,763.73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton-86 atom,” a definition which stood until 1983.

Finally, in 1983, a new standard was adopted: the distance light travels in 1/299,792,458th of a second.

Although light is an electromagnetic wave with in-phase oscillating electric and magnetic fields perpendicular to the direction of light’s propagation, the speed of light is wavelength-independent: 299,792,458 m/s in a vacuum. If you can measure the distance that light of any wavelength travels in 1/299,792,458th of a second, you can precisely measure and know how long “1 meter” is from anywhere in the Universe.

Because the speed of light in a vacuum is always constant, this definition is universal.

The longer a photon’s wavelength is, the lower in energy it is. But all photons, regardless of wavelength/energy, move at the same speed: the speed of light. This is, surprisingly, irrespective of the motion of the observer relative to light; the speed of all forms of light is measured to always be the same for all observers.

Mostly Mute Monday tells a scientific story in images, visuals, and no more than 200 words.

This article How the “meter” came to be exactly one meter long is featured on Big Think.

Introduction from Zach Rausch:

One of the most surprising patterns in the global mental health data has been the sharp decline in adolescent mental health in the region often said to be the happiest in the world: Scandinavia. These countries have strong social safety nets and a population that embraces free play and childhood independence. However, many Scandinavian parents, educators, and politicians transferred that mentality to the virtual world, eagerly adopting new digital technologies for children, and allowing kids unfettered access to roam free online.

Just like in the Anglosphere, screens, smartphones and social media reshaped adolescence in the Nordic countries starting around 2012, and a decline in teen mental health quickly followed, as we showed in our post on mental health trends in Finland, Iceland, Denmark, Norway, and Sweden.

What’s notable about Sweden isn’t the effect that the phone-based childhood had on its kids — it’s how they’re responding and changing course.

Today’s post is written by Linda Åkeson McGurk, a Swedish-American journalist, speaker, and bestselling author of There’s No Such Thing as Bad Weather and The Open-Air Life, two books that have inspired readers all over the world to embrace nature as a way of life. Linda has spent over a decade advocating for children’s right to outdoor play, and helping families trade screen time for green time, including through her Substack, The Open-Air Life.

In this essay, she gives us an inside look at how Sweden first embraced, and then reset, its relationship with smartphones, social media, and other emerging digital technologies. Sweden is a small and nimble nation with a history of experimentation with social and educational policies — so they are able to make sharp changes in short periods. That makes it one of the most important countries to watch. If their new policies work, including rolling out bell-to-bell phone-free schools, reintroducing textbooks, and pulling back on screens in schools, the world will have a powerful example of how to roll back the phone-based childhood and restore the play-based childhood. Go Sweden!

— Zach

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Sweden Went All in on Screens in Childhood. Now It’s Pulling the Plug.

By Linda McGurk

Sweden isn’t just the land of fika, flat-pack furniture, and the Nobel Prize — it’s also one of the most tech-forward countries on Earth. Spotify, Minecraft, Candy Crush, and the famous YouTuber PewDiePie, who has more than 110 million followers, all hail from here. Broadband is universal, Wi-Fi is lightning-fast, and no Swede wants to be accused of being a late adopter.

So, when I moved back to my native Sweden in 2018 after spending 15 years in the U.S., I knew I was returning to a digital wonderland. Even so, I was stunned to see how thoroughly digital devices had infiltrated every corner of daily life — especially childhood. At the time, a quarter of Swedish babies under 12 months (!) were using the internet. Two-thirds of 9-year-olds had cellphones. And 97% of all 12- to 15-year-olds were on Snapchat.

Even though the official age limit for Snapchat is 13, the girls in my daughter’s fifth-grade class were no exception, and soon my daughter was the only one left out of the class Snapchat group. When I tried to raise the issue with other parents, I was met with blank stares. Soon, I felt like I was the only parent in Sweden trying to limit my children’s screen time and access to social media. Anyone who questioned the nation’s blind faith in digital childhood was treated like a moral panic peddler and cultural reactionary, not unlike those who once claimed that jazz music was the work of the devil.

Yet in recent years, the country has awoken to the risks of rapid digitalization and a childhood saturated in screentime. This top-to-bottom reversal can provide a crucial blueprint for other tech-smitten nations struggling to balance the digital age with children’s well-being.

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The Nature-Based Childhood Versus the Digital Blindspot

In her book The Danish Secret to Happy Kids, author Helen Russell argues that because Nordic countries’ social codex traditionally gave children lots of freedom to play outdoors (a positive), they misguidedly granted children the same wide-ranging freedom online. Until very recently, Sweden’s Public Health Institute had no screen-time guidelines. Not even the Swedish Agency for the Media — whose primary task is to protect minors from harmful media use and increase media literacy in the general population — had any advice for parents. Russell calls this lack of awareness of the effects of excessive smartphone and social media use a “digital blindspot.”

To my surprise, digital devices had even made their way into the Swedish universal preschool system, which is internationally renowned for its focus on child-led outdoor play year-round. In 2019, the government went a step further by mandating the use of digital tools in the national preschool curriculum. The fear that Sweden’s 1- to 5-year-olds might fall behind in the race toward an AI-powered future was palpable. And with that, screens were challenging one of the most quintessentially Scandinavian things: the nature-based childhood.

Meanwhile, the public school system seemed woefully unprepared to deal with the consequences of the fast and furious digital revolution. By the time my oldest daughter entered eighth grade in 2021, phones went everywhere with kids, even into classrooms. Just like in the U.S., the result was chaos. Almost daily, my daughter told me about students texting, playing games, scrolling on social media, snapping selfies, and taking calls during lessons. Teachers had been demoted to smartphone police, trying to teach algebra to kids hooked on Roblox. Distraction was the new normal – and it showed in school results.

In the 2022 international PISA assessment, Swedish 15-year-olds recorded their lowest scores in math and reading in a decade, with more than a quarter of the students falling into the low-performing category in math. When the Swedish National Agency for Education analyzed the results, they concluded that the students with the highest digital media use for things other than learning, both at school and at home, performed the worst. An OECD report went even further, noting that nearly 4 in 10 Swedish students Swedish students are distracted by digital devices in math class. Teachers saw the same trend from the front lines. Nearly 9 in 10 said that smartphones were harming students’ learning, stamina and attention spans.

When I asked my daughter’s teacher why phones weren’t collected at the start of the day, he sighed: “We try to limit phones in the classroom with the younger kids, but the eighth and ninth graders are kind of set in their ways. It is what it is.”

I couldn’t believe it. How could a country that had always taken pride in its progressive policies on children’s well-being lack awareness and concern about how near-constant digital stimulation might affect learning and adolescent brain development?

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The Turning Point

But after years of digital free fall, the tide in Sweden began to turn. The first signs of a reversal came in late 2022, when then-Minister of Schools Lotta Edholm called the digitalization of Swedish schools “an experiment” that wasn’t scientifically based and that harmed children’s learning. Then, the Public Health Institute made a course correction by issuing Sweden’s first-ever screen time guidelines in 2024. Their recommendations were both clear and pragmatic:

• Ages 0–2: Ideally, no screen time at all, aside from video calls with family.

• Ages 2–5: No more than one hour per day, with content tailored to the child’s age and developmental stage.

• Ages 6–12: One to two hours per day, with parents encouraged to stay involved—know what your child is watching or playing, make sure age limits are respected, and talk about what happens online.

• Ages 13–18: Two to three hours per day, while paying attention to how screen use affects well-being. Parents are urged to take an active interest in their teens’ digital lives and to help them find a healthy balance between online and offline activities.

The guidelines also warn about algorithm-driven apps that are addictive by design and can lead to problematic use — especially among younger children.

No More Phones in Schools

At the same time, Sweden tightened its school laws. Phones are now banned from classrooms unless specifically needed, and starting in 2026, a nationwide school phone ban will take effect for the full school day. The government isn’t stopping there. They’re also backing away from screens in schools in general, instead increasing funding for physical textbooks and school libraries.

“We’re reintroducing books, pencils, and paper as the default tools for learning in the classroom,” said then-Minister of Education, Johan Pehrson during an online summit on ed-tech. While Pehrson said he initially received pushback and was accused of being “old-fashioned,” the consensus has shifted, and the government now has broad public support for their agenda to reduce screen time in schools.

That’s not all. Citing concerns about sleep deprivation, worsening mental health, and plummeting school results among teenagers — and encouraged by the example set by Australia — the Swedish government is now considering introducing an age limit on social media.

Parents Push Back

Change didn’t come from the top alone. Across Sweden, parents are starting to rebel against Big Tech’s grip on childhood.

In the small town of Viken, two mothers launched a pact to delay smartphones until age 14. Within weeks, 250 people — about 5% of the town’s population — had signed on. In a different part of the country, parents created a similar pact to protect children against screen addiction and harmful social media content. Both initiatives were inspired by the newly founded organization Ki-DS, which aims to change the norms around smartphones based on the four principles of The Anxious Generation: No smartphones before 14, no social media before 16, phone-free schools and more independence and free play in the real world. So far, parents in over 200 Swedish towns have signed the pledge.

Prominent influencers, such as tech entrepreneur and investor Sara Wimmercranz, have helped change the conversation around screens as well. Wimmercranz made headlines when she went public about limiting screen time for her four children to Saturdays and keeping the family’s summer vacations screen free. Now, going smartphone free or completely screen free during the summer holiday is trending.

The evidence of a turnaround is more than anecdotal. When the Swedish Agency for the Media published their latest report on children’s media use in September 2025, it showed:

• Among 9-12-year-olds, the average daily use of digital devices has decreased by 40 minutes per day since 2022. The use is also decreasing among children in other age groups.

• The share of 9-year-olds that don’t have a cell phone has almost doubled since 2022, a trend that is also apparent among 0–8-year-olds.

• Social media use is decreasing among children under the age of 13.

• Parents’ concern about children’s digital media use is increasing, especially among parents of young children.

Another telltale sign of the times is that one of Sweden’s largest electronics chains reported that the sales of “dumb phones” tripled from 2022 to 2024.

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What Sweden’s Example Can Teach Other Nations

The other day, I received a brochure in the mailbox titled “How do you talk about screens at home?” It was from the Public Health Institute of Sweden and was packed with tips and information about screen use and what families can do to encourage healthy habits. It was exactly the kind of support I’d wished for seven years earlier, when my children were still young and we had just made the move across the Atlantic.

Sweden’s story is one of a society that looked at itself in the mirror and changed course. The lessons from the Swedish experience are simple but profound:

• Policy matters. National bans on phones in schools ensure an environment conducive to learning and connection, allow students to engage more fully, and take pressure off of teachers who previously had to police device usage.

• Official guidance empowers parents. Clear, research-based recommendations make it easier to set, justify, and enforce limits.

• Community action works. Parents joining forces — village by village — can shift cultural norms faster than we think.

Once a country that prided itself on being the fastest to digitalize, Sweden is now proving that progress sometimes means knowing when you’ve taken a wrong turn, so you can double back and undo the mistake. As my daughter turns 18, it’s too soon to know exactly how Sweden’s radical digital experiment has shaped her generation, but the course reversal makes me hopeful about the future for Sweden’s children and — if other countries follow Sweden’s lead — for those around the world.

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