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A team of scientists is exploring ways to use dark craters at the lunar poles as sites for ultrastable lasers to aid in surface and near-lunar navigation. The group, led by Physicist Jun Ye, an expert on lasers and precision measurements, were discussing the types of instruments that Artemis astronauts could install and use during their time on the Moon.

Here’s the latest opinion/comedy bit from Friday’s Real Time show with Bill Maher, with the episode called “Let’s be frank.”  Maher starts out by citing the recent Democratic Party Autopsy (here) about why the party lost the Presidency and Congress in 2024. But he then faults both parties for having politicians in office who won’t be honest (surprise!).

Honesty, he avers, can be found only in books politicians write after they have left office. Maher gives several examples, including Republicans who admit, after they leave office, that Trump is paying off the January 6 insurrectionists with a “slush fund.” And don’t forget, he adds, Eisenhower’s warning about the “military industrial complex,” issued just three days before he left office.

The key diagnosis, Maher says, was made by the late Barney Frank when he was in hospice. It’s cited in the Times of Israel:

“The key to liberal democracy being able to come back is to get rid of the perception that we have allowed to grow, that the entire Democratic Party is committed to a series of very drastic social reconstructions that go beyond the politically acceptable,

Maher says, “And there, in one sentence, is the autopsy the Democrats have been so desperately searching for.”  True! And of course this explains the capitalized “Frank” in the title.

The theme, then, is that Democrats say the truth about the party only when they have nothing to lose for speaking up.

Finally, Maher notes that some red states are better than his own “progressive” state—California—in education and in green energy.  The last bit: “Democrats: these are your issues: education, race, the environment. And I say this with love: you’re losing to the Waffle House car-on-the-lawn states.”  Well, we’ll see how the Democrats do in this fall’s midterms, though the most crucial election is in 2028.

The guests for this episode were astrophysicist Neil deGrasse Tyson, MS Now news correspondent Katy Tur, and former Speaker of the House Kevin McCarthy. Tyson is not shown in this segment.

I don’t wholeheartedly embrace AI, for I think it will be the death of liberal education.  In both the humanities and science, I fear that students will lose any ability they have to write, and will not improve their writing because they’ll be using bots.  This will degrade their ability to communicate. (Scientists too need to communicate, and if they rely solely on bots, which can write papers for them, they’ll also degrade their ability to think.)  Take-home assignments will vanish (AI can do them, and are doing them now), and all that’s left are in-class verbal participation and in-class exams.  This is fine for students who just think of college as a way to purchase accreditation and not a chance to glory in the joys of learning, but so be it.

However, AI is good for some things, including analyzing data, doing statistics, doing preliminary literature searches, and, in the article from the WSJ screenshot below, solving difficult math problems.  The article shows that a problem posed by the famous and eccentric Hungarian mathematician Paul Erdös—the “unit distance problem” has been solved by AI. Open AI, which created the program that did it, describes it this way—but it’s not that simple:

For nearly 80 years, mathematicians have studied a deceptively simple question: if you place nn points in the plane, how many pairs of points can be exactly distance 1 apart?

This is the planar unit distance problem, first posed by Paul Erdős in 1946. It is one of the best-known questions in combinatorial geometry, easy to state and remarkably difficult to resolve. The 2005 book Research Problems in Discrete Geometry, by Brass, Moser, and Pach, calls it “possibly the best known (and simplest to explain) problem in combinatorial geometry.” Noga Alon, a leading combinatorialist at Princeton, describes it as “one of Erdős’ favorite problems.” Erdős even offered a monetary prize for resolving this problem.

The “distance 1” thing confused me, and Wikipedia explains it a different way:

A problem posed by Paul Erdős known as the unit distance problem asks for the maximum possible number of unit-distance pairs determined by n points in the Euclidean plane; equivalently, it asks for the maximum number of edges in a unit distance graph on n vertices.

It gives a figure described as “a unit distance graph with 16 vertices and 40 edges”.

By David Eppstein – Own work, CC0/

Wikipedia describes such unit distance graphs this way:

“In mathematics, particularly geometric graph theory, a unit distance graph is a graph formed from a collection of points in the Euclidean plane by connecting two points whenever the distance between them is exactly one.”

That’s what is confusing me, for if the theorem deals only with points in a two-dimensional plane, why aren’t unconnected dots not joined that are closer than some connected dots? (Look at the four dots around the center of the graph above. None of them are connected to each other, though more distant one are.)  I presume some math-savvy reader will enlighten us.

Anyway, Open AI and the WSJ tells us that the problem has been solved by AI. If you want to see the solutions, open AI says this:

The proof is available here ⁠(opens in a new window). The companion paper by leading external mathematicians is available here⁠ (opens in a new window). You can find an abridged version of the model’s chain of thought here⁠ (opens in a new window).

But the WSJ gives more comprehensible details.  Click screenshot to read (if you subscribe):

An excerpt:

“If you are a mathematician,” one of the world’s leading mathematicians recently wrote, “you may want to make sure you are sitting down before reading further.”

And you’ll definitely need to sit down if you’re not a mathematician.

Because a famous math problem that stumped humans for the better part of a century has finally been toppled—by AI.

Not long ago, the most advanced AI models couldn’t do basic math. By last year, they were performing at gold-medal levels at the International Mathematical Olympiad. Now they are solving classic problems in combinatorial geometry using algebraic number theory. In no time at all, artificial intelligence has gone from stupid to frighteningly smart.

But even mathematicians were astonished when OpenAI announced that one of its models resolved a puzzle known as the unit distance problem without the help of any humans scribbling a bunch of equations on chalkboards.

It was fed this prompt:

And produced this proof, giving the maximum number of unit-distance pairs:

Apparently the proof was accepted by mathematicians.  More from the WSJ:

And everyone in math lost their minds.

For those who aren’t fluent in numbers, OpenAI helped translate its findings by presenting them alongside 19 pages of companion remarks from prominent mathematicians.

. . .Just looking at formulas is enough to hurt my brain, but I wanted to know more about what the AI found, how we humans missed it—and why this breakthrough matters to those of us who would like to permanently distance ourselves from math problems.

When I spoke with OpenAI employees, they told me this result would have sounded completely bananas one year ago.

“Forget one year ago,” researcher Sebastien Bubeck said. “A month ago.”

There are endorsements by mathematicians, and a history of the problem, which Erdös considered quite difficult.  So difficult, in fact, that he offered what was then a pretty hefty sum for anybody who could solve it: $500. I think the money will be given to the OpenAI team.

OpenAI’s researchers were stunned. They had given this Erdős problem to an internal model as a test of its capabilities—to find out whether it was better than previous models. They found out how much better it was once they took a peek at the solution. “I initially didn’t believe it,” said Mehtaab Sawhney, a Columbia mathematician at OpenAI. So they searched for errors, verified the results with outsiders and checked the AI’s work using the company’s AI coding agent. “With enough reading and enough Codexing,” Sawhney said, “it seemed believable—and pretty remarkable.”

Long before AI, mathematicians who solved Erdős problems often framed their checks instead of cashing them. For them, the money was worth less than the glory. When I asked OpenAI researchers about their plans for the prize, they hadn’t given it much thought.

But they did have lots of thoughts about my next question: Why did AI succeed where humans failed?

The first explanation is that this particular solution happens to be highly counterintuitive.

Most people who tackled this problem tried to prove Erdős’s conjecture, rather than disprove it. Only by defying conventional wisdom and experimenting with seemingly improbable strategies did the model find an unexpected path forward.

The second is that humans specialize while AI synthesizes.

While mathematicians tend to focus on their specific areas of expertise, AI models use their vast knowledge to spot connections that we couldn’t possibly see ourselves. In this case, that meant pulling from both algebraic number theory and discrete geometry, which have about as much in common as the marathon and pole vault.

The third explanation is that AI has time, attention, patience, focus and the persistence to stick with methods that humans might abandon—and the solution to this Erdős problem demanded it.

“It’s the kind of idea that you try for a bit, it doesn’t work, and you think maybe you were just too hopeful,” said Mark Sellke, a Harvard statistician at OpenAI. “So you give up and move on.”

AI doesn’t move on. It keeps plugging away without taking breaks to eat, sleep, answer emails, pick the kids up from school and watch the Knicks.

And it can think coherently for so long that even an abridged version of the model’s “chain of thought” ran more than 75,000 words—the length of the first “Harry Potter” book.

Was it an elegant proof? Well, the article implies “no,” but it’s apparently a proof:

“It’s fair to say that we haven’t seen yet the spark of genius that you could attribute to some of the grandest proofs in the history of humanity,” Bubeck told me.

And how long did the computation take? Less than a day and a half:

After reading it, a former OpenAI researcher did some back-of-the-envelope math and estimated it took less than 32 hours and $1,000 in tokens, a bargain for a result of this caliber. The researchers wouldn’t confirm the exact amount of time and compute, but Bubeck described the costs as “really nothing crazy at all.”

At any rate, this is what AI is good for, and I wonder if, say, it could solve Fermat’s Last Theorem, which took Andrew Wiles eight years of work to solve (he was knighted for it).  And I wonder if there are any seemingly intractable math problems that can’t be solved by AI, especially if they were or will be solved by humans.

Now I don’t think there are any practical implications of this results, but that’s true of much mathematical theory. I’m just amazed at what AI can do.

From People magazine (also at the UPI), we hear about a brave moggy whjo chased off a coyote.  Click on the screenshot to read:

An excerpt:

A Pico Rivera, California, resident captured some surprising footage: a cat fighting off a coyote in the middle of the day.

“I was in shock,” Debbie Beltran, the cat’s owner, told KTLA-TV, after viewing the video. “It took me a while to see—is that our cat or somebody else’s? And no, it’s our cat.”

Beltran said she was at work on May 1 when a neighbor sent security camera footage of her cat ferociously fighting a coyote outside. The video shows the cat standing its ground outside the family’s yard on Manzanar Avenue before it climbs a tree and escapes the coyote.

“Coyotes usually come out when the sun goes down,” Beltran said. “So to see this happen in broad daylight, that was shocking.”

Beltran said her cat, named Mama, has been with her family for about 5 years and is believed to be about 10 years old. She notes that Mama has always been a courageous cat who doesn’t back down from a fight.

“She’s always been feisty, this type of cat, and has got into fights before, so it doesn’t surprise me,” the pet parent told KABC.

Unfortunately, this isn’t the first time a coyote has attacked one of Beltran’s pets. She said that last year, one of her cats died in a coyote attack. Now, she’s giving Mama some extra attention since her caught-on-camera battle.

The video is below (turn off the closed captions, as they interfere with seeing the scrap).  Mama is a brave cat: watch at her bristle, hump her back, and chase the d*g! However, cats should really be kept indoors because not all predators are so timorous.

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From IHeartCats, we here about a high-tech way Dubai has developed to feed street cats. Click headline below to read.

An excerpt with a video below:

As people stroll through Dubai’s carefully maintained parks and busy public spaces, a quieter sign of compassion is beginning to appear beside the city’s modern landscape. New feeding stations for stray animals are being introduced across several locations, giving homeless cats a cleaner and more dependable place to find food and water. For years, many residents relied on leaving bowls wherever they could stop to help, often hoping hungry street cats would discover them in time. Now, Dubai is taking a more organized approach that blends kindness, sanitation, and public care into one thoughtful effort designed to support both animals and the shared spaces around them.

Dubai has launched a pilot program featuring 12 feeding units placed in parks and other public areas. The project is designed to support stray animals while also improving cleanliness and organization in shared spaces. For years, many residents and volunteers have cared for street cats on their own, stopping to leave food and water wherever they could. While compassionate, those efforts often created scattered feeding spots that were difficult to maintain.

Now, the city is taking a more structured approach.

The stations aim to make feeding more consistent and sanitary while helping caretakers provide support in designated locations. It reflects a growing recognition that animal welfare is connected to a city’s overall health and appearance. Instead of treating stray-cat care as an informal act left entirely to volunteers, Dubai is weaving compassion into its public infrastructure.

For the cats wandering through busy streets and quiet parks, the change could mean something deeply important: reliability.

Street animals often survive day by day, never knowing when food or water will appear. Many endure extreme heat, exhaustion, and long stretches of uncertainty. Having fixed feeding stations creates a sense of stability for animals that spend their lives navigating harsh outdoor conditions. Even a simple sheltered feeding spot can offer relief and comfort.

Dubai’s decision also highlights how cities are beginning to rethink the relationship between urban development and animal care. Modern public spaces are usually designed around people first, but this initiative acknowledges that stray animals are part of the environment, too.

The feeding stations are intended to reduce mess and discourage random food waste while still allowing residents to help animals responsibly. By centralizing feeding efforts, the city can better manage sanitation concerns without removing the compassion that inspired people to feed the cats in the first place.

The idea transforms what was once a scattered, individual effort into something shared and supported at a civic level.

Not only that, but the station combines feeding with recycling: if you put a can or bottle into the station, cat food is dispensed into the station. See the video below.  Great idea!

 

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From The Animal Rescue Site we hear of an unholy interspecific friendship between a cat and a d*g species: “Wild fox befriends cat“, by Malorie Thompson.  Here’s an excerpt, with a video below:

Cats and foxes seem like two of the same, but it’s rare that we see them interact.

They’re both sly and cunning, playful and adorable. Yet, they’re different species and they likely rarely cross paths in a meaningful way.

However, a wildlife photographer managed to capture a sweet exchange between the two animals and you have to see it to believe it.

Turkish wildlife photographer Ali ihsan Öztürk (@aliihsanozturk.65) shared a video of a cat and a fox hanging out on Instagram and it’s really something special.

He captioned the post (translated): “Fox and cat’s friendship. I couldn’t believe even while taking the picture. what a beautiful friendship.”

In the video, you can see the cat come up behind the fox and nuzzle the wild animal. Surprisingly, the fox didn’t seem to mind one bit and took it as an invitation for friendship!

The two animals continued to nuzzle each other in a playful way. It’s easy to see why Ali was so surprised to witness it!

Below is the Facebook post, which you can also see by clicking on the picture. Here’s the entire text:

In January 2026, a story began spreading online that many people could not stop thinking about: two stray animals who soon became known as the “street brothers.”

A fox and a cat had somehow learned to survive together outdoors. They shared warmth, protection, and the feeling of not being alone. Life on the street was hard, but they always stayed close to each other. The fox, a little bigger and stronger, often let the injured cat lie right by his side. On cold nights, it almost seemed as if he was quietly keeping watch so nothing would happen to his small companion.

When rescuers finally brought them to safety, the cat received the medical care it urgently needed. But at the shelter, something became obvious right away: whenever the two were separated, both became visibly stressed. Restlessness, searching, whining — as if the most important support in their lives had suddenly been taken away. Their closeness had long become more than a habit. It was their home.

So the team did everything they could to keep them together. Eventually, their story reached a kindhearted person who did not want a half-solution. He did not adopt only the cat — he took in the fox too, so the two would never be torn apart again.

Their journey is a reminder of what loyalty really means. And that friendship sometimes appears where no one expects it. Family does not always have to be the same species — sometimes it is simply the same bond holding two hearts together.

Fox-and-cat-friends videos are not rare: here are two more. All of these, oddly, feature cats that are mostly white.

*****************’

Lagniappe: From Reese: “Our Michael” from Archaeology & Art on Facebook, featuring an old photograph that was apparently for sale on eBay but that has been sold. Lovely cat!  Here’s the whole text and the dead link:

Oct, 1938: our Micheal [sic]

The love radiating from the phrase “our Michael” alone is enough to warm our hearts.

The photographer and story are unclear. The source of this vintage photo is an old eBay listing, but the link isn’t active:

http://www.ebay.com/…/Antique…/391002853535…

h/t: Michael, Reese

Building a permanent base on the Moon sounds like an engineering problem. Design the habitat, sort the power supply, figure out life support, and you're most of the way there. But the engineers who've spent time thinking hard about this will tell you the real challenge isn't the hardware — it's the humans inside it. Now researchers have built a virtual Moon base and run tens of thousands of simulated missions inside it, studying not the rocket engines or the radiation shielding, but the astronauts themselves. What they found could reshape how we plan humanity's return to the lunar surface.

As traditional chip miniaturization slows, researchers have found a way to pack more computing power into the same space by stacking silicon circuits in multiple layers. The new process uses ultra-thin silicon membranes and low-temperature manufacturing techniques to overcome a major obstacle that has long blocked the production of true 3D chips.

There is plenty of intriguing sci-fi on offer this month, whether it’s solar-powered cities from Adrian Tchaikovsky or a strange future from M. John Harrison

Our final Skeptoid Adventure of 2026 takes us to the Yucatán coast to explore the Mysteries of the Maya. So, in anticipation of that, we're playing an episode from the archive that takes us to the heart of Mesoamerica: "Finding the Black Olmec" -- Enjoy!

And this Adventure takes place December 6th-13th and links up seamlessly with the New Orleans Escapade for those who are interested!

www.skeptoid.com/adventures

Learn about your ad choices: dovetail.prx.org/ad-choices

By stacking custom-designed silver nanoparticles like nanoscale LEGO bricks, scientists stabilized a mysterious crystal phase that had never been observed before. The material not only solves a longstanding puzzle in materials science but also exhibits promising quantum properties at room temperature.

By stacking custom-designed silver nanoparticles like nanoscale LEGO bricks, scientists stabilized a mysterious crystal phase that had never been observed before. The material not only solves a longstanding puzzle in materials science but also exhibits promising quantum properties at room temperature.

Particles of light cannot be divided into smaller particles, but if you try to snip off the end of one, instead of shortening it multiplies

A new room-temperature quantum device uses twisted light to entangle photons and electrons, overcoming one of the biggest hurdles in quantum technology. The breakthrough could pave the way for smaller, cheaper quantum systems with applications ranging from secure communications to future AI and computing platforms.

A new room-temperature quantum device uses twisted light to entangle photons and electrons, overcoming one of the biggest hurdles in quantum technology. The breakthrough could pave the way for smaller, cheaper quantum systems with applications ranging from secure communications to future AI and computing platforms.

A cloaked alien invasion force is approaching Earth and coming up on Mars. The first officer looks through a viewfinder and says, “Captain, the fourth planet’s atmosphere is behaving strangely. As though it were trying to block incoming energy.” The captain takes a moment, then his (already big) eyes get wide and he exclaims, “It’s a defense shield! The Earthlings are hiding on the fourth planet and are prepared to attack us! Abort the invasion!” The first officer responds, “Aye aye, Captain!”

The Sun has a heartbeat. Every eleven years it swells with magnetic fury, hurling solar flares and charged particles into space, sparking auroral displays and threatening power grids, all before quietening down again. We've tracked this rhythm for centuries. But now, scientists listening to sound waves deep inside our local star have found something deeply unexpected, that heartbeat is changing. And nobody yet knows what it means.

According to a mathematical model of how people weigh up different outcomes, the optimal strategy is to be ambitious, but not overly so

A decades-old mystery about Saturn has finally been solved thanks to the James Webb Space Telescope. Scientists discovered that Saturn’s changing “rotation rate” was never caused by the planet speeding up or slowing down, but by powerful winds high in its atmosphere. Webb’s unprecedented observations revealed that Saturn’s northern lights actively heat the atmosphere, creating winds that generate electrical currents, which then power the aurora all over again in a self-sustaining cycle.

Quantum Backrooms is a horror game in which the player explores eerie rooms. The twist is that the rooms have been generated by a quantum computer

When it comes to understanding Earth and our changing environment, space is the place. Not only does it give us an overall holistic view of the planet below, but satellite-based imagery can transcend national boundaries and give us an understanding of key changes that often go unseen at ground level. Now, the European Space Agency (ESA) has chosen two new missions to address key questions in Earth environmental science: Hibidis and SOVA-S.

We're increasingly prioritising our own needs over those of the wider community, which may be causing us to love our partners less intensely