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taylorvich writes:

https://phys.org/news/2024-11-himalayas-formation-destroyed-continental-crust.html

Earth's continents are slowly moving across the planet's surface due to plate tectonics, culminating in regions of crustal expansion and collision. In the latter case, high temperatures and pressures lead to the reworking of the crust, affecting its composition, as well as that of the underlying mantle. Furthermore, when two continental plates collide, distinct topographic features are produced, namely mountain ranges, which are surficial manifests of Earth's thickened crust.

Three such collision zones form the Himalaya-Tibetan Plateau, the European Alps and the Zagros Mountains in Iran, Iraq and Turkey, originating during the Cenozoic (last 66 million years). New research, published in Earth and Planetary Science Letters, has attempted to quantify the amount of continental crust lost to the mantle when two plates collide at each of these boundaries.

To do so, Dr. Ziyi Zhu, Research Fellow at Monash University, Australia, and colleagues developed a theoretical model for the mass/volume balance of continental crust and compared the amount of shortened crust with the crust being vertically thickened, laterally extruded and eroded at the surface.

Simplifying the utility of each of these parameters in the calculations, Dr. Zhu says, "Imagine squeezing a soft chocolate bar: the material compressed (horizontal shortening) forms a pile (vertical thickening).

"Additionally, the crust can move in directions perpendicular to the compression (extrusion) or undergo erosion. If crustal mass is conserved, the mass of the shortened crust should balance with the mass of the thickened crust, along with any crust lost to erosion or lateral extrusion. Any imbalance indicates that the missing crust likely sinks into the mantle."

The research team identified that at least 30% of continental crust was lost to the mantle during the formation of the Himalaya-Tibetan Plateau and Zagros Mountains (potentially up to 64% for the latter, depending upon the initial crust thickness), while up to 50% of the Alps' volume may have been destroyed. Importantly, this loss to the mantle had double the destructive effect than that of surface erosion, which is estimated based on the volumes of sediment fans associated with each mountain range.

Journal Reference:
Ziyi Zhu, et. al.,Quantifying the loss of continental crust into the mantle from volume/mass balance calculations in modern collisional mountains, Earth and Planetary Science Letters Volume 648, 15 December 2024, 119070 (DOI: https://linkinghub.elsevier.com/retrieve/pii/S0012821X24005028)

Original Submission

upstart writes:

Senators Say TSA's Facial Recognition Program Is Out of Control, Here's How to Opt Out:

A bipartisan group of 12 senators has urged the Transportation Security Administration's inspector general to investigate the agency's use of facial recognition, saying it poses a significant threat to privacy and civil liberties.

Their letter comes just before one of the busiest travel periods of the year when millions of Americans are expected to pass through the nation's airports.

"This technology will soon be in use at hundreds of major and mid-size airports without an independent evaluation of the technology's precision or an audit of whether there are sufficient safeguards in place to protect passenger privacy," the senators wrote.

The letter was signed by Jeffrey Merkley (D-OR), John Kennedy (R-LA), Ed Markey (D-MA), Ted Cruz (R-TX), Roger Marshall (R-Kansas), Ron Wyden (D-OR),  Steve Daines (R-MT), Elizabeth Warren (D-MA), Bernie Sanders (I-VT), Cynthia Lummis (R-WY), Chris Van Hollen (D-MD), and Peter Welch (D-VT).

While the TSA's facial recognition program is currently optional and only in a few dozen airports, the agency announced in June that it plans to expand the technology to more than 430 airports. And the senators' letter quotes a talk given by TSA Administrator David Pekoske in 2023 in which he said "we will get to the point where we require biometrics across the board."

[...] To opt out of a face scan at an airport, a traveler need only say that they decline facial recognition. They can then proceed normally through security by presenting an identification document, such as a driver's license or passport.

Original Submission

Ingar writes:

Intel Chief Executive Pat Gelsinger has been forced out less than four years after taking the helm of the company, handing control to two lieutenants as the faltering American chipmaking icon searches for a permanent replacement. Gelsinger, whose career has spanned more than 40 years, also stepped down from the company's board.

As reported by several news outlets: Reuters, The New York Times, The Guardian.

Original Submission

Arthur T Knackerbracket has processed the following story:

The reach of the China-linked Salt Typhoon gang extends beyond telecommunications giants in the United States, and its arsenal includes several backdoors – including a brand-new malware dubbed GhostSpider – according to Trend Micro researchers.

While the crew has made headlines recently for hacking "thousands and thousands" of devices at US telcos, research published on Monday by Trend Micro's threat intel team suggests Salt Typhoon (which Trend tracks as Earth Estries) has also hit more than 20 organizations globally since 2023. These span various sectors – including technology, consulting, chemical and transportation industries, government agencies, and non-profit organizations (NGOs) in the US, the Asia-Pacific region, the Middle East, and South Africa.

Affected countries include Afghanistan, Brazil, Eswatini, India, Indonesia, Malaysia, Pakistan, the Philippines, South Africa, Taiwan, Thailand, the US, and Vietnam.

It's "one of the most aggressive Chinese advanced persistent threat (APT) groups," Trend Micro's Leon Chang, Theo Chen, Lenart Bermejo, and Ted Lee wrote.

"We found that in 2023, the attackers had also targeted consulting firms and NGOs that work with the US federal government and military," the threat intel team observed.

These intrusions not only compromised telcos' database and cloud servers, but also attacked the firms' suppliers – in at least one instance implanting the Demodex rootkit on machines used by a major contractor to a dominant regional telecommunications provider. Trend Micro's analysts think that shows Salt Typhoon wanted to gain access to more targets.

Original Submission

Arthur T Knackerbracket writes:

Arthur T Knackerbracket has processed the following story:

One of the best features Google Maps offers is incident reporting. Users have the ability to report anything from crashes to lane closures and more. Speed trap reports are particularly handy as they can alert you to the presence of a hidden police officer. A recent update, however, has replaced the “Speed trap” option with something new.

[...] It seems that Google is aware of this misnomer and is making a change to the option. In a new update, the tech giant has quietly removed “Speed trap” and replaced it with a more appropriate, if not generic, “Police” option. In addition, the “Police” option sits higher on the list than where the “Speed trap” option was located. This brings incident reports in line with what Google showed us in an announcement back in July.

Original Submission

upstart writes:

QNAP firmware update leaves NAS owners locked out of their boxes:

A recent firmware pushed to QNAP network attached storage (NAS) devices left a number of owners unable to access their storage systems. The company has pulled back the firmware and issued a fixed version, but the company's response has left some users feeling less confident in the boxes into which they put all their digital stuff.

As seen on a QNAP community thread, and as announced by QNAP itself, the QNAP operating system, QTS, received update 5.2.2.2950, build 20241114, at some point around November 19. After QNAP "received feedbacks from some users reporting issues with device functionality after installation," the firm says it withdrew it, "conducted a comprehensive investigation," and re-released a fixed version "within 24 hours."

The community thread sees many more users of different systems having problems than the shortlist ("limited models of TS-x53D series and TS-x51 series") released by QNAP. Issues reported included owners being rejected as an authorized user, devices reporting issues with booting, and claims of Python not being installed to run some apps and services.

QNAP says affected users can either downgrade their devices (presumably to then upgrade once more to the fixed update) or contact support for help. Response from QNAP support, as told by users on forums and social media, has not measured up to the nature of losing access to an entire backup system.

Ars has reached out to QNAP for comment and will update this post with response.

oops.

Original Submission

Arthur T Knackerbracket has processed the following story:

ICE buys location info from data brokers to evade warrant requirements. It slurps data from utility companies to locate immigrants who need electricity, heat, and internet connections but would rather not be hassled for trying to exist and earn a living by providing this same information directly to the US government.

The operative theory appears to be that immigrants here illegally aren’t protected by the US Constitution. But that’s simply not true. Rights are extended to people living in our borders, whether or not they’re US citizens. However, none of that is going to matter if Trump succeeds in deploying his mass deportation plans — ones that are long on rhetoric and short on actual planning at the moment.

Rest assured, the round-ups will outpace the planning following Trump’s re-ascension. ICE tends to be very proactive when it feels the person in the Oval Office has its back. “Going forward” means “starting now,” as this New Yorker article written by Ronan Farrow points out. Be sure you don’t overlook what’s being said in the last sentence of the article’s opening paragraph.

Nice. So, we’re doing business with a company that will only allow the US government to target US citizens. While it’s great that it’s preventing outside countries from doing this (which is a claim I’m not inclined to believe), it’s definitely shitty that it’s offering a bespoke version to the DHS and ICE for the express purpose of plug-and-play domestic surveillance.

Then there’s the first sentence of the paragraph, which indicates this was in motion two months ahead of the election, which suggests two equally disturbing things. Either the outgoing administration was fine with expanded domestic surveillance or DHS felt it should get the ball rolling because the victor of the 2024 election was likely to be supportive of expanded domestic surveillance. Perhaps the purchasing department was just running a Trump re-election parlay. Or maybe the DHS felt pretty confident Kamala Harris wouldn’t object to mass surveillance, even while she argued against mass deportations. Not great!

taylorvich writes:

https://newatlas.com/automotive/mercedes-reinvents-brakes-ev-in-drive/

In the simplest terms, nearly every modern car on the planet uses disk brakes: a rotor attached to a hub with a caliper with brake pads fixed to the control arm at each wheel. The driver presses the brake pedal and hydraulic fluid is pushed down the brake lines into the caliper, expanding the pistons and pushing the brake pads against the rotor, slowing down the rotation of the rotor connected to the hub, thus slowing down the wheel.

There are other systems, like drum brakes, air brakes, band brakes, the Flintstones method, et cetera, that have also been around since the dawn of the automotive industry. The concept almost always remains the same: using friction to slow down. And so it doesn't go unsaid, yes, there are compression brake systems as well, but that's entirely different.

Mercedes-Benz has put a new spin on an age-old concept with what it calls "in-drive brakes" for electric vehicles. The system being developed at the company's research and development department in Sindelfingen, Germany, integrates the brakes right into the drivetrain, in an arrangement that works very much like a transmission brake. It resembles clutch plates – but with a unique twist.

There are no calipers, instead a circular brake pad connected directly to the output shaft of the electric motor is pressed against a stationary water-cooled ring, all of which is in an enclosed system.

According to Mercedes, the in-drive brake system shouldn't require servicing for the life of the vehicle, potentially saving the owner thousands of dollars in brake repairs and replacements. Even the brake dust is collected in a small inner compartment that won't require emptying.

Brake dust is a major contributor to pollution, particularly in urban areas with lots of stop-and-go traffic. And if you've ever driven down a long, steep grade like the Grapevine, just north of Los Angeles, California, you're no stranger to the smell of brake dust – and the discomfort in your nasal passages. EV motors inherently act as a brake when the accelerator is released, as EV motors have the ability to regenerate electricity back into the batteries, slowing the vehicle down in the process. An actual brake system is still needed, however.

Though the in-drive brake is still undergoing testing, Mercedes reckons that brake fade will be a non-issue as the system is water-cooled. Given the in-drive brake system relocates all the necessary "slow down" bits away from the wheels, unsprung weight (weight that isn't carried by the chassis, and instead spins or moves with the wheels, creating gyroscopic forces) is significantly reduced, making the vehicle both handle better and improve the ride. Wheels could also be made more aerodynamically efficient without the constraints of rotors and calipers.

Original Submission

upstart writes:

ISPs tell FCC that mistreated users would switch to one of their many other options:

Lobby groups for Internet service providers claim that ISPs' customer service is so good already that the government shouldn't consider any new regulations to mandate improvements. They also claim ISPs face so much competition that market forces require providers to treat their customers well or lose them to competitors.

Cable lobby group NCTA-The Internet & Television Association told the Federal Communications Commission in a filing that "providing high-quality products and services and a positive customer experience is a competitive necessity in today's robust communications marketplace. To attract and retain customers, NCTA's cable operator members continuously strive to ensure that the customer support they provide is effective and user-friendly. Given these strong marketplace imperatives, new regulations that would micromanage providers' customer service operations are unnecessary."

Lobby groups filed comments in response to an FCC review of customer service that was announced last month, before the presidential election. While the FCC's current Democratic leadership is interested in regulating customer service practices, the Republicans who will soon take over opposed the inquiry.

USTelecom, which represents telcos such as AT&T and Verizon, said that "the competitive broadband marketplace leaves providers of broadband and other communications services no choice but to provide their customers with not only high-quality broadband, but also high-quality customer service."

"If a provider fails to efficiently resolve an issue, they risk losing not only that customer—and not just for the one service, but potentially for all of the bundled services offered to that customer—but also any prospective customers that come across a negative review online. Because of this, broadband providers know that their success is dependent upon providing and maintaining excellent customer service," USTelecom wrote.

While the FCC Notice of Inquiry said that providers should "offer live customer service representative support by phone within a reasonable timeframe," USTelecom's filing touted the customer service abilities of AI chatbots. "AI chat agents will only get better at addressing customers' needs more quickly over time—and if providers fail to provide the customer service and engagement options that their customers expect and fail to resolve their customers' concerns, they may soon find that the consumer is no longer a customer, having switched to another competitive offering," the lobby group said.

The lobby groups' description may surprise the many Internet users suffering from little competition and poor customer service, such as CenturyLink users who had to go without service for over a month because of the ISP's failure to fix outages. The FCC received very different takes on the state of ISP customer service from regulators in California and Oregon.

The Mt. Hood Cable Regulatory Commission in northwest Oregon, where Comcast is the dominant provider, told the FCC that local residents complain about automated customer service representatives; spending hours on hold while attempting to navigate automated voice systems; billing problems including "getting charged after cancelling service, unexpected price increases, and being charged for equipment that was returned," and service not being restored quickly after outages.

The California Public Utilities Commission (CPUC) told the FCC that it performed a recent analysis finding "that only a fraction of California households enjoy access to a highly competitive market for [broadband Internet service], with only 26 percent of households having a choice between two or more broadband providers utilizing either cable modem or fiber optic technologies." The California agency said the result "suggests that competitive forces alone are insufficient to guarantee service quality for customers who depend upon these services."

CPUC said its current rulemaking efforts for California "will establish standards for service outages, repair response time, and access to live representatives." The agency told the FCC that if it adopts new customer service rules for the whole US, it should "permit state and local governments to set customer service standards that exceed the adopted standards."

upstart writes:

OpenAI denies deleting evidence, asks why NYT didn’t back up data:

OpenAI keeps deleting data that could allegedly prove the AI company violated copyright laws by training ChatGPT on authors' works. Apparently largely unintentional, the sloppy practice is seemingly dragging out early court battles that could determine whether AI training is fair use.

Most recently, The New York Times accused OpenAI of unintentionally erasing programs and search results that the newspaper believed could be used as evidence of copyright abuse.

The NYT apparently spent more than 150 hours extracting training data, while following a model inspection protocol that OpenAI set up precisely to avoid conducting potentially damning searches of its own database. This process began in October, but by mid-November, the NYT discovered that some of the data gathered had been erased due to what OpenAI called a "glitch."

Looking to update the court about potential delays in discovery, the NYT asked OpenAI to collaborate on a joint filing admitting the deletion occurred. But OpenAI declined, instead filing a separate response calling the newspaper's accusation that evidence was deleted "exaggerated" and blaming the NYT for the technical problem that triggered the data deleting.

OpenAI denied deleting "any evidence," instead admitting only that file-system information was "inadvertently removed" after the NYT requested a change that resulted in "self-inflicted wounds." According to OpenAI, the tech problem emerged because NYT was hoping to speed up its searches and requested a change to the model inspection set-up that OpenAI warned "would yield no speed improvements and might even hinder performance."

The AI company accused the NYT of negligence during discovery, "repeatedly running flawed code" while conducting searches of URLs and phrases from various newspaper articles and failing to back up their data. Allegedly the change that NYT requested "resulted in removing the folder structure and some file names on one hard drive," which "was supposed to be used as a temporary cache for storing OpenAI data, but evidently was also used by Plaintiffs to save some of their search results (apparently without any backups)."

Once OpenAI figured out what happened, data was restored, OpenAI said. But the NYT alleged that the only data that OpenAI could recover did "not include the original folder structure and original file names" and therefore "is unreliable and cannot be used to determine where the News Plaintiffs' copied articles were used to build Defendants' models."

In response, OpenAI suggested that the NYT could simply take a few days and re-run the searches, insisting, "contrary to Plaintiffs' insinuations, there is no reason to think that the contents of any files were lost." But the NYT does not seem happy about having to retread any part of model inspection, continually frustrated by OpenAI's expectation that plaintiffs must come up with search terms when OpenAI understands its models best.

OpenAI claimed that it has consulted on search terms and been "forced to pour enormous resources" into supporting the NYT's model inspection efforts while continuing to avoid saying how much it's costing. Previously, the NYT accused OpenAI of seeking to profit off these searches, attempting to charge retail prices instead of being transparent about actual costs.

Now, OpenAI appears to be more willing to conduct searches on behalf of NYT that it previously sought to avoid. In its filing, OpenAI asked the court to order news plaintiffs to "collaborate with OpenAI to develop a plan for reasonable, targeted searches to be executed either by Plaintiffs or OpenAI."

How that might proceed will be discussed at a hearing on December 3. OpenAI said it was committed to preventing future technical issues and was "committed to resolving these issues efficiently and equitably."

taylorvich writes:

https://spectrum.ieee.org/semiconductor-fabrication

In 1970, Bill Harding envisioned a fully automated wafer-fabrication line that would produce integrated circuits in less than one day. Not only was such a goal gutsy 54 years ago, it would be bold even in today's billion-dollar fabs, where the fabrication time of an advanced IC is measured in weeks, not days. Back then, ICs, such as random-access memory chips, were typically produced in a monthlong stop-and-go march through dozens of manual work stations.

At the time, Harding was the manager of IBM's Manufacturing Research group, in East Fishkill, N.Y. The project he would lead to make his vision a reality, all but unknown today, was called Project SWIFT. To achieve such an amazingly short turnaround time required a level of automation that could only be accomplished by a paradigm shift in the design of integrated-circuit manufacturing lines. Harding and his team accomplished it, achieving advances that would eventually be reflected throughout the global semiconductor industry. Many of SWIFT's groundbreaking innovations are now commonplace in today's highly automated chip fabrication plants, but SWIFT's incredibly short turnaround time has never been equaled.

SWIFT averaged 5 hours to complete each layer of its fabrication process, while the fastest modern fabs take 19 hours per processing layer, and the industry average is 36 hours. Although today's integrated circuits are built with many more layers, on larger wafers the size of small pizzas, and the processing is more complex, those factors do not altogether close the gap. Harding's automated manufacturing line was really, truly, swift.

I encountered Harding for the first time in 1962, and hoped it would be the last. IBM was gearing up to produce its first completely solid-state computer, the System/360. It was a somewhat rocky encounter. "What the hell good is that?" he bellowed at me as I demonstrated how tiny, unpackaged semiconductor dice could be automatically handled in bulk for testing and sorting.

Original Submission

upstart writes:

Supreme Court wants US input on whether ISPs should be liable for users' piracy:

The Supreme Court signaled it may take up a case that could determine whether Internet service providers must terminate users who are accused of copyright infringement. In an order issued today, the court invited the Department of Justice's solicitor general to file a brief "expressing the views of the United States."

In Sony Music Entertainment v. Cox Communications, the major record labels argue that cable provider Cox should be held liable for failing to terminate users who were repeatedly flagged for infringement based on their IP addresses being connected to torrent downloads. There was a mixed ruling at the US Court of Appeals for the 4th Circuit as the appeals court affirmed a jury's finding that Cox was guilty of willful contributory infringement but reversed a verdict on vicarious infringement "because Cox did not profit from its subscribers' acts of infringement."

That ruling vacated a $1 billion damages award and ordered a new damages trial. Cox and Sony are both seeking a Supreme Court review. Cox wants to overturn the finding of willful contributory infringement, while Sony wants to reinstate the $1 billion verdict.

The Supreme Court asking for US input on Sony v. Cox could be a precursor to the high court taking up the case. For example, the court last year asked the solicitor general to weigh in on Texas and Florida laws that restricted how social media companies can moderate their platforms. The court subsequently took up the case and vacated lower-court rulings, making it clear that content moderation is protected by the First Amendment.

Cox has said that letting the piracy ruling stand "would force ISPs to terminate Internet service to households or businesses based on unproven allegations of infringing activity, and put them in a position of having to police their networks." Cox said that ISPs "have no way of verifying whether a bot-generated notice is accurate" and that even if the notices are accurate, terminating an account would punish every user in a household where only one person may have illegally downloaded copyrighted files.

Record labels urged the court to reinstate the vicarious infringement verdict. "As the District Court explained, the jury had ample evidence that Cox profited from its subscribers' infringement, including evidence 'that when deciding whether to terminate a subscriber for repeat infringement, Cox considered the subscriber's monthly payments,' and 'Cox repeatedly declined to terminate infringing subscribers' Internet service in order to continue collecting their monthly fees,'" the record labels' petition said.

Another potentially important copyright case involves the record labels and Grande, an ISP owned by Astound Broadband. The conservative-leaning US Court of Appeals for the 5th Circuit ruled last month that Grande violated the law by failing to terminate subscribers accused of being repeat infringers. The 5th Circuit also ordered a new trial on damages because it said a $46.8 million award was too high. Grande and the record labels are both seeking en banc rehearings of the 5th Circuit panel ruling.

But will they listen? And note the phrasing: whether Internet service providers must terminate users who are accused of copyright infringement.

Original Submission

upstart writes:

X says The Onion can't have Alex Jones' Infowars accounts:

X claims in court filings that it still owns Infowars' X accounts and can't be sold without its permission.

Well that's a bit of a spanner in the works.  Previously : The Onion Buys InfoWars - No Seriously! - SoylentNews:

The satirical website The Onion purchased InfoWars on Thursday, a capstone on years of litigation and bankruptcy proceedings following InfoWars founder Alex Jones' defamation of families associated with the Sandy Hook Elementary School massacre.

Those families backed The Onion's bid to purchase InfoWars' intellectual property, including its website, customer lists and inventory, certain social media accounts and the production equipment used to put Jones on the air. The Connecticut families agreed to forgo a portion of their recovery to increase the overall value of The Onion's bid, enabling its success.

MORE: Alex Jones still must pay $1B judgment: Judge

The families said the purchase would put an end to Jones' misinformation campaign.

"We were told this outcome would be nearly impossible, but we are no strangers to impossible fights. The world needs to see that having a platform does not mean you are above accountability -- the dissolution of Alex Jones' assets and the death of Infowars is the justice we have long awaited and fought for," said Robbie Parker, whose daughter Emilie was killed in the Sandy Hook shooting.

In 2022, the families that brought the case against Jones in Connecticut secured a $1.4 billion verdict in their defamation lawsuit. A Texas bankruptcy court ruled on the liquidation of Jones' assets in June of this year, handing over control to an independent trustee tasked with selling them off to generate the greatest possible value for the families.

hubie writes:

New filing shows electricity demand would be flat without the industry:

Ever since data centers started spreading across the Virginia landscape like an invasive pest, one important question has remained unanswered: How much does the industry's insatiable demand for energy impact other utility customers? Under pressure from the SCC [Virginia State Corporation Commission], this month Dominion Energy Virginia finally provided the answer we feared: Ordinary Virginia customers are subsidizing Big Tech with both their money and their health.

Dominion previously hid data centers among the rest of its customer base, making it impossible to figure out if residents were paying more than their fair share of the costs of building new generation and transmission lines. Worse, if data centers are the reason for burning more fossil fuels, then they are also responsible for residents being subjected to pollution that is supposed to be eliminated under the 2020 Virginia Clean Economy Act (VCEA). The VCEA calls for most coal plants in the state to be closed by the end of this year – which is not happening – and sets rigorous conditions before utilities can build any new fossil fuel plants.

[...] Even before the 2024 IRP was filed, though, the SCC directed the utility to file a supplement. It was obvious the IRP would project higher costs and increased use of fossil fuels. How much of that, the SCC demanded to know, is attributable to data centers?

A lot, as it turns out. Though Dominion continues to obfuscate key facts, the document it filed on November 15 shows future data center growth will drive up utility spending by about 20%. Dominion did not take the analysis further to show the effect on residential rates.

The filing also shows that but for new data centers, peak demand would actually decrease slightly over the next few years, from 17,353 MW this year to 17,280 MW in 2027, before beginning a gentle rise to 17,818 MW in 2034 and 18,608 MW in 2039.

In other words, without data centers, electricity use in Dominion territory would scarcely budge over the next decade. Indeed, the slight decrease over the next three years is especially interesting because near-term numbers tend to be the most reliable, with projections getting more speculative the further out you look.

upstart writes:

Teen Mathematicians Tie Knots Through a Mind-Blowing Fractal:

In the fall of 2021, Malors Espinosa set out to devise a special type of math problem. As with any good research question, it would have to be thought-provoking, its solution nontrivial — something others would want to study. But an additional constraint stumped him. Malors, then a graduate student in mathematics at the University of Toronto, wanted high school students to be able to prove it.

For years, Malors had been running summer workshops for local high schoolers, teaching them about basic ideas in mathematical research and showing them how to write proofs. But a few of his students seemed ready to do more — to find out what it means to do math when there is no answer key. They just needed the right question to guide them.

[...]

Menger's statement didn't distinguish between homeomorphic curves. His proof only guaranteed, for instance, that the circle could be found in his sponge — not that all homeomorphic knots could be, their loops and tangles still intact. Malors wanted to prove that you could find every knot within the sponge.

It seemed like the right mashup to excite young mathematicians. They'd recently had fun learning about knots in his seminar. And who doesn't love a fractal? The question was whether the problem would be approachable. "I really hoped there was an answer," Malors said.

There was. After just a few months of weekly Zoom meetings with Malors, three of his high school students — Joshua Broden, Noah Nazareth and Niko Voth — were able to show that all knots can indeed be found inside the Menger sponge. Moreover, they found that the same can likely be said of another related fractal, too.

"It's a clever way of putting things together," said Radmila Sazdanovic, a topologist at North Carolina State University who was not involved in the work. In revisiting Menger's century-old theorem, she added, Malors — who usually does research in the disparate field of number theory — had apparently asked a question that no one thought to ask before. "This is a very, very original idea," she said.