August 7, 2026

04b Theory and Analysis

Democrats once undermined the Army. Now they undermine the nation.– www.theblaze.com

pgnewser October 23, 2025 0

Blurb:

America again stands on the edge of betrayal, watching mobs assault federal officers while judges call it “restraint.”

This is not new. Between 1876 and 1878, the same script played out as those sworn to uphold the law were branded as tyrants and those undermining it claimed the mantle of freedom. When the federal government lost the will to enforce its own laws, violence filled the vacuum.

The Left “understood that if they can get control of the educational system, they can change the country”– legalinsurrection.com

pgnewser October 23, 2025 0

Blurb:

… We covered the situation in the Middle East and the ‘ceasefire’ deal, the possibility NYC will elect a socialist, immigration policy, and the rise of antisemitism particularly on the right.

(transcript autogenerated may contain transcription errors, lightly edited for transcript clarity)

Shines (06:10):

And one of the things, William, I’m really concerned about is even here in our own country, I took a little heat for saying this. … Why would we allow individuals to come into our country whose objective is Sharia law that is antithetical to the constitutional republic that we have in this nation? Why are we not able to talk like this in a civil way and then at the same time prohibit individuals that would be so divisive that they’ll tear this nation apart if we don’t do something? Am I going too far, William, for making that assertion?

WAJ (07:18):

No. And we have not only almost 1400 years of history, we have current events. Look at what has happened in London. Look at what has happened in Paris. We don’t want to become London and Paris. We want to continue to be America.

And it’s a tension that we have because we do have a constitution and everybody has individual rights. On the other hand, the Constitution is not a suicide pact, and we’re entitled to maintain a republic that upholds that constitution. And so by allowing people in who are not committed to that, by allowing people in who do not view our constitution as valid, by allowing people in who come for the very purpose of subverting our society, we are committing suicide.

Is America Headed for Revolution? • Stimson Center– www.stimson.org

pgnewser October 23, 2025 0

Blurb:

Charlie Kirk’s killing last month has sparked fears that the United States is headed to an all-out second civil war or revolution. According to a YouGov survey earlier this year, “more Americans than not believe it is likely that the United States will see a civil war over the next decade” while several hundred political scientists and historians in an April 2025 survey saw the U.S. slipping into authoritarianism with Trump’s second term. Trump’s deployment of the military at home, combined with his vow to suppress “the enemy within” while his domestic advisor, Stephen Miller labels the Democratic Party a domestic extremist organization, can easily be seen as setting the stage for an authoritarian takeover.

How Race-Based Districts Rig Elections Before the First Vote Is Cast– www.breitbart.com

pgnewser October 22, 2025 0

Blurb:

Voting security is always a hot topic around election time, but manipulation of our electoral system is a bigger problem that we have to worry about all the time.

On the most recent episode of The Drill Down podcast, we are not talking about stolen ballots, “ballot harvesting,” or other shenanigans that can happen during an election, but about how congressional districts are both drawn and apportioned. Two things recently in the news raise questions about how we do those things, and whether it’s still the best way.

As host Peter Schweizer asks, “What if an election can be rigged before the first ballot is even cast?”

Defeating Mamdani requires crossing party lines– www.americanthinker.com

pgnewser October 22, 2025 0

Blurb:

When it comes to politics and economics, a surprisingly large number of voters either cannot recognize charlatans or suffer from amnesia. That is, all too often, many of these people fail to understand and remember the basis for success and failure in public policy, and they get drawn to the siren call of alluring, but “risky” new candidates at election time.

How is it possible that New York City, America’s leading city of capitalism, finance, and business, could elect a mayoral candidate, Zhoran Mamdani, who, while known to identify as a democratic socialist, has an easily verifiable hard-core Marxist background. Mamdani’s academic life was immersed in Marxism, embracing the analytical framework of class struggle, oppression, labor and power structures, and historical materialism. His studies and work also included Leninist perspectives on colonialism and post-colonialism. In addition to Marx and Lenin, Mamdani embraced leftist figures such as Frantz Fanon and Antonio Gramsci, whose ideas on cultural hegemony, colonialism and underdevelopment are aligned with Marxist critiques.

Plants self-organize in a ‘hidden order,’ echoing pattern found across nature– www.livescience.com

pgnewser October 22, 2025 0

Blurb:

Scientists have uncovered a “hidden order” in drylands across the planet, where plants follow disordered hyperuniformity — a layout that looks random and disorganized up close but adheres to a clear pattern when viewed from farther away.

The findings explain phenomena like “tiger bush” in West Africa, where bands of plants look like tiger stripes from above, or “fairy circles” in Namibia that look like spots from far away but are actually clumps of plants. These plants are self-organized in a way that helps them cope with drought and function in extreme conditions.

A giant wave is rippling through the Milky Way, and scientists don’t know why– www.sciencedaily.com

pgnewser October 22, 2025 0

Blurb:

Our Milky Way is constantly in motion: it spins, it tilts, and, as new observations reveal, it ripples. Data collected by the European Space Agency’s Gaia space telescope show that our galaxy is not only rotating and wobbling but also sending out a vast wave that travels outward from its center.

For about a century, astronomers have known that the Milky Way’s stars orbit its core, and Gaia has precisely tracked their speeds and trajectories. Since the 1950s, scientists have also recognized that the galactic disc is not flat but warped. Then in 2020, Gaia uncovered that this warped disc slowly oscillates over time, similar to the motion of a spinning top.

AI Is Changing What High School STEM Students Study– www.wired.com

pgnewser October 21, 2025 0

Blurb:

In the early 2010s, nearly every STEM-savvy college-bound kid heard the same advice: Learn to code. Python was the new Latin. Computer science was the ticket to a stable, well-paid, future-proof life.

But in 2025, the glow has dimmed. “Learn to code” now sounds a little like “learn shorthand.” Teenagers still want jobs in tech, but they no longer see a single path to get there. AI seems poised to snatch up coding jobs, and there aren’t a plethora of AP classes in vibe coding. Their teachers are scrambling to keep up.

“There’s a move from taking as much computer science as you can to now trying to get in as many statistics courses” as possible, says Benjamin Rubenstein, an assistant principal at New York’s Manhattan Village Academy. Rubenstein has spent 20 years in New York City classrooms, long enough to watch the “STEM pipeline” morph into a network of branching paths instead of one straight line. For his students, studying stats feels more practical.

Nuclear stocks surge after Army launches program to deploy small reactors– www.cnbc.com

pgnewser October 15, 2025 0

Blurb:

Nuclear stocks rallied Wednesday after the U.S. Army launched a program to deploy small reactors.

Shares of NuScale, a small reactor developer, soared 17%. Oklo and Nano Nuclear were up nearly 7% and 4%, resepectively. The uranium company Centrus was up 13%.

The U.S. Army on Tuesday launched a program to build micro nuclear reactors in partnership with the Defense Innovation Unit. The microreactors will be commercially owned and operated with the goal of helping developers scale up their businesses, according to the Army.

AI Could Make it Harder to Establish Blame for Medical Failings, Experts Say– www.madinamerica.com

pgnewser October 14, 2025 0

Blurb:

From The Guardian: “The use of artificial intelligence in healthcare could create a legally complex blame game when it comes to establishing liability for medical failings, experts have warned.

The development of AI for clinical use has boomed, with researchers creating a host of tools, from algorithms to help interpret scans to systems that can aid with diagnoses. AI is also being developed to help manage hospitals, from optimising bed capacity to tackling supply chains.

But while experts say the technology could bring myriad benefits for healthcare, they say there is also cause for concern, from a lack of testing of the effectiveness of AI tools to questions over who is responsible should a patient have a negative outcome.

Are Abortion Pills Contaminating Our Water?– www.lifenews.com

pgnewser October 14, 2025 0

Blurb:

As the use of the mifepristone chemical abortion pill continues to rise in the U.S., concerns are growing that residue from the powerful drug as well as the remains of aborted babies are contaminating the water supply and may be contributing to fertility problems, as well as other health concerns.

Recently released research by Liberty Counsel Action (LCA) pointed out that when mifepristone was originally approved by the Food and Drug Administration (FDA) in 2000, it was predicted that the impact of the drug on the environment would be minimal, and therefore “no further study was completed.” As LCA noted, since mothers who take the abortion pill are instructed to deliver their dead baby into their toilet at home, the assessment “failed to address the issue of how the fetal remains would be disposed of, essentially ignoring the reality that in many cases, said remains would enter U.S. water systems in violation of various fetal disposal and medical waste laws.”

Earth enters ‘new reality’ as coral reefs reach first climate tipping point– phys.org

pgnewser October 14, 2025 0

Blurb:

The world faces a “new reality” as we have reached the first of many Earth system tipping points that will cause catastrophic harm unless humanity takes urgent action, according to a report released by the University of Exeter and international partners.

With ministers gathering ahead of the COP30 summit, the second Global Tipping Points Report finds that warm-water coral reefs—on which nearly a billion people and a quarter of all marine life depend—are passing their tipping point.

If Anyone’s Causing A ‘Judicial Crisis,’ It’s Rogue Judges– thefederalist.com

pgnewser October 14, 2025 0

Blurb:

Since returning to office, President Trump has faced an onslaught of leftist-backed lawfare seeking to grind the implementation of his voters’ agenda to a halt. Unsurprisingly, many of these lawsuits have been filed in districts predominated by Democrat-appointed judges, who have been more than happy to issue a myriad of preliminary injunctions and temporary restraining orders blocking enforcement of the administration’s policies.

Now, with the U.S. Supreme Court largely agreeing to shut down this lower court judicial coup for the time being, a number of rogue judges have taken to anonymously attacking the high court for stopping the crisis they helped create.

Innovation. `Bone-02' — A glue that heals fractures in just 3 ...

Bone Glue Could Revolutionize Emergency Medical Healthcare

pgnewser October 9, 2025 1

Chinese researchers have developed a glue that, when applied, turns into, effectively, human bone. Lead researcher Lin Xianfeng said the glue has the potential power to “achieve precise fixation within two to three minutes.” If it proves to be as affective as possible, Bone-02 could not only rapidly heal broken bones, it could save millions of lives.

Researchers ecstatic over medical breakthrough that could change the way we heal: ‘Potential for use in emergency fracture treatment in battlefields or disaster zones’  

from The Cool Down

Blurb:

A cutting-edge medical breakthrough could help change the way that doctors are able to treat fractures.

As reported in Interesting Engineering, a team of Chinese researchers has developed Bone-02, a dissolvable bone glue that aims to streamline the healing process in fractures. The technology is inspired by the way oysters attach to surfaces underwater.

Led by Lin Xianfeng, an associate chief orthopedic surgeon, the research team sought to reduce the number of potential complications that arise in traditional fracture treatments. According to Lin, the groundbreaking adhesive has the ability to “achieve precise fixation within two to three minutes.”

Research into Bone-02 began in 2016 after the team began to look for methods to combat the wet, blood-rich environment of the human body. Lin explained that he took inspiration from marine species after observing oysters that were effectively adhered to a bridge’s underwater structure despite the force of the waves hitting against them. Oysters are able to stick to underwater surfaces by secreting an organic cement onto the hard surface, which then hardens and binds the oyster to its new home.

Are AI robots the future of parenting in China? | CNN

AI Toys Coming to America, Look at China for what’s to come here

pgnewser October 9, 2025 1

Parents in the US brace as China’s AI toy trend goes global

from www.techspot.com

Blurb:

The market for AI toys in China is predicted to grow faster than any other consumer AI sector, writes MIT Technology Review, reaching $14 billion by 2030. That’s not surprising when there are around 1,500 AI toy companies operating in the country as of October 2025.

 

Can Lutnick’s Chip-for-Chip Idea Work?– warontherocks.com

pgnewser October 9, 2025 0

Blurb:

The Commerce Department’s imminent Section 232 investigation — launched in April and expected to conclude soon — may fundamentally shift how the United States acquires semiconductors. The chips America imports range from commodity devices embedded in household appliances to the expensive, high-performance AI processors that power the AI boom, designed in America by Nvidia, but manufactured in Asia.

Taiwan and Korea sit at the center of this challenge. Together, they produce the majority of semiconductors used by the United States across nearly every category. This concentration represents a major national security risk, given China’s preparations and repeated threats to use force against Taiwan and antagonism toward South Korea.

Commerce Secretary Howard Lutnick phrased the situation thus in a recent interview: “If you can’t make your own chips, how can you defend yourself?”

Tariffs are one tool to address this exposure, designed to boost demand for chips manufactured in the United States. But they are not enough. Lutnick offers a second measure, called “chip for chip.” It would tie tariff waivers directly to verifiable domestic production milestones, incentivizing U.S. firms to act more in the national interest.

However, Lutnick’s ‘chip-for-chip’ framework could succeed only if Washington pairs it with enforceable production benchmarks and demand-side incentives. Otherwise, it risks becoming another half-measure in America’s decades-long struggle to rebuild semiconductor sovereignty.

Texas conservatives defend decision for DEI audit of UT system’s gender studies courses– www.thecollegefix.com

pgnewser October 9, 2025 0

Blurb:

Key Takeaways

  • Proponents argue that the audit reflects a broader accountability effort to align curricula with state priorities, while critics, including academic freedom advocates, warn it undermines faculty autonomy and academic integrity.
  • The audit comes shortly after the Texas Tech System Chancellor announced a mandate that in-class instruction must note there are only two sexes.

A recently announced audit of the University of Texas System’s gender studies course has academic freedom advocates sounding the alarm and conservatives defending a broader agenda for accountability and reform under a recently passed anti-DEI law.

“It has been a priority for lawmakers in Texas to return our universities to their role as institutions of free speech, merit-based achievement and open inquiry and end the culture of ideological indoctrination that has proliferated on many campuses, dividing students by race and gender and stifling debate and free expression,” Texas Public Policy Foundation spokesperson Sherry Sylvester told The College Fix in an interview.

Senate Bill 37, signed into law last year, gave the Board of Regents oversight powers to review and approve the curricula and degree programs within the system, which enrolls some 260,000 students at academic and health institutions across the state.

‘Squeezed light’ might be the secret to building the quantum internet– www.techexplorist.com

pgnewser October 9, 2025 0

Blurb:

Imagine a future where the internet isn’t just fast, it’s fundamentally different. Where information doesn’t travel through cables in bits and bytes, but dances across space in entangled photons, instantaneously linking quantum computers continents apart. In this shimmering vision of tomorrow, the backbone of communication is no longer copper or fiber; it’s quantum light.

At the heart of this revolution is a peculiar phenomenon known as squeezed light, and a team of researchers from the U.S. Department of Energy’s Fermi National Accelerator Laboratory and the California Institute of Technology believes it may be the key to unlocking scalable quantum networks. Their latest study, led by Fermilab scientist Alexandru Macridin, marks a pivotal step toward building a quantum internet, one that could transform scientific research, cryptography, and computing itself.

Quantum networks rely on entangled qubits: pairs of quantum bits that remain mysteriously connected, no matter how far apart they are. In quantum physics, entanglement is the ghostly thread that links particles across space, such that a change in one instantly affects the other. It’s a phenomenon Einstein famously referred to as “spooky action at a distance,” and it forms the cornerstone of quantum communication.

from www.techexplorist.com

Donald Trump vs US states: President says Chicago mayor, Illinois governor ‘should be in jail’ – ICE row escalates– timesofindia.indiatimes.com

pgnewser October 9, 2025 0

Blurb:

US President Donald Trump has called for the imprisonment of Chicago mayor Brandon Johnson and Illinois governor JB Pritzker, accusing them of failing to protect federal immigration officers. The remarks, posted on Trump’s social media platform Truth Social, come amid ongoing political tensions over immigration enforcement and the deployment of federal troops in Democratic-led cities.“Chicago Mayor should be in jail for failing to protect ICE Officers! Governor Pritzker also!” Trump wrote, referring to US immigration and customs enforcement personnel operating in the city.

Trump’s comments follow a recent executive order by Johnson that designates city property as an “ICE Free Zone,” restricting federal immigration agents from using municipal facilities. The move was seen as a direct pushback against federal immigration operations within the city.Trump’s statement adds to a broader dispute over the use of the national guard in Democrat-led states. Hundreds of Texas national guard soldiers have reportedly assembled at a military facility near Chicago, despite vocal opposition from state leadership, including Johnson and Pritzker.The administration has not accused either Johnson or Pritzker of any wrongdoing legally. Both leaders have opposed Trump’s immigration policies and criticized what they see as the federal government’s overreach. Pritzker has previously accused Trump of trying to provoke unrest as a means to justify military deployments.

The People's Lawyers': Attorneys General Letitia James and Dana ...

NY Hopes to become a Social Media Cop, and Letitia James is the Wanna-be Chief

pgnewser October 7, 2025 0

The People's Lawyers': Attorneys General Letitia James and Dana ...

NY’s unconstitutional “Stop Hiding Hate” act takes effect January 1, 2026, and Letitia James is expecting social media companies to submit their hate speech standards biannually. The key element of the unconstitutional law lies in the requirement by social media companies to effectively show how they’re fighting “hate” on their platform, a term that is highly subjective. A Democrat’s Hate is a Republican’s righteous truth, and vice versa.

Letitia James has informed social media companies of her intention to enforce this Soviet-styled law, setting up a legal showdown for January 1, 2026. The social media companies face potential fines for every violation of the Orwellian law.

A regulatory analysis website, regulatoryoversight.com, summed up the regulations in the law: “Social media companies are required to submit reports twice a year to the New York AG’s office. These reports must include statements on their terms of service, including whether the policy defines terms such as hate speech, racism, extremism, and radicalization, among others. The company must also describe its policy and how it enforces it, such as how the company uses automated process and addresses user reports to address conduct that violates the policy.”

New York’s “Stop Hiding Hate” Act: What It Means for Social Media Companies – regulatoryoversight.com
Source Link
Excerpt:

On October 2, New York Attorney General (AG) Letitia James announced that, in accordance with the “Stop Hiding Hate” Act, social media companies are now required to report their content moderation policies to her office, with first reports due no later than January 1, 2026. This legislation, sponsored by Senator Brad Hoylman-Sigal and Assemblymember Grace Lee and signed into law by Governor Kathy Hochul, mandates that platforms operating in New York with more than $100 million in gross annual revenue must post their content moderation policies publicly, provide consumers with a contact to report violations of the policy, and submit biannual reports to James’ office concerning compliance.

Lockheed, Verizon testing 5G-linked drone swarm for intel collection

‘Swarms of Killer Robots’: Why AI is Terrifying the American Military – Politico

pgnewser October 7, 2025 0

Lockheed, Verizon testing 5G-linked drone swarm for intel collection

‘Swarms of Killer Robots’: Why AI is Terrifying the American Military – Politico
Source Link
Excerpt:

Artificial intelligence technology is poised to transform national security. In the United States, experts and policymakers are already experimenting with large language models that can aid in strategic decision-making in conflicts and autonomous weapons systems (or, as they are more commonly called, “killer robots”) that can make real-time decisions about what to target and whether to use lethal force.

But these new technologies also pose enormous risks. The Pentagon is filled with some of the country’s most sensitive information. Putting that information in the hands of AI tools makes it more vulnerable, both to foreign hackers and to malicious inside actors who want to leak information, as AI can comb through and summarize massive amounts of information better than any human. A misaligned AI agent can also quickly lead to decision-making that unnecessarily escalates conflict.

Trump Opens the White House Doors to Foreign Regimes and Their Dirty Money– www.thenation.com

pgnewser October 7, 2025 0

Trump Opens the White House Doors to Foreign Regimes and Their Dirty Money– www.thenation.com
Source Link
Excerpt:

Lobbyists for foreign countries have long helped other governments influence US policy, but nothing compares to the brazen corruption of the second administration of Trump.

Given that anyone anywhere can quietly bankroll President Donald Trump via his “memecoin,” it’s fair to say that we’ve never seen a White House so saturated in foreign money.

(Paul Yeung / Bloomberg via Getty Images)

It’s difficult to overstate how significantly the world of foreign lobbying has transformed in the past few months. An industry that was once relegated to backrooms and back channels is now blasted out in public statements and social media posts. From India to Oman to Romania and beyond, governments are lavishing Donald Trump with luxury jets, high-rise towers, resorts, and crypto investments—and the president is unashamed, even bragging about it. Eight months into Trump’s second administration, it’s difficult to keep track of all the unprecedented ways that regimes have tried to curry favor with him.

Gun Control Zealots Stand By ‘Two Bullets’ Jay Jones– thefederalist.com

pgnewser October 7, 2025 0

Gun Control Zealots Stand By ‘Two Bullets’ Jay Jones– thefederalist.com
Source Link
Excerpt:

Moms Demand Action bills itself as a “grassroots movement of Americans fighting for public safety measures that can protect people from gun violence.” The nonprofit’s website notes that former Monsanto communications executive Shannon Watts started Moms Demand Action the “day after the Sandy Hook Tragedy in 2012… with the message that all Americans can and should do more to reduce guns violence.”

But Shannon and her gun-control organization have been curiously quiet about leftist Virginia attorney general candidate and former commonwealth delegate Jay Jones, who reportedly was fond of fantasizing about putting “two bullets” in the head of a Republican politician he loathed.

As of Monday evening, Jones proudly included Moms Demand Action’s logo — including the leftist group’s coveted Gun Sense Candidate seal of approval — on his AG campaign page. Moms says its Gun Sense Candidate program “is meant to signal to our ten million supporters, volunteers, and gun safety voters across the country that, if elected, a candidate will govern with gun safety in mind.”

I wonder if Jones had gun safety in mind when he wrote in 2022 of then-state House Speaker Todd Gilbert, a Republican, that if Jones were given the choice to kill three people with two bullets — Adolf Hitler, Cambodian dictator Pol Pot, or Gilbert, the longtime Virginia House member would get “two bullets to the head.”

Violent predators are exploiting gender ideology to continue their heinous crimes– www.lifesitenews.com

pgnewser October 7, 2025 0

Violent predators are exploiting gender ideology to continue their heinous crimes– www.lifesitenews.com
Source Link
Excerpt:

If you are a violent criminal seeking to escape from the full consequences of your misdeeds, identifying as transgender is the way to go.

It worked well for the attempted assassin of Brett Kavanaugh, who got a mere eight-year prison sentence instead of the 30 years requested by the Department of Justice, with the judge referencing his freshly minted transgender identity as one of the mitigating factors at sentencing last week.

It also worked for convicted pedophile Christopher Williams, who was placed in the Washington Correctional Center for Women after identifying as transgender. A September 29 report from Reduxx revealed that Williams has brutally assaulted a female inmate, striking her multiple times in the head. Williams was accused of sexually assaulting another female inmate last year.

As Reduxx reported based on testimony from the victim, “the two were in a common area on August 7 when Williams, who stands 6’3″, began punching her in the face in an apparent retaliation against her for calling him a ‘rapist.’ Jones, in contrast, is 5’4″.” The female inmate had tried to avoid Williams, who began to stalk her by sitting near her whenever he could. He attacked her from behind while she was standing at a microwave, throwing her onto the ground and smashing her in the back of the head.

“I was kicked and punched continuously. At this point, I saw who was doing this – Christopher Williams. I was immediately in fear for my life, trying to block while protecting my face and head, kicking out with my feet,” the woman, who remains unnamed for safety reasons, told Reduxx.

A Wargame to Take Taiwan, from China’s Perspective– warontherocks.com

pgnewser October 7, 2025 0

A Wargame to Take Taiwan, from China’s Perspective– warontherocks.com
Source Link
Excerpt:

In August 2025, 25 international experts gathered at Syracuse University to do something unusual: plan China’s invasion of Taiwan. For two days, academics, policy analysts, and current and former U.S. officials abandoned their typical defensive postures and attempted to inhabit Beijing’s offensive strategic mindset in a wargame. They debated not how America should respond to Chinese aggression, but how China might overcome the obstacles that have so far kept it from attacking the island nation.

This role reversal yielded an uncomfortable insight. The invasion scenarios that dominate U.S. military planning — involving massive amphibious assaults on Taiwan and preemptive strikes on American bases — may fundamentally misread Beijing’s calculus. As the wargame revealed, analysts seeking to understand China’s intentions should pay greater attention to plausible alternative military pathways to reunification that involve far less force and far more political calculation.

Climate change: News, features and articles | Live Science

EU Signals its about to clamp down on Human Action in the name of saving the Planet from Climate Chage

pgnewser October 6, 2025 0

Climate change: News, features and articles | Live Science

Climate change threatens Europe’s resources, European Union warns – India Today
Source Link
Excerpt:

The European Environment Agency said biodiversity in Europe is declining due to unsustainable production and consumption, especially in the food system.

Due to over-exploitation of natural resources, pollution and invasive alien species, more than 80 per cent of protected habitats are in a poor or bad state, it said,

“The degradation of our natural world jeopardises the European way of life,” the agency said in its report: “Europe’s environment 2025”.

“Europe is critically dependent on natural resources for economic security, to which climate change and environmental degradation pose a direct threat.”

Europe is the world’s fastest-warming continent and is experiencing worsening droughts and other extreme weather events.

But governments are grappling with other priorities including industrial competitiveness, and negotiations on EU climate targets have stoked divisions between richer and poorer countries.

Study finds that by age 3 kids prefer nature's fractal patterns ...

Mathematicians Discover Prime Number Pattern in Fractal Chaos– www.scientificamerican.com

pgnewser October 6, 2025 0

Study finds that by age 3 kids prefer nature's fractal patterns ...

Mathematicians Discover Prime Number Pattern in Fractal Chaos– www.scientificamerican.com
Source Link
Excerpt:

Prime numbers are sometimes called math’s “atoms” because they can be divided by only themselves and 1. For two millennia, mathematicians have wondered if the prime numbers are truly random, or if some unknown pattern underlies their ordering. Recently number theorists have proposed several surprising conjectures on prime patterns—in particular, probabilistic patterns that show up in large groups of the mathematical atoms.

The patterns in the primes trace back to an 1859 hypothesis involving the legendary Riemann zeta function. Mathematician Bernhard Riemann derived a function that counts the number of primes up to a number x. It includes three main ingredients: a smooth estimate, a set of corrective terms coming from the Riemann zeta function, and a small error term.

Much has been written about the Riemann zeta function, but the most important thing to know is that it provides a correction to the smooth estimate. To do so, it takes on a wavy pattern, sometimes raising the count, sometimes lowering it. These corrective oscillations are determined by the locations of the zeros of the Riemann zeta function. In fact, the celebrated Riemann hypothesis claims that all such zeros lie on a “critical line” where the real part equals 1⁄2.