How Earth’s Core Waves Transformed Japan Post-2011 Earthquake

Kesennuma fishing port after the 2011 Tohoku earthquake

Kesennuma Fishing Port: The Aftermath of the 2011 Tohoku Pacific Coast Earthquake

Image Credit: Carolyn Cole/Los Angeles Times via Getty Images

<p>On March 11, 2011, just 15 minutes after Japan experienced the powerful magnitude-9 Tohoku earthquake, most of the country shifted eastward by approximately half a centimeter. This significant geographical change was driven by formidable seismic waves that traveled 5,800 kilometers deep to the Earth's core before bouncing back to the surface.</p>

<p>While a shift of five millimeters may appear minor against the catastrophic backdrop of the earthquake—which caused severe local land movements, resulting in the meltdown of three reactors at the Fukushima Daiichi nuclear power plant and a devastating 40-meter tsunami—it highlights a complex geological phenomenon.</p>

<p>This remarkable movement spanned 3,000 kilometers, nearly seven times longer than the earthquake's primary rupture line and surpassing any previously recorded land displacement.</p>

<p>Park Sun Young from the University of Chicago notes that this event is unique due to its timing and pattern: "No normal earthquake took place at that moment. This widespread 5-millimeter eastward displacement occurred almost simultaneously across most of Japan."</p>

<p>The changes were not only vast but also influenced the oceans, showcasing the extensive impact of the earthquake across the entire nation.</p>

<p>"It’s not just a limited 'edge' moving," Park explained. "The eastward shift is widespread across Japan, particularly where GPS stations are located. If we had greater density of instruments on the ocean floor, we could better assess this offshore movement, but on land, these changes are evident throughout Japan."</p>

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<p>By meticulously analyzing a wealth of GPS and seismic data obtained during this disaster, Park and colleagues uncovered the mechanisms behind such enormous movements and the reasons for the rupture occurring 15 minutes post-main shock.</p>

<p>Typically, earthquakes generate waves that penetrate the Earth's interior and rebound off the core, but these waves weaken significantly before reaching the surface. In the case of the Tohoku earthquake, the shock was so powerful that the waves remained strong enough upon returning to the surface, causing widespread shaking as four adjoining tectonic plates moved synchronously.</p>

<p>"We believe the intense shaking from the initial Tohoku earthquake compromised the stability of plate boundaries, rendering them more vulnerable to movement when reflection waves arrive," Professor Park stated.</p>

<p>This event suggests a previously unrecognized mechanism for post-earthquake rupture, indicating a need for awareness regarding potential seismic hazards triggered by waves traveling deeper following large earthquakes across extended distances—possibly leading to additional earthquakes.</p>

<p>Further research is crucial for comprehending how such phenomena affect other locations globally with similar geological traits, according to Robin Lee of the University of Canterbury, New Zealand.</p>

<p>("This demonstrates that significant earthquakes can initiate widespread delayed faulting within minutes and across much larger areas than anticipated," Lee pointed out.)</p>

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Source: www.newscientist.com

How AI Has Transformed Mathematics: The Biggest Breakthrough in Math History

Plane Unit Distance Problem

The Plane Unit Distance Problem explores the maximum number of equally sized lines connecting points on an infinite paper.

Noga Alon et al. 2026, OpenAI

An 80-year-old mathematical conjecture, known as the plane unit distance problem, has been solved by OpenAI’s advanced artificial intelligence model. This breakthrough is igniting discussion around the immense mathematical capabilities of AI.

“This is a problem I never expected to see solved in my lifetime,” states Mischa Rudnev from the University of Bristol, UK. “It’s a groundbreaking achievement.”

Tim Gowers commented that the solution represents a “significant milestone in AI mathematics.” He noted in a paper that had it been submitted by a human, it would be accepted without hesitation, highlighting that such groundbreaking evidence of AI-generated solutions is rare.

The plane unit distance problem was deemed by the 20th-century mathematician Paul Erdős as his “most important contribution” to geometry. The challenge lies in determining the maximum number of lines of equal length that can connect numerous dots placed on an infinite paper.

Erdős believed that the optimal arrangement for maximum connections would be a grid layout, suggesting that the number of lines would surpass the number of points only marginally. Persistent efforts to prove his assertion or to discover alternative patterns yielded minimal advances, with the most recent improvements occurring over 40 years ago.

OpenAI’s model revealed that Erdős’s hypothesis was significantly underestimated, demonstrating that a more irregular arrangement of points can yield far more connections.

“Initially, I could hardly believe the results,” remarks Will Sawin from Princeton University. “It convinced me that this achievement is the most remarkable in the realm of AI mathematics so far.”

Details on how the OpenAI model diverges from publicly available AI technology and its training methods remain undisclosed. However, researchers have mentioned that the model is “general purpose” and was not specifically trained for mathematical applications.

AI employed strategies from algebraic number theory to establish extensive lattices in dimensions far exceeding two-dimensional configurations. By creating these more sophisticated shapes, AI translates them into two dimensions to generate representations of the higher dimensions.

“The counterexamples produced by AI are intricate, and while the foundational ideas exist in existing literature, the synthesis to achieve them required ingenuity,” explains Kevin Buzzard from Imperial College London.

While the magnitude of this result is undeniable, it underscores a gap in mathematicians’ consideration of Erdős’s original predictions. Samuel Mansfield from the University of Manchester, England, notes that the complexity of executing an experiment to challenge the conjecture would have eluded many geometry experts lacking advanced number theory knowledge. “This highlights a necessity for interdisciplinary expertise,” he adds. “In hindsight, AI’s adaptability in this area may not be surprising.”

Rudnev emphasized that the problem’s allure lies in its “pure intellectual challenge,” and although it may not directly influence other unresolved questions, it has inspired further research. Sawin, after examining the proof, utilized the techniques unearthed by AI to advance the number of connectable points.

“Similar to many other AI milestones, it didn’t take long for human researchers to internalize, comprehend, and extend upon the AI-derived arguments,” commented Buzzard. “This contrasts sharply with human discoveries that often require extensive validation periods.

Topics:

  • Artificial Intelligence/
  • Mathematics

Source: www.newscientist.com