Sergio 🇲🇽🇩🇪

@AJENews @AJEnglish 👏👏👏👏👏👏👏👏👏👏👏

BREAKING: Spain will ask the European Union to end its association agreement with Israel over alleged violations of international law, Prime Minister Pedro Sanchez said. 🔴LIVE updates: aje.news/w7b54q

Wenn wir mit offenen Augen durch unser Land fahren, sehen wir überall Erfolgspotenziale. Nutzen wir diese Potenziale, lösen wir die Bremsen. Sorgen wir gemeinsam dafür, dass dies das Jahrzehnt wird, in dem Europa und Deutschland zu neuer Stärke finden.

The Fibonacci sequence (0,1,1,2,3,5,8,13…) isn’t just math — it’s a universal pattern. As it grows, ratios of terms approach the Golden Ratio (Φ ≈1.618), a harmony found in spirals, plants, shells, galaxies & even DNA. [🎞️ thevisualalchemy]

'The First Six Books of The Elements of Euclid - With Colored Diagrams And Symbols': a reproduction of Oliver Byrne’s celebrated work from 1847 plus interactive diagrams, cross references, and posters designed by N. Rougeux Go to➡️c82.net/euclid/ #iteachmath #MTBoS

@Microinteracti1 @WaltonTiger 💯👏🏻👏🏻👏🏻👏🏻

Donald Trump: “NATO is nothing without America.” Meloni: “Perfect. Then Europe will close the U.S. bases, tear up the sweetheart trade deals, and, just to make the message land, boycott McDonald’s too.” That is the blunt reality: if Washington wants to talk like protection is a one way favor, Europe can answer like a partner with leverage, not a dependent begging for permission. And honestly, that tone is long overdue. When someone says “you are nothing without me,” the correct reply is not gratitude. It is boundaries.

🚨: For the first time, physicists have unified space and time quantum mechanics

@sanchezcastejon @kanezadiane @LaVanguardia 💯👏🏻

Si Trump ocupa Groenlandia hará de Putin el hombre más feliz. Europa debe avanzar en su proceso de integración y dotarse de una defensa realmente común. Mi entrevista en @LaVanguardia: lavanguardia.com/politica/20260…

@EmmanuelMacron 💯👏🏻

La France est attachée à la souveraineté et à l’indépendance des Nations, en Europe comme ailleurs. Cela préside à nos choix. Cela fonde notre attachement aux Nations unies et à notre Charte. C’est à ce titre que nous soutenons et continuerons de soutenir l’Ukraine, et que nous avons bâti une coalition des volontaires pour une paix robuste et durable, pour défendre ces principes et notre sécurité. C’est à ce titre aussi que nous avons décidé de nous joindre à l’exercice décidé par le Danemark au Groenland. Nous l’assumons. Aussi car il en va de la sécurité en Arctique et aux confins de notre Europe. Aucune intimidation ni menace ne saurait nous influencer, ni en Ukraine, ni au Groenland, ni ailleurs dans le monde lorsque nous sommes confrontés à de telles situations. Les menaces tarifaires sont inacceptables et n’ont pas leur place dans ce contexte. Les Européens y répondront de façon unie et coordonnée si elles étaient confirmées. Nous saurons faire respecter la souveraineté européenne. C’est dans cet esprit que je m’entretiendrai avec nos partenaires européens.

@EmmanuelMacron 💯👏🏻

France is committed to the sovereignty and independence of nations, in Europe and elsewhere. This guides our choices. It underpins our commitment to the United Nations and to its Charter. It is on this basis that we support, and will continue to support Ukraine and that we have built a coalition of the willing for a robust and lasting peace, to defend these principles and our security. It is also on this basis that we decided to take part in the exercise organized by Denmark in Greenland. We fully assume this decision, because security in the Arctic and at the outer edges of our Europe is at stake. No intimidation or threat will influence us—neither in Ukraine, nor in Greenland, nor anywhere else in the world when we are confronted with such situations. Tariff threats are unacceptable and have no place in this context. Europeans will respond in a united and coordinated manner should they be confirmed. We will ensure that European sovereignty is upheld. It is in this spirit that I will engage with our European partners.

@vonderleyen @RobinStanfill2 💯👏🏻

Territorial integrity and sovereignty are fundamental principles of international law. They are essential for Europe and for the international community as a whole. We have consistently underlined our shared transatlantic interest in peace and security in the Arctic, including through NATO. The pre-coordinated Danish exercise, conducted with allies, responds to the need to strengthen Arctic security and poses no threat to anyone. The EU stands in full solidarity with Denmark and the people of Greenland. Dialogue remains essential, and we are committed to building on the process begun already last week between the Kingdom of Denmark and the US. Tariffs would undermine transatlantic relations and risk a dangerous downward spiral. Europe will remain united, coordinated, and committed to upholding its sovereignty.

Square-free numbers are integers that are not divisible by the square of any prime, meaning no prime factor appears more than once in their prime factorization. They play a central role in number theory because they encode the “simplest” multiplicative structures. The Riemann zeta function ζ(s), defined as the sum ∑ₙ n⁻ˢ, is deeply connected to square-free numbers through its Euler product representation, which expresses ζ(s) as a product over all primes. By using Möbius inversion, one can isolate the contribution of square-free numbers and show that the probability a randomly chosen integer is square-free is 1/ζ(2)=6/π². More generally, generating functions involving the Möbius function and ζ(s) allow mathematicians to count and study square-free numbers and understand their distribution. These connections reveal how the zeta function encodes subtle arithmetic structure, linking prime factorization, randomness in integers, and deep analytic properties of ζ(s). Image: share.google/xXE1RhQl4O31ZN…

On 14 January 2025, the LIGO's detectors captured GW250114, a gravitational wave signal (GWS) caused by two black holes' coalescence, each about 30 times the size of our Sun. With a signal-to-noise ratio of 80, as opposed to 26 for GW150914 a decade ago, GW250114 is the most clearly recorded signal to date, allowing us to test Einstein and Hawking's ideas with unprecedented precision. Ten years after the historic, Nobel-winning discovery of GW150914, LIGO is now more sensitive, giving scientists (and us) a sharp snapshot of this new merger. The two black holes coalescence, with respectively 33.6 and 32.2 solar masses, formed a black hole of 63 solar masses. During the “ringdown,” the final phase when the new black hole vibrates like a bell, scientists picked up: - the main oscillation (247 Hz); - a fleeting “overtone,” a secondary vibration at a slightly different frequency, fading away in less than one cycle. This confirms the no-hair theorem: black holes are simple objects, described only by mass and spin, in line with Einstein's general relativity. The observed frequencies align with the Kerr spectrum within ±30%: an extraordinary result. In addition, GW250114 confirms Hawking's area theorem, also known as the 2nd law of black hole mechanics, which states that the black hole horizon area cannot decrease in time. Furthermore, the area of a black hole's event horizon is directly proportional to its entropy, linking the theorem to the second law of thermodynamics. The initial area of the two black holes (about 240,000 km², the size of the UK) grew to 400,000 km² in the final black hole (roughly Sweden's size). This increase, confirmed with 99.994% confidence, suggests black holes behave as thermodynamic systems, a step toward a quantum theory of gravity. GW250114 reminds us that black holes follow precise rules, and each signal brings us closer to learn more about the universe. However the future of LIGO is at risk: possible budget cuts could shut down one of its stations, with easily imaginable deleterious consequences. -------------------------- Image: "Gravitational waves that emanate from colliding black holes bear clues about these unseen objects." Credits: Maggie Chiang/Simons Foundation Sources Research Paper➡️journals.aps.org/prl/abstract/1… ➡️arstechnica.com/science/2025/0… ➡️science.org/content/articl…

🚨: Scientists believe we may have received a signal from a parallel universe via a WORMHOLE

🚨: We might be living inside a 2 billion light-year void, and it could help clear up one of the biggest mysteries in cosmology

@Earstohearyou 💯⚫⚪ The Maya conceived the world as a great cosmic sphere divided into several planes. At its center was the Earth, surrounded by thirteen heavens and nine levels of the underworld (Xibalbá). This idea reflected a rounded universe, in constant motion and balance.

From the sphere, the ORIGIN of all form, arise the 5 Platonic Solids of pure GEOMETRY - mental constructs shaping our reality. Mathematically FAWLESS, the sum of their internal angles always resolves to 9, the number of COMPLETION mirroring the infinite cycles of life. Yet HIDDEN within them is a sixth: the Star tetrahedron or MERKABA, the union of body and spirit, matter and light. "The laws of nature are written by the hand of God in the language of mathematics." ~ Galileo

Writing is perhaps the greatest of human inventions, binding together people, citizens of distant epochs, who never knew each other. Books break the shackles of time, proof that humans can work magic. -- Carl Sagan, Cosmos (1980) #scritturebrevi #VentagliDiParole #ThePhotoHour

@Earstohearyou o bʼakʼtun 🙏🏻

Cycles of RISE and FALL ripple through history… Atlantis mirrored realms we inhabit, giants once walked among us, and cosmic CYCLES mark inevitable change. Humanity shapes the aether - when love declines, imbalance follows, and CATACLYSM is born. With each cycle of destruction and renewal, do we SHRINK… or rise with the power of love to restore balance to these ever decreasing cycles?

An international team led by the @IAC_Astrofisica alongside the @ULL has uncovered a sensational cosmic drama unfolding in our own galaxy. The binary star system known as V Sagittae is performing an extraordinary “stellar dance”: a superdense white dwarf is ravenously siphoning material from its slightly larger companion at a rate never seen before. This dramatic feeding frenzy has ignited the system to extraordinary brightness, illuminating a surrounding ring of gas formed from debris it can no longer absorb. Every 12.3 hours, the two stars whirl ever closer in this celestial tango. Astronomers believe that this violent interaction may soon crescendo into a nova, an explosion bright enough to become visible to the naked eye from Earth, even from a distance of around 10,000 light-years. Should gravity complete its fatal embrace, the pair could merge in a supernova so luminous that it might even be visible during the day. By employing the Very Large Telescope (VLT) of the @ESO, researchers captured this cosmic spectacle in unprecedented detail. The discovery of the glowing gas ring encircling both stars offers fresh insight into how such extreme binary systems evolve and ultimately explode. The findings helped solve a century-long mystery surrounding V Sagittae, one of the brightest and most enigmatic binary systems known. 👉 academic.oup.com/mnras/advance-…

@Earstohearyou 🙏🏻🙌🏻

You may change your mental vibrations by an effort of WILL in the direction of deliberately fixing the Attention upon a more desirable state. Will directs the ATTENTION, and Attention changes the Vibration. Cultivate the Art of Attention by means of the Will, and you have solved the secret of the MASTERY of Moods and Mental States ~ Kybalion

Sunset from space