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🚨BREAKING: France wiped Google and Microsoft off 2.5 million government computers.
Germany moved 30,000 PCs off Windows. Denmark dropped Microsoft Office.
Here's exactly what they switched to and how to do the same: – at New York, USA
Merlions Keep, Phill Shade retweeted
Oh Captain my Captain. You will forever be remembered.
tiktok.com/t/ZPLyoKuJh/
🤖 Made with AI
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The Taylor series of f at a is ∑ f⁽ⁿ⁾(a)(x − a)ⁿ/n!, built from the derivatives of f at one point.
Cut at degree n, it matches f and its first n derivatives at a, with error shrinking like (x − a)ⁿ⁺¹. For eˣ the coefficients are 1/n!; for sin x only odd powers survive, with alternating signs.
Smoothness is not enough: e^(−1/x²), set to 0 at 0, has every derivative 0 there, so its series is 0. Functions equal to their series are called analytic.
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Why do bubbles squeeze themselves into hexagons instead of staying round?
When bubbles crowd together, round shapes waste space. Their shared walls rearrange to reduce surface energy, and in a flat foam, three films meet at exactly 120°.
The surprising part? No bubble needs to know geometry. The physics creates the pattern.
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The golden ratio hides inside a single triangle and refuses to leave.
φ = (1 + √5)/2 satisfies φ² = φ + 1, so every power collapses into the two before it. That same relation produces the Fibonacci sequence when you scale by successive powers and take the nearest integer.
A golden triangle simply embeds the identity geometrically: each base is the longer side of the next, and the angles lock so the ratio never drifts. The continued fraction and nested radical are just the same equation written in different clothes.
One number, infinite ways of saying it is exactly itself plus its reciprocal.
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Buckingham Palace Honours Sir Patrick Stewart (1940–2026) with Star Trek Theme Tune 🕊️
The Band of the Grenadier Guards performs the iconic Star Trek theme at Buckingham Palace in honour of Sir Patrick Stewart, following the sad news of his passing.
Queen Elizabeth II knighted Sir Patrick Stewart in 2010, recognising his outstanding contribution to drama and the arts 🇬🇧
🎥 @KingsGuardTours
📆 30 October 2026
📍 Buckingham Palace
#SirPatrickStewart #StarTrek #GrenadierGuards #BuckinghamPalace #BritishArmyMusic
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ALT Four-panel comic titled “The power of the nap” by purr.in.ink. A fluffy black cat lies on a bookshelf beside three books, with one front paw dangling over the edge. In the first three panels, the scene is dark and grey as the cat’s eyes grow rounder and wider. The text reads: “The world… may be terrible. But when we sleep…” In the final panel, the cat closes its eyes peacefully, and the scene changes to soft lavender, blue and pastel colours. The text concludes: “we sleep.”
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Replying to @TheTrekCentral
Don't know who did this. But, thank you.
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One quantity, eight faces, one irreversible arrow.
Clausius dS = δQ_rev / T and Boltzmann S = k_B ln Ω both track growing disorder through heat and microstates.
Gibbs S = −k_B ∑ p_i ln p_i, Shannon H = −∑ p_i log₂ p_i, and von Neumann forms show the same measure of missing information.
Black-hole S_BH = k_B c³ A /(4 G ħ) ties entropy to area, while ΔS_universe ≥ 0 unites every definition.
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How can a cat be both alive and dead, or two particles share a fate across the universe?
These nine ideas capture quantum mechanics:
- Superposition mixes states until measured,
- Entanglement correlates distant systems instantly,
- Wave-particle duality produces interference,
- Tunneling lets particles cross forbidden barriers,
- The uncertainty principle bounds simultaneous precision,
- Quantization restricts energy to discrete levels, s
- Spin is intrinsic angular momentum,
- Hilbert space is the arena for state vectors, and
- Virtual particles mediate interactions.
They enable quantum computers, MRI imaging, and secure cryptography. The universe runs on amplitudes, not certainties.
Which concept most changed how you see physical reality?
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SIR PATRICK STEWART (1940-2026)
Before everything else, Patrick was defined by being born and bred in Yorkshire, the proud county in the north of England which he loved to the end. You could hear it in his accented voice and in the stern honesty with which he told you what he thought and felt. Yorkshiremen have no truck with half-truths or avoidance of big issues. He wore his heart on his sleeve, which made him a man to rely on, to admire and in my case, love.
We first met as ambitious young actors with the Royal Shakespeare Company half a century ago but we weren’t in the same productions. My first strong memory was a few years later, meeting him in the street in central London when he told me about an offer to take over a leading part in 'Star Trek'. “But Patrick think of your stage career in the UK. Do you really want to risk—getting lost in Hollywood for years and years?”. Well, he took the risk and thank goodness for us all that he did for not just his devoted Trekkies but film and theatre audiences, who marvelled at his using international celebrity to star in a string of cinema successes ('X-Men' of course) and in great classical plays by Shakespeare, Ibsen, Arthur Miller, Peter Shaffer, Pinter and Beckett at Stratford-upon-Avon, in London’s West End and on Broadway.
America was his adopted home, where he met his adored Sunny who has cared for him through sickness and health, through thick and thin. But he never forsook his origins: and the proudest achievement of the most respected and beloved actor of his generation on either side of the Atlantic, was his appointment as Chancellor of Huddersfield University in Yorkshire.
His farewell performance in 'Avengers: Doomsday' is yet to be seen.
Ian McKellen 29 October 2026
Photo: University of Huddersfield
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This is what radiation looks like.
A piece of uranium in a chamber filled with cooled ethanol vapor creates visible condensation trails as the alpha particles it emits collide with and ionize the gas molecules.
📽: Cloudylabs





























