Every physics teacher you had lied a little. An electron isn’t a tiny dot flying down a line, it’s this.
This is a Gaussian wave packet, the simplest quantum particle there is, straight from the Schrödinger equation. The blue spiral is the wavefunction. The red dot is where a classical ball would be.
The bell tells you where it probably is. The twist tells you how fast it’s moving. Squeeze one and the other blurs. Not because our instruments are bad. Because the universe doesn’t allow both.
“Philosophy is written in this grand book, the universe, which stands continually open before our eyes… It is written in the language of mathematics.”
- Galileo Galilei
Каждый школьный учебник показывает атом водорода как статичный шарик или «облачко». Это ложь. Даже в основном состоянии электрон не стоит на месте.
Вот что на самом деле рисует уравнение Паули.
Маленькая цветная фигурка в углу — та самая орбиталь, которую тебе показывали. Всё остальное — вероятность тока. Оранжевый крутится против часовой, синий — по часовой. Белый — почти стоит.
Это не электрон, который бегает по орбите. Это математика «где его вероятнее всего найти». И эта математика отказывается сидеть спокойно.
В обычном уравнении Шрёдингера волновая функция основного состояния 1s — вещественная. Поэтому классический ток вероятности там равен нулю. Но когда ты добавляешь спин (через уравнение Паули или Дирака), появляется дополнительный член. Даже в «идеально неподвижном» основном состоянии течёт ток, потому что спин электрона сам по себе создаёт циркуляцию.
Плотность вероятности |ψ|² при этом стационарна — она не меняется со временем. Но ток внутри неё есть. Это как река, которая стоит на месте как целое, но внутри вода постоянно движется.
Именно этот ток даёт магнитный момент атома. Не «электрон крутится вокруг ядра», а математика вероятности, которая отказывается быть статичной.
Ни один электрон не «вращается» по классической траектории. Но квантовая вероятность всё равно течёт.
Физика никогда не была такой простой, как рисовали в учебнике.
TKA...
🤗 woles : 🚫
😀 start roadmap to UTBK : ✅💯
Klean yg lg warming up bwt 2027 final endgame, khusus mtk, cek link di bio yahh 👆
#tka#utbk2027#snbt#pkpm
Big investigation coming out.
For months I have been working through more than 1,000 pages of declassified German archives on what many call the genocide against communists in Indonesia in 1965.
The involvement of the US and Britain is widely reported. But there was another player that financed and armed this massacre: Germany.
To this day, Germany refuses to acknowledge what it knew and denies any direct involvement. Its own archives show it knew everything. Bonn was told about the army's test killings of communists in January 1965, almost nine months before the massacre began.
In two days I will publish the full investigation, with hundreds of declassified documents and testimonies from victims and perpetrators of the killings.
Today Berlin sends weapons to Israel and sees no genocide in Gaza. Sixty years ago it sent weapons to Indonesia and saw none there either. Same state. Same lie.
The full investigation will be on https://t.co/pMW5GBnvBd, online from 30 September 2026.
The documentary I produced in 2021 will be released in a remastered version on the same day on my YouTube channel: https://t.co/aHX9hvoOAQ
Both the investigation and the documentary will be published in several languages.
Stay tuned.
New video: The Sicilian Najdorf Is Actually EASY With This Simple Setup
The Najdorf looks complicated because White has countless options.
But Fischer and Kasparov often relied on the same practical setup:
0:00 Why the Najdorf gives Black active play without endless memorization
2:45 The simple setup Fischer and Kasparov trusted
3:20 The early trap hidden inside Black’s central move
4:30 The knight jump that can unexpectedly win White’s queen
5:07 The complete setup—and Black’s clear middlegame plan
7:30 Why White cannot allow Black’s queenside pawns to advance
8:50 How Black can stop White’s scary-looking kingside attack
9:29 The central breakthrough that signals Black is taking over
12:07 The Tal-style pawn sacrifice that tears open White’s king
16:17 The brilliant move that allows White to capture Black’s queen
The number π is about circles. So why is it hiding inside the bell curve, the shape behind coin flips, test scores, and measurement error?
The bell curve is the graph of e^(-x²), and the total area under it is one of the most important numbers in statistics.
There is a catch. That curve has no formula for its area. You cannot integrate it with any standard method. It beats every trick in a calculus course.
The way around it feels like cheating. Take the flat curve and spin it into three dimensions, into a smooth bell. Then measure that bell's volume two different ways.
Slice it into thin sheets, and the volume comes out as the flat area you wanted, squared. Sweep it around in rings instead, and the volume comes out as exactly π. The circles you swept through left it behind.
Set the two equal. The area under the bell curve is the square root of π.
π was never only about circles. It was hiding inside randomness all along.
most people think mathematics is about being good with numbers. it isn’t.
mathematics is the discipline of seeing patterns.
• patterns in change.
• patterns in structure.
• patterns in logic.
• patterns in uncertainty.
build a mathematical mind by Albert rutherford argues that mathematical thinking is a skill, not a talent.
you develop it by asking:
• what stays the same?
• what changes?
• what repeats?
• what constrains the system?
• what is the simplest rule that explains this?
that is why mathematics reaches so far beyond the classroom.
the same pattern-recognition machinery powers engineering, programming, physics, finance, and science.
a mathematical mind doesn’t memorize formulas.
it learns to compress complexity into structure.
A poor clerk in India, no degree, no training, mailed his math to the top professors in Britain. Almost all of them threw the letters away. One did not, and the clerk turned out to have rediscovered the deepest unsolved problem on Earth by himself.
His name was Srinivasa Ramanujan.
The problem is about prime numbers, the ones divisible only by one and themselves. 2, 3, 5, 7, 11. They look scattered with no pattern, and in 2000 years nobody has found a formula for the next one.
Every bank login, every encrypted message, every card payment you make rests on that apparent chaos. If someone found the hidden order in the primes, they could break most of the security on the planet.
That hidden order has a name. The Riemann hypothesis. It says the primes are not random at all, that underneath the scatter runs a perfect structure, a kind of music.
It has stood unproven for over 150 years. The best minds alive have thrown themselves at it and broken. There is a million dollar prize for a proof, and it sits untouched.
Ramanujan, alone in India with no library and no teacher, walked straight into the edge of this thing. He filled notebooks with results he could not formally prove, that took the rest of the world decades to catch up to.
Your gut reads the primes as noise. Wrong. The whole bet of modern mathematics is that the noise is a song nobody has learned to read yet.
The lecture is free. Millions have watched it and walked away entertained. Almost nobody sits with the real point. The man who saw furthest into it had no credentials at all, and the men with every credential mailed his genius into the bin.
The math is free. The eye to see structure where everyone else sees chaos, that took a self taught clerk from Madras, and it still cannot be bought.
Jujur walaupun kocak asli ini edukasinya damkar gunung kidul (Ig/damkarmatgunungkidul) bener lho, wilayah gunung kidul ketika kemarau tuh bener2 kering dan banyak dedaunan gugur karena sebagian besar wilayahnya itu hutan jati yang gugur in daun nya di musim kemarau, sekalinya kebakaran terjadi bisa2 meluas ga terkendali dengan cepat banget. Stay safe ya warga gunung kidul, wes rasah bakar uwuh sek pas kemarau 😃
@LiumangtuCrypto Economic is the study of lack
The world is abundant
Abundance is everywhere
Limited minds
Limited thinking
Limited dreaming
Limited imagination
Limited education
And the government does this on purpose
Is endemic in every educational text book
Fundamentally flawed
THE INVISIBLE ENGINE BEHIND EVERY GREAT FILM INDUSTRY:
1. Hollywood → Fear. Fear of irrelevance, fear of failure, fear of losing the spotlight. That anxiety built the most powerful entertainment machine on earth.
2. Bollywood → Emotion. Every story, every song, every scene is designed to make you feel something at full volume.
3. Nollywood → Necessity. No studios, no budgets, no infrastructure. Just stories that needed to be told and people who refused to wait.
4. Korean Cinema → Obsession. With craft, with detail, with saying something true about society even when it is uncomfortable.
5. French Cinema → Intellect. Film is not entertainment there. It is philosophy with a camera.
6. Italian Cinema → Beauty. Even poverty, even tragedy, even violence had to look extraordinary on screen.
7. Japanese Cinema → Silence. What is not said, not shown, not explained carries more weight than anything on screen.
8. Iranian Cinema → Restraint. Working under censorship, Iranian filmmakers learned to say everything by showing almost nothing.
9. British Cinema → Class. Every British film, underneath the surface, is really about where you come from and whether you can escape it.
10. Chinese Cinema → Scale. Landscapes, armies, dynasties. Everything framed to remind you how vast history really is.
11. German Cinema → Darkness. From Expressionism to modern thrillers, Germany has always been most honest when exploring what humans are capable of.
12. Scandinavian Cinema → Isolation. Cold landscapes, quiet people, and an honesty about loneliness that the rest of the world finds difficult to film.
13. Spanish Cinema → Surrealism. Reality was never quite enough. Spanish directors always needed to bend it slightly to tell the truth.
14. Mexican Cinema → Mythology. Ancient symbols, family wounds, and magical realism woven so naturally you forget where history ends and imagination begins.
15. Turkish Cinema → Contradiction. Between tradition and modernity, East and West, faith and freedom. The tension never resolves and that is exactly what makes it compelling.
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Minta tolong yang lihat di-retweet ya 🫶
Btw aku domisili pemalang (jateng) ya
#JumatBerkah#zonauang