Olivia
Online
Christ van Wijck
@Wellofknowledge
Retired ICT-pro.
Don't try to scam me. I may look like an old idiot, but that's just the outside :)
Drunen - The Netherlands
Joined June 2009
649 Following
577 Followers
86.6K Posts
Four sites used by the Russian FSB were reportedly struck in the Strilkove area in the occupied part of Kherson region.
It is reported that 15 FSB officers were killed and around 30 more wounded.
There has been no official confirmation yet.
💥 Ten Russian UAV control points and ground operator stations neutralized. One S-400 Triumf and one Buk-M3 air defense system destroyed, along with a Nebo-U radar.
That is one week of work by Ukraine's Defence Forces: taking apart the means Russia planned to use against our cities.
Between September 13 and 20, our forces struck seven key military facilities where Russian drones were produced, stored, or prepared for launch. Production shops in temporarily occupied Siverskodonetsk. Bases and launch sites in Sochi and Kursk. Locations in occupied Donetsk.
We are working to remove the root cause of the air raid alerts: Russia's ability to strike our cities. Every hit strips the enemy of the material resources to wage this war.
Insane video of a Russian air defence system Pantsir being deployed right above Moscows busiest highway right next to an oil refinery.
Satellite imagery of the Kuibyshev Oil Refinery in Samara clearly shows damage to the fuel storage tanks.
However, footage filmed at the site after the attack shows separate fires and damage in opposite parts of the refinery, so the tanks were not the only targets hit. But the currently available satellite images are not detailed enough to identify all of those impact points.
Beautiful properties of Pascal Triangle
1/ Igor 'Strelkov' Girkin warns that Russia inevitably faces a "terrible future" after Putin, with the possibility of "sullen, cocaine-addicted gangsters with sadistic, perverted tendencies" – people like the late Yevgeny Prigozhin – taking over a disintegrating country. ⬇️
Ukrainian heavy bomber drones dropped kamikaze ground robots 10 km behind Russian lines in northern Donetsk region. First operation of this kind in the world.
Assault troops freed two villages and cleared a third after the robots landed — Oboronka. 1/
MIT professor Denis Auroux teaches the one optimization trick behind every AI model at OpenAI, Google DeepMind, and Meta - and why every quant at Two Sigma uses it to build $10 billion trading strategies.
It's called Lagrange multipliers. One lecture. Changes how you see every optimization problem.
Most optimization is simple: minimize a function, set derivatives to zero, done.
But real problems have constraints.
Build the smallest pyramid with a fixed volume. Train a neural network with a fixed compute budget. Find the portfolio with the highest return at exactly this level of risk.
You can't just set derivatives to zero anymore. The constraint changes everything.
Watch the moment (around 6 min in):
He draws a hyperbola on the board and asks: what is the closest point to the origin?
You could solve for y in terms of x and substitute. But that only works when the constraint is simple.
Instead, he draws the level curves of the distance function as circles around the origin. Then he shrinks the circles until one of them just barely touches the hyperbola.
That touching point - where the circle is tangent to the hyperbola - is the answer.
And the geometric key: at that point, both curves have the same tangent line. Which means their gradient vectors are parallel.
That's the entire method. Gradient of f equals lambda times gradient of g.
This is the math behind every Support Vector Machine at Google and Meta - the algorithm that classifies billions of images and ads daily.
SVMs are literally a Lagrange multiplier problem. Maximize the margin between classes subject to the constraint that all points are correctly classified.
Every time Instagram decides what ad to show you, it runs this calculation.
Neural network training with weight constraints, portfolio optimization at Bridgewater, drug molecule design at Pfizer - all Lagrange multipliers.
OpenAI's RLHF method that made ChatGPT actually useful is constrained optimization at its core.
The lecture ends with a harder problem: build a pyramid with a fixed volume and minimum surface area. Where do you place the top?
Lagrange multipliers give the answer in a few lines: the top should sit directly above the incenter of the triangle - the point equidistant from all three sides.
A result that would take pages of geometry falls out of one equation.
MIT 18.02, Lecture 13. Denis Auroux. Free on YouTube.
bookmark this if you're learning calculus or machine learning
Ten million people have watched an Australian high school teacher accidentally destroy the entire personal finance industry.
He filmed the lesson on a whiteboard in a regular Sydney classroom and put it on YouTube.
Robo-advisors charge two percent a year to hide the exact equation he teaches for free in seven minutes.
His name is Eddie Woo. He is a Sydney high school math teacher and one of ten finalists for the 2018 Global Teacher Prize.
For years he has been filming his regular lessons for students who missed class.
His entire framework fits on a napkin.
Every growth process has three parts: rate, time, result. The exponent is time. The logarithm pulls it out. Every doubling takes the same amount of time. Divide 72 by your annual return to get years to double. Linear charts lie. Log charts do not.
That last rule alone has probably cost the retirement industry a hundred million dollars in unbought pensions.
"The greatest shortcoming of the human race is our inability to understand the exponential function."
That is Al Bartlett, the physicist behind the most-watched lecture on exponential growth in history. Woo teaches the same idea in seven minutes.
Founders build financial models on linear axes and are surprised when the market grows ten times before their next investor meeting. Retail investors move in and out of the stock market and lose the exact number of doublings that would have made them rich.
The lesson is free on YouTube. Every textbook chapter on logarithms is a hundred years old.
Woo still teaches high school in Sydney. Almost none of the ten million viewers have ever divided 72 by their portfolio's return.
The math is free. The willingness to actually work out how many doublings you have left is the entire edge.
James Maynard won the Fields Medal in 2022 - the Nobel Prize of mathematics, awarded once every 4 years to mathematicians under 40.
He teaches this Oxford lecture on the one number that tells you everything about a matrix - and why Google built a $2 trillion company on it, why Goldman Sachs pays $400k starting salaries to people who understand it, and why every AI lab on earth can't function without it.
The number is called the determinant.
Most students memorize the formula and move on. Maynard teaches where it actually comes from.
Take any shape - a square, a triangle, anything. Apply a linear transformation. The shape gets stretched, rotated, skewed.
The determinant is exactly the factor by which the area changes.
That's it. One number. Describes the entire transformation.
Watch the moment (around 6 min in):
He draws a unit square on the plane. Area = 1.
He applies a linear transformation. The square becomes a parallelogram.
The parallelogram has some area C. Every other shape you feed into this transformation - triangles, circles, anything - also gets its area scaled by exactly C.
That constant C is the determinant.
This is why the determinant matters in practice.
At Google, PageRank multiplies matrices billions of times. The determinant tells engineers whether the system is stable or collapsing.
At Two Sigma and D.E. Shaw, portfolio risk models use matrix operations constantly. A determinant of zero means the model has broken down - the positions are perfectly correlated and diversification is gone. That mistake cost funds billions in 2008.
In neural networks, every layer of a transformer like GPT is a matrix multiplication. Vanishing or exploding determinants are why deep networks were nearly impossible to train before 2015. Fixing this problem made OpenAI worth $300 billion.
But Maynard goes further than the formula.
He strips the determinant down to three abstract properties:
Linear in each column
Zero when two columns are identical
Equals 1 for the identity matrix
Then he proves that anything satisfying these three rules must be the determinant.
No formula memorized. Just logic.
This is what Oxford mathematics looks like at the first-year level. The Fields Medal winner is in the room, and the starting point is "what should the determinant be?"
Oxford Mathematics, Linear Algebra II. James Maynard. Free on YouTube.
bookmark this if you're learning linear algebra
NEW: US President Donald Trump reportedly decided to refrain from striking Houthi targets in Yemen “for the time being” on September 20. (1/2)
Other Key Takeaways:
The Islamic Revolutionary Guards Corps (IRGC) is reportedly supporting Houthi efforts to develop infrastructure in the Houthis’ newly captured territory along Yemen’s southwestern coast that the group could use to consolidate its recent territorial gains around the Bab al Mandeb and establish long-term leverage over international shipping. Two Houthi military sources told AFP on September 19 that IRGC personnel visited recently captured Houthi territory along Yemen’s Red Sea coastline and supervised Houthi efforts to construct tunnels along the mountainous terrain surrounding the port city of Mokha in Taiz Governorate.
Iranian Supreme National Security Council Secretary Major General Mohsen Rezaei used his September 20 interview with Qatari outlet Al Jazeera to further Iran’s ongoing effort to sow divisions between the United States and its Gulf allies. Rezaei also sought to portray Iran as a cooperative regional security partner to Gulf states, likely as part of an Iranian effort to secure recognized control of the Strait of Hormuz among other Persian Gulf littoral states.
Rezaei also claimed that Iran tested a new anti-ship missile armed with a cluster munition warhead in a recent Iranian attack targeting the USS George Washington aircraft carrier on September 5. The missile did not impact the warship but struck “near” the vessel, according to Rezaei.
Russia planned to deepen Russian economic support for Iran and deepen sanctions evasion collaboration between 2024 and 2026, according to the 44-page plan Fox News obtained and published on September 20.
A series of explosions struck an ammunition depot at a Syrian army site near Al-Eis in southern Aleppo, leaving civilians injured.
New details on the damage to the Moscow Oil Refinery: both of its primary crude-processing units, in total accounting for 53% of capacity, caught fire during the September 20 strike, - Reuters
Crude processing has now completely stopped, yet again.
P.S: After the previous strikes on June 18 industry sources estimated that full repairs would take at least six months.
By the time of a September 20 strikes Russia managed to restart only part of the refinery, with the plant reportedly operating at around one-third of capacity by mid-August — only for both units to be hit again.
Kurt Gödel, the logician behind the incompleteness theorems, also constructed a formal argument for God’s existence.
He never published it.
Using modal logic, Gödel defined God as a being possessing every “positive” property. The argument then rests on a striking premise: if such a being is possible, its existence is necessary.
Gödel showed the proof to Dana Scott around 1970.
The argument remains controversial. Its axioms, especially the notion of a “positive property,” are open to philosophical criticism. Some formulations also lead to modal collapse, where every truth becomes necessary.
It is not an accepted mathematical proof of God.
It is a remarkable example of how far formal logic can be pushed.
A former Morgan Stanley trader walks into MIT with colleagues from Harvard Management sitting in the back row.
He shows why following the "optimal" portfolio strategy cost funds $57 billion in a single month in 2008 - and what Harry Markowitz's Nobel Prize actually got wrong.
Harry Markowitz won the Nobel Prize in 1990 for Modern Portfolio Theory.
The idea: find the combination of assets that gives you the highest return for the lowest risk. Plot every asset on a chart. Draw the efficient frontier. Done.
Goldman Sachs, Two Sigma, every major fund uses this framework.
But the professor shows a problem nobody talks about.
Watch the moment (around 1:05:00 in):
He shows a video of the London Millennium Bridge.
Engineers designed it perfectly. Accounted for every known force. Built with cutting-edge technology.
It started swaying violently the first day people walked on it.
What went wrong? When the bridge moved slightly, pedestrians instinctively adjusted their step to keep balance. Which synchronized their movement. Which amplified the sway. Which made more people sync up.
The bridge nearly collapsed because everyone was individually optimizing - and that destroyed the system.
This is exactly what happened in 2008. Every major fund ran the same optimal portfolio model. When markets moved, they all hit the same stop-losses at the same time. The selling synchronized. The whole system crashed.
Funds that were up 20% in January were down 40% by October. The math was correct. The strategy was optimal. And it nearly broke the global financial system.
The lecture also covers a result that sounds impossible.
Take two assets. Asset A doubles in year one, then drops 50% in year two. Net result: zero.
Asset B drops 50% in year one, then doubles in year two. Net result: also zero.
But a 50/50 portfolio of A and B, rebalanced each year, returns 25%.
Both assets went nowhere. The portfolio made money. That's the math of diversification - the closest thing to a free lunch in investing.
Then he introduces risk parity - the approach Bridgewater's Ray Dalio used to build a $150 billion fund.
Standard 60/40 portfolios put 60% of capital in stocks, 40% in bonds. But stocks are three times more volatile than bonds. So 90% of the actual risk comes from equities.
Risk parity flips this. Equal risk, not equal capital. Then lever up to hit your return target.
The Sharpe ratio - your risk-adjusted return - stays the same when you add leverage. That's the math that made risk parity famous and made Bridgewater the largest hedge fund on earth.
The lecture closes with Claude Shannon - the father of information theory, the man who invented the mathematics behind every computer and phone on earth - who spent his later years at MIT trying to solve portfolio optimization.
His debate with Paul Samuelson about the Kelly Criterion is still unresolved.
If Shannon couldn't crack it, the problem is still open.
MIT 18.S096, Lecture 16. Free on YouTube.
bookmark this if you're studying quantitative finance
⚡️ Russia is blocking the delivery of food and medicine to the occupied part of the Kherson region, — Ministry of Foreign Affairs (MZS).
The most difficult situation is in Oleshky: about 2,000 people remain there, including 50 children. The city has no electricity or gas, and food, medicine, and other aid have not been delivered for a month. People report searching for leftover food and gathering grass to survive.
Russia is also obstructing the evacuation of civilians and does not allow humanitarian missions. Ukraine is pushing for organized evacuation and access for humanitarian organizations.
👉 Follow @blyskavka_ua
Polish FM Sikorski: Ukraine destroyed an estimated 30-40% of Russia's refining capacity practically without an air force. I told the Russians, as a deterrent: we have more combat aircraft than you.
President Trump pulled back Sunday from joining Saudi Arabia’s war against the Houthis after considering strikes last week - New York Times
Most of his inner circle is reportedly deeply skeptical or outright opposed to joining the fight.
Foundation models grew up on the open web, scraped into giant corpora like Common Crawl. Everything that lay unlocked went in: washing-machine manuals, strangers arguing about the right way to cook rice. What the models learned: how people perform for an audience ↓
Ukraine is pushing back in northern Donetsk, in a region Russia has spent years trying to capture.
The Third Army Corps says its ongoing “Vivaldi” counteroffensive has retaken Shandryholove, Derylove, and Drobysheve and regained 50 square kilometers of territory that had been occupied by Russia.
Open-source analyst Clément Molin called it “one of the most important victories for Ukraine in 2026,” saying the gains could delay Russia’s planned offensive in the northern Donbas.
The corps says “Vivaldi” is only in its second phase, out of four “seasons.”
🔗Read more: https://t.co/aqMD34TBki
Last Seen Users on Sotwe
Trends for you
Most Popular Users
Elon Musk 
@elonmusk
241.7M followers
Barack Obama
@barackobama
119M followers
Cristiano Ronaldo
@cristiano
114.4M followers
Donald J. Trump
@realdonaldtrump
111.9M followers
Narendra Modi
@narendramodi
107.2M followers
Rihanna
@rihanna
98.7M followers
NASA
@nasa
92.4M followers
Justin Bieber
@justinbieber
91.8M followers
KATY PERRY
@katyperry
90M followers
Taylor Swift
@taylorswift13
83.9M followers
Lady Gaga
@ladygaga
75.4M followers
Virat Kohli
@imvkohli
73.3M followers
Kim Kardashian
@kimkardashian
70.9M followers
YouTube
@youtube
68.8M followers
Neymar Jr
@neymarjr
66.3M followers
Bill Gates
@billgates
65.1M followers
Selena Gomez
@selenagomez
63M followers
The Ellen Show
@theellenshow
62.3M followers
CNN
@cnn
61.8M followers
X
@x
60.7M followers