F.H.

Engineer / Start Up / Investing

[Mathematica @mathemetica]

Why does a magnetic field appear between a charging capacitor’s plates - where no current flows?

- Gauss’s law of magnetism
∮ 𝐁 · d𝐀 = 0
says magnetic lines always form closed loops; no monopoles exist.
- Gauss’s law of electricity
∮ 𝐄 · d𝐀 = qᵢₙ / ε₀
lets electric lines start and stop on charges.
- Ampère’s law fails for changing fields. Maxwell added displacement current, giving
∮ 𝐁 · d𝐥 = μ₀(I + ε₀ dΦ_E/dt).

That single term yields electromagnetic waves: the foundation of every radio, Wi-Fi and MRI signal.
The universe runs on closed loops and one clever correction.

[The Scientific Lens @LensScientific]

The Faces of e

Leonhard Euler introduced the symbol e in the 18th century, but the number itself appeared earlier in the work of Jacob Bernoulli, while studying compound interest. Euler later showed how naturally this constant appears across mathematics.

[Massimo @Rainmaker1973]

Rubiks cube and graph theory.

[🎞️ jagarikin]

[fintex @_yusufknl]

As someone who reads every transformer paper that drops, this Fourier series lecture is the closest thing to a Google FNet explainer I've ever seen released for free.

Everyone thinks attention is what makes transformers powerful. Google replaced attention with a 200-year-old Fourier transform. It nearly matched BERT and ran 7x faster.

25 minutes. Bookmark & watch today. Then read the article below - I broke down the 5 pieces of math the AI hype skips.

[F.H. @_Don_Haag_]

@seriengruender Mietauto holen, aber gründlich die Reifen vorher checken, wenn die schon Schäden vor allem an der Seite haben, wird versucht dir das bei Rückgabe anzuhängen. Nachts vorsichtig Fahren, es gibt teilweise brutale Schlaglöcher.

[Calc Consulting @CalcCon]

Yurii Nesterov is a Belgian-Ukrainian mathematician and one of the founders of modern optimization theory. His work has had an enormous impact on machine learning, artificial intelligence, engineering, operations research, economics, and scientific computing.

He just recently received the Carl Friedrich Gauss Prize, one of the highest honors in applied mathematics, recognizing mathematical work that has had exceptional real-world impact.

His work laid the foundations to today's NN optimizers (Adam, AdamW, RMSProp, etc.) While the not identical to Nesterov's algorithm, many build directly on ideas that he introduced. Epecially acceleration and momentum. His work fundamentally changed how we think about designing optimization algorithms.

[F.H. @_Don_Haag_]

Great!

[Philosophy Of Physics @PhilosophyOfPhy]

Visualization of Maxwell’s equations.

Showing electric flux from charge, divergence-free magnetic fields, electromagnetic induction, displacement current, and coupled electric and magnetic fields propagating through vacuum as light.

[Philosophy Of Physics @PhilosophyOfPhy]

In 1926, Erwin Schrödinger introduced the equation that became the dynamical law of non-relativistic quantum mechanics:

iℏ ∂ψ/∂t = [−ℏ²/(2m)∇² + V]ψ

It does not describe a particle following one definite path. It describes how the wavefunction evolves and therefore how the probabilities of possible experimental outcomes change with time.

[F.H. @_Don_Haag_]

@Karl_Lauterbach https://t.co/PRW9IOggUH

[Hayek-Club Weimar @WeimarClub]

Deutsche Auswanderung 1820–heute.

Drei große Wellen. Immer dann, wenn der Leviathan besonders gierig war.
1854: Steuern, Militärpflicht, Bürokratie.
1881: Der Obrigkeitsstaat auf Steroiden. Weltkriege, Hyperinflation, NS-Diktatur, Nachkriegssozialismus – jedes Mal dasselbe Muster: Der Staat dehnt sich aus, die Freiheit schrumpft, die Produktiven verschwinden.

Und jetzt? 2016–2025: Rekordzahlen. Nicht, weil die Deutschen plötzlich Abenteurer geworden sind, sondern weil der Sozialstaat, der Energiewende-Irrsinn, die Masseneinwanderung, die Enteignung durch Inflation und Steuern, die Regulierungswut und die moralische Erpressung jedes freien Geistes unerträglich geworden sind.

Wer will in einem Land bleiben, das ihn als Melkkuh behandelt? Freiwilliger Tausch, Privateigentum, freie Vereinbarung – das ist die einzige moralische Grundlage von Gesellschaft. Der Staat ist ein Kartell mit Gewaltmonopol. Wer kann, stimmt mit den Füßen ab.

[Philosophy Of Physics @PhilosophyOfPhy]

In 1928, Paul Dirac found a way to describe the electron using both quantum mechanics and special relativity. The equation worked beautifully, but it also permitted negative-energy states with no obvious place in the known universe.

Dirac initially tried to identify the strange result with the proton. That interpretation failed. In 1931, he proposed something far more radical: an anti-electron, possessing the electron’s mass but the opposite electric charge.

One year later, Carl Anderson found it in cosmic rays. Inside a cloud chamber, its track curved like an electron’s, but in the opposite direction. The new particle became known as the positron.

Antimatter was not imagined first and then inserted into mathematics. The mathematics revealed a possibility that experiment had not yet seen.

Sometimes an equation does not merely describe reality. It tells us that reality contains more than human intuition allowed.

( 📷 1932 cloud chamber photograph taken by physicist Carl Anderson, which provided the first direct evidence for the existence of the positron. )

[F.H. @_Don_Haag_]

@RikiRealEstate Bolsena

[John Ziegler @Zigmanfreud]

This video provides a really good explanation for why rank & file MAGA are stronger believers than the media/influencer class of MAGA, as well as why Penn Staters are, counter intuitively, the very worst subjects when it comes to learning that the “Penn State Scandal” is a fraud.

[F.H. @_Don_Haag_]

@MathiasPriebe Das entspricht einer Erhöhung vom Basiswert von 15,789%

[Massimo @Rainmaker1973]

When you start a chess game, you have 20 possible moves available. After the first full move (White then Black), there are already over 400 possible positions. By the third move, that number jumps to around 8,900, and after the fourth it reaches nearly 200,000.

By the time you get to move #40, the total number of possible games explodes to roughly 10⁴⁰, a number comparable to the total number of atoms in the observable universe.

[Simon Betschinger @SBetschinger]

Anleitung: So führt man ein Land in den Bankrott.

WELT: "Sozialstaat. Ich habe mir ausgerechnet, was ich mit Bürgergeld bekäme, und bin schockiert... komme ich auf eine gesamte Leistung des Staates an mich in Höhe von rund 70.000 Euro jährlich. Das ist netto für kaum einen Erwerbstätigen zu erwirtschaften."

Ein teuflisches Anreizsystem:

- Anreiz dem Arbeitsmarkt fernzubleiben
- Ummoralisch hohe Besteuerung von Arbeitnehmern reduziert deren Leistungsbereitschaft
- Anreiz für Einwanderung in die Sozialsysteme

[Anna Vero Wendland @VeroWendland]

Der ehemalige EnBW-Manager @UlrichGraeber im Gespräch mit @thinkBTO räumt reihenweise Legenden der Atomgegner ab & liefert auch einige Überraschungen, zB seine zutreffende Analyse, dass der Eso-Wahn vom „soft energy path“ der Grünen nur deswegen in der 🇩🇪 Ingenieursnation➡️

[sparbuchfeinde @sparbuchfeinde]

Die gesetzliche Rente wird in den nächsten 2-3 Jahren das sichere(!) politische Ende der beiden ehemaligen Volksparteien CDU und SPD einleiten.

Die Faktenlage dazu ist eindeutig. Die Realität zu niederschmetternd. Vor allem in Ostdeutschland.

Ein Thread.

[Mathelirium @mathelirium]

String Theory Lecture 2

In Conformal Gauge, the String Becomes a Wave Equation

Episode 1 showed the geometric jump

point particle -> worldline
string -> worldsheet

Episode 2 is the dynamical jump.

The Nambu-Goto action measures the area of the worldsheet,

S = −T ∫ dτ dσ √[−det hₐᵦ]

but the square-root determinant is awkward to work with. So we usually rewrite the same classical theory in Polyakov form,

S = −(T/2) ∫ dτ dσ √[−γ] γᵃᵇ ∂ₐXᵘ ∂ᵦXᵤ

Here Xᵘ(τ,σ) tells us where each point of the string’s worldsheet sits in spacetime, and γₐᵦ is the metric we put on the worldsheet.

The power of this form is that we can choose a convenient gauge. In conformal gauge, the equations of motion simplify to

(∂²/∂τ² − ∂²/∂σ²) Xᵘ = 0

So the string’s spacetime coordinates behave like waves living on the worldsheet.

The τ-derivative measures how the string changes in worldsheet time.
The σ-derivative measures how it bends along its own length.

For a closed string, σ is periodic

Xᵘ(τ, σ + 2π) = Xᵘ(τ,σ)

and the wave equation splits into two traveling pieces,

Xᵘ(τ,σ) = Fᵘ(τ + σ) + Gᵘ(τ − σ)

One family moves one way around the string and the other moves the opposite way. These are the left-moving and right-moving modes.

In the render, the bright loop is the string at the present moment. The glowing cylinder behind it is the worldsheet it has swept out. The cyan curves trace one traveling family, and the gold curves trace the other. They are the visual version of τ + σ and τ − σ.

Therefore, the theory has an internal wave equation, and its normal modes are the raw material for the string spectrum.

#StringTheory #TheoreticalPhysics #ConformalGauge #Worldsheet #WaveEquation #Physics #Mathematics #MathematicalPhysics #QuantumGravity #ScienceVisuals

[F.H. @_Don_Haag_]

@75Jamin https://t.co/IpvVHLhWHN

[Rothmus 🏴 @Rothmus]

1. Compared to what?

2. At what cost?

3. What hard evidence do you have?

Few ideas on the Left that can pass all 3.

Because there are no utopian solutions out there, only trade-offs.

The boundaries are defined by what we can tolerate.