Subhash Bhardwaj

Air Veteran

[Rishi Bagree @rishibagree]

Just one common man was enough to neutralise the entire Umar Khalid gang

[Tech with Mak @techNmak]

Richard Feynman called Euler's formula "the most remarkable formula in mathematics."

And there's a fascinating engineering reason why this equation is so important.

e^(iθ) = cos(θ) + i·sin(θ)

It connects exponential functions, imaginary numbers, trigonometry, and rotation through a single mathematical relationship.

But its usefulness goes much further.

Consider a sinusoidal signal:
x(t) = A cos(ωt + φ)

Using Euler's formula, we can represent it as the real part of a complex exponential:
A e^(i(ωt + φ))

Why would engineers use this representation?

Because differentiating e^(iωt) simply multiplies it by iω. Phase shifts can be represented through complex multiplication.

For linear, time-invariant electrical circuits in sinusoidal steady state, this allows differential equations to be reduced to algebraic equations.

Engineers use this mathematics in phasor analysis, AC circuit calculations, impedance, and frequency-response analysis.

The same complex-exponential representation is fundamental to Fourier analysis, signal processing, communication systems, and the study of mechanical vibrations.

Feynman also described the complex-plane representation of numbers as the unification of algebra and geometry.

And that's what makes Euler's formula so remarkable.

An equation connecting imaginary numbers and circular motion provides a practical way to analyze real electrical signals, oscillations, and physical systems.

[Zentrale Ermittlungsstelle @ZentraleV]

Das Wort zum Sonntag:

Islamist: Wer sich so kleidet, begeht eine Sünde.
Frau: Es gibt 54 muslimische Länder, und trotzdem kommen sie zu mir nach Hause und behaupten, Speck und Hunde seien anstößig. Tut mir leid, aber die können sich zur Hölle scheren.

[Selfless Cricket @SelflessCricket]

Every Hindu in Kerala needs to watch this video. I repeat, every single Hindu in Kerala needs to watch this video.

[Ashok Shrivastav @AshokShrivasta6]

Thank You Neha

[The Universe @TheUniverse_CBS]

You are not the same person after you've seen aurora explose like this-dancing all around you in the sky.

You will remember, and you will want more!

Last September on our aurora tour!

[desi mojito @desimojito]

Pakistanis and Bangladeshis protesting in London against Gyanesh Kumar because their names were deleted from the voter list 😂😂

[Deliriumm @0xDeliriumm]

ashish vaswani - indian-american researcher at google brain - published "attention is all you need" in june 2017 with 7 co-authors. the paper introduced the transformer architecture, the self-attention mechanism, and multi-head attention in 15 pages. it has been cited 140,000 times. it created a $4.6T industry. none of the 8 authors fully understood what they had built.

this october 2026 paper is the first document that shows exactly what happens inside the model they created - layer by layer, token by token, attention head by attention head.

P(x_{t+1} | x_{≤t}) = f_θ(x_{≤t}). one equation. the entire intelligence of GPT-4, claude, gemini reduces to this. predict the next token. repeat.

somewhere between the repetition and the scale, something that looks like understanding appears.

input text enters as tokens. each token becomes an embedding vector. the sequence passes through N transformer blocks - each applying h = σ(Wx + b). layer after layer. the network is not reading. it is computing.

the attention mechanism is where it stops being a calculator. Attention(Q,K,V) = SoftMax(QK^T/√d_k)V. every token votes on every other token simultaneously.

"the future of AI is" doesn't process left to right. all five tokens attend to each other in one matrix operation. the model outputs a probability distribution. tomorrow: 0.42. brighter: 0.28. more: 0.18. one token chosen. repeat 500 times per response.

layer 1 encodes surface features. layer 8 encodes syntactic structure. layer 16 encodes semantic clusters. layer 32 encodes abstract concepts.

nobody designed this. it emerged from gradient descent across billions of parameters.

below 10^9 parameters - flat performance curves. above 10^10 - non-linear jumps in reasoning, code generation, language understanding. capabilities that weren't present at smaller scale suddenly appear. not gradually. as phase transitions.

google paid vaswani to write a paper about sequence transduction. he accidentally wrote the architecture every major AI lab has been scaling for 9 years.

vaswani left google in 2023 to start his own company. the paper he left behind is the foundation of $4.6T in market value.

the 8 researchers who wrote it in 2017 didn't know what they had.

this paper does.

save this.

[Sandhya Yadav @Sandhyayadav_1]

सुन लो चमचों और तिलचट्टों ये भी एक देश की #GenZ है..

#NarendraModi #PmModi #SanatanDharma #RahulGandhi #Cockroach

[SanataniRiddhi @Ridhu417Sharma]

हम हिन्दू है तो मुल्ली तू मनुस्मृति लाएगी?🧐

[Pakistan Untold @pakistan_untold]

When I counter-question your faith: BLASPHEMY!
When you mock my faith: COMEDY!

Pakistani Hindus: 😢

[Kreately.in @KreatelyMedia]

Asgar Ali, Afjal Ali, Afser Ali, Haider Ali, and Sarwar Ali arrested for destroying Durga Puja pandal.

📍Dengahri Jamalpur, Manikpur, Pratapgarh, UP

[Amy Mek @AmyMek]

Islam’s War on the West

Bullets in France, Ballots in America - And America Is Worse Off!

France is being taken over physically and violently - churches burned and vandalized, riots, no-go zones. You can still see it happening.

America is WORSE OFF because the same process is quieter and further advanced. Churches are bought and converted. Parallel communities are built. They capture schools, political offices, and laws from the inside.

They skip the bullets because Americans are armed, so they use ballots, real estate, and institutions instead.

France had 8 mosques in 1975. Now 2,600.

America went from ~100 to over 4,000.

In France, the takeover is still physical and visible. In America, a larger one is already happening from within, and most people still don’t grasp how far it’s gone.

This November, Americans need to vote like their lives depend on it.

[Dr. Eli David @DrEliDavid]

As France is burning, I keep thinking of what the UAE Foreign Minister said a few years ago 👇

He accurately predicted this.

[MATLAB @MATLAB]

How can a collection of sine waves become a sawtooth wave?

This MATLAB visualization, created with the MATLAB Agentic Toolkit, shows how a Fourier series is built one harmonic at a time.

As each harmonic is added, you can watch the waveform take shape 🌊⤵

[Trisha @GoldWisdomh]

In Hinduism, Kāma is not just lust or sexual desire.

It's part of a 4,000-year-old conversation about what makes human life worth living.

Ancient Hindu thinkers described FOUR fundamental aims of life.

And know the surprising part? Read it.

1. The Four Aims of Life

[Dr. Suresh Chavhanke “Sudarshan News” @SureshChavhanke]

फराह खान को सेक्युलर बताने वालो देखो

[Trishul Warrior @Trishulwarrior]

A pattern reminiscent of 'grooming gangs' has emerged in India; a 15-year-old Dalit girl, who had gone missing from the holy city of Ujjain, has been found in Indore.

The girl, who belongs to a Hindu family, had gone missing two days earlier. When the police arrived in Indore in search of her, they were shocked to find her wearing a burqa.

Upon questioning the accused, it was revealed that six months ago, a man named Iman had lured the girl into a romantic trap, established a physical relationship with her, and subsequently abandoned her. Following this, Iman had tasked his friend, Moin, with keeping tabs on the girl.

During this period, the girl's Muslim female friends attempted to influence and incite her, ensuring that the relationship remained undisturbed.

Subsequently, Moin and his family members quietly sent the girl to the homes of their relatives in Indore—a process in which two of her Muslim female friends provided full assistance.

The police discovered that the girl had been learning Islamic customs for some time, with the help of her Muslim female friends.

Note: The image has been generated using AI and is provided for illustrative purposes only.

[Math Pulse @themathpulse]

An umbrella drawn by two chains of rotating circles, one setting x and the other y. One circle per axis is off by up to 34.4% of its height, 10 circles by 5.17%, 100 circles by 0.422%.