BerkhJadamba

Welcome to the things I love. As you scroll, I will tell you why each one pulls me in, how it leads to the next, and what I have made along the way.

r 24.00 rstime ×1.02

rs=2GMc2r_s = \frac{2GM}{c^2}dτdt=1−rsr\frac{d\tau}{dt} = \sqrt{1 - \frac{r_s}{r}}

Past the photon sphere, at 1.5 Schwarzschild radii, light itself can orbit.

Beyond the horizon every path leads inward. Let’s go through.

01 Cosmos

On the other side, a universe.

≈ 380,000 years

  1. First light

    The universe cools enough for atoms to form and light streams free. We still see it: the cosmic microwave background.

    T∝1aT0≈2.725 KT \propto \frac{1}{a} \qquad T_0 \approx 2.725\,\text{K}

  2. The first stars

    After the dark ages, gravity gathers hydrogen until the first stars ignite.

    MJ∝T3/2ρ1/2M_J \propto \frac{T^{3/2}}{\rho^{1/2}}

  3. The cosmic web

    Dark matter and gas collapse into filaments and clusters, while space itself keeps expanding.

    H2=8πG3ρ−kc2a2+Λc23H^2 = \frac{8\pi G}{3}\rho - \frac{kc^2}{a^2} + \frac{\Lambda c^2}{3}

  4. Today

    Galaxies strung along a web of filaments and voids. Move your cursor — you are a gravitational well now.

    v=H0 dH0≈70 km/sMpcv = H_0\, d \qquad H_0 \approx 70\ \tfrac{\text{km/s}}{\text{Mpc}}

Move to bend spacetime · press and hold to deepen the well

Olympiad platformLive

Astrolemma

An astronomy problem bank for olympiad preparation.

Astrolemma offers astrophysics problem sets, solutions and resources for olympiad preparation — built for students who want to think like astrophysicists.

Tags: Astrophysics · Education · Web

02 Powers of ten

Down the scales.

Thirty-nine orders of magnitude, from a galaxy to a quark. Every object is drawn at its true relative size — keep scrolling.

10²¹ m

A spiral galaxy

A hundred billion stars or more, wound into spiral arms and held together by gravity — most of it dark matter.

v(r)=GM(r)rv(r) = \sqrt{\frac{G M(r)}{r}}

10¹² m

The inner Solar System

Four rocky planets, a belt of debris and Jupiter. Sunlight takes about 43 minutes to reach it.

T2=4π2GM a3T^2 = \frac{4\pi^2}{GM}\, a^3

Click empty space to launch a comet

10⁷ m

Earth

12,742 kilometres across. Most of its atoms were forged inside earlier generations of stars.

g=GMR2≈9.81 m/s2g = \frac{GM}{R^2} \approx 9.81\ \text{m/s}^2

Click the Earth to step inside

10⁻¹ m

The human scale

Where physics turns into engineering — forces, materials and the things we build to extend ourselves.

σ=FA\sigma = \frac{F}{A}

Hover to flex · click to grip

10⁻⁹ m

Matter, ordered

Look closely at most solids, metals included, and you find atoms stacked in a repeating crystal lattice.

nλ=2dsin⁡θn\lambda = 2d \sin\theta

10⁻¹⁰ m

An atom

The electron does not orbit. It is a cloud of probability, |ψ|², shaped by its quantum numbers.

H^ψ=EψEn=−13.6 eVn2\hat{H}\psi = E\psi \qquad E_n = -\frac{13.6\ \text{eV}}{n^2}

Click to excite the electron

10⁻¹⁴ m

A nucleus

Protons and neutrons, tens of thousands of times smaller than the atom, bound by the residual strong force.

EB=Δm c2E_B = \Delta m\, c^2

10⁻¹⁵ m

Inside a proton

Two up quarks and a down, tied together by gluon fields. Stretch one: the field stores about 1 GeV per femtometre — roughly 16 tonnes of force.

V(r)≈−43αsr+κrV(r) \approx -\frac{4}{3}\frac{\alpha_s}{r} + \kappa r

Drag a quark to stretch the gluon string

≤ 10⁻¹⁸ m

Quarks

As far as any experiment can tell, they are points. The bottom of the ladder — for now.

Computational physics

Physics Simulation

Physical law, turned into something you can play with.

A physics simulation project: modelling a physical system numerically and visualising how it evolves in real time.

Tags: Physics · Simulation

Hardware prototypePrototype

3D Prosthetics Prototype

Engineering at the human scale.

A prototype prosthetic designed in 3D — where physics, materials and the human body meet.

Tags: 3D design · Prototyping · Engineering

03 Fields

Charge, field, light.

  1. Charge

    Up, up, down: +⅔ +⅔ −⅓. Charge fills the space around it with an electric field, and every other charge feels it.

    F=14πε0q1q2r2F = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r^2}

  2. Maxwell’s equations

    Four lines describe every electric and magnetic phenomenon. A changing magnetic field makes an electric one, and the reverse.

    ∇⋅E=ρε0\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}∇⋅B=0\nabla \cdot \mathbf{B} = 0∇×E=−∂B∂t\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}∇×B=μ0J+μ0ε0∂E∂t\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}

  3. Waves

    Shake a charge and the disturbance travels: E and B regenerating each other at the speed of light. That is what light is.

    c=1μ0ε0≈3.00×108 m/sc = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \approx 3.00 \times 10^8\ \text{m/s}

  4. Why electricity

    Four equations describe every spark, magnet and beam of light, and electrical engineering lets me build with them. The same physics fires inside every neuron, so the brain comes next.

Your cursor bends the field · click to shake the charges

Move to tune the wavelength · click to send a pulse

04 Neurons

Electricity, alive.

  1. The electrical cell

    A neuron is a living circuit: a membrane holding about −70 mV, with branches that gather input from thousands of others.

    E=RTzFln⁡[X]o[X]iE = \frac{RT}{zF} \ln\frac{[X]_{o}}{[X]_{i}}

  2. Action potential

    Push the voltage past threshold and the cell fires: a spike races down the axon to its synapses, then the cell rests.

    CdVdt=−∑igi(V−Ei)+IC \frac{dV}{dt} = -\sum_i g_i (V - E_i) + I

  3. A network

    Each spike nudges the next cell towards its own threshold. From that, somehow, come memory, attention and thought.

    Δwij=η xi xj\Delta w_{ij} = \eta\, x_i\, x_j

  4. Why the brain

    This is the part I love most. A brain is cells passing electrical pulses, yet it remembers, imagines and feels. Building machines that learn is how I try to understand it.

Hover a cell to make it fire · click to stimulate

05 Signal

Minds,
compiled.

spikes → bits

everything is information

information → networks that learn

hover a neuron · click or tap to run a forward pass

Machine-learning researchResearch

Sentiment Analysis for Mongolian

Teaching machines to read sentiment in the Mongolian language.

Machine-learning research on sentiment analysis for Mongolian — a low-resource language with comparatively few labelled datasets and tools.

Tags: Machine learning · NLP · Mongolian

06 Consciousness

Neuroscience, into AI, towards consciousness.

My long-term goal is to carry what we learn from the brain into artificial intelligence, and to study consciousness itself: the one horizon we look out from but never see.

Every journey here ends at a horizon. Let’s start the next one.

Neuroscience, AI, electromagnetism, simulations or olympiad problems: I’d love to hear from you.

Projects

4 entries · more on the way