# ManySpace — a prerequisite map and study system for math, physics and AI

Canonical: https://manyspace.aporia.systems/
Updated: 2026-10-13

Choose a goal and see every prerequisite between you and it. Mathematics, physics and AI/ML, a daily plan, memory-model reviews and free interactive tools.

## Subjects

- [Mathematics](https://manyspace.aporia.systems/subjects/mathematics): From natural numbers and fractions through calculus, linear algebra, probability and proof.
- [Physics](https://manyspace.aporia.systems/subjects/physics): Mechanics, waves, electromagnetism, thermodynamics, modern physics, each tied to the mathematics it needs.
- [AI & ML](https://manyspace.aporia.systems/subjects/ai): Models, optimisation, neural networks and attention, with every prerequisite in the mathematics side visible.

## Free tools

- [Derivative Visualizer](https://manyspace.aporia.systems/tools/derivative): The derivative is a limit you can watch: shrink h and see the secant become the tangent.
- [Integral Explorer](https://manyspace.aporia.systems/tools/integral): The definite integral is just area — tiled, summed, and refined until the rectangles disappear into it.
- [Unit Circle Explorer](https://manyspace.aporia.systems/tools/unit-circle): Sine and cosine are not buttons on a calculator — they are the shadows of one point on one circle.
- [Complex Plane Explorer](https://manyspace.aporia.systems/tools/complex-plane): A complex number is an arrow: how far (modulus) and which way (argument). Multiplication turns and stretches.
- [Probability Lab](https://manyspace.aporia.systems/tools/probability): One flip tells you nothing. A thousand flips tell you p. Flip the coin and watch luck average out.
- [Bayes Lab](https://manyspace.aporia.systems/tools/bayes): A 95%-accurate test can still cry wolf 5 times out of 6. The crowd decides what a positive means — move the prior and watch.
- [Eigen Explorer](https://manyspace.aporia.systems/tools/eigenvectors): Most directions come out of a matrix bent. A few come out only stretched — turn v until you find them.
- [Fourier Series](https://manyspace.aporia.systems/tools/fourier-series): Every repeating wave is a stack of pure sines. Add harmonics one at a time and watch a square wave assemble itself — bumps, ringing, and all.
- [Projectile Motion Lab](https://manyspace.aporia.systems/tools/projectile-motion): Speed, angle, gravity — three knobs, one arc. Sweep them and find the angle that flies farthest.
- [Orbit & Gravity](https://manyspace.aporia.systems/tools/orbit): Every launch buys a fate: too slow falls home, just right loops forever, too fast never returns. Aim the arrow and scrub the flight.
- [Gradient Descent Playground](https://manyspace.aporia.systems/tools/gradient-descent): One walker, one bowl, one knob that matters. Find the step size that flies — and the one that explodes.
- [Loss Function Explorer](https://manyspace.aporia.systems/tools/loss-functions): Every loss is an opinion about error: MSE panics at outliers, MAE counts calmly, log-loss fears confident mistakes.
- [k-Means Visualizer](https://manyspace.aporia.systems/tools/k-means): Clustering is a loop, not an oracle: assign every point to its nearest center, move each center to its mean, repeat.
- [Logistic Regression](https://manyspace.aporia.systems/tools/logistic-regression): A straight line, a squash function, and two clouds of dots: draw the boundary by hand, then let gradient descent show you its own.
- [Forward Pass](https://manyspace.aporia.systems/tools/neural-network): Two inputs, three hidden neurons, one output — nothing hidden. Push an input and watch every neuron answer at once.
- [Backpropagation](https://manyspace.aporia.systems/tools/backpropagation): The forward pass makes a prediction; backprop decides how much to blame each weight. Follow one blame path from loss to weight.
- [Attention Visualizer](https://manyspace.aporia.systems/tools/attention): Attention is a spotlight: each word decides how much of every other word to mix into itself.
- [Tokenization Explorer](https://manyspace.aporia.systems/tools/tokenization): Type a sentence and watch a simplified toy tokenizer split it into pieces: suffixes peel off, numbers become digits, and tokens turn out to be neither words nor characters.

- [Pricing](https://manyspace.aporia.systems/pricing)
- [About](https://manyspace.aporia.systems/about)