Experiments

live demo

UUID v7 inspector

Generate a UUID v7 and watch the timestamp hiding in its first 48 bits. The reason your database indexes love them.

live demo

Diffie–Hellman playground

Watch two parties agree on a secret while you see every byte they exchange — then switch sides and try to break it as Eve.

live demo

Least squares playground

Drag the points around and watch the best-fit line argue back — then see the same fit as the bottom of a bowl-shaped loss surface.

live demo

Linear regression playground

Resample noisy data from a known line and watch the OLS fit jitter around the truth — with a confidence band and a cloud of fits that makes variance something you can see.

live demo

Gradient descent playground

Roll downhill on a loss surface: dial the learning rate up until the steps overshoot and diverge, and watch the trajectory pick its way across a bowl, a ravine, or a saddle.

live demo

Logistic regression playground

Slide two classes apart and watch a fitted sigmoid steepen into confidence — or overlap them and see it flatten as cross-entropy climbs. The decision boundary is a single point where the S-curve crosses one-half.

live demo

Cross entropy playground

Drag the predicted probability and watch the −log(p) loss spike — then push a predicted distribution against a one-hot truth and see cross entropy and KL react.

live demo

Softmax playground

Drag the logit bars, turn the temperature knob, and watch raw scores become a probability distribution that always sums to one — plus the log-sum-exp stability trick.

live demo

ReLU playground

Tilt the leaky slope to watch ReLU's variants morph near zero — then stack a handful of ReLU bumps into a piecewise-linear curve and tune it toward a target.

live demo

Adam playground

Race SGD, momentum, RMSProp and Adam across the same loss surface from the same start — and watch memory and per-parameter scaling earn their keep.

live demo

A matrix is a verb playground

Drag the four entries of a 2×2 matrix and watch it warp a grid live — the determinant is right there as the area it stretches or flips.

live demo

The four fundamental subspaces playground

Drag a target b around the output space and watch it fall inside or outside the column space — the reachable set — as the solvable/not-solvable badge flips.

live demo

The shadow of a vector playground

Drag the vector b and watch its shadow b̂ slide along a fixed subspace while the gold residual b − b̂ holds its right angle — projection you can feel with your hand.

live demo

Eigenvectors playground

Set a 2×2 matrix and watch which directions on the unit circle refuse to turn — the eigenvectors — then step power iteration onto the dominant one.

live demo

Positive definite playground

Set the three entries of a symmetric 2×2 matrix and watch the contour map of its quadratic form bend from a bowl to a saddle — with the eigenvalues and definiteness verdict updating live.

live demo

SVD playground

Set a 2×2 matrix and watch it map the unit circle to an ellipse in three acts — rotate, stretch, rotate — with the singular values as the ellipse's semi-axes.

live demo

PCA playground

Scatter a 2-D point cloud and watch its principal axes swing to follow — PC1 along the direction of greatest variance, PC2 perpendicular — then project onto PC1 and see how little of the story you lose.

live demo

RAIDZ1 reconstruction

Kill one disk in a single-parity stripe and watch it come back as the XOR of the survivors — then try to kill a second and watch the one equation refuse.

live demo

RAIDZ2 reconstruction

Take out two disks at once and watch RAIDZ2 solve a 2×2 system over GF(2⁸) — two independent syndromes P and Q, a nonzero determinant, one field inverse.