Every fit tells two lies. A rigid model — a straight line — is too stiff to trace a curved law, so its fits all miss the same way no matter which sample they see. That systematic miss is bias.
A flexible model — a high-degree polynomial — is supple enough to thread every point, so it chases the random noise. Re-roll that noise and its fit lurches somewhere new. Puff the bellows and watch the ghost fits fan out: that spread is variance.
Test error is bias² + variance + irreducible noise. It dives as you add flexibility, then climbs as variance takes over — the U-shaped curve at the heart of the field. The lowest point is the sweet spot.
The ridge dial (L2 regularization) shrinks the coefficients toward zero, trading a sliver of bias for a large cut in variance. It crushes the fan without ever lowering the degree — which is exactly why ridge regression exists.
The simulation stopped unexpectedly — the lesson continues without it. You can move on; nothing you did was wrong.