The hundred-eyed watchman
The fullest telling is in the first book of Ovid's Metamorphoses, the Latin epic he finished around AD 8. Jupiter had caught Io, daughter of the river god Inachus, under a blanket of dark mist, and when his wife Juno came down to see what the mist was hiding, he turned the girl into a gleaming white heifer. Juno admired the animal and asked for it as a gift, and Jupiter couldn't refuse without giving himself away. She handed the heifer to Argus, son of Arestor, to guard. His head was ringed with a hundred eyes, which took their rest two at a time, in turn, while the others stayed at their posts and kept watch (1.625–627). Wherever he stood he was looking at Io; even with his back turned, he had her before his eyes. From a mountain top he watched in every direction (1.666–667).
Jupiter sent his son Mercury, the Greek Hermes, to kill him. Mercury laid aside his wings and his cap, kept only his sleep-bringing wand, and came down as a herdsman driving goats and playing a pipe of reeds. Argus, charmed by the new sound, invited him to sit beside him on his rock. Mercury talked and played the day away, but however many eyes gave in to sleep, some stayed awake, and Argus asked how the pipe had been invented. So Mercury began the story of the nymph Syrinx, who fled from the god Pan and was turned into marsh reeds, from which Pan made the first pipe (1.689–712). Before the story was finished, every eye had closed (1.713–714). Mercury deepened the sleep with a stroke of his wand, struck Argus with a curved sword where the head meets the neck, and threw him bleeding from the rock. Centumque oculos nox occupat una, Ovid writes: one night takes all hundred eyes (1.721). Juno gathered them up and set them in the feathers of her bird, filling its tail with starry jewels (1.722–723). In the next book she drives her chariot through the sky behind peacocks, newly painted, Ovid adds, since Argus was killed (2.531–533).
The Greek writers disagree about almost every number. A fragment of the lost Aegimius, a poem attributed to Hesiod and quoted in the ancient marginal notes on Euripides' Phoenician Women, gives Argus four eyes that look every way, and says that sleep never fell on them. Aeschylus calls him the all-seeing, panoptēs (Suppliants 303–304), and in Prometheus Bound the myriad-eyed herdsman whose ghost still stings and hounds Io after his death (567–573). The Library attributed to Apollodorus says he had eyes all over his body, and gives him a career as a monster-slayer: he killed a bull that ravaged Arcadia and wore its hide, killed a satyr who stole the Arcadians' cattle, and caught the serpent-woman Echidna asleep and killed her (2.1.2). Its Hermes doesn't bother with music. Because an informer called Hierax had blabbed, Hermes couldn't steal the heifer quietly, so he killed Argus with a thrown stone (2.1.3). That, says the Library, is why he is called Argeiphontes, “slayer of Argus”, the name Homer already uses for Hermes (Iliad 2.103). And in Moschus's Europa, a poem of the second century BC, the peacock springs from the watchman's blood (lines 58–61).
However many eyes the tellers give him, every version agrees on the essential point: Argus never trusts a single eye. Each glimpse is noisy and some eyes are always asleep, yet the watch as a whole misses nothing. That's this course in one image. Every eye is a sample. One tells you little; the average of a hundred has a standard error ten times smaller than any single eye, and a likelihood tells you how much each glimpse should count. And notice how Hermes won. He didn't fight the eyes one by one: he told all of them the same story, until they failed together. Averaging defeats independent errors, not shared ones. If every pair of eyes makes errors with correlation , the variance of their average can never fall below , however many eyes you add.
How the battle works
Argus is made of every idea in this course: odds and evidence, distributions and sampling, variances of sums, the multivariate Gaussian, the laws of averages, maximum likelihood, information, priors and posteriors, and honest evaluation. The questions are drawn at random from a pool written for this battle, spanning all nine chambers. Many ask you to calculate, so keep pen and paper, or a Python prompt, within reach.
- Land 8 correct answers to close all of Argus's eyes.
- Every wrong answer costs one of your 3 lives. Lose them all and you retreat, but you can always return.
- There are no retries within a question. Think, then strike.
- Victory earns a large XP bounty, the Hermes's Lullaby badge, the legendary card The Peacock's Tail and your certificate of completion. Win without taking a single wound for an extra reward.
After the labyrinth
Look back at how far the thread has come. You began by weighing evidence, with odds that multiply and log-odds that add, and built a spam filter from them. You described uncertainty with distributions and learned to draw from any of them with nothing but uniform noise. You added up variances, and that arithmetic told you how to initialise a deep network. You read covariance matrices as ellipses and noised data the way a diffusion model does. You watched averages settle, and settle into a bell curve. You fitted models by maximum likelihood and found squared error and cross-entropy inside it, measured surprise in bits, derived the bound a variational autoencoder maximises, and watched priors turn into regularisers and posteriors into strategies. Finally, you learned to tell a real improvement from a lucky seed. That's the mathematics of learning from noisy data.
Your next labyrinth puts it to work. Neural Networks from First Principles builds a network from a single neuron and trains it, and this course runs underneath every step: the cross-entropy loss is a negative log-likelihood, a good initialisation is a variance argument, a minibatch gradient is a sample mean with a standard error, and the error bars on an experiment are standard errors too. You'll recognise the machinery on every page.