How much can one trial teach?
Separate surprise from learning, watch mass cancel Fisher curvature, and find pi in the price of coding an unknown coin.
Explore the survey 18 min All fields By Field · Formal worlds Survey · 2 interactive demos Survey · 2 interactive demos Survey · 2 interactive demos Survey · 2 interactive demos With an interactive demo Survey · 2 interactive demos Survey · 4 interactive demos Survey · 2 interactive demos Survey · 2 interactive demos Survey · 2 interactive demos Keep crossing boundaries
Information Theory
What survives a summary, a code, or a noisy channel?
Follow evidence geometry into learning, compression, noisy channels, and quantum messages.
8 readings · 3 subfieldsEntropy & distinguishability
How much can a trial teach, and how distinguishable are two messages?
Entropy · Mutual information · Rate-distortion theory
When a channel carries mass
Read channel overlap as cone mass, turn a Lorentz factor into an error exponent, and discover when forgetting labels costs information.
Explore the survey 22 minHow life prepares for an uncertain world
Let a receptor learn by waiting, then grow a population across two possible futures.
Explore the survey 15 minHow far apart are two quantum messages?
Turn a quantum receiver, derive a mass-to-error law, and discover how one average state can hide many different messages.
Explore the survey 17 minMove to ask a better question
Move a sensor, combine cues, and discover what the next reading can reveal.
Read the article 12 minA compass can hide two destinations
Compare directional populations that share one average but tell different stories.
Explore the survey 10 minPhysical Statistics
Connect probability, momentum, and learning through four interactive statistical experiments.
Explore the survey 25 minCodes & channels
How do cone mass and rapidity enter the work of a code?
Compression · Universal coding · Channel coding
How much can one trial teach?
Separate surprise from learning, watch mass cancel Fisher curvature, and find pi in the price of coding an unknown coin.
Explore the survey 18 minWhen a channel carries mass
Read channel overlap as cone mass, turn a Lorentz factor into an error exponent, and discover when forgetting labels costs information.
Explore the survey 22 minA decoder that computes in rapidity
Build a decoder from two cone operations: multiply velocities to check parity, add rapidities to combine messages, and watch information polarize.
Explore the survey 17 minQuantum information
How does a quantum message become distinguishable from another?
Quantum information theory · Entanglement · Mixedness