Milo interactive mathematics landscape.

MILO / LIGHT LESSON

Mathematics

A shared language.

Move the light and follow its path to the eye.

SOURCEPATHSURFACEFIELDSIGHTINFERENCE
MOVE THE LIGHT
MODEL MODEL · GEOMETRIC OPTICS · RAY PATHS

CONTINUE THE STUDY

Papers and
instruments.

The papers set out the mathematics and its limits. In the instruments, you can change a variable and follow what happens.

MILO / RESEARCH & EXPLORATION

THE COUPLING LENS

Read by sweep and return.

A one-holed hyperbolic surface used to read by sweep and return.

DERIVED GEOMETRY · PROPOSED READING

MILO / RESEARCH & EXPLORATION

APPROACH GEOMETRY

Follow the approach to a basin.

How unabsorbed factors create flat regions and affect basin commitment.

GRADIENT-FLOW ANSATZ · NUMERICAL STUDY
α(d, β)= 1 + d/(d + β)β = 6/23 · CONVERGENCE, NOT COMPLETION

MILO / RESEARCH & EXPLORATION

A COUPLING CALCULUS

A proposed calculus for asymmetry.

Read asymmetry and stop when the estimate converges; the system may still change.

PROGRAMME · NOT A THEOREM

MILO / RESEARCH & EXPLORATION

THE LASER READ

Reconstruct a field from line integrals.

Line integrals become a reconstructed field.

COMPUTED CT · SYNTHETIC INPUT
OPEN FULL COMPOSITION ↗︎

MILO / RESEARCH & EXPLORATION

TWO LIVE MAPS

Compare paths from a finite sample.

A path can be sampled and still remain unresolved.

MODELED · FINITE SAMPLE
OPEN FULL COMPOSITION ↗︎

MILO / RESEARCH & EXPLORATION

THE PERIODIC ATLAS

Follow the elements along a helix.

Hydrogen anchors an authored helical ordering.

AUTHORED HYPOTHESIS · MODELED DISPLAY

Path

A source emits light. A varying refractive medium changes its geometric-optics path.

Surface

Local geometry supplies surface normals. Material response reflects, scatters, or transmits incoming light. Topology describes global connections rather than optical bending.

Field

An analytic one-dimensional vacuum pulse shows perpendicular electric and magnetic fields travelling together.

Sight

The eye samples incoming light. Photon-like points represent idealized detection events, not known microscopic trajectories.

Inference

Perception infers a world from incomplete optical evidence.