Start with a shape you can reason about.
Use a familiar surface to build an intuition for paths, symmetry, and dimensions—then carry that intuition into spacetime geometry.
Find your next visual question
There is no required background. Begin with a surface, a path, or a projection—whichever makes you curious.
Mobius Strip
Twist a strip until it has one continuous side.
chi = 0, non-orientable Open the model →Klein Bottle
Walk around a closed non-orientable surface with no interior.
chi = 0, no inside/outside split Open the model →Crosscap Particles
Explore particle-like topology from compact non-orientable defects.
Pin structure, holonomy labels Open the model →Real Projective Plane
See antipodal identification through a Boy surface immersion.
S2 / (x ~ -x) Open the model →Closed Curves
Trace homotopy classes and holonomy around compact surfaces.
loops, winding, transport Open the model →4D Immersions
Project a rotating four-dimensional frame into ordinary 3D.
projection from R4 to R3 Open the model →Geometry is a way to ask better questions.
These models introduce the visual language behind a research hypothesis: particle-like behavior may arise from persistent geometric and topological structure, not only from objects placed in space.
Read the hypothesis in plain language, then follow the references when you want the mathematical detail.
Read the hypothesis