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Your Universe of Digital Possibilities
A source is hidden in a patch of sky smaller than any telescope could resolve. Make the whole Earth into one: a handful of dishes, turning with the planet, each pair sampling one Fourier coefficient of the sky — and CLEAN drawing a black hole’s shadow out of the gaps. It is the scanner’s theorem pointed outward. Rebuild the sky from its fringes alone, then turn around.
The correlation of the signals at two points — two dishes — is the Fourier transform of the source’s brightness, read at their separation in wavelengths. An interferometer never sees the sky; it hears one coefficient of its transform per baseline, per moment.
The theorem The Scan runs on, read from the other side. A scanner sends its beam through a body and gets one spoke of the body’s Fourier plane per angle; a radio telescope scanned across the Sun in strips — Bracewell, 1956 — gets one spoke of the sky’s. Turn the scanner and the spokes fill the plane; let the Earth turn the baselines and the tracks do. The scanner and the telescope are the same theorem, pointed in opposite directions.
The finest detail a telescope separates is about the wavelength over its size — or, for an array, over its longest baseline. At 1.3 mm across the Earth that is some 25 micro-arcseconds: a grapefruit on the Moon. The shortest baselines set the largest scale it can see at all.
The dirty image is the sky convolved with the dirty beam B. Find its brightest point, subtract a fraction γ of the beam there, record a delta-function component; repeat. Then convolve the components with a clean Gaussian beam and add back the residual. It is a prior — the sky is a sum of points — and it fills the unsampled uv plane with it.
The dark disc is bigger than the horizon itself: any ray aimed inside the critical impact parameter bcrit is swallowed. Lensing magnifies the rs horizon into a √27 ≈ 5.2 rs silhouette — the ring the Event Horizon Telescope photographed in 2019.
This is the Orfeo Edition’s last shadow, and it closes the ring. Walk the ten back from here. The Void counted muons and waited for 5σ from every side; The Fix heard four clocks all wrong by the same amount; The Core read the Earth’s interior from times on a curve and its silence; The Line found a star’s make-up in the light it withholds; The Mirror took a known blur back out of a flawed telescope; The Hologram froze a wave’s phase into fringes; The Phase rebuilt a crystal from the magnitudes alone; The Pixel asked how few numbers can hold a picture. And here the dishes sample the sky’s Fourier plane along the tracks the Earth draws, and leave the rest — the dirty beam — exactly as The Scan left its missing wedge: the same theorem, the same null space, the scanner turned inside-out to face the sky. Every one of them saw only shadows; none turned around until the evidence was in.