Every way of seeing the world

Dichromatic — two cones, no red — plus a tapetum lucidum that returns photons to the retina for a second pass.

S(λ) = exp(-((λ - λ_peak)² / (2σ²))) ; tapetum_gain ∈ [1, 130]

16 photoreceptor channels spanning 300–720 nm plus 4 polarization channels. UV-fluorescent patches that humans see as plain coral light up as blue-violet glow in the mantis view.

S_n(λ) = exp(-((λ - λ_n)² / (2σ²)))   for n ∈ {1, …, 16}

Trichromat with UV — three Gaussian cones at 350, 440, 540 nm replace human RGB. Flowers paint UV-reflective "nectar guides" invisible to us; for the bee, every sunflower has a runway.

S_uv(λ), S_blue(λ), S_green(λ) = exp(-((λ - λ_n)² / (2σ²)))

Active sonar. The bat broadcasts an ultrasonic chirp and ranges the world from the round-trip echo time. The world's first FMCW radar — 50 million years old. Five EML files: chirp, echo, Doppler, beam, matched filter.

range(t) = c · Δt / 2 ;   c = 343 m/s

Underwater FMCW sonar — the same matched-filter math the bat uses, but at 1500 m/s in seawater instead of 343 in air. ~4.4× the reach for the same time budget; click rate ramps up as targets close in.

range(t) = c · Δt / 2 ;   c = 1500 m/s

Asymmetric ear placement — one higher than the other — turns the inter-aural time delay into a 3D localization vector. Hunts mice in pure darkness, by sound alone.

Δt = d · sin(θ) / c   ⇒   θ = arcsin(c · Δt / d)

300 M olfactory receptors vs the human 6 M, plus a stereo-nostril gradient cue. Trace explosive plume invisible to human noses; legible to dogs across the test domain.

r(c) = c / (c + K_d)   (Michaelis-Menten)

The web is the sensor. Standing waves, mechanical bandpass filter, direction-of-arrival from inter-radial delay, prey-vs-wind classifier from frequency content. Passive analog signal processing.

G(f) = 1 / √(1 + ((f² - f₀²) / (f · Δf))²)

The ampullae of Lorenzini detect electric fields down to 5 nV/cm. A buried fish is invisible in turbid water but its bioelectric dipole pulls the shark in to within 30 cm.

|E| = p · |cos θ| / (4πε r³)

Active electroreception — the eel generates its own dipole field and reads how nearby objects distort it. Conductive prey raise |E| at the skin electrodes; insulating rocks lower it. Inverse problem: object class from the polarity of the perturbation pattern. Impedance imaging.

ΔE / E ≈ Γ · (a / r)³ ,  Γ = (σ_obj − σ_w) / (σ_obj + 2σ_w)

Cryptochrome proteins in the retina form radical pairs whose recombination rate depends on Earth's magnetic field direction. Quantum biology you can fly with.

Φ(B,θ) = ⅓ + (2/15)κ(3·cos²(θ) - 1)

The loreal pit organ is a biological bolometer — a thin membrane suspended in air, heated by IR radiation, sensed by mechanoreceptors. 0.003 °C resolution.

B(λ, T) = (2hc² / λ⁵) · 1 / (exp(hc / λkT) - 1)   (Planck)