Chapter 11

Rocky Has Sonar

Passive echolocation and Fourier transform

Grace discovers Rocky doesn't see with light but with sound: passive echolocation. Aluminum is "transparent" to Rocky. Using Fourier analysis, Grace begins decoding the Eridians' musical language.

Sonar instead of vision: how Rocky "sees"

In the book

Rocky can't distinguish ink marks but can "see" through an aluminum plate. Grace deduces he uses passive sonar.

The science behind it

Humans perceive the environment with photons (light). Rocky uses sound waves. On his planet, with 29 atm of ammonia and possibly no surface light, optical vision never evolved.

Unlike bats and dolphins (active sonar: emit pulses and listen for echoes), Rocky uses passive sonar: his brain processes ambient sound bouncing off objects.

A thin aluminum sheet blocks nearly all light but transmits sound perfectly. To Rocky, the Hail Mary's metal hull is as transparent as a glass window to us.

Ink marks on a measuring tape produce no relief, so sonar can't detect them. Only physical relief is "visible" to sonar. That's why the Eridian clock has raised numbers (3 mm high).

Key terms

Echolocation
Perceiving the environment using sound waves. Active: emit and listen for echoes. Passive: only listen to ambient sound.
Passive sonar
Perception system that doesn't emit its own signals. Analyzes existing ambient sound.

Fourier transform: decoding the language

In the book

Grace installs Fourier analysis on his laptop. When Rocky speaks, the software shows each chord's frequencies.

The science behind it

The Fourier transform is an algorithm that decomposes any complex signal into its component frequencies. Record a piano chord, and the algorithm tells you exactly which notes compose it.

Human speech is chaotic: constantly changing formants, noisy consonants, blending vowels. It's hard to cleanly decompose.

Eridian chords have discrete, stable frequencies: each "phoneme" is a precise combination of notes. The Fourier algorithm identifies them unambiguously.

5 simultaneous notes in a chord implies 5 independent "vocal cords." Grace can transcribe each word as a list of numerical frequencies and build a dictionary.

Key terms

Fourier transform
Algorithm decomposing a signal into pure frequencies. Fundamental in audio, image, and signal processing.
Formant
Resonant frequency of the vocal tract. Different formant combinations produce different vowels.
Phoneme
Minimum sound unit in a language. In English: /a/, /b/, /k/... In Eridian: frequency chords.

Try it yourself

Fourier Visualizer: Eridian Language

Select notes to create an Eridian "chord." The Fourier transform decomposes sound into frequencies.

261.6
293.7
329.6
349.2
392
440
493.9
523.3