Diogenes Laertius: Stoic sound as spreading waves, and Epicurean motion below sense
Source: English Wikisource, R. D. Hicks’s 1925 translation, Book VII and Book X; local verbatim excerpt
.txt; retrieved and verified 2026-09-18. Metadata: Diogenes Laertius compiled in the third century CE, reporting Stoic doctrine from the third century BCE onward and quoting Epicurus (341–270 BCE) verbatim in Book X. The Epicurus letter is a primary document inside a later compilation, and the Stoic report is doxography rather than a quoted text. Extraction: footnotes and Greek glosses removed, section numbers kept in square brackets. Rights: Hicks 1925; Wikisource text. The repository already holds Book IX from the same edition.
What it supplies
A Greek wave theory of sound, three centuries before Praśastapāda. VII.158:
We hear when the air between the sonant body and the organ of hearing suffers concussion, a vibration which spreads spherically and then forms waves and strikes upon the ears, just as the water in a reservoir forms wavy circles when a stone is thrown into it.
That is the vīcī-santāna, the ripple series, in Stoic dress and with the same image, and it stands beside the Vaiśeṣika derivation of sound from sound. The collection therefore now holds the water-ring model of propagation in both traditions, which makes the convergence a datum rather than a recollection. The preceding sentence gives the Stoic account of sight by a cone of tensioned air, “the thing seen is reported to us by the medium of the air stretching out towards it, as if by a stick”, so the same passage has both modalities carried by a medium.
An explicit ancient statement that observed continuity of motion fails below the threshold of observation. Epicurus, Letter to Herodotus 61–62, after arguing that atoms all travel at equal speed through the void, “quick as the speed of thought”:
the atoms in the aggregates are travelling in one direction during the shortest continuous time, albeit they move in different directions in times so short as to be appreciable only by the reason, but frequently collide until the continuity of their motion is appreciated by sense. For the assumption that beyond the range of direct observation even the minute times conceivable by reason will present continuity of motion is not true in the case before us.
This is the closest ancient statement to what the theorems of this programme say about records. A motion that presents itself as continuous to sense is a succession at times below sense, and Epicurus names the fallacy of extrapolating the observed continuity downward. He draws the boundary where sense fails; the theorems draw it at a mesh computed from the mark cost.
Passage anchors
| Location | Text | Supplies |
|---|---|---|
| VII.157–158 | cone of air to the eye “as if by a stick”; hearing as a concussion that “spreads spherically and then forms waves” | Both sight and sound carried by a medium; the water-ring image |
| X.61 | atoms of every size travel at equal speed through the void when unobstructed | An ancient speed law for the unobstructed case |
| X.62 | continuity of motion appreciated by sense, denied at times “appreciable only by the reason” | Apparent continuity above a threshold, succession below it |
Coverage and limits
Reading level passage for the three locations;
metadata for the rest. The Greek is not stored, and Hicks’s
rendering of the Epicurean sentence is known to be difficult; a critical
text of the Letter to Herodotus, such as Arrighetti or Dorandi,
is what a close argument would need. The related Epicurean doctrine of
minimal parts of the atom, at Herodotus 56–59, is not covered
here, and Lucretius on the simulacra is not covered at all.