This quotation, or rather the sense of it, is generally attributed to Heraclitus, a Greek philosopher of Ephesus (near modern Kuşadası, Turkey) who was active around 500 BCE. He proposed a doctrine that things are constantly changing, the flux doctrine.
The above quotation is attributed to Plato’s statement about Heraclitus’s work:
“Heraclitus, I believe, says that all things pass and nothing stays, and comparing existing things to the flow of a river, he says you could not step twice into the same river.”
(Plato Cratylus 402a, as cited in Graham, Daniel W., “Heraclitus”, The Stanford Encyclopedia of Philosophy (Fall 2015 Edition), Edward N. Zalta (ed.),
URL = <https://plato.stanford.edu/archives/fall2015/entries/heraclitus/>.
Graham (2015, op.cit. above), suggests however, that an interpretation of Heraclitus’s reference to the river, “is not that all things are changing so that we cannot encounter them twice, but something much more subtle and profound. It is that some things stay the same only by changing”. He suggests that, for example, a human body only achieves constancy, by virtue of its constant metabolism. Therefore while Heraclitus believed in flux, not as destructive of constancy, rather as a necessary condition of constancy.
This is an interesting concept related to the earlier exercise of the Square Mile, in which I tried to examine how environments change over time. However while the visual appearance alters, it could be considered that, in the case of my study, Glossop as a town remained constant – only by changing over time as economic and technological developments affected it.