bean (n.)youdaoicibaDictYouDict
Old English bean "bean, pea, legume," from Proto-Germanic *bauno (cognates: Old Norse baun, Middle Dutch bone, Dutch boon, Old High German bona, German Bohne), and related to Latin faba "bean;" Greek phakos "lentil;" Albanian bathë "horse-bean;" Old Prussian babo, Russian bob "bean," but the original form is obscure; perhaps from a PIE reduplicated base *bha-bha-

As a metaphor for "something of small value" it is attested from c. 1300. Meaning "head" is U.S. baseball slang c. 1905 (in bean-ball "a pitch thrown at the head"); thus slang verb bean meaning "to hit on the head," attested from 1910.

The notion of lucky or magic beans in English folklore is from the exotic beans or large seeds that wash up occasionally in Cornwall and western Scotland, carried from the Caribbean or South America by the Gulf Stream. They were cherished, believed to ward off the evil eye and aid in childbirth.

Slang bean-counter "accountant" recorded by 1971. To not know beans (American English, 1933) is perhaps from the "of little worth" sense, but may have a connection to colloquial expression recorded around Somerset, to know how many beans make five "be a clever fellow."
gulf (n.)youdaoicibaDictYouDict
late 14c., "profound depth," from Old French golf "a gulf, whirlpool," from Italian golfo "a gulf, a bay," from Late Latin colfos, from Greek kolpos "bay, gulf of the sea," earlier "trough between waves, fold of a loose garment," originally "bosom," the common notion being "curved shape." This is from PIE *kwelp- "to arch, to vault" (compare Old English hwealf, a-hwielfan "to overwhelm"). Latin sinus underwent the same development, being used first for "bosom," later for "gulf" (and in Medieval Latin, "hollow curve or cavity in the body"). The geographic sense "large tract of water extending into the land" (larger than a bay, smaller than a sea, but the distinction is not exact and not always observed) is in English from c. 1400, replacing Old English sæ-earm. Figurative sense of "a wide interval" is from 1550s. The U.S. Gulf States so called from 1836. The Gulf Stream (1775) takes its name from the Gulf of Mexico.
stream (n.)youdaoicibaDictYouDict
Old English stream "a course of water," from Proto-Germanic *straumaz (cognates: Old Saxon strom, Old Norse straumr, Danish strøm, Swedish ström, Norwegian straum, Old Frisian stram, Dutch stroom, Old High German stroum, German Strom "current, river"), from PIE root *sreu- "to flow" (see rheum).

From early 12c. as "anything issuing from a source and flowing continuously." Meaning "current in the sea" (as in Gulf Stream) is recorded from late 14c., as is the sense of "steady current in a river." Stream of consciousness in lit crit first recorded 1930, originally in psychology (1855). Stream of thought is from 1890.