mush n.

"soft mixture, mass of ingredients beaten or stirred together," late Old English *masc (in masc-wyrt "mash-wort, infused malt"), from Proto-Germanic *maisk- (source also of Swedish mäsk "grains for pigs," German Maisch "crushed grapes, infused malt," Old English meox "dung, filth"), possibly from PIE root *meik- "to mix."

Originally a word in brewing; general sense of "anything reduced to a soft pulpy consistency" is recorded from 1590s, as is the figurative sense "confused mixture, muddle." Short for mashed potatoes it is attested from 1904.

"to walk with measured steps or a regular tread," either individually or as a body, early 15c., from Old French marcher "to stride, march, walk," originally "to trample, tread underfoot," a word of uncertain origin. Perhaps from Frankish *markon or some other Germanic source related to Middle English march (n.) "borderland" (see march (n.2)). Or possibly from Gallo-Roman *marcare, from Latin marcus "hammer," via notion of "tramping the feet."

The transitive meaning "cause to march, cause to move in military order" is from 1590s. Sense of "cause (someone) to go (somewhere) at one's command" is by 1884. Related: Marched; marching. Marching band is attested by 1852. Italian marciare, Spanish marchar are said to be from French.