The phrase "hath one nose grindstone" may not be a common expression, but there are several synonyms that can convey a similar meaning. One such synonym is a "single-minded focus" on a particular task or goal. This means being fully committed and dedicated towards achieving one objective, without letting distractions or other priorities interfere. Another synonym is "tunnel vision," which implies a narrow and limited perspective, where only one thing is in focus, often to the detriment of other important aspects. Additionally, "obsession" can be a synonym as it refers to a strong and persistent fascination with something, often to the point of becoming unhealthily fixated on it.