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The slender little end is the smallest part of anything.
Note: First things first. This proverb is also an Irish version of the 80-20 rule. The 80-20 rule is based on the Pareto Distribution. Wilfredo Pareto discovered in the later part of the nineteenth century that about 80% of the wealth of a country is usually controlled by about 20% to 40% of the population. This skewed distribution of wealth has been generalized into other areas, e.g., 60% to 80% of revenues are generated by 20% to 40% of one's customers, 60% to 80% of any job is completed with the first 20 to 40% of effort. So don't start with the end of a job, with the tail of any job; jump into the meat of it first.
Note also: This weeks' proverb contains an idiomatic homage to St. Patrick, the patron saint of Ireland and the first bishop of Armagh. The phrase "cuid Pháidín don mheacain" is translated as "the smallest part (or share) of anything." It literally means "Patrick's share of the root." Páid is an abbreviated form of Patrick. Páidín is the diminutive form. So the allusion is to a young St. Patrick.
Young St. Patrick was a slave of an Antrim chieftain named Miliucc, who ruled an area around Slemish Mountain. Tending the flocks, far from his home in Celtic Britannia, he prayed and fasted for redemption. In Patrick's Confession, he wrote of a dream in which a voice told him "Thou fastest well, soon thy will go to thy Fatherland." He fled to Wexford where he convinced a sea captain to allow him to escape to the continent. In northern Gaul, young Patrick and his party wandered in a dessert on the verge of starvation. All were amazed that Patrick always eat less than his comrades. On the verge of starvation, Patrick convinced his party to pray for redemption. Shortly afterward, they chanced upon a wild herd of pigs.
Patrick brought this fasting devotion back to Ireland to his ministry of the Gaels. Each Lent, he would fast in solitude at "the places where no man dwells." In 441 B.C., for example, he climbed a steep mountain on the shores of Clew Bay in what is now County Mayo. There he abstained from meat and fasted, living on meager roots, for forty days and nights. Since then the mountain has been called Croagh Phádraig. Pilgrims climb this mountain every March 17 in his memory, some barefoot, others on their knees. His memory is further honored in the Irish idiom that equates "Patrick's share of the root" with the "smallest part of anything."