Difficulty and Involution

noun

• An effort that is inconvenient.
  • usage: "I went to a lot of trouble"; "he won without any trouble"; "had difficulty walking"; "finished the test only with great difficulty"
  • synonyms: trouble
• A factor causing trouble in achieving a positive result or tending to produce a negative result.
  • usage: "serious difficulties were encountered in obtaining a pure reagent"
• A condition or state of affairs almost beyond one's ability to deal with and requiring great effort to bear or overcome.
  • usage: "grappling with financial difficulties"
• The quality of being difficult.
  • usage: "they agreed about the difficulty of the climb"
  • synonyms: difficultness

• (n.) Embarrassment of affairs, especially financial affairs; -- usually in the plural; as, to be in difficulties.
• (n.) A controversy; a falling out; a disagreement; an objection; a cavil.
• (n.) Something difficult; a thing hard to do or to understand; that which occasions labor or perplexity, and requires skill and perseverance to overcome, solve or achieve; a hard enterprise; an obstacle; an impediment; as, the difficulties of a science; difficulties in theology.
• (n.) The state of being difficult or hard to do; hardness; arduousness; -- opposed to easiness or facility; as, the difficulty of a task or enterprise; a work of difficulty.

noun

• Reduction in size of an organ or part (as in the return of the uterus to normal size after childbirth. )
• A long and intricate and complicated grammatical construction.
• Marked by elaborately complex detail.
  • synonyms: elaborateness, elaboration, intricacy
• The act of sharing in the activities of a group.
  • usage: "the teacher tried to increase his students' engagement in class activities"
  • synonyms: engagement, participation, involvement
• The process of raising a quantity to some assigned power.
  • synonyms: exponentiation
• The action of enfolding something.
  • synonyms: enfolding

• (n.) The state of being entangled or involved; complication; entanglement.
• (n.) The act of involving or infolding.
• (n.) The return of an enlarged part or organ to its normal size, as of the uterus after pregnancy.
• (n.) The relation which exists between three or more sets of points, a.a', b.b', c.c', so related to a point O on the line, that the product Oa.Oa' = Ob.Ob' = Oc.Oc' is constant. Sets of lines or surfaces possessing corresponding properties may be in involution.
• (n.) That in which anything is involved, folded or wrapped; envelope.
• (n.) The act or process of raising a quantity to any power assigned; the multiplication of a quantity into itself a given number of times; -- the reverse of evolution.
• (n.) The insertion of one or more clauses between the subject and the verb, in a way that involves or complicates the construction.