"So what are you actually trying to say about Straight Lines and Trinities?"
If you think of breeze and the sails of sailing ships you might be able to think of breeze as influence. If you then address Charles Pierce's Semiotics - signs, symbols and communication - where he insisted that "action, or influence, which is, or involves, a cooperation of three subjects, such as a sign, its object, and its interpretant, this trirelative - three related subjects - are an influence that cannot be resolved into actions between pairs." You might now conclude that minds are propelled by a breeze called triads or trinities that use words as symbols as they are blown into the corridors of meanings. And here, you as the interpretant are a third participating influence, or breeze along with the sign which is the word CAT and its object, an actual breathing cat that needs to be fed or whatever.
Unlike de Saussure, who concentrated his poststructural thinking on language around the signifier - the spoken word C-A-T - and the signified - the abstract image and understanding of cat that dwells in your mind - Pierce was of the opinion the whole combination that connects the cat form to the cat idea - the you - should not be underestimated and therefore in the study of semiotics there was a tri-relative - three related subjects - influence that could not be resolved by the actions of bi-relative - two related subjects.
Pierce died in 1914, de Saussure died in 1913.
"And your point?"
Since those days, not so long ago, scientists of the mind and their terrifying machines, have determined that when the brain is engaged in routine task-solving, or cognitive custom and practice, it relies on predictable, boring apparently linear pathways that draw straight lines from Problem A to Solution B through a tri-relative process. (1) the Problem, (2) The solution, and (3) the subject, you or I, who more often has already mentally examined, carefully shelved and sanctified the solution to the problem long enough for it be classified as a habit of thinking that has achieved the status of "True."
So when stuck in a loop of depression, or stuck in the loop of a failing belief system of predetermined solutions, those "There is no alternative" doctrines of the locust relieve common sense of its purpose by maintaining a triad that keeps the line straight, endless, unchanging until blessed release produces no actual somewhere else to go.
But when the brain stops to actually think, it enters a genuinely creative state which neuroimaging suggests is a radically non-linear series of events. The brain turns to the wishy-washy parts responsible for daydreaming, sometimes called memory-blending, and explores the glory of unconstrained association.
To do this, a mind intentionally breaks the triadic logic of "Given A and B, C must follow." The straight lines are gone, replaced by friction, anxiety, ambiguity, and a wandering that allows thoughts to drift out into the wilderness where unexpected connections hide behind or under rocks waiting to be presented as a possibility, sometimes called "hope" or "dreaming" or "the solution."