I don't think of a straight string of dots as finding its "essence" in a straight line (sounds kinda metaphysical to me...). This suggests that dot strings find their "fulfillment" in the line. ("Analog" would be a better word than "fulfillment" here, IMHO.) Whatever the case, sometimes our problem requires that we think in terms of dots (points), and sometimes in terms of line. Thus the two are non-equivalent, and not in a condition where one's essence lies in or depends on the other. Point and line have meanings of their own, and typically are associated with different dimensions; point, zero dimensions; line, one dimension.
If you're interested in concept formation, I'd recommend Kant's Critique of Pure Reason (See, e.g., his remarks on synthetic a priori concepts), and not the Objectivist literature.
How come you slipped "divine intervention" into this piece? Just because I'm Christian? I feel reasonably sure that God is confident that the gift of reason He indued in me from creation is sufficient for me to handle problems like this.
betty boop. Of course you have the capability to identify and distinguish existents and to conceptualize patterns. You’re making my point. Most simple identification has been done subconsciously since you were an infant. Some is probably instinctual. But Plato and Aristotle didn’t have the science to understand molecules, forces, protons and neurons so they imagined otherworldly mechanisms (divine intervention) that reflected form onto matter or that allowed us to perceive an “essence” in it. Rand used the term “essence” tongue in cheek in that quote above.
That example of a line for instance… It’s composed of existents that we’ve distinguished and named electrons and protons. We’ve identified their various arrangements and forces in their relationships and named them molecules. We rearranged them into a new version of what we call pigments, and ordered them into a specific instance of a pattern that we conceptualize as a line. It’s an amazing process, but there’s no reason I’m aware of to believe that it doesn’t occur naturally. Absent that, evidence supporting natural explanations is compelling.
The term “divine intervention” is not a slight. There should be no problem with people believing in it, only with calling it evidence based. Just don’t misrepresent evidence supported natural explanations as misguided or faith-based. Have enough confidence in your ideology without needing to misrepresent mine.