Now, of course I had no option but to post a just-found formista quote that links conceptualization and algebra with genius to spare. I’m predictable and then some.
Conceptualization is man’s method of organizing sensory material. To form a concept, one isolates two or more similar concretes from the rest of one’s perceptual field, and integrates them into a single mental unit, symbolized by a word. A concept subsumes an unlimited number of instances: the concretes one isolated, and all others (past, present, and future) which are similar to them.
Similarity is the key to this process. The mind can retain the characteristics of similar concretes without specifying their measurements, which vary from case to case. "A concept is a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted."
The basic principle of concept-formation (which states that the omitted measurements must exist in some quantity, but may exist in any quantity) is the equivalent of the basic principle of algebra, which states that algebraic symbols must be given some numerical value, but may be given any value. In this sense and respect, perceptual awareness is the arithmetic, but conceptual awareness is the algebra of cognition.
Ayn Rand, Introduction to Objectivist Epistemology
Dr. Leonard Peikoff, The Philosophy of Objectivism: A Brief Summary PDF
I shall read Ayn Rand soon, I can feel it’s just about the right momement for us to meet. (She surely is one polemical woman: there’s no shortage to people advising you against her and her massive — as in, it has so many damn references ((~100) that it needs two-columns for footnotes — ↓pedia↓ is currently protected until the bickering quiets down.))