The matrix of abstract thought

The following paragraphs are from section 4.3 “The child is father to the man” in “The Evolution of Cognition” [1]:

In general we assume that the growth of thinking and knowledge in individuals is epigenetic, that later mechanisms of thought are constructed from the materials made available by earlier mechanisms (Benzon and Hays 1988: 314-319). In particular we remain partial to the concept of stages pioneered by Jean Piaget (Piaget and Inhelder 1969). The abstractions one begins learning in adolescence are based on the more concrete structures of thought acquired earlier. The preadolescent matrix will vary from rank to rank.

Let us begin by considering Rank 2. The child of Rank 2 parents will be exposed to the Rank 2 cultural environment of those parents. Much of that world will be as mysterious to the Rank 2 child as the world of Rank 1 adults is mysterious to the Rank 1 child. But, for example, the Rank 2 child can see his parents read and write, while the Rank 1 child cannot, for that is a mystery which doesn't exist in the Rank 1 world.

Consider, specifically, the language to which a Rank 2 child is exposed. It will have a more deeply developed system of superordinate and subordinate categories, including categories such as plant and animal. The child may not have an immediate grasp of the conceptual structure underlying these categories—such ontological knowledge develops gradually (Keil 1979) — but he or she can learn to use those words correctly in many contexts and that knowledge will be a good foundation on which to construct the appropriate abstract justification for the categories. The conceptual environment of the Rank 2 child is thus significantly different from that of the Rank 1 child, and the difference is of the sort which will make it easier for the Rank 2 child to acquire the abstractions necessary for a Rank 2 adult.

Consider the world of a very young child. In our culture (21st century America) the child will be playing with alphabet blocks before she can talk. She won’t understand the significance of those images, but she will be thoroughly familiar with them. Similarly, she will be familiar with simple picture books. This is laying a foundation, a matrix, that eases the way for reading and writing a few years later.

My guess is that it will be difficult, though perhaps not impossible, for an adult of rank N to acquire ideas of rank N+1, certainly more difficult than raising a child to N+1 thought in a rank N+1 environment. Why? Because that rank N adult will not have a N+1 preadolescent matrix.

This has some bearing on the difficulty of paradigm change (in Kuhn’s sense). Changing from one paradigm to another within a given rank will be easier than changing from a paradigm of rank N to one of rank N+1. How many of the cases considered by Kuhn involve rankshift between paradigms vs. change from one paradigm to another within rank? I’m guessing that most of them were rankshift changes. That’s what’s difficult, moving from one rank to another.

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Here’s the last two paragraphs from “The Evolution of Cognition”:

We expect childhood exposure to computing to have a similar effect. But we do not as yet see anything significant happening on a large scale. There may be computers in every primary school in the nation, and in a small percentage of homes, but children do not spend much time on these computers. And most, if not all, of the time they do spend is devoted to using the computer in the most superficial way, not in learning to program it. And that, programming, is where the major benefit lies. It is in programming that the child has to deal with control structure, the element which is new to Rank 4 thought.

We know that children can learn to program, that they enjoy doing so, and that a suitable programming environment helps them to learn (Kay 1977, Pappert 1980). Seymour Pappert argues that programming allows children to master abstract concepts at an earlier age. In general it seems obvious to us that a generation of 20-year-olds who have been programming computers since they were 4 or 5 years old are going to think differently than we do. Most of what they have learned they will have learned from us. But they will have learned it in a different way. Their ontology will be different from ours. Concepts which tax our abilities may be routine for them, just as the calculus, which taxed the abilities of Leibniz and Newton, is routine for us. These children will have learned to learn Rank 4 concepts.

How many of the people currently running the world – in government or private industry – grew up programming computers from a young age, before adolescence? Very few, I warrant, very few.

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[1] William Benzon and David Hays, The Evolution of Cognition, Journal of Social and Biological Structures 13(4): 297-320, 1990, https://www.academia.edu/243486/The_Evolution_of_Cognition.