Yes, there’s a lot of nonsense in universities; yes, there are a lot of people going to university that will benefit very little — if at all — from going there; yes, the [insert problem here] problem happens and it’s a shame.
But!
But nevertheless, there’s an important function for universities in the productive economy (as opposed to being long vacations for the rich that the non-rich get to enjoy by going into non-dischargeable-in-bankruptcy debt). And that function is more important for the middle-skilled than for the upper-skilled.
(Throughout this post we’ll be using “skilled” instead of “smart,” because smart misses a number of performance-determining factors. There’s an appendix covering those factors after the post.)
The usual logic is that universities should only be for the really skilled, with the middle-skilled going into trades or technical schools. And there’s nothing wrong with the trades or technical schools, especially with the extant shape of university education in some countries and their financing by sluicing guaranteed loans through the students.
But universities do two things that are of most importance to the middle-skilled: they develop advanced thinking tools (cognitive artifacts) and teach these to people who wouldn’t learn them otherwise.
Cognitive artifacts as multipliers of talent and skill
Let’s say we are budding digital circuit designers and have to build a circuit to implement a function of three inputs, the one in the left in this figure:
Because it’s the 1970s and we need to save electronic components, we first must simplify the function. This will be the problem used to illustrate the advantage of thinking tools (cognitive artifacts) here.1
If we don’t have tools designed to help humans simplify logic tables, we go back to first principles. (This is true for all domains, not just digital circuit design.) The first principles here are the rules of logic, so first we convert that table into a logic formula, using the digital circuit convention of multiplication for conjunction, sum for disjunction, and a bar for negation.
The top line of the middle column in the above figure is that function; to implement it directly we’d need three inverters, four 3-input AND gates, and one 4-input OR gate.
By applying the rules of logic, we can simplify that to the bottom line of the middle column, which requires only two inverters, two 2-input AND gates, and one 2-input OR gate. That’s a pretty good improvement.
Despite the simplicity of this example (which had to be simple for illustration), using the rules of logic is difficult and error-prone, and some people in the lower band of the middle-skilled distribution are prone to errors when manipulating symbolic formulas of all kinds.
Enter a cognitive artifact known as a Karnaugh map, illustrated on the right in the figure above.
Using a rote method to fill the map from the table, clustering the 1s by visual inspection (following some simple rules), and then translating the clusters into formulas (following some simple rules), makes it much easier to simplify the function.
The result is the same: the red cluster in the top half of the map is equivalent to the first two steps in the derivation using the rules, and the cluster in the bottom is equivalent to the last two steps. But unlike the rules-based derivation, they are obtained without thinking about the rules, just “fill the map and cluster the 1s.”
Cognitive artifacts: replacing thinking with rote work, to help achieve similar results.
Expanding the number of capable people by training
Using a cognitive artifact (Karnaugh maps) more people can simplify the function than those who can do so by following the rules of logic. And that’s the point of developing these artifacts: so that rote methods can be used to replace thinking, as much as possible.
For illustration let’s say we know distribution of the skill scores (talent, intelligence, skills) in the population; we’ll standardize it as an index, say it’s a Normal distribution with an average of 100 and standard deviation 15, like the one below (only half shown).
To illustrate the power of cognitive tools, let’s say only people with an index of 120 or above can simplify logic functions using the rules of logic. That means that only 9% of the population can do it.
Very few of these 9% of the population can develop a general-purpose tool (one in nine), and in the absence of a formal education system, for example in an apprenticeship system, only the apprentices of these one-in-nine out of 9% will learn the tool. That is if the master decides to share the secret, which isn’t guaranteed; and apprentices are likely to be selected from a limited catchment pool.2
Enter formal education with a research arm. Or as we like to call them, universities.
The numbers still apply, but once Karnaugh makes his maps known to the world, by publishing them (which is why that’s a requirement in academic environments), these maps can now be taught to many more people than those who could use formal logic.
If we assume that it takes a skill score index of 105 to learn how to use these maps, with the help of a teacher, teaching materials, practice problems, and time to practice (instead of doing work for the master, as apprentices do), we now have a situation where 37% of the population can simplify logic functions.
If we view universities as places where cognitive artifacts are created and taught, the idea that they should be “reserved” to the high-skilled gets turned on its head: it’s the expansion of the capabilities of the middle-skilled that has the highest impact.
Now, if only universities focussed on creating and teaching cognitive artifacts, that would be great.
Appendix: Performance theory, fresh from the 1980s.
This figure pretty much says it all: performance in any task is a function of ability, opportunity, and motivation (plus outside random factors):
There seem to be many people who believe talking about IQ makes them appear smart (while what they say proves the opposite) and many others who want to feel superior based on putative population-level differences.
Many of these people seem to be invested in zeroing out the entirety of knowledge collected on the influence of the other factors, which is why in the above (and in general), we use “skill score” as the individual index of potential performance, to counter that trend.
It’s not just skill, it has to be a skill score, something that combines the skill, the other abilities, and the motivational aspects. From the viewpoint of people who like solving logic puzzles, that’s what “IQ” tests are, a specific type of skill score, where the skill is solving the simple puzzles that compose an “IQ” test.
The cognitive artifacts, as indicated in the figure above, are force-multiplier tools, which allow people who couldn’t otherwise do a task (they couldn’t simplify the function if they had to use the rules of logic) to do so with the tools (they can with Karnaugh maps).
This is basically high-school material, at best; it needs to be because it’s an illustration that can be followed by people who didn’t get an EECS degree — granted, a major personal failure of theirs, but we’re accepting of all comers here.
It’s saddening to see people still pushing for apprenticeships as the main element in advanced education. Internships, apprenticeships, trial periods, acclimation periods to a job are all very well and good, but they are periods to learn the specific requirements of a job.
Formal education (meaning the use of techniques, support materials, practice problems, and testing materials all designed to impart and validate knowledge) has inordinate advantages for creating the foundations for those periods, as has been demonstrated by the history of STEM and of the introduction of formal training in the trades.
Note that formal training in anything includes a healthy dose of practice; sadly, many people think it refers to lectures. Formal just means that the training period has a different form from that of the period in which the knowledge is put to work for real.