Learning does not mirror Teaching

An implicit assumption in most educational infrastructure is that teaching and learning are closely similar processes, perhaps even mirror images of each other. In the abstract at least, there is a transfer of knowledge from teacher to learner. It’s even possible that once a learner has assimilated enough taught knowledge, they could ‘switch polarity’ and become a teacher. No, this is not another well crafted advocacy for sweeping reform in the educational system. I am neither qualified nor motivated to deliver such a thing. I just want to say a few words in the context of some aspects of computational thinking. There are several ways to categorize programming languages: procedural, declarative, functional, concatenative, syntonic, object oriented, data oriented, etc. My point is merely this: teaching is declarative, learning is syntonic.

The ability to acquire and the ability to impart are wholly different talents. The former may exist in the most liberal manner without the latter.
– Horace Mann

When we start out, we immediately inherit a vast and exponentially expanding body of human knowledge. This is our birthright, it does not belong to gate keepers or authorities who mete out crumbs as they see fit. Academia has the task of adding to and curating this knowledge – it doesn’t own it.

The unifying term ‘education’ implies a deep connection, a yin-yang, almost mathematical sort of symmetry between teaching and learning. This symmetry is a perception that is eagerly supported by academia, it’s an intuitive and widely held view, a ‘central dogma’. There is little evidence for it, however. It should be remembered that mathematics is only shorthand for the complexity of nature. Nature is a realm of computation and evolution, and mathematics is one of the tools that enables a vastly simplified model of reality to be held in a three-pound hominid brain. It is often said that mathematical concepts such as π and the Fibonacci Sequence are seen everywhere in nature. That’s true, but they’re seen by who? Snails and daisies, or humans? The fact that we see a pattern does not necessarily mean that a ‘Deep Truth’ has been discovered. Anthropomorphizing nature is a mistake. Furthermore, it is difficult to see even a logical similarity between Plato in the olive groves of Athens and the result of many millions of years of evolution by variation and natural selection.

There is one aspect of teaching though, that is highly influential on learning. That is in a teacher’s capacity to inspire.

If you want to build a ship, don’t drum up people to collect wood and don’t assign them tasks and work, but rather teach them to long for the endless immensity of the sea.
– Antoine de Saint-Exupéry

Human knowledge may be a birthright, but the storage and delivery systems for that knowledge are subject to the laws of socio-economics just like every other industry. Papyrus, the printing press, telegraphy, telephony, electronic media, and ultimately the Internet has been the path of technology.

While not able to exactly lay out a guaranteed path, a teacher can describe the landscape, list known boundary conditions, and illustrate and clarify goals and heuristics. Teaching is therefore, a formal, objective, descriptive task. In programming parlance, it is ‘declarative’.


Learning stuff is a very different topic from teaching. We have basically the same neurology as people did way back when banging rocks together was high technology. We evolved to find food, avoid predators, and reproduce. Of course, when intelligence arrived on the scene, things became ‘non-linear’. When social behaviour and language arrived, Alice tumbled down the rabbit hole.

The smartphone is a testament to language, science, and technology, but not increased individual intelligence. In 1965, a good pocket radio had a handful of transistors. Today’s smartphone has over a billion. People haven’t gotten a hundred million times smarter in the last 50 years (at least I know that I haven’t). Buckminster Fuller’s “Knowledge Doubling Curve” goes from 100 years around 1900, to 25 years around 1950, to 1 year today, to months/weeks/days/hours? soon. Accurate predictions are difficult because human activity is now blending with machine learning, and it’s a whole new ball game. If the central dogma that teaching and learning are symmetrical ever was true, it is becoming less true with each passing year.

So how do human learners continue to even be relevant? Well, the good news is that the same evolved learning capacity we’ve always had is applicable to any level of abstraction. In fact, perhaps a serious exploration of exactly what ‘level of abstraction’ means would be a good thing for young minds. An associated idea is that ‘things’ are not of primary importance, but rather that the connections between things are. Metaphors are examples of such connections. If we can conceptualize atoms and galaxies in terms of table-top models, we have a shot at comprehension. Also, people can learn on their own using reasoning, common sense (bootstrapping), reverse engineering, and intelligent trial and error.

The key element to learning is experience. It makes little difference how logical or well laid out an argument is if the learner has no connection to it. That’s what is meant by ‘syntonic learning’:

Educators sometimes hold up an ideal of knowledge as having the kind of coherence defined by formal logic. But these ideals bear little resemblance to the way in which most people experience themselves. The subjective experience of knowledge is more similar to the chaos and controversy of competing agents than to the certitude and orderliness of p’s implying q’s. The discrepancy between our experience of ourselves and our idealizations of knowledge has an effect: It intimidates us, it lessens the sense of our own competence, and it leads us into counterproductive strategies for learning and thinking.
– Seymour Papert

A body of knowledge is much more compelling if it can be explored subjectively, at the learner’s own speed and depth, because memorability is a big part of learning:

When you make the finding yourself – even if you’re the last person on Earth to see the light – you’ll never forget it.
– Carl Sagan

Teaching does not and cannot encompass learning:

What we become depends on what we read after all of the professors have finished with us. The greatest university of all is a collection of books.
– Thomas Carlyle

Learning is not containable in bricks and mortar or bureaucracy. It is very simply, what every human does whenever free to do so. ‘Education’ is really just another word for ‘learning’:

Self-education is, I firmly believe, the only kind of education there is.
– Isaac Asimov

It may be tempting to assert that Socratic dialectic is a suitable substitute for syntonicity. However, the former, while undeniably powerful and valuable, still involves knowledge transfer between human minds. This, by necessity, requires formalism, symbolism, and formulae. Syntonicity, on the other hand, requires nothing but a human mind exploring reality, with the aid of machine computation (algorithms) if necessary. Learning is therefore, an informal, subjective, experiential task. In programming parlance, it is ‘syntonic’.

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