Exponential acceleration in free learning

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This text is part of: "I would never send my kids to school" by Piotr Wozniak (2017)

Goals in learning

There is an ancient concern about free learning that dates back to the invention of the concept of school. How can we direct learning in free learning if learning is free? How can we accomplish goals?

If schooling it to bring a child from Point A to Point B, school is a strong competitor to free learning, at least in theory. Free learning maximizes the total value of knowledge by the reliance on the learn drive. A key component to that maximization is the speed of learning, which increases dramatically in free learning due to the maximization of learntropy. In free learning, we do not determine who a child is gonna be. We just let the process go spontaneously. The goals emerge in the process. So does the destiny. Nobody is born a doctor. The dream of helping people emerges gradually with the development of interests in proportion to the growth of knowledge.

Due to a dramatically faster learning rate, it is possible that a free learning child will go in its own direction and will lag in reference to the theoretical A->B trajectory (where B is the goal). However, all it takes to recover from the lag is to make an own decision to "get to B". If that decision is free from frustrating comparisons with peers, free learning powered by the knowledge valuation network recalibrated for point B will make it relatively easy to achieve goals (assuming they are set to be achievable).

For example, a great deal of unschoolers decide to take on SAT exams at later stages of development. Due to the their free capital of knowledge and excellent self-learning skills, unschoolers find that goal remarkably easy and even enjoyable. At the same time, rigorously schooled kids might be at the end of their tether, while striving for the exactly same goal. For a kid schooled against its own inclinations (as expressed by the learn drive), a failure at SAT may receive monumental lifetime dimensions. This is because schooling feels like an investment, while unschooling feels like fun. Easy come, easy go. For a schooled child, a failure in an exam feels like the failure of self.

Not everyone can be Bill Gates, but for an increasing number of kids, tests and certificates are secondary. A 12-year-old programmer can think of starting up his company without the need to prove his skills to anyone. The test of his skills will come in sales of his apps. The same is true of a young talented novelist. An increasing number of colleges treat unschoolers favorably. They come with a unique set of skills in problem solving or in navigating uncertainty and complexity.

Last but not least, all the above considerations are born on the assumption that the student is incapable of setting ambitious goals for herself. In real life, if we allow of sufficiently long time for self-growth, the emergence of knowledge will translate into the emergence of goals.

The problem of goal setting in education is largely born of the culturally imprinted role of school: delivering children to an adult goal. In the reality of free learning, rich environments and freedom are all that is needed to solve this seemingly expensive dilemma.

In educational goal setting, schools create a fake problem and then take credit for solving it

Explosive breakthroughs in free learning

The main advantage of free learning is a dramatically wider stream of well-consolidated knowledge. This is not a well-targeted knowledge like at school or in SuperMemo. This is the knowledge that fits well in the jigsaw puzzle of prior knowledge. It is mnemonic, coherent and durable. It is sticky in that it powers a rich learn drive.

What we often observe in free learning is a rapid unexpected exponential spurt of growth in an area that seems stagnant (e.g. stepwise progression in reading). Even if free learning is largely extinct in schooled populations, we can observe it in most kids before they go to school, for example in speech development. In kids with speech delays, the sharp turn in particularly easy to notice: from a mute to a chatterbox in a few months. The same phenomenon can be observed in walking or in biking even though these are based on procedural learning. The mechanisms of knowledge crystallization behind all those sharp upturns is the same.

Once kids go to school, those exponential explosions tend to disappear. They may still show up under the radar. For example, if the kid makes a rapid progress in a computer game, nobody in the adult world seems to notice or even care. However, in unschoolers or in democratic schools, we can see those learning explosions at later ages as well. For example, we can see it in learning to read in democratic school, where spontaneous reading without instruction often comes pretty late.

We can see exponential progress when learning foreign languages abroad, where long period of stagnation may turn into a sudden spurt of growth when vestigial comprehension, motivation, and new learning enter a positive feedback loop.

Learning explosions are possible at middle age too. If they are rare, it is only because we tend to settle into a comfy lifestyle with fewer challenges.

Exponential acceleration in free learning
Exponential acceleration in free learning

Figure: Exponential acceleration in free learning: The illusive superiority of direct instruction underlies the Prussian model of schooling. The immediately observable advantage in achieving set goals is wrongly translated to a strategy for achieving long-term goals, such as well-rounded education. Explosive accelerations are a norm in free learning, unschooling or in democratic schools. The main reason why this explosive educational property is marginalized is the lack of human control over the accomplished goals. The problem is most pronounced in societies with poor emphasis on freedom, and high emphasis on discipline, homogeneity, social order, and the like

Crystallization metaphor

The underlying mechanics of the explosive learning process can easily be explained in terms of knowledge crystallization in sparsely connected and yet rich semantic networks. If the process of establishing connections in a semantic net is compared with the process of molecule alignment in crystallization, the explosive emergence of high quality knowledge becomes obvious (see: Knowledge crystallization metaphor).

Schooling can be seen as a laborious, slow, linear, and saturative growth towards the target. Crystals are formed layer by layer, and keeping the structure clear from interference is always a battle.

In contrast, in free learning, it is cheap to create a great deal of incoherent mini-crystals that can later form larger structures by spontaneous rapid crystallization. A large number of seemingly irrelevant pieces of information can quickly crystallize into a coherent network. The explosive nature of that crystallization can easily be explained by a chain reaction, in which connections between neighboring crystals of knowledge facilitate further connections in the neighborhood.

A simple visualization of the process can be done with a supercooled beer crystallization trick. With supercooled beer, all it takes it one strong shake and the liquid crystallizes almost instantly. This type of explosive crystallization in learning is what gives kids the label of marvelous learning machines. In the light of childhood amnesia, calling kids "sponges of knowledge" is a misnomer. Their brains cannot compete with adult brains in terms of memorization. The only trick the kid uses is free learning. This free learning leads to exponential accelerations that amaze the adult world. Sadly, without understanding the underlying process, we take the best tools of learning away, and coerce kids into academic instruction. This in turn will earn them another label: lazy! (see: Myth: students are lazy).

Kids are not fantastic learners, their amazing learning outcomes stem from freedom

Jigsaw puzzle metaphor

Jigsaw puzzle metaphor can also be used to explain exponential spurts in learning. Schooling can be compared to a laborious analysis of a linear stream of jigsaw puzzle pieces provided by a teacher in a well-ordered sequence determined by the curriculum. That stream, in theory should make it possible to align pieces one by one. However, the gap between the determinations of the learn drive and the determinations of the curriculum keeps increasing from year to year. While reasonably happy first graders learn to attach new letters of the alphabet to their body of knowledge, 4-5 years later, most of kids sit their classes deathly bored due to poor comprehension, or a total lack of interest. This can best be seen in learning foreign languages when high school graduates often cannot compete with a native 4-year-olds (I was one of them graduates).

In contrast, free learning is more reminiscent of how we efficiently solve jigsaw puzzles. We look at the whole constellation of pieces and make educated decisions about which pieces are more likely to fit. We pick those and attempt a match. This is how the learn drive works: intelligent knowledge matching. Needless to say, that free approach brings much faster growth of the puzzle, and the growth trajectory may be very hard to predict in advance. In free learning, a child will build a great deal of jigsaw puzzle islands, and those islands are the key to the exponential explosion.

Once a large number of pieces of the puzzle form islands, the exponential progress is possible because one piece can instantly connect big swathes of the previously assembled sections. The student can see the big picture that makes further work much easier. It is reminiscent of the epiphany that comes from realizing the meaning of the entire puzzle.

In other words, high speed of learning at first comes from the parallel assembly (as opposed to a linear stream of pieces at school), seeming lack of progress comes from incoherence (before the islands of knowledge get connected, they cannot be used efficiently), the acceleration comes from rapid re-assembly of previously formed islands of knowledge, and the final spurt comes from the epiphany: the realization of the meaning of the entire puzzle.

TV tuning metaphor

In ancient times, tuning in to a TV signal would gradually convert a gray image of static into a nice sharp TV picture. In schooling, we aim at building the whole perfect image pixel by pixel in a systematic manner, from the top row, from left to right. Any disruption to that process may lead to a spotty image. In that idealized image of education, it is important to be fast with recovery while getting sick. This is due to the fact that sickness leads to possible loss of pixels in the perfect image. In free learning, all forms of acceleration and slowdown on demand are a norm. The speed of learning is optimum.

A government spokesman will appeal to teachers' conscience: "if you go on a strike today, the kids may miss exponentiation and be left with a gap in knowledge for life" (actual words of spokeswoman Joanna Kopcińska, Poland, Mar 12, 2019).

In free learning, we randomly assemble areas of the image long before we have a general idea of what the TV picture shows.

The generalizing capacity of neural networks may suddenly trigger a recognition upon the arrival of a tiny piece of data. The same capacity may be used in recognizing the entire TV image. Once the sharpness is tuned in well enough, a sudden epiphany may reveal the underlying image. The same kind of epiphany occurs on a smaller scale at tiny subareas of knowledge again and again. Small epiphanies in one area, may contribute to bigger epiphanies at the higher level. This is how the chain reaction of the learning progress develops.

House building metaphor

In the effort to abolish the old Prussian school model, Sal Khan and his Khan Academy are quintessential contributors and a source of inspiration. However, one of the metaphors used by Sal Khan in the lecture circuit is misleading. When speaking of the problem of schooling, Khan uses a metaphor in which builders fail to build the second floor of the house and are forced, like at school, to build the third floor. When learning mathematics, this obviously leads to dismal comprehension. You cannot understand exponentiation if you do not know how to add numbers.

The problem with the metaphor is that when it is taken too literally, it may actually speak against free learning. After all, free learning is best expressed in terms of freedom, e.g. open market, while direct instruction leads to structured learning that may follow a strict path of the curriculum. It is hard to imagine a cathedral emerging in the place of a bazaar.

The key to resolving this metaphorical paradox is to understand that learning leads to knowledge which forms a semantic network in the mind. As such, the sequence of learning is essential for comprehension, and free learning optimizes comprehension to perfection by simply rejecting boring or abstruse material on input. In architecture though, the constraints imposed on the graph that illustrates the growth of the semantic network are more rigid: they are limited by the laws of physics. We cannot build the roof of the cathedral before laying the foundations.

A modern resolution to the constraints of physics is open source architecture. In open source architecture before we move to the construction phase, we can generate complex designs using open source subcomponents.

If we use open source architecture as a metaphor, we can indeed start building houses from the roof. It is just a matter of interest, available subcomponents, and imagination. A child can also learn exponentiation by watching bacteria grow in a test tube, or see how stones on a beach are scattered along a negative exponential function of the distance from the groynes. The rudimentary understanding of exponential functions requires little or no understanding of 3+3. I dare say that understanding math should come well ahead of the deployment of formulas.

In open source architecture, we can also see the exponential explosion of progress. In early phases, when there are no components to work with, developers need to design all bolts and boards from scratch. It will be a while before the first design of the first house emerges. However, once components multiply and more complex structures crystallize, we can see an exponential increase in the availability of designs ready for construction. With a bit of luck, a modern cathedral or two will also emerge. The exponential progress will turn into a logistic S-curve only when we run out of available architects. Human learning is also limited by the properties of memory, however, with spaced repetition, saturation is deferred. In theory, with the use of SuperMemo, the lifelong learning progress curve is almost linear.

Open source architecture allows of growth spurts in design
Open source architecture allows of growth spurts in design

Figure: Sal Khan's house building metaphor may be misconstrued. It does not imply the need for school or direct instruction. Where it insists on the ordered sequence of learning, it under-emphasizes multiple branching nodes in the graph of possible design decisions or learning options. In open source architecture, building homes may avail of crowdsourcing. When the semantic net of knowledge is freed of physical constraints of actual construction, house design is a better analogy of learning. Free learning, as much as free design, allows of unplanned creative growth characterized by unexpected exponential spurts of acceleration

Exponential learning in SuperMemo

SuperMemo insert. What is SuperMemo?
The lesson for users of SuperMemo is that free learning should be the guidance to spaced repetition as well. It happens all too often that schools and curriculum are the guidance in SuperMemo. As a result, instead of improving the learning process, SuperMemo contributes to making the school experience even more harrowing. Not only is the sequence of learning far from the optimum, the costs are multiplied by the efficiency of spaced repetition that dramatically increases the costs of retaining incoherent knowledge. With wrong criteria, SuperMemo efficiently boosts inefficient learning.

Instead, in SuperMemo, we should mimic free learning by binding essential pieces of knowledge with high retention links stored in SuperMemo. In other words, we need to learn first, freely, and then store knowledge for spaced repetition only when its usefulness has been proven in free learning. The natural process that makes the above possible is incremental reading, which interleaves free learning of new knowledge with making it rock solid for life with spaced review.

Linear memorization of sequential databases is not different from schooling, and may reduce the overall efficiency of learning. The fact that SuperMemo ensures high retention can only worsen the cost of learning along the old principle garbage in, garbage out (GIGO). Even in Advanced English 2018 that I recommend to everyone, after 30 year of ordinal adjustments (for perfect sorting), student's own extensions are essential for coherent learning

For more texts on memory, learning, sleep, creativity, and problem solving, see Super Memory Guru