Knowledge crystallization

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

Self-directed learning underappreciated

The system of schooling has a powerful side effect of undermining the appreciation of self-directed learning. Regular and systematic coercive instruction leads to the withering of skills and interests needed for effective self-directed development. Schooling suppresses the learn drive.

The ignorance of the power of the learn drive and the power of the emergence in building coherent knowledge is omnipresent. All good educators, good teachers, and good students understand that self-directed learning has amazing values. However, for a societal breakthrough, we need to have a majority voice. Students worry that without school they will get lazy. They might be right. One of the reasons schools fail is that they undermine self-motivation, self-discipline, and they suppress the learn drive. Unless we learn independently from early ages, a corruption of self-discipline might set in. Teachers worry students would go astray or stay monothematic. They say "school broadens horizons". Parents fear the kids would spend all their days playing videogames. They get their proof when kids exhausted from schooling spend all their evenings on the computer. The good example of democratic schools remains amazingly invisible in the cacophony of pressures of the modern world. The success of homeschoolers is attributed to selective parenting, privileged upbringing, etc. Peter Gray has spent a lifetime investigating self-directed learning and self-development. His "Free to learn" could convince a brain-damaged ameba. The benefits are obvious and yet societies and schools still stick to the old Prussian dogma.

My convictions come from practising self-learning from birth. There was only one big obstacle in that self-learning process: compulsory schooling. This chapter visualizes the error of schooling by employing a crystallization metaphor.

From jigsaw puzzle to a crystal

The jigsaw puzzle metaphor of the learn drive explains that each piece of knowledge is like a piece of jigsaw puzzle. It needs to fit the puzzle, i.e. the knowledge of the individual. Students get a happy reward for each fitting piece. They get unhappy and helpless if they are forced to combine an unfit piece that finds no match on the surface of the knowledge.

Schools have a good program for building up the jigsaw puzzle from the very basics to the complete set. However, instead of relying on the learn drive, they pour pieces of a jigsaw from a bucket. The speed of flow is the same for everyone and goes far beyond the well-documented brain capacity to absorb new information. All students are supposed to drink from the same bucket and get constantly pushed to look for matching pieces of the jigsaw. Many get lost in the process and most consider school an unhappy experience as a result.

To illustrate the progression of unconstrained self-directed learning, I came up with a knowledge crystallization metaphor. A similar process of fitting pieces of information to the surface of knowledge occurs in attaching molecules to the surface of a crystal in crystallization. New molecules can attach to the surface of the crystal only given the right circumstances. Crystallization can be a good metaphor for comparison of free learning with schooling. I hope it will help many see why kids learn faster on their own, and how that early organic process can be extended to later ages.

Crystallization metaphor

Imagine a baby brain as a solution of salt, and the ideal adult brain as a solid spotless crystal of knowledge. Imagine the crystallization process. In the solution of salt, tiny crystals can form. Imagine those as nuggets of knowledge. The idea of schooling is to systematically add layers to the crystal so that it could gradually, perhaps over two decades, grow into that clear crystallic structure. The problem with that approach is that it is highly inefficient at best, and does not work at all at worst.

Now imagine how a baby learns. The crystallization in a baby brain is determined by the exposure to the outside world as perceived by the senses. This exposure can be compared to running currents of saltier water through a baby's brain. High concentration solution will result in nucleation: tiny crystals forming at all impurities, which stand for seeds of inspiration. For a baby, a red spot on the wall may be this type of impurity. The baby will circle the spot until it figures out if it is an edible tomato or just a piece of dry paint. In a young brain, hundreds, and then thousands of crystals will form. The best formula for crystallization is to add more salty water and give it some time. Provide exposure and wait. Nothing else! The more seeds of crystal grow, the greater the surface of knowledge, the faster the crystallization. Large surfaces help new pieces of knowledge stick.

Schooling is supposed to pick a good crystal candidate and keep growing its surface. This process is meticulous and well-programmed. It is determined by national or state curriculum which tells children what they need to learn. The problem is that this monocrystal schooling is always limited by the slow-growing surface of that perfectly programmed crystal. When kids are allowed to explore on their own, their exposure is less organized, more random, more extensive. However, it makes it possible to grow many more crystals. They may be small and incoherent, but their strength is in numbers and in their surface area. The greater the surface of crystals, the more new knowledge can stick.

Crystallization of the world view

If you talk to a 5-year-old you may be surprised with detailed technical knowledge harbored in the young brain. The kid may know a word or two about politics. I saw a precocious 4-year-old pretending to read the news on the radio and spewing "fake news" that amazed me with their similarity to the real world. However, those young smarts are just an illusion. Kids do not have a coherent world view. They will not have it for many years. Their knowledge is like a murky solution full of tiny crystals that do not fit well together. They know details, they do not have a good big picture. They know the trees, but they do not understand the forest. This is the natural and welcome side effect of growing thousands of incoherent crystals. In the ideal case, the murkiness of the semi-liquid mix of the salt solution with thousands of tiny crystals is not a problem. Gradually, in thousands of places, incoherences get fixed. Those incoherences are points of interest. The child will want to know why things do not match and what explains the inconsistency. This keeps a young brain buzzing and asking questions. Tiny crystals align and form bigger structures. The whole murky mass of knowledge gradually becomes clearer and more organized. Uneven surfaces get polished by forgetting. Smaller crystals find a match and unify in the process of memory optimization in sleep. The child can slowly see the image of reality in a way that is more and more adult-like.

Unconnected crystals can make highly intelligent people prone to gaffes. Every island of ignorance is a possible gaffe. Unconnected areas of knowledge are particularly dangerous. This can make a knowledgeable 70-year-old senator blunder like a schoolboy. It can happen to anyone.

Schooling disrupts crystallization

The huge problem with education is that before common sense develops, before a kid can connect its multiple crystals into a coherent structure, we send kids to school. We begin focusing on the central crystal. We drill ABCs and 123s. In the meantime, the whole multitude of tiny crystals built in childhood dissolves through forgetting. We channel kids into the singular track of schooling.

The school may begin with a great deal of early stress. However, it may equally well begin with early enthusiasm and early success. There is a central core where the big crystal of wisdom is supposed to grow: reading and counting. Layer by layer, the curriculum is supposed to add perfectly coherent structures of knowledge. However, some kids get to school too early. They do not have necessary impurities or mini-crystals to begin with. Letters and numbers are too abstract. They know colors, cars, animals, or even understand how the earth orbits the sun. But numbers somehow do not stick to their memory. Instead of building crystals, teachers try to make sand pies in dry sand. All dry sand structures tend to collapse soon after being shaped. They can be shaped over and over again and there is no progress. There is nothing crystal about sand pies. Herein the dangerous process may begin. Instead of growing a pure crystal, schooling will start building up an impure but rigid lattice of salt and dry sand. That lattice will have three negative aspects: (1) it stays impure, (2) its surface stays small, and (3) the child cannot grow its dozens of baby crystals because all its mental energy is devoted to trying to stick new layers to the impure crystal of the curriculum. In addition to a perpetual lack of progress, building sand pies inevitably leads to toxic memories and school hate.

For most kids, with prolonged effort, letters and numbers start making sense, but the process of adding dry sand to the structure will continue. Before a kid gets a chance to make order in the dirty crystal, the system will try to add more dry sand. The teacher may try to drill the multiplication table and add more sandy layers to the structure that was shaky in the first place. The bigger the surface of that salt-and-sand mix, the crumblier the structure.

A bad teacher can add a lot of sand and may totally block certain areas of knowledge from further development. It takes a lot of thawing and cleanup to restore passions in damaged areas. A change of a teacher can turn a kid who loved math or English into someone who hates the same subject.

In the end, instead of adding new layers of crystal, the whole educational effort starts looking like firefighting. There is little time to build the crystal because there are always portions of the sandy edifice that crumble and need repair. At some point, it becomes clear that further progress is unlikely. This is when many kids drop out from the system. They feel they won't benefit much from school anymore. They are labelled or label themselves as school failure. And this is just the beginning of where the whole problem of schooling resides

Crystallization metaphor of schooling and unschooling

Figure: In perfect schooling we create a perfect crystal of knowledge. In college, we add an extra crystal of specialization. In reality though, learning looks a bit less perfect. For most kids, knowledge never builds sufficient coherence and falls apart due to interference (i.e. fast forgetting). As a result, in real schooling, knowledge asymptotically reaches a certain volume and keeps churning around from that point on with little progress in stability or coherence. In contrast, in free learning, the acquisition of knowledge is chaotic and uneven. However, as long as it is based on the learn drive, the volume of knowledge is very large. Individual crystals of knowledge collide, and build consistency and coherence. This in turn helps stability and further integration of knowledge. By the time of college, in terms of volume, free learners should know far more than ordinary students. Free knowledge has multiple areas of strength, and multiple areas of weakness. However, it superior in coherence. This is why it is more applicable in problem solving

Crystallizing power of an electric passion

Neurobiologists will tell you that there is a huge constellation of well-known and well-researched brain states. Even more, there are multiple states for individual structures of the brain. Good learning requires a good symphony in between all brain states.

Now imagine that your salt solution has its optimum concentration and we apply an optimum electric field to stimulate nucleation. In other words, we can change the state of the solution with the help of the electric field to speed up or slow down the process of forming crystals. The same can happen in the brain. For optimum knowledge crystallization, we do not need any complex apparatus. The optimum brain field is well known to everyone. It is easy to recognize. Here are some good signs of the optimum learning brain state in a child: interest, smiles, sparkles in the eyes, passion, and focus. The electric field can cause homogenous nucleation too. This means that the crystals can form spontaneously without the need to add impurities. Those spontaneous crystals are nothing else but little brain "errors" that we call creativity. When a kid starts fidgeting at school, he will be reprimanded or drugged. In the optimum brain state, at high alertness, fidgeting should be a natural consequence of losing patience with a boring lecture, drifting attention, craving for learn drive reward, which initiates creative processes that will spill onto the motor system. This natural healthy process will be proportional to giftedness, and alertness. In other words, those who are most gifted and in the best brain state are most likely to be penalized for all shortcomings of the education system. Like the brain in REM sleep, with the motor system paralyzed, while creating new neural connections, the little baby brain will send random creative signals all over its structures. This will result in fidgeting, looking for solutions, wandering eyes, random limb movements, etc. Those are the signs schools try to extinguish. Fidgeting is combated like a dangerous wildfire. In other words, schools will combat the signs of that most precious thing in self-directed learning: creativity. Creative fidgeting is the time when new crystal seeds form. They begin their dendritic growth, and form regular fractals of rock-solid knowledge. This is the best ground for growing more crystals. This is the platform for further natural acceleration of learning! Creative homogeneous nucleation of knowledge is what makes for the great surface to build new crystal lattices. This is the chance kids lose when attending a classroom lecture, and when exposed to knowledge that sparks nothing but boredom. This is the root of learned helplessness and, potentially, a springboard to an unhappy life.

Maximum speed of learning

Maximum speed of learning will come with large surfaces of crystals ready to build new lattice layers.

In the ideal case, we should let a slow river of knowledge flow through a child's brain. This cannot be a meaningless stream of nonsensical syllables. The river must spark passions. The current must be slow enough for nuggets of knowledge to stick. You cannot drink knowledge from a firehose.

The river of knowledge is the river of the concentrated salt solution. We should amplify or just enable polarizing electric field of the excitement and passion. We should then see the crystals grow and self-organize. For a little child, early in development, all knowledge is of value and there is no need to direct that process towards reading, or counting, or anything else. Whatever sticks to the crystal structure will be used in the future to grow more crystals. Whatever does not stick is of little concern either. In the window of childhood amnesia, and well beyond it, all knowledge will be forgotten and recycled anyway. The crystals are in constant motion. There is no worry the kid will lag behind its own potential because all losses in goals and the direction will be well-compensated by the speed of learning coming from the enthusiasm and the unrestrained experience. Naturally, if the kid does not read or count, we all start worrying at some point. Danny Greenberg or Peter Gray might disagree. In democratic schools all kids learn to read, eventually. Basic illiteracy may slow down further progress. This is why a gentle trajectory corrector, for example a loving parent, might operate within the push zone to help correct the course.

Minor corrections should help the kid understand the value of areas and concepts that can serve best as springboards into the future. However, if the kid is unwilling at 3, there is no point in nagging him every month. It makes more sense to try at 4, then at 5, then at 7 or 8. A bothersome corrector violates the fundamental law of learning. This does not qualify as a push within the optimum push zone.

What if the kid lags with more complex concepts? Should we not start pushing in the area of math at least? Or physics?

It is true that not all kids will gravitate towards calculus. Unschooling may leave a gap there. However, schooling is no remedy. Most of adults know little or no calculus. All years of drilling at school have no effect anyway. Early math instruction does more damage than good.

Pushing kids is mostly an expression of parental dreams, not actual needs of the kid. Some people will never know trigonometry. They may be experts in economics, or even computer science, but their interests will still never align with triangles. Forcing trigonometry on a teen will only increase the dislike of the subject. Nothing works better than a realization that trigonometry might be useful for a job or skill one is truly interested in or truly needs. Trigonometry might even be useful to get to the next level in some exciting educational videogame.

As all kids differ through their different experiences, their crystals will differ and different passions will dominate. This is when kids may slowly start specializing in specific areas. This process does not have to begin at any specific moment of time. This does not need to be the start of vocational school or college. This should be a natural process based on the learn drive and individual needs or interests.

Pressure cracks

When there is too much external pressure to acquire new knowledge, the crystal can crack. The human brain has natural generalization powers. This helps re-crystallize cracks in the structure, e.g. at differently polarized crystal boundaries. Generalization makes human knowledge easy to employ. However, it also has negative side effects such as the confirmation bias, and tunnel vision. The natural way to break a wrongly formed crystal is to add knowledge that contradicts some of the prior knowledge. Strive for consistency is a natural neural process. Consistent and coherent knowledge is best achieved with intense lifelong self-directed learning.

Where crystal cracks lead to higher consistency and cohesion, they are welcome. However, the same process happens when a teacher forces a student to memorize vast portions of the material before a test. Large volumes of knowledge with insufficient comprehension will cause the crystal to crack. The bigger the volume of contradictions, the bigger the increase in cracks. Cracks are worse than just forgetting. Forgetting fosters generalization, while crystal cracks just cause the knowledge to crumble. This is how learning can destroy prior learning via the process called interference. Learning without comprehension can ravage prior learning. This is what happens in the school system on a daily basis. A nicely-formed crystallic structure can crack, soak in impurities, and prevent further crystal growth. This is why the crystals of knowledge tend to stagnate under pressure of compulsory schooling. In schooling, after a few years, the rate of gaining new knowledge is balanced by the destruction of old knowledge due to knowledge interference and forgetting. This process will affect all individuals sooner or later, even those who learn with comprehension. There is a natural limit to how much we can learn. The best tool to indefinitely postpone the point of saturation is spaced repetition. In theory, it makes it possible to attach new crystals till the day we die. However, spaced repetition employed to perpetuate cracked crystal will make matters worse. In theory, SuperMemo can freeze a bad crystal structure with negative outcomes that can span years.

Knowledge ecosystems

As for tunnel vision that stifles creativity, it is unavoidable. For science to progress, we need individual scientists with rock-solid models of reality and strong convictions. It helps if the models are correct, but wrong models need their advocates too.

If what we know is wrong, and what is wrong solidifies into a perfect crystal, we might never be able to jump out of the box and see a different interpretation. It may take a team of scientists to disprove a solid model residing in a single human brain.

If all crystals were the same in all brains due to uniform schooling, they would all be resistant to the same forces. Differently formed crystals crack in different places under different influences. This allows of a collective evolution of global wisdom. Differences and impurities allowed of Copernicus to follow Ptolemy, and Einstein to follow Newton. If Ptolemaic system crystallized too well and was perpetuated by perfect schooling, we would not have communication satellites today, and I would not make this book available free on the web.

There is value to educating new generations. There is some value to ignorance and forgetting. Most of all, there is a huge value in a diversified dendritic process of self-directed learning and the evolutionary power of competing points of view. Homogeneous education is a major stumbling block on the way towards future creative breakthroughs.

Pearl crystallization

Multifocal crystallization is great for keeping the surface of knowledge large and learning fast. However, human brain processes information via a narrow channel of attention. We do not take a snapshot of reality to crystallize many grains of knowledge at the same time. Instead, we work on a single crystal adding new layers molecule by molecule. The formula for growing pearls is based on an obsessive focused attention on a single crystal. Obsessive attention in a creative child is achieved with passion and interest. The same hyperactive kid that will fidget beyond control during a boring lecture is also able to sit for hours tinkering with a spoilt cell phone. That's what Ellen Winner calls the rage to master. What may be diagnosed as ADHD in a classroom turns out to be a symptom of giftedness in solitude.

Too much love can hurt pearl crystallization. Parents who want to see their kid happy will shower her with gifts at Christmas. In a mountain of 20 toys, 15-17 may turn out to be a waste of plastic and labor. The kid will always focus on 2-3 of his favorites and dump the rest. This core toy will be used to build pearls of knowledge.

However, the same wasteful set of 20 toys can be turned around into a highly educational tool for the exact same kid. I jokingly call it: "incremental toy giving". Toys can all be of value if they are delivered in 3-5 day intervals (spaced presentation), esp. if they are sorted from the least likely to be favored. The adult brain works better with spaced exposure to novelty (e.g. as in incremental reading). In a similar fashion, so does the kid brain. Even in reference to toys. Next Christmas, many of the toys can be reused with the help of forgetting. Toys tossed first can be hidden and revisited a year later. Parents can use the spacing effect to help kids build new crystal grains that might have partly disintegrated due to forgetting.

A little pearl grows best on a scratch in a container that holds our salt solution. A single toy tossed to a baby room is like a scratch. If there are no other toys or distractions (e.g. TV), the kid may focus entirely on play and grow a little pearl by extracting all creative juices from a single toy. If things go well, the toy may even sprout some dendritic crystals that will serve as a basis for future interests and inspirations. On the other hand, leaving the kid in a toy room is like making dozens of tiny scratches of which few will ever have a chance to grow productively. The kid may keep switching attention from toy to toy and never truly gain from the experience (compare: Futility of schooling). Stimulation isn't always good. It can become overstimulation. Naturally, taking a kid to a toy room for the sake of picking The Toy with the help of baby's self-directed investigation is a great idea! For more see: Incremental toy giving

Spaced presentation optimizes exposure, while self-direction optimizes fun. The kid will often prefer to kick around a beer can rather than to tinker with that expensive toy cell phone. That's a saving for a parent and a gain for the kid. Baby brain knows best which crystals are mature for further growth.

At later ages, the same problem may arise in cultivated parenting when the kid is shunted from classes in piano, then violin, and then even tuba? One instrument should be enough. Music tutoring time should also be limited. If the kid does not practise on her own there is little chance she will be a virtuoso. Tutors should become mentors, rather than executioners of coercive learning. Naturally, inter-mingling tuba with aikido is a great idea. Those are different forms of learning that need to be cultivated on their own.

For growing pearls of knowledge in young brains, parents can tinker with the environment to ensure it forms a natural optimum push zone for self-directed learning. Low exposure leads to no learning, high exposure leads to interference and crumbling crystals. Then there is always that goldilock zone of exposure that makes a young brain thrive on its own.


Knowledge crystallization metaphor explains how knowledge is built into coherent structures in a way similar to building crystals.

Perfect education is supposed to build a perfect crystal, but it never works this way. In reality, schooling builds incoherent tiny crystals of stunted knowledge. Self-directed learning leads to organic crystal growth with a large surface that effectively activates the learn drive.

This is what we do wrong by enforcing compulsory schooling:

  • suppressing self-directed learning: growing one crystal, instead of letting many crystals sprout naturally
  • wrong learning-forgetting balance: trying to add too many molecules at too many locations on the crystal's surface
  • suppressing creativity (e.g. discipline, ADHD medication): slowing down nucleation and dendritic growth
  • low level of comprehension: trying to fuse local crystals together before they are ready. Building irregular lattices that crumble
  • knowledge interference: adding cracks to crystals by piling up excess knowledge that leads to excess pressure. Knowledge interference destroys previously formed structures through crystal crumbling
Solution: Self-directed learning employs natural neural mechanisms to optimally dose new knowledge, in optimum brain states, to build optimal semantic tree that makes further learning easy and pleasurable