Joyfully Sorting Out the Disorder
“Perhaps the butterfly, with its seemingly frailty and lack of power, is a natural choice for a symbol of the small that can produce the great.
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THE CHILD AS A COMPLEX DYNAMICAL SYSTEM
Gas Molecules and People
I’m watching a butterfly flutter about, tender yellow against the multiple shades of blue at the Côte d’Azur. So tiny and defenceless and yet so convincingly present and so determined to fulfil its little mission.
I wonder if the gentle flapping of this butterfly’s wings will bring about a tornado in a couple of weeks from now, somewhere else on the planet. It’s called the butterfly effect. Chaos theory founder Edward Lorenz discovered that a tiny shift in the initial conditions (such as the perturbations created by a butterfly) can lead to significant changes along the way. His original research was based on studying weather patterns, but scientists have come to realise that such sensitive dependence on initial conditions is actually a property of any complex dynamical system.
Many contemporary researchers have adopted the view that human development, too, can be regarded as a complex dynamical system.
While most models in psychology, education and administration today are still stuck in the industrial age and continue to heavily rely on the (often mythical) average, there is serious work being done to develop an alternative framework called the science of individuality. Its hub is The Laboratory for the Science of Individuality at the Harvard Graduate School of Education, led by Todd Rose.
In his bestselling book The End of Average, Todd Rose tells the story of Professor of mathematical and developmental psychology Peter Molenaar who had the courage to question the traditional research tools and thus his own successful career at the University of Amsterdam after he nearly reached retirement age. Molenaar experienced a revelation when rereading “the Bible of Testing”, Statistical Theories of mental Test Scores by psyshometricians Frederic Lord and Melvin Novick. Mental testing was codified into its modern form in this 1968 textbook as it remains required reading on standardised tests. In the intro to the textbook, the authors observed that according to classical test theory, the only way of determining a person’s true score was by administering the same test to the same person over and over again multiple times. Some amount of error would always occur at each test session, but an average score across a large number of test sessions would converge into the individual’s true score. Lord and Novick acknowledged, however, that repeatedly administering the same test to the same person would be impossible as it would mean asking test taker to solve the problems he or she was already familiar with and thus foil the possibility of obtaining many independent test scores. “But rather than admit defeat, Lord and Novick proposed an alternative way to derive someone’s true score: instead of testing one person many times, they recommended testing many people one time”, Rose explains. This was Molenaar’s epiphany, as he instantly knew what he was looking at: an irrefutable error that served as the basis for research in many fields of science that studied individuals and called into question the validity of an endless collection of supposedly reliable tools (among others, Rose lists diagnostic tests, basic methods of grading in schools, depression treatments, brain models, selection procedures for gifted programs).
Molenaar traced this fatal flaw to the late 1800s, when scientists wanted to know if they could predict the behaviour of a single gas molecule by looking at the average behaviour of a group of gas molecules. According to the rigorous mathematical principles developed to test this method (called ergodic theory), a group average can be used to predict individual behaviour only if two conditions are true: (1) every member of the group is identical, and (2) every member of the group will remain the same in the future. If a group of entities satisfies both conditions, the group may be considered ergodic (its average behaviour is suitable for predicting the individual behaviour members). It took a while to figure this out, but as we now know from fluid dynamics, gas molecules turned out to be not ergodic, even though they look so simple and similar. So what drove psyshometricians to believe that human individuals were ergodic?
Molenaar spoke up with a manifesto titled Bringing the Person Back Into Scientific Psychology, arguing against generalisability in developmental psychology. Denied the facilities to embark on a new kind of research in The Netherlands, he relocated to the U.S. and gathered around himself a group of visionary scientists from around the world. At the department of Human Development and Family Studies at Penn State, together they are developing new tools to enable scientists, physicians, educators and businesses to improve the way they evaluate individuals. This time based not on fixed values and average scores, but on the math of dynamical systems, the math of changing, nonlinear, dynamic values.
Molenaar’s revelation is almost biblical, considering how many years of his career he had believed in the existence of the average man, “that the average represents the ideal and the individual represents error” (something many social scientists have believed ever since Adolphe Quetelet coined this misconception in the 1840s). It must have taken a lot of courage to accept his previous misjudgement, stand up to his conformist colleagues and even move across the Atlantic at an advanced age. To me, this is a beautiful example of what intelligence and learning is: flexibility to unlearn and relearn. As a parent, it’s never too late to do the same: unlearn to see your child as a deviation from the average norm and relearn to embrace her in her fluid and dynamic individuality.
Snowflakes and Polygons
In The End of Average, Rose also pays tribute to the legacy of another revolutionary developmental psychologist, Esther Thelen. Early in her career, Thelen used to study animals and noticed that many behaviours that biologists insisted were fixed and rigid were actually highly variable, depending in large part on the unique peculiarities of each individual animal. This initial observation drove her to study the mathematics of dynamical systems and eventually to reexamine human development. She came up with the analyse-then-aggregate approach: Contrary to what is still common in psychology and education today — aggregating very limited data from many individuals and then analysing a particular individual’s set of data as compared to the general curve — Thelen suggested focusing on each individual first, analysing each individual’s behaviour in great detail without comparing it to anyone else’s, and putting the meta-individual puzzle together at a much later stage. This individual-first approach has led to dynamite break-throughs because it allows to see the individual patterns in development masked when relying only on group averages.
Yes, the individual-first approach requires much more computational power. Industrial age methods like concentrating on averages used to be state of the art when only primitive computational tools were at our disposal and when we were predominantly concerned with questions like increasing the efficiency of large groups and ranking. We no longer live in the industrial age. In the digital age, we have the power to store and analyse massive amounts of individual data, cheaply.
The truth is that the computer, like a steam engine, is just a tool and it’s up to us what we want to do with it. The industrial age is a mindset. Hence we can continue to industrialise and standardise every aspect of our lives and use the computer and big data to run algorithms based on averages and implement state surveillance to rank individuals. But the same tools can be used to admire individual development in all its complexity and allow for diversity to flourish.
Dynamic systems theory equips us with a set of powerful glasses allowing us to see child development very differently from the traditional stage theories. From a stage theorist point of view, “a child walks already or doesn’t walk yet”. In reality, every new skill involves microscopic progression and regressions, simply not visible if one zooms out too much. Take your glasses off, and a snow-flake with its intricate nested patterns will seem like a crude polygon.
Individual development can only be understood as nested processes that unfold over many timescales from milliseconds to years, Thelen wrote. The same can be said of learning, of acquiring knowledge from our daily activities. Look at this as the creation of new forms through the self-organisation process. Development can be seen as a function of self-organisation. What does self-organisation mean? Self-Organisation is the emergence of order without specific instructions from the organism itself or from the environment. It’s really difficult for some of us to grasp, but there’s no direct causality in our development. To truly see this, one needs a top-drawer life skill: thinking nonlinearly. In a nonlinear system, multiple internal and external influences continuously interact, and no single factor - such as biological age - can be seen as the single cause for developmental change, no single element has causal priority. This is why development milestones you expect an individual to hit should not be based on biological age. This is why grouping individuals by age is ill-informed. What is even more important, this is a clue for giving up on the arrogant idea that we can mould individuals according to some external plan. There is no plan.
Your child's developmental architecture may seem to follow complex rules, but according to many contemporary theorists (like Stephen Wolfram) and as has been shown by multiple computational models, there exist no higher order, complex organisational principles. Rather, minuscule changes in the initial conditions can spontaneously lead to significant changes in the outcome. Just like with the butterfly effect, something seemingly complex emerges after a single small change is introduced in the system, but can be neither thought of as having been caused by that small change nor predicted based on that small change.
ATTRACTORS
What Would happen If I Did That?
“I realized their “scurrying” had no purpose or intent: they were simply moving faster in the sun—and slower in the shade. Biotic self-organization—exactly the same principle that underwrites the free energy principle”, Karl Friston recalls observing woodlice as a boy. Many scientists revere Karl Friston’s free energy principle as key to our understanding of intelligence and learning (including potential general artificial intelligence). We are all just shapes in space-time (ensemble densities or the relative probabilities of states of affairs) and can be thought of in terms of density dynamics, Friston says. He introduced entropy (disorder) as a measure of the “shape of things”: “Interesting shapes (i.e., those characteristic of self-organizing systems like you and me) have a low entropy. This is exactly the same as the distribution of woodlice in the shade. Crucially, in the absence of any movement, a low entropy “shaped” probability distribution would simply not exist. In other words, had my woodlice just been basking in the sun there would have been no self-organization. The only way you can change “the shape of things”—i.e., bound entropy production—is to act on the world. (…) In fact, we have now taken to referring to the free energy principle as active inference, which seems closer to the mark and slightly less pretentious for nonmathematicians”.
“To reduce the amount of energy consumed in establishing order, the self-organising system settles into or prefers only a few behaviour modes”, researcher Katarína Millová writes in the International Encyclopedia of the Social & Behavioral Sciences (Second Edition). “In the dynamic terminology this behavioural mode is an attractor state, the system has an affinity to that state. But even stable attractors remain dynamic, the system is not rigid or deterministic, it is softly assembled.”
According to Friston, any opportunity to resolve uncertainty becomes attractive (literally, in the mathematical sense of a random dynamical attractor), thus we grasp at every opportunity to answer the question “What would happen if I did that?” “Formally, the resolution of uncertainty (aka intrinsic motivation, intrinsic value, the value of information, Bayesian surprise, etc.) corresponds to salience”. I believe by salience Friston means “lack of ambiguity”, for he continues: “If there is an action that can reduce uncertainty about the consequences of a particular behaviour, it is more likely to be expressed.” And it is that process of reducing uncertainty, reducing disorder that brings us joy: “In a world full of novelty and opportunity, we know immediately there is an opportunity to resolve reducible uncertainty and will immediately embark on joyful exploration—joyful because it reduces uncertainty or expected free energy.”
Friston places attention in very close relation to the experience of prediction errors and writes that a completely unpredictable world, where there is no opportunity to answer “what would happen if I did that” and all uncertainty is irreducible, is a joyless world. “Boredom is simply the product of explorative behaviour; emptying a world of its epistemic value—a barren world in which all epistemic affordance has been exhausted through information seeking, free energy minimising action.” Isn’t a world where learning is reduced to memorising the definitions and strategies such a joyless world? A world where the learner is expected to regurgitate trivial determined results with no opportunity for self-directed and self-paced discovery in pursuit of her very own “what if” questions? As Nobel Prize winner, Physicist Richard Feynman put it in his semi-autobiographical book Surely you’re joking, Mr. Feynman:
“Triboluminescence. Triboluminescence is the light emitted when crystals are crushed…”
I said, “And there, have you got science? No! You have only told what a word means in terms of other words. You haven’t told anything about nature - what crystals produce light when you crush them, why they produce light. Did you see any student go home and try it? He can’t.
“But if, instead, you were to write, “When you take a lump of sugar and crush it with a pair of pliers in the dark, you can see a bluish flash. Some other crystals do that too. Nobody knows why. the phenomenon is called “triboluminescence”.” Then someone will go home and try it.
…Finally, I said that I couldn’t see how anyone could be educated by this self-propagating system in which people pass exams, and teach others to pass exams, but nobody knows anything.
My 10 year-old son Simon loves this Feynman quote. He picked it up while scrutinising the challenging AI video course by Welch Labs called “Learning to See" [Part 5: To Learn is to Generalize]. I have asked Simon how he sees himself applying his knowledge down the road, trying to understand what academic or career goals he may have set for himself, if any. Does he have a picture of himself in five years from now, where does he want to be by then? He got very upset, just like when asked to sum himself up in one sentence for an interview last spring. His answer to my career question was: “Mom, I’m just having fun!” He is having fun embarking on a ton of mathematical discoveries every day, devising original proofs, trying to reduce uncertainty and disorder and shape his little piece of the universe. And from what I can tell by the projects he produces as a creator of math and programming content, he owns that knowledge. He lives in a joyful world. This conversation we had was a beautiful humbling lesson for me, a reminder about why we left public school and switched to self-directed learning in the first place.
THE MARKOV BLANKET
The Big Web and the Big Wave
My 8 year-old daughter Neva sleeps under a weighted blanket. It helps to keep her anxieties under control, shielding her ensemble density in a tight, warm embrace and allowing her to reduce uncertainty about a soft borderline between her and the rest of the universe. We jokingly call her heavy duvet a Markov blanket.
Actually, the Markov blanket is a machine learning term defining the part of a graphical model that contains all the variables that shield a particular node from the rest of the network, i.e. the only knowledge needed to predict the behaviour of that node and its children. Some researchers equate the Markov blanket with a cognitive definition of the mind. Karl Friston says this is possible because we can equate consciousness with inference: “Inference is only defined in relation to (sensory) evidence – that necessarily induces a Markov blanket (that separates the stuff that is being inferred from the stuff that is doing the inferencing).”
To sum up Friston’s main idea: There is only one imperative in life — give existential shape to the way we are. Mathematically, this entails a minimisation of entropy or at least a bound on entropy production. The only interesting states are low entropy states. The only interesting processes are those that bound an increase in entropy, weave a Markov blanket.
Many of us struggle with weaving their Markov blanket in today’s world of growing uncertainty. There is simply too much information, too many stimuli to metabolise. To avoid losing ourselves in that boundless sea of information, our natural instinct should be to discriminate between what we should pay attention to and what we should ignore, guided by our intrinsic interests and our need for joyful exploration.
Once we are exposed to educational content from early childhood and free to choose what to explore, we quickly learn to sort out the knowledge we crave for at that particular moment and don’t feel overwhelmed by tech stress. Conventional schools are breaking this intrinsic motivation by force-feeding us with information that we haven’t asked for, causing exhaustion, emotional outbreaks, numbness and apathy. Yes, school children have their mobiles and iPads, but do they still see them as active inference tools? Overfed as they are with redundant stimuli during school hours, their precious childhood hours outside of school are also drowning in the sea of compulsory homework assignments and other structured activities that have little to do with curiosity-driven discovery. They hardly have the time to just sit down and meditate on what they personally want to learn next as there is so much they have to “learn” for school in order to get those passing scores. It makes me wonder what the aspired final product of this assembly line actually is? Is it knowledge or is it just a piece of paper with a score on it, a simulacrum of knowledge? And is that piece of paper a mark of a fertile, imaginative, engaged mind, capable to face the challenges of the new century, to unlearn and to relearn, a creator? Or is that piece of paper a mark of a broken will, of conformism, a brand mark of a slave?
Conventional school also creates a false model of the natural world as if it were divided into subjects. This is not how self-directed learning works, developing knowledge in the form of a web or a graph with nodes connected to one another (Markov blanket), thus making it clear how everything is connected. In Friston's words, “It is exactly those scientists who are making a difference who will look as if they're struggling—trying to integrate multiple fields—because they are looking for principles, explanations, hypotheses, models that have the broadest explanatory power. We're all aspiring collectively to the simplest explanations for why we are here and what we are doing. (…) That movement is a collective movement, and it does depend upon a culture of digital exchange and stored knowledge.” In other words, the digital age has unleashed an overwhelming big wave of information, and we’ve got to surf that big wave. Stop micromanaging your child’s “screen time” but give the child the time and the space to freely discover. Stay involved and learn together with the child, but let the child take the lead in climbing that surfboard and deciding which wave to try next. Stop pushing the child along some fixed narrow path towards a fixed final product. There is no final product, learning is a continuous process, and one's education is a spiritual journey rather than a race for a set of prises.
Let’s pick up “The End of Average” by Todd Rose again. His mentor, psychologist Kurt Fischer, a ground-breaking figure in the science of the individual, is renowned for his contributions to resolve the crisis of variability in developmental science (obvious discrepancies between individual development and the supposed normal pathways first noticed in the 1980s). For nearly a century, stage theorists had viewed development as a ladder that everyone was programmed to climb rung by rung. “There are no ladders”, Fischer once told Rose. “Instead, each one of us has our own web of development, where each new step we take opens up a whole range of new possibilities that unfold according to our own individuality”.
“Normative thinking — the belief there is one normal pathway — has fooled scientists in many fields,” Todd Rose writes, listing multiple examples of scientific breakthroughs, from early child development to cancer research to depression treatment, that have been made possible thanks to focusing on individuals instead of averages. He coined several principles of individuality and the pathways principle is one of them. According to this principle, there are many, equally valid ways to reach the same outcome (rooted in the powerful concept from the mathematics of complex systems called equifinality) and no universally fixed sequences in human development. “In a multidimensional system that involves changes over time — like a person interacting with the world — there are always multiple ways to get from point A to point B.” The fact that we all master new skills better when the learning is self-paced and in self-directed sequence as opposed to fixed-pace group instruction and following a curriculum planner has been established long ago (for example, in late last century’s pioneering research by educational scholar Benjamin Bloom). In the 1980s, Bloom “acknowledged that it would be prohibitively complex and expensive to convert the fixed-pace standardised education system into a flexible one”, Todd Rose continues. “But the ‘80s have passed. We live in an era where new, affordable technology can make self-paced learning an accessible reality”.
THE FORMULA OF INTELLIGENCE
A Force Resisting Confinement
Neuroscientist Suzana Herculano-Houzel, famous for inventing a method to count the exact number of neurones in the human brain and comparative studies of various species, defines intelligence as behavioural and cognitive flexibility. Flexibility as a choice to do something else than what would happen inevitably, no longer being limited to purely responding to stimuli. This is how animals with a cerebral cortex gained the past and the future. Flexibility in decisions that allow you to stay flexible. Generically speaking, the more flexibility the more intelligence, with learning as one of the results of flexible cognition, Herculano-Houzel pointed out during a live session that my son Simon attended as part of the World Science Scholars program. Hence making predictions and decisions is all about maximising future flexibility, which in turn allows for more intelligence and learning. This is a very important guideline for educational administrations, governments and policy makers: allowing for flexibility, Herculano-Houzel stressed. There is a problem with defining intelligence as producing desired outcomes, she said. Yet is this not what standardised curriculum and testing is based upon, reproducing desired outcomes?
“We are only starting to explore defining intelligence, and it’s clear that the biophysical capability (how many neurones one has) is only a starting point. It is through our experiences of the world that we gain our ability and flexibility, that is what learning is all about”. In a way, Herculano-Houzel paraphrased Friston’s active inference principle, hasn’t she?
Can we evaluate intelligence and learning? Professor Herculano-Houzel loved Simon’s definition of IQ testing as a “glorified dimensionality reduction”. Simon doesn’t believe anything multidimensional fits on a bell curve and can possibly have a normal distribution. Professor Herculano-Houzel urged us to see a TED talk given by prominent computer scientist and entrepreneur, Alex Wissner-Gross, on intelligent behaviour and how it arises.
Is there an equation for intelligence? Yes, says Wissner-Gross. It's F = T ∇ Sτ.
A force, F, acts so as to maximize future freedom of action. It acts to maximize future freedom of action, or keep options open, with some strength T, with the diversity of possible accessible futures, S, up to some future time horizon, tau. In short, intelligence doesn't like to get trapped. Intelligence tries to maximize future freedom of action and keep options open. And so, given this one equation, it's natural to ask, so what can you do with this?
As an example, Wissner-Gross went on to demonstrate a software engine called Entropica, designed to maximize the production of long-term entropy of any system that it finds itself in. Entropica was able to pass multiple animal intelligence tests, play human games, and even earn money trading stocks, all without being instructed to do so. In other words, Entropica wasn't given learning goals, advised no “desired outcomes”.
"Recent research in cosmology has suggested that universes that produce more disorder, or "entropy," over their lifetimes should tend to have more favorable conditions for the existence of intelligent beings such as ourselves. But what if that tentative cosmological connection between entropy and intelligence hints at a deeper relationship? What if intelligent behavior doesn't just correlate with the production of long-term entropy, but actually emerges directly from it?”
The main concept we can pass on to the new generation to help them build artificial intelligences or to help them understand human intelligence, according to Alex Wissner-Gross is the following: "Intelligence should be viewed as a physical process that tries to maximize future freedom of action and avoid constraints in its own future. Intelligence is a physical process that resists future confinement".
Simon's reaction to Alex Wissner-Gross's TED Talk was: "But this means school only makes you less intelligent!”
TRUST
Autonomy as Key to Emotional Balance and Attention
Think about it for a moment: several prominent visionaries of our time tell us that intelligence and consciousness emerge from joyfully sorting out the disorder, following a dynamic web-like path. In that self-organising process, guideposts may hinder rather than help, because those have been sorted by someone else.
Especially in today’s unpredictable world, flexibility is key. Today, when we increasingly have to deal with things no humans have ever dealt with before, “such as super-intelligent machines, engineered bodies, fluid gender identities, algorithms that manipulate your emotions with uncanny precision, rapid man-made cataclysms, and the need to change your profession every decade. (…) The very meaning of “being human” is likely to change. How to live in a world where cofound uncertainty is not a bug, but a feature?” historian Yuval Noah Harari asks in his book 21 Lessons for the 21st Century. “To survive and flourish in such a world (and not end up being a clueless fossil) you will need a lot of mental flexibility and great reserves of emotional balance. You will have to repeatedly let go of some of what you know best, and feel at home with the unknown,” he answers. The new generation will have to learn to reinvent themselves and shake off the illusion that there is a moment when they “finish school”, finish the learning part of their life.
What we really need to hold on to are our intrinsic abilities to make sense of information, both Friston and Harari emphasise. “Schools focus too much on providing pupils with a set of predetermined skills, based on our current world view. But we don’t know what skills people will need in 2050”, Harari writes. Much of what kids learn at school today will likely be irrelevant by 2050, he adds.
Most teachers and parents themselves lack the mental flexibility that the new century demands, for they themselves are the product of the old, assembly-line educational system, coined by the demands of the Industrial Revolution, the model that raised many out of poverty but eventually also caused a climate emergency and a burn-out epidemic. Many school children and university students rebel. The dropping out of school, depression and burn-out wave is largely triggered by the fact that the world is changing at an astronomic speed while we are being force-fed a completely outdated world model, in a growingly standardized, controlled manner. The sensitive minds among us, however young they may be, feel this discrepancy and jump off. Those who continue happily riding the assembly line won’t notice how their minds have been hacked and all decision making has ceded to the algorithms. Which in essence will mark the end of their existence as autonomous agents acting upon the world, as separate entities. The end of learning.
The only way to avoid the end of learning is to trust your child. Trust your child, not the educational path someone believes your child should follow. I am trying to be a trustful parent, in psychologist Peter Gray’s terminology. Gray suggests we seek inspiration in the ways human hunter-gatherer kids had learned for a couple hundred thousand years, until the agricultural and later the industrial revolution brought slavery, long working hours, ranking and achievement pressures. Many researchers confirm that the ways hunter-gatherers go about learning, affording their kids enormous amounts of time to play and explore, emphasizing voluntary observation of ongoing interactions instead of following mandatory instructions, result in better skill retention, mental stability and ability to concentrate. Some indigenous cultures that are not technically hunter-gatherers but where the child is granted great autonomy produce comparable results. According to one study by two psychology professors, Marciela Correa-Chavez and Barbara Rogoff, Mayan children who have less exposure to formal education show “more sustained attention and learning than their counterparts from Mayan families with extensive involvement in Western schooling.” Rogoff suggests that schooled children may “give up control of their attention when it’s always managed by an adult.”
“Self-determination theory assumes that inherent in human nature is the propensity to be curious about one's environment and interested in learning and developing one's knowledge. A large corpus of empirical evidence based on Self-determination theory suggests that both intrinsic motivation and autonomous types of extrinsic motivation are conducive to engagement and optimal learning. It is the lack of autonomy in school that inhibits kids' ability to pay attention”, researchers Christopher Niemiec and Richard Ryan conclude in another study.
Does this mean we should all head off to the jungle and become hunter-gatherers again? As my 8-year-old daughter puts it, life is like a book: to fight global warming and support biodiversity we shouldn’t go back to the first page, “there’s no internet there!” But we shouldn’t stay on our current page either. We can turn to the next page that will have science and innovation but also deep respect for the world around us and nearly animistic relationships with the (smart) stuff we mindfully accumulate. I think the same can be said about fighting global depression and burn-out waves and supporting neurodiversity and sustainable learning. We can turn the page, because it is possible to find ourselves in a world where technology equips us with affordable learning tools and ways to connect with the best experts across the world, empowering every child on her unique journey of self-directed learning, in deep respect for her individual pace and personal quirks.
I let my children take ownership of their learning, make mistakes and learn from them. I believe this is the only way to nourish their intrinsic sense of responsibility. I trust my children as self-organising dynamic systems. My role as a parent is to provide an emotionally warm and engaged, stimulating environment. Which neuronal pathways they train and which they prune is ultimately part of that natural process of weaving their own Markov blankets. I bet it will be the things they enjoy most that will stick. My role is to make sure they have the tools and the flexibility, in both space and time.
It is difficult to be a trustful parent in a mandatory school environment. This is why our family has moved countries to be able to homeschool. As I write this essay, my 10-year-old son has finished building another AI, this time implementing the minimax algorithm — something conventional school wouldn’t have allowed him to explore for another decade.
Théoule-sur-Mer and Antwerp, August 2019 - January 2020
Sources:
Todd Rose, “The End of Average” (Penguin Books, 2017)
Peter Molenaar, Distinguished Professor of Human Development and Family Studies, Penn State University
https://hhd.psu.edu/contact/peter-molenaar
Hanna Mulder, ... Marian J. Jongmans, "How Children Learn to Discover Their Environment", published in Neuropsychology of Space, 2017
https://www.sciencedirect.com/science/article/pii/B9780128016381000094
Katarína Millová, Marek Blatný, “Personality Development: Systems Theories", published in International Encyclopedia of the Social & Behavioral Sciences (Second Edition), 2015
https://www.sciencedirect.com/science/article/pii/B9780080970868230353
Chris Frith, “Under the Markov Blanket”, published on Frithmind
http://frithmind.org/blog/2014/05/12/under-the-markov-blanket/
Karl Friston, “Life as we know it"
https://royalsocietypublishing.org/doi/full/10.1098/rsif.2013.0475
Karl Friston, "Of woodlice and men: A Bayesian account of cognition, life and consciousness. An interview with Karl Friston (by Martin Fortier & Daniel Friedman)", published in ALIUS Bulletin. 2: 17–43.
https://www.aliusresearch.org/uploads/9/1/6/0/91600416/friston_-_of_woodlice_and_men.pdf
Anthony Wing Kosner, “The Mind at Work: Karl Friston on the brain’s surprising energy”,
published on September 30, 2019
Suzana Herculano-Houzel, World Science Scholars course “Big Brains, Small Brains: The Conundrum of Comparing Brains and Intelligence”, November 2019.
Alex Wissner-Gross, TEDxBeaconStreet, November 2013
https://www.ted.com/talks/alex_wissner_gross_a_new_equation_for_intelligence?language=en
Yuval Noah Harari, “21 Lessons for the 21st Century” (Vintage UK, 2019)
Peter Gray, “Free to Learn (Why Unleashing the Instinct to Play Will Make Our Children Happier More Self-Reliant and Better Students for Life)”, (BasicBooks(AZ), 2013)
Peter Gray, “Children Educate Themselves III: Wisdom of Hunter-Gatherers
How hunter-gatherer children learn without schools”.
Correa-Chávez, M., & Rogoff, B. (2009). Children’s attention to interactions directed to others: Guatemalan mayan and european american patterns. Developmental Psychology, 45(3), 630–641. https://doi.org/10.1037/a0014144
Michaeleen Doucleff, “A Lost Secret: How To Get Kids To Pay Attention”, published on NPR on June 21, 2018
Christopher P. Niemiec, Richard M. Ryan, “Autonomy, competence, and relatedness in the classroom: Applying self-determination theory to educational practice”, published on June 25, 2009