Seymour Papert: The Gears of my Childhood

Original: The Gears of my Childhood

How can we restructure maths to make it more lovable and learnable!? What would success look like?

Seymour covers a lot of ground brilliantly in his 4 page Preface to Mindstorms! His personal learning story which then morphs into a pathway to universal powerful, learning opportunities

He traces his personal learning journey from early childhood when he played around with car gears in the back shed. Seymour fell in LOVE with the gears. He found “particular pleasure” in the differential gear due to its complexity, “the motion in the transmission shaft can be distributed in many different ways to the two wheels depending on what resistance they encounter”. He argues that this love affair became a vehicle for him to later on master school maths. “I clearly remember two examples from school maths. I saw multiplication tables as gears, and my first brush with equations in two variables (eg. 3x + 4y = 10) immediately evoked the differential.”

Another CRUCIAL piece of information about the gears. Good learning materials have a dual nature. They can carry both advanced maths ideas AND sensory motor ‘body knowledge’. You can be the gear.

So far, this is a story of one person’s unique pathway to maths mastery. But not everyone will fall in love with gears:

“One day I was surprised to discover that some adults – even most adults – did not understand or even care about the magic of the gears”

This led him to think:

“How could what was so simple for me be incomprehensible to other people?”

Seymour’s reflection on this question is revealing. He rejected the viewpoint of his proud father that he was clever because he knew people who could do other things he found hard who didn’t understand the differential.

But it slowly led him to what he still sees as the fundamental fact about learning: “Anything is easy if you can assimilate it to your collection of models. If you can’t, anything can be painfully difficult.”

This leads to further questions for educators: How can we create conditions where learners develop useful mental models? How do intellectual structures grow out of one another?

Having a physical manifestation helps here – be it a floor turtle, a Robocup competition vehicle made from LEGO or an attractive shape designed in Turtle Art and then 3D printed.

And to repeat: Seymour fell in love with the gears. He stresses that you need love. He gently criticises Piaget here who focused more on the cognitive than affect.

By the way, later the slogan became hard fun. Whether you prefer love, hard fun or play is ok the underlying message is the important thing: if we like it we will persist in learning it.

When computers came along Seymour envisaged that they could play the role for everyone that the gears played for him. His belief is that many more will fall in love with a cleverly constructed computer based learning environment that taps into natural ways of learning. Hence Seymour helped to invent Turtle Graphics. The computer (Protean machine) can take on a thousand different forms. It can be the universal machine for learners to fall in love with. An incredible leap! Profound yes, True? We shall see.

Of course, since the computer can take on a thousand different forms it can also be used in bad ways:

• Computer as universal machine
• Children’s learning machine
• Game playing machine
• School administrative systems
• Surveillance capitalism machine
• Tik Tok trivial and sinister machine
• Some blame social media for the mental health decline in youth (Jonathan Haidt, The Anxious Generation)

Spawner of revolutions …universal communication and computation (internet, smart phone – banned in schools because too distracting for the youth.

Seymour’s optimistic pathway is one amongst many. Creative learning systems are always there but never dominant in society overall.

I understood this part of Seymour’s message, that the turtle is body syntonic and offers an engaging, a path to mathematical abstraction. Logo / Scratch provides students with a far better chance of falling in love with maths.

What I didn’t grasp firmly enough was the embodiment aspect. I did run a LEGO TC logo group for a while in the 80s but drifted off that path because of the logistic / cost factors of establishing that in the curriculum. More recently, I've corrected that error, after reading Gershenfeld's book, Designing Reality.

In our age, where individual data points have taken on more importance how do we measure or evaluate the mental models that Seymour sees as the most fundamental measure of learning new, useful things? This question was unresolved in Seymour’s view:

“If any ‘scientific’ educational psychologist had tried to ‘measure’ the effects (of Seymour’s encounter with gears) he would probably have failed … A ‘pre-’ and ‘post-’ test at age two would have missed them.”

It’s hard to measure mental models! I see that as the most important challenge arising from Seymour’s article:

“Thus the “law of learning” must be about how intellectual structures grow out of one another and about how, in the process, they acquire both logical and emotional forms”

This is the subject of Marvin Minsky’s book Society Of Mind

theory of instruction confronts theory of mind

A research question arising from consideration of Direct Instruction

 My current research question:
Why is Zig Engelmann's Direct Instruction (DI), a comprehensively trialled educational theory of instruction based on logical inference with rigorous empirical checks on performance and curriculum design successful in practice given that our minds apparently develop through a process of fluid analogies, as argued by Artificial Intelligence researchers Marvin Minsky and Douglas Hofstadter?

There appears to be convincing evidence for the success of DI in practice. Zig  Engelmann has put Chapter 5: Follow Through Evaluation of his book, Teaching Needy Kids in our Backward System, on line which provides a blow by blow account of how Project Follow Through findings were suppressed by "progressives" back in the 1970s

Here are some conflicting statements from the different schools of thought on logical thinking:

 Engelmann and Carnine. Could John Stuart Mill have saved our schools? (2011)

“If the examples presented to teach something are capable of generating only one inference or meaning, that is what all learners will learn, regardless of other differences among individual learners (9) … From our perspective, the most fundamental fact about the learner's mind is that it is totally logical in its learning operations. This is directly inferred from the learner's most elementary performance” (57)

Marvin Minsky, Society Of Mind (1987)

“Logical Thinking The popular but unsound theory that much of human reasoning proceeds in accord with clear-cut rules that lead to foolproof conclusions. In my view, we employ logical reasoning only in special forms of adult thought, which are used mainly to summarise what has already been discovered. Most of our ordinary mental work – that is, our commonsense reasoning – is based more on 'thinking by analogy' - that is, applying to our present circumstances our representations of seemingly similar previous experiences” (329)

I have been thinking about this question and discussing it with whoever is willing to discuss it. I can provide further reading references as an addition to this blog post for anyone who requests that. If anyone reading this feels they have an answer or relevant references then please post them in comments.

I'm not happy until I've theorised a learning approach and I become a little obsessive until I feel I've got to the bottom of it. From what I've read a theory of logical empiricism is incomplete when evaluated with a modern theory of mind. That doesn't mean that DI doesn't work - the evidence seems compelling - but it still worries me because there might be hidden implications for some aspects of learning.

why left brain/ right brain theories won't go away

Here's my theory about why left brain/ right brain theories which overreach won't go away.

First up, people love to describe themselves as either left brained (logical, mathematical) or right brained (creative, artistic, wholistic). Why? Because that provides a convenient biological explanation about why they are good at some things and not good at other things. "I can't learn this because my brain won't let me". That has a nicer feel to it than "I can't learn this because (a) I can't be bothered (b) it's not important to me (c) some other reason".

Secondly, people worry about the state of the world: economic inequality, wars, environmental catastrophe, crappy politicians, insanity / delusions, apparent failed alternatives in other social forms that temporarily deluded millions (eg. communism), suicide bombers, 9/11, religion etc. Well, to explain all this requires a lot of hard thinking and it is embarrassing to be a member of the human race given the reality that we are collectively quite immature and still working out how to govern ourselves in a semi competent fashion. So, it's reassuring to have a biological theory that the left brain and right brain are somehow out of sync or causing us to focus on the wrong things rather than doing the hard work of actually figuring out the real factors that determine our social development.

So, that's my theory of why left brain/ right brain theories which overreach won't go away.

Reference:
The Master and His Emissary: The Divided Brain and the Making of the Western World by Ian McGilchrist (the Introduction can be downloaded for free)

  Reception to the above book as documented by wikipedia. Mostly very positive reviews by influential people, with the notable exception of The Economist.

  The human brain: Right and left. The Economist review, which is the one I like.

Modern myths of learning: The creative right brain
Sensible review of the history and current state of the science

 What Marvin Minsky said about half brain theories in his 1987 book, Society of Mind:

The two hemispheres of the brain look so alike that they were long assumed to be identical. Then it was found that after those cross connections are destroyed, usually only the left brain can recognise or speak words, and only the right brain can draw pictures. More recently, when modern methods found other differences between these two sides, it seems to me that some psychologists went mad - and tried to match those differences to every mentalistic two part theory that was ever conceived. Our culture soon became entranced by this revival of an old idea in modern guise: that our minds are meeting grounds for pairs of antiprinciples. On one side stands the Logical, across from the Analogical. The left side brain is Rational; the right side is Emotional. No wonder so many seized upon this pseudoscientific scheme: it gave new life to every dead idea of how to cleave the mental world into two halves as nicely as a peach.

What's wrong with this is that each brain has many parts, not only two. And though there are many differences, we also ought to ask about why those left-right brain halves are actually so similar. What functions might this serve? ...
(see sec 11.8 Half Brains and 11.9 Dumbbell Theories for more details)

Yes, some psychologists went mad, and some are still going mad.

minsky 9: the self

Overview of Chapter 9 of The Emotion Machine (summary, online draft, buy)

The Single Self idea keeps us from wasting time about difficult questions about our mind

How does vision work? "Your Self simply peers out through your eyes"
How does memory work? "Your Self knows how to recollect what might be relevant"

Sometimes physicists strive to construct a single model or a grand unified theory. Nevertheless, physics contains many different subjects and each has its own (useful) way of describing the world. Whenever a subject becomes important to us we tend to build multiple models. This diversity is a principle source of our resourcefulness

We each make multiple models of ourselves

Our subpersonalities will frequently need to compete for control of higher level processes

William James (1890) on recalling childhood:

"... that child is a foreign creature with which our present self is no more identified in feeling than it is with some stranger's living child today ..."

Daniel Dennett (1991) on Self:

"... like spider webs, our tales are spun by us; our human consciousness, and our narrative selfhood, is their product, not their source ... their effect on any audience ... is to encourage them to posit a unified agent whose words they are, about whom they are ... a 'centre of narrative gravity'"

Instead of asking about our Identity it is better to ask, "Which of my models of myself best serves my present purposes?"

Personality traits

We describe people as having character traits - disciplined, honest, attentive, friendly

Possible causes for personal traits:
Inborn, genetic -
Learned -
Investment principle - hard to displace tried and trusted methods that work
Archetypes and Self-Ideals - our cultural heroes and villains
Self control - to keep ourselves from constantly changing our goals and priorities

Nevertheless, the concept of traits can be treacherous, for example, the generalities of astrology influence many

Self Control

To achieve long range goals you need self control. But self control is hard. We use tricks to achieve self control, we threaten or bribe ourselves, "I'll be ashamed if I give in to this", "I'll be proud if I can accomplish this"

Why must we use devious tricks to control or Ways to Think, instead of just choosing to do what you want to do?

Directness would be too dangerous (see Chapter 3) We would probably die if one part of our mind could take over the rest. In emergencies our instincts need to take over

Many of us spend much of our lives seeking ways to make our minds behave

Dumbbell ideas and dispositions

People like two part distinctions. Minksy provides many examples, both of traits (eg. solitary v. sociable) and of alleged characteristics of right and left brain thinking (eg. rational v. intuitive). Many things seem to come in opposing pairs.

Minsky thinks two part distinctions are too simple:

"...it usually makes little sense to commit ourselves, for all future times, about which objects to like and dislike - or about which persons, places, goals or beliefs we should seek to avoid, or accept or reject - because all such decisions should also depend on contexts ....most dumbbell distinctions ... appear to be so simple and clear that they seem to be all that you need - and that tempts you to stop. Yet most of the novel ideas in this book came from finding that two parts are rarely enough - and eventually my rule became: when thinking about psychology, one should never start with less than three different parts or hypotheses!"

Why do we like the idea of a self?

What leads us to the strange idea that our thoughts cannot just proceed by themselves, but need something else to control them? We use words like "Me" and "I" to keep us from thinking about what we are!

Various ways in which the Single-Self concept is useful to us:
Localised body is consistent with Single-Self
Private mind - the idea (illusion?) that only you hold the keys to the strong closed box of your private mind
Explaining our minds - if we can think "I perceive the things that I see" then it keeps us from wasting time on questions about perception that we don't know the answer to
Moral responsibility - to justify our laws and moral codes we assume that Selves are responsible for intentional deeds
Centralised economy / Decisiveness - "Thats enough thinking, I've made my decision!"
Causal attribution - we like to attribute causes
Attention and focus - we often think we have a single stream of consciousness to which we attend
Social relations - others think of themselves as Single Selves, we might be seen as weird if we didn't play along!

Our minds are messy. We spend large parts of our lives tidying them up - selecting, suppressing, refining

What is pleasure and why do we like it?

Emotions are hard to describe because they seem hard to split into parts. Hence there seems to be nothing to use as pieces of explanation

Minsky argues that pleasure is a suitcase word for quite a few different processes:

• Satisfaction - achieving an ambition
• Exploration - a quest, the pleasure is not only at the end
• Goal suppression - critics and other goals suppressed
• Relief - if the goal was the elimination of an irritation

Pleasure and satisfaction refer to extensive networks of processes we don't yet understand. We tend to treat complex, hard to grasp things as single and indivisible.

The pleasure of exploration

Adventurousness is an antidote for exploring unfamiliar terrain, which can lead to pain and distress. Learning by small incremental positively rewarded steps is limited

When we are learning a new technique, we need to work harder with fewer rewards, while enduring the additional stress of being confused and disoriented. We may have to abandon older techniques which have served us well. We may arouse a sense of loss or grief and a temptation to quit. Such learners have trained themselves to enjoy discomfort

Exploring the contradiction of enjoying discomfort: Pleasure is not a basic all or nothing thing just as the Self is not a single thing. Some parts of the mind may be uncomfortable but other parts enjoy forcing those first parts to work for them: "Good, this is a chance to experience awkwardness and to discover new kinds of mistakes"

We can envisage pleasure as negative, in the way it can suppress competing goals

What makes feelings so hard to describe?

The alleged mysteries of "subjective experience" or "directness of experience" arises from the inability of our higher level processes to detect all the intermediate steps involved in these experiences, eg. touching, redness. Some philosophers (dualists) conclude that materialist explanations of such things is impossible. Minsky argues that they have not worked hard enough to imagine adequate models of those processes.

How important is "privileged access" to our own mind? Sometimes our self assessments are inept, our friends may have better ideas of our real state

The sense of having an experience

Perception or Sensations are not "basic" (see Chapter 5). More signals flow down to the sensory cortex than in the opposite direction, presumably to help us see what we expect to see. We frequently "see" things that do not exist, eg. this square:

How is a human mind organised?

Each normal child eventually learns to:

• recognise, represent and reflect upon some of his own internal states
• self reflect on some of his intentions and feeling
• identify with aspects of how others behave

Summary of the kinds of structures would support these developments:

1) Deal with various situations by activating certain sets of resources, which are different Ways to Think
2) How would we determine which resources to select?
(a) for simple situations use use If--> Do rules
(b) for more versatile situations use Critic --> Selector schemes

3) The adult mind develops multiple levels of functioning and each level contains Critics and Selectors (See Chapters 5,6,7)

4) Various Ways to Think might also have levels of different symbolic expressiveness (See Chapter 8)
5) Our model needs to have room for answers to questions we haven't thought of asking yet. Envision the mind as a decentralised cloud of yet unimagined processes, interacting in still unspecified ways

Central and Peripheral Controls

We have various "alarmers" which interrupt higher level processes. Sometimes our thinking processes "break down". Some examples:

• trouble recalling past events
• trouble solving an urgent problem
• cannot decide which action to take
• lost track of what you were trying to do
• a surprise happens

But we are capable of rapid recovery

Mental Bugs and Parasites

Examples of mental parasites include self reproducing sets of ideas (memes) which can displace competing ideas - doctrines, philosophies, faiths, beliefs

The dignity of complexity

Our brains have evolved in a process that has taken 30 million centuries

Some of our sources of human resourcefulness come from three vastly different time scales:

• Genetic endowment
• Cultural heritage
• Individual experience

Most of our commonsense knowledge may be embodied as metaphors in the form of panalogies (See Chapter 6)

We have multiple descriptions of things - and can quickly switch among them
We make memory records of what we've done - so that later we can reflect on them
Whenever one of our Ways to Think fails, we can switch to another
We split hard problems into smaller parts, and keep track of them with our context stacks
We manage to control our minds with all sorts of bribes, incentives and threats

Our minds have bugs! For example, our powerful imagination can lead us to set out on extensive but futile quests!

minsky 8: resourcefulness

Overview of Chapter 8 of The Emotion Machine (summary, online draft, buy)

Before Alan Turing we did not know about a single machine that could emulate other machines. Turing opened the door to developing a machine which can have multiple Ways to Think

We have multiple ways of estimating distances - remembering typical sizes, overlaps, context, binocular vision, perceived speed. Each method is imperfect but taken together we can usually avoid serious mistakes. We effortlessly switch between methods choosing the more appropriate one for each different situation. This might also apply to how we think.

Panalogy (a word invented by Minsky meaning parallel analogy, also discussed in Chapter 6)

Panalogies are corresponding features of different meanings which are connected to the same parts of one larger structure. Minsky suggests that our brain architecture has evolved structures which make it easy to link knowledge fragments in this way.

Examples:

• Whenever you think about your Self, you are reflecting about a panalogy of mental models of yourself
• Sight is intertwined with memory, we fill in huge chunks from memory when "seeing" (without realising)
• We rarely make entirely new ideas, instead we modify existing ideas

This creates both speed (swapping between multiple meanings) and also the potential for confusion and ambiguity. It might explain the importance of metaphor and analogy in our thinking. Hence ambiguity becomes a virtue and not a fault because much of our human resourcefulness comes from using analogies that result from this.

How do people learn so rapidly?

Sometimes we learn new tricks from a single exposure (whereas a dog may require hundreds of lessons). A difference engine could be converted into a copying machine, so the structure in long term memory becomes the same as the one in short term memory


Minsky thinks our minds are like computers in this respect. Short term memory is expensive and limited.

"... a blow to the head can cause a person to lose all memory of what happened before and including that accident ... transfer to long term memory may take a day or more and require sleep"

Other reasons why long term memories may require much time and processing:
Retrieval - it may have to be linked to an existing panalogy, otherwise how could it be retrieved?
Credit Assignment - to be useful it would need to be linked to other relevant panalogies
Real Estate problem - finding a place for new memories would not be simple (might involve destruction)
Copying complex descriptions - hard to think of plausible schemes for making complex, linked memories

Learning involved many varied skills, such as:

• Adding new If --> Do --> Then rules
• Changing low level connections
• Making new subgoals for goals
• Choosing better search techniques
• Changing high level descriptions
• Making new Suppressors and Censors
• Making new Selectors and Critics
• Linking older fragments of knowledge
• Making new kinds of analogies
• Making new models and virtual worlds
  

Credit Assignment

Behaviourism is limited. Learning complex things cannot be explained by reinforcement or if-do rules

Minsky speculates that we might use higher level processes to decide what to learn from each incident by reflecting on our recent thoughts. These processes could be used to make such "credit assignments":

• choosing how to represent a situation will affect which future ones will seem similar
• learn only the parts of your thinking that helped, and forgot those which were irrelevant
• connect each new fragment of knowledge so that you can access it when it is relevant

The quality of our credit assignments might account for our "intelligence" (a suitcase word). The section about Poincare's unconscious processes (7-7) pointed out that this might take days. There is an incubation period.

We need more research about what kind of credit assignments infants can make, how children develop better techniques, how long such processes persist and the extent to which we can control them

Transfer of learning to other realms:

Some children seem to transfer their learning to other realms, while others don't

Transfer of learning might be superior for those who make better credit assignments. To gain more from each experience, it would not be wise for us to remember too many details but only those aspects that were relevant to our goals. Also what we learn from an experience might be more profound if we assign credit to the earlier choices we made that selected our winning strategy

Creativity and Genius

Genius consists of unusual combinations of otherwise common ingredients:

• genetics
• fortunate mental accidents
• learn how to praise self internally
• intense positive attention from parents
• isolation from other children
• mental management
• enduring discomfort when replacing a Way to Think
• selecting which new idea to develop

Memories and Representations

Minsky defines representation to mean any structure inside one's brain that one can use to answer some questions

What distinguishes us from other animals? It is our ability to treat ideas as though they were things, our ability to conceptualise. Minsky argues that there must be representation structures (networks) inside our brains. Knowledge fragments don't have meanings unless they are linked. He discusses various possible ways to represent knowledge:

• Describing events as stories or scripts
• Describing structures with semantic networks
• Using trans-frames to represent actions
• Using frames to embody commonsense knowledge
• Learning by building "knowledge Lines"

Connectionist and Statistical Representations

He contrasts two different ways to represent an apple, through a semantic (symbolic) network and a connectionist network


Connectionist networks (based on numbers showing strength of associations) can learn to recognise many important types of patterns, without any need for a person to program them. But number based networks have limitations. Every relationship is reduced to a number or strength so there remains almost no trace of the evidence that led to it, eg. the number 12 could represent all sorts of things

Minsky:

I see the popularity (of Connectionist Networks). in recent years, as having retarded the search for higher level ideas about human psychological machinery... research on commonsense thinking kept advancing until about 1980, but then it was clearly recognised that further progress would need ways to acquire and organise millions of fragments of commonsense knowledge. That prospect seemed so daunting that most researchers decided to try, instead, to invent machines that could learn, by themselves, all the knowledge that they would need - in short, to invent new kinds of "baby machines" ...

Quite a few of these learning machines did indeed learn to do some useful things, but none of them went on to develop higher-level reflective Ways to Think - and I suspect that this was mainly because they tried to represent knowledge in numerical terms....

... I do not mean to suggest that such networks are not important ... it seems safe to assume that many of the low level processes in our brains must use some form of Connectionist Networks (pp. 289-91)

How do we learn new representations?

Kant 1787: ... experience and sensory knowledge is only part of knowledge ... cognition adds new knowledge

Minsky thinks we are born with primitive forms of structures like K-lines, Frames and Semantic Networks which are then built on to create representations

Which representations to use for which purposes?

A dialogue between different approaches to the best way to represent knowledge:

Mathematician: It is always best to express things with logic
Connectionist: No, logic is far too inflexible to represent commonsense knowledge. Instead, you ought to use Connectionist Networks
Linguist: No, because Connectionist Nets are even more rigid. They represent things in numerical ways that are hard to convert to useful abstractions. Instead, why not simply use everyday language - with its unrivaled expressiveness
Conceptualist: No, language is much too ambiguous. You should use Semantic Networks instead - in which ideas get connected by definite concepts!
Statistician: Those linkages are too definite and don't express the uncertainties we face, so you need to use probabilities
Mathematician: All such informal schemes are so unconstrained that they can be self contradictory. Only logic can ensure us against those circular inconsistencies

minsky 7: thinking

Overview of Chapter 7 of The Emotion Machine (summary, online draft, buy)

Our ability to think in different ways (new Ways to Think) distinguishes us from other animals. However, we rarely ask good questions about what thinking is or what chooses which subjects we think about. Thinking often just happens smoothly.

How do we explain things such as long term plans, reminding ourselves of things to do, choosing among conflicting goals and whether to quit or persist?

The Critic-Selector Model of Mind

Minsky discusses various possibilities about how to resolve conflicts when more than one Critic-Selector is aroused and compete for resources.

Central Problems for Human Psychology

Small group in depth studies (eg. Piaget) are more valuable than large group statistical studies to the development of psychology. In large group studies small but vital details are overlooked.

The research that Minsky thinks needs to be done:

• What are the principal Problem Types that our mental Critics recognise?
• What are the major Ways to Think that or mental Selectors engage?
• How are our brains organised to manage all those processes?

What are Some Useful Ways to Think?

Knowing How
Searching Extensively

Reasoning by Analogy
Dividing and Conquering
Reformulating
Planning

First solve a different problem ->
Simplifying
Elevating
Changing the subject

Reflective ->
Wishful thinking
Self reflection
Impersonation

Others ->
Logical contradiction
Logical reasoning
External representation
Imagination

Social ->
Cry for help
Ask for help

Last resort ->
Resignation

What Are Some Useful Types of Critics?

These mirror the Levels of Mental Activities, from Chapter 5

Innate Reactions and Built-in Alarms - some alarms are hard to ignore, eg. a babies cry
Learned Reactive Critics - eg. moving to a quieter environment
Deliberative Critics - thinking about what went wrong
Reflective Critics - diagnosticians which verify progress or suggest alternatives
Self-Reflective Critics - various forms of self criticism
Self-Conscious Critics - these affect one's image of oneself, eg. I'm losing track of what I am doing (Confusion)

How Do We Learn New Selectors and Critics?

We can improve our Ways to Think by creating higher level Selectors and Critics that help to reduce the size of the searches we make. Most "theories of learning" do not address this

Poincare's Unconscious Processes

Minsky includes several great quotes from mathematician Henri Poincare (1913) about his unconscious learning process. These stages are described:

• Preparation -
• Incubation -
• Revelation -
• Evaluation -

Incubation and Revelation occur without our being aware of them. We don't really understand how they work.

How do we organise and change our collection of Critics and Ways to Think? We don't know. These issues should be recognised as central to the development of psychology.

Do We Normally Think "Bipolarly"?

Common sense thinking may consist of a brief "micro-manic" phase producing a few ideas, followed by a brief "micro-depressive" phase looking for flaws - all taking place so quickly the reflective systems don't notice it

minsky 6: common sense

Overview of Chapter 6 of The Emotion Machine (summary, online draft, buy)

Comparing what computers can do (play chess) with what humans can do which computers can't yet do (make a bed, read a book or babysit) provides us with insights about humans. Computer programs don't have commonsense knowledge, eg. when someone says, "a package is tied up with string", this includes "obvious" facts about the nature of string and packages (eg. with string you can pull but not push a thing)

Computer programs are not self aware of their goals - whether they are achieved or at what quality or cost. Computer programs are not as resourceful as humans, when "stuck", eg. they don't reason by analogies

What Do We Mean by Common Sense?

Minsky provides an extensive account of the common sense knowledge involved in answering a phone call. We aren't normally aware of how much we know

He introduces a new word, panalogy, which means parallel analogy

"Charles gave Joan the book"

• Physical Realm - book moves from Charles to Joan
• Social Realm - is Charles generous or hoping to ingratiate himself?
• Dominion Realm - Joan now controls the book

Here we have three meanings of the word "give". Our brains may structurally connect analogous items of knowledge from different realms (points of view). This might explain how we can easily switch without even being conscious of it between these different meanings

Multiple meanings are sometimes seen as a defect because of their ambiguities. The panalogy concept reframes them as a strength

It is hard to categorise commonsense knowledge. The scheme favoured by Minsky is along the lines of the kinds of thinking that can be applied to the categories:

• Positive expertise
• Negative expertise
• Debugging skills - knowing alternatives when usual methods fail
• Adaptive skills - how to adapt old knowledge to new situations

Could we build a "baby-machine", a machine that will gradually learn more by itself? Such programs have been tried but have failed to develop good new ways to represent knowledge. A machine will fail to learn the right things from most of its experiences. Minsky argues that learning requires selectivity and appropriate "credit assignments". You cannot learn things that you can't represent

Building intelligent machines becomes stuck due to not having ways to overcome problems like:
The Optimisation Paradox: difficult to improve once you work well
The Investment Principle: reliance on existing processes makes it hard to develop alternatives
The Complexity Barrier: changing complex systems has unexpected side effects

At any rate, good new ways to represent knowledge are usually not quickly and widely adopted:

• you need new skills to work with them efficiently
• such skills take time and performance will probably worsen during the changeover period

Evolution is more about rejecting bad changes than selecting beneficial changes. Most species evolve to occupy narrow, specialised niches. Evolution can learn to avoid common mistakes but usually not uncommon mistakes - except by evolving language systems.

We first need to evolve ways to protect against changes that cause bad side effects. Excellent method here is to split system into parts that can evolve more independently. eg. organs

Remembering

Our Amnesia of Infancy leads us to develop simplistic views of what memories are and how they work. Minsky argues for goal based organisation (accomplishment) rather than descriptive organisation (data base and matches):

POSITIVES

• What kinds of goals might this item serve?
• In which situations might it be relevant?
• How has it been applied in the past?

NEGATIVES

• What are its most likely side effects?
• How much will it cost to use it?
• What are its common exceptions and bugs?

SOURCES AND LINKS

• Was it learned from a reliable source?
• Is it likely to be outdated soon?
• Which other people are likely to know it?

Intentions and Goals

What is "self control", responsibility or intention? Moralists, Psychiatrists and Jurists argue about this.

Sometimes a goal can seem like a physical force, hard to resist, even though part of us does not want to do it. The goal may conflict with our high level values. There is no reason to expect that all our goals should be consistent.

Difference Engines

Psychology words don't meaningfully describe goals, they just pass the meaning onto another word that needs to be explained (want, motive, desire, purpose, aim, hope, aspire, yearn, crave). We need to talk about the underlying machinery:

"A system will seem to have a goal when it persists at applying different techniques until the present situation changes into a certain other condition"

Motives and goals could be explained as consisting of these three things:
Aim - description of a possible future situation
Resourcefulness - methods to reduce the difference between the present situation and the future situation
Persistence - keep applying those methods


When you hear a story you react most to how it differs from what you expected. Some names for this include accommodation, adaptation, acclimatization, habituation, becoming accustomed
Our eyes normally make small motions which helps maintain an image. Our systems mainly react to change.

Roger Schank, Tell Me a Story (1990) has conjectured that representing events as stories may be one of our principal ways to learn and remember

Making Decisions

When people say, "I used my free will to make that decision," this is roughly the same as saying, "some process stopped my deliberations and made me adopt what seemed best at the moment". "Free will" is not a process we use to make a decision, but one that we use to stop other processes! "My decison was free" is similar to "I don't want to know what decided me"

Reasoning by Analogy

Minsky identifies reasoning by analogy as one of the main methods by which we solve new problems. Why does analogy work so well? According to Douglas Lenet it is because there is a lot of common causality in the world.

Positive vs. Negative Expertise

We see things as positive because we censor or suppress other processes that would see them as unpleasant.

Minsky simulates a dialogue with a teacher who believes in positive reinforcement and small steps. Such an approach is not bad in itself but limited:

• difficult tasks almost always involve episodes of distress and discomfort
• reinforcement can lead to rigidity, lack of adaption
• other processes may fail when the "normal way" is abandoned
• the development of higher level managerial resources is put on hold

We must learn to "enjoy" some suffering when learning new things that need large scale changes in how we think. It's a mistake to make education too pleasant.

minsky 5: levels of mental activities

Overview of Chapter 5 of The Emotion Machine (summary, online draft, buy)

Minsky proposes a 6 level model of mind, which is described in some detail (for a little more detail see the wiki):


Psychologist: I find it hard to see the difference between your top most three levels
Student: No theory should have more parts than it needs

Minsky: The boundaries are indistinct but psychology is not like maths or science. When you know that your theory is incomplete then leave some room for other ideas you might need later!

Individualist: Where is the Self that makes our decisions? What decides which goals we'll pursue?

Minsky: It would be dangerous to locate all control in one single place because then all could be lost from a single mistake. Our minds use multiple ways to control themselves. Freud anticipated this with his ideas of superego, ego and id

Imagination:
"We don't see things as they are. We see things as we are" - Anais Nin

... most of what we think we see comes from our knowledge and our imagination

Abraham Lincoln (vague patches of darkness and light)

We don't know how our brains achieve this. "Seeing" seems simple because the rest of our minds are blind to the processes that do it for us. Perception is complex and invisible

More abstract, higher level descriptions are more powerful and efficient. Minsky is arguing for the importance of higher level semantics here as compared with inefficient processing of visual images

We internalise prediction machines. Nevertheless, such a system will never be very resourceful until it knows a great deal about the world it is in. This leads into the next chapter (Common Sense)

Related:
Dennett's Creatures is a bit similar to Minsky's model of mind
Skinnerian creatures ask themselves, "What do I do next?"
Popperian creatures ask themselves, "What do I think about next?"
Gregorian creatures ask themselves, "How can I learn to think better about what to think about next?"

minsky 4: consciousness

Overview of Chapter 4 of The Emotion Machine (summary, online draft, buy)

Consciousness is a suitcase word. It can mean such diverse things as a unifier, self awareness, identity, an animator of the mind, a provider of meaning or a detector of feelings. It refers to many different mental activities that don't have a single cause or origin

We need a way to divide the mind into parts that is more meaningful than crude folk psychology "dumbbell" (two part distinctions) such as conscious v. unconscious, premeditated v. impulsive, etc. For example, the "unconscious" state may represent various different states. Information may be inaccessible for a variety of reasons such as simple failure to retrieve, active censorship or "sublimated" into a form which can't be recognised (to borrow Freud's terminology)

Minsky uses the Plato / Socrates shadows on the cave allegory to discuss a possible structure of our minds.

Imagine we have an A-Brain and a B-Brain. The A-Brain receives signals from external world via organs such as eyes, ears, nose and skin - and can react to those signals by making our muscles move. The A-Brain has no sense of what the events mean.

The B-Brain receives and reacts to signals from A-Brain. However, the B-Brain has no direct connection to the outer world, so it is like the prisoners in Plato's cave, who see only shadows on the wall. The B-Brain mistakes A's descriptions for real things

For example, if B sees that A has got stuck at repeating itself, it might suffice for B to instruct A to change its strategy. To acquire its skills the B brain may need a C brain to help (eg. it's not always appropriate to stop repeating oneself, especially when crossing a road)

Student: Would not this raise increasingly difficult questions, because each higher level would need to be smarter and wiser?
Minsky: No, C-Brain could act as a "manager" who has no special expertise about particular jobs but could still give "general" guidance, like: "If B's descriptions seem too vague, C tells it to use more specific details", etc.

Minsky proposes six levels of processes:


The organism principle

Student:

Does your theory really need so many different levels? Are you sure that you can't make do with fewer of them? Indeed, why should we need any "levels" at all - instead of a single, big, cross connected network of resources?

The Organism Principle: When a system evolves to become more complex, this always involves a compromise. If its parts become too separate, then the system's abilities will be limited. But if there are too many interconnections, then each change in one part will disrupt many others

Hence, our bodies are composed of distinctive separate parts we call "organs". This also applies to the brain organ. New design is built on top of old design: "... large parts of our brains work mainly to correct mistakes that other parts make ..."

Psychology is hard because each "law of thought" has exceptions. It will never be like physics which has "unified theories" which work flawlessly.

Minsky's proposed solution to consciousness being a suitcase word: We must try to design - as opposed to define - machines that can do what human minds do. DESIGN not DEFINE

Consciousness seems mysterious because we exaggerate our perceptiveness. Most processes are hidden from us. We see things less as they are and more with a view to how they are used (eg. hammer, ball). Our minds did not evolve to serve as instruments for observing themselves

There are many suitcase words in psychology: attention, emotion, perception, consciousness, thinking, feeling, self, intelligence, pleasure, pain, happiness

Why do people, including scientists, look for a single concept, process or thing to explain multiple aspects of mind? They prefer one large problem rather than dozens or hundreds of smaller problems

Aaron Sloman:

"People are too impatient. They want a three-line definition of consciousness and a five-line proof that a computational system can or cannot have consciousness. And they want it today. They don't want to do the hard work of unraveling complex and muddled concepts that we already have, and exploring new variants that could emerge from precisely specified architectures for behaving systems"

How do we initiate what we call consciousness?

Most mental processes don't cause us to think or reflect about why or how. But when those low level processes don't function well or when they encounter obstacles the high-level activities start up with these properties: self models, serial processes, symbolic descriptions and recent memories. A trouble detecting critic (T) might operate as shown:


If you reverse the trouble detector, then you have a consciousness detector, ie. a part of our brain that sends signals to other parts including our language system which then invents words to describe this condition, such as: conscious, attentive, aware, alert, me, myself, deliberate, intentional, free will

Our higher level descriptions are mainly stable, they have been formed previously. Hence it's an illusion to think we live in the present moment!

The Immanence Illusion: For most of the questions you would otherwise ask, some answers will have already arrived before the higher levels of your mind have had enough time to ask for them. Our Critics may recognise a problem and start retrieving the knowledge you need before your other processes have had time to ask questions about it

Some philosphers regard explaining "subjective experience" as the hardest problem in psychology: the quality of deep blue, the sensation of middle C. Minsky argues that terms like experience or inner life refer to big suitcases of different phenomena. Our "insights" from inside our mind are frequently wrong. If consciousness means "awareness of our internal processes" then it doesn't live up to its reputation

Minsky uses the word model in this book to mean "a mental representation that can be used to answer some questions about some other, more complex thing or idea". We have multiple models: professional, political, beliefs about abilities, ideas about social roles, moral and ethical views. Our thinking depends on (a) quality of models; (b) how good our ways of choosing which model to use in different situations

"Free will" might mean "I have no model that explains how I made the choice I made"

The Cartesian Theater is the idea that our minds contain a central stage on which various actors perform while we (the self) watches and then makes decisions. This popular idea is analysed and debunked. The spatial metaphor is deeply held and hard to abandon

The idea that we live in the here and now, moving steadily into the future - is an illusion! "Real time" is a process of zigzagging through memories as we assess our progress on goals, hopes, plans and regrets!

Dennett and Kinsbourne (1992):

"... there is no single, definitive 'stream of consciousness', only a parallel stream of conflicting and continuously revised contents"

There are problems with thinking too much about how we think, to be too self aware would be very tedious! Minsky employs an amusing and enlightening dialogue with HAL to illustrate:

... interpreting those records is so tedious ... I often hear people say things like, "I'm trying to get in touch with myself." ... take my word for it, they would not like the result of accomplishing this

minsky 3: from pain to suffering

Overview of Chapter 3 of The Emotion Machine (summary, online draft, buy)

"Emotions are different Ways to Think."

When I reread this chapter it seemed to have two separate parts:
Sections 3-1 to 3-4 is an extended discussion of whether pain and suffering is a mystery
Sections 3-5 to 3-8 is building on Freud's idea that our minds are battlegrounds between basic instincts and higher ideals

What is the connection between these two parts? I think Minsky is using pain and suffering as one example of basic instincts. This sets the scene for the contrast of the Freudian conflict later in the chapter.

Pain and pleasure have many similar qualities. They both constrict one's range of attention, both have connections with how we learn, both reduce the priorities of one's other goals. Pain protects our bodies but destroys our minds. In an evolutionary sense this might be a programming bug that evolved before our higher level intellects

The extended discussion on pain, suffering and grief is very interesting and punctuated with some great quotes (from Woody Allen, Dennett, Shakespeare and Oscar Wilde). Minsky is a great writer as well as having great ideas.

One deficiency of behaviourism is that it only observed the actions of what people do while ignoring questions about what people do not do. Negative expertise is a very large part of every person's precious collection of commonsense knowledge. Negative expertise might work through Critics, each of which learns to recognise some particular kind of potential mistake

Types of Critics:

• Corrector - declares you are doing something dangerous
• Suppressor - interrupts before you begin an action
• Censor - prevents "incorrect" ideas occurring to you in certain situations

Freud was on the right track. The human mind is like a battleground, there are continual conflicts between our animal instincts and our acquired ideals


Human thinking does not proceed in any single, uniform way

On the issue of controlling our moods:

If you could switch all your Critics off then nothing would seem to have any faults ... everything now seems glorious

If you turned too many Critics on, you'd see imperfection everywhere ... ugliness ... if you found fault with your goals themselves, you'd feel no urge to straighten things out, or to respond to any encouragement

Sometimes we use one emotional state to combat another emotional state. For example, you might call up an image of a Challenger to use jealousy, anger or shame to combat sleep

Why do we need such fantasies, why aren't we more rational?

• concept of "rational" itself is a kind of fantasy because our thinking is never based on just pure logic
• directness would be too dangerous, if we could turn Hunger off we might starve; if we could turn Anger on we might fight all the time; if we could extinguish Sleep then we might wear out bodies out (these considerations shaped our evolution)

minsky 2: attachments and goals

Overview of Chapter 2 of The Emotion Machine (summary, online draft, buy)

This chapter is about how people choose which goals to pursue, through the strong self conscious feelings such as Pride and Shame. Pride or Shame (as distinct from not so strong emotions such as Pleasure or Dissatisfaction) play a unique role in determining our values, goals or ends (as distinct from learning methods of how to achieve a goal once we have it)

A sketch of a difference engine, which works to reduce the difference between your present situation and a goal, is introduced

Imprimers: a new word is introduced by Minsky (derived from imprinting):

"An imprimer is one of those persons to whom a child has become attached"

The "caregiver" word is not sufficient since attachments can form without physical care

Limits of behaviourism: The idea of learning by being "reinforced" by success or by "trial and error" does not explain how we develop completely new goals or "values" or "ideals". It would be potentially dangerous if strangers could easily alter our higher level goals.

Several different ways in which a child might change:

• Positive experience
• Negative experience
• Aversion learning: when a stranger scolds ...
• Attachment praise: imprimer praises
• Attachment censure: imprimer scolds
• Internal impriming

How could we elevate a goal? By moving it up the 6 level model, eg. from Deliberative thinking to Self-Conscious emotions



"The problem we faced" and "the action we took" are not simple objects that we can connect. Minsky argues that we also need to make structures which represent both external events and relevant internal mental events. We need reflective resources to choose which things to remember out of all the things we were doing when solving a particular problem. Minsky calls these "credit assignments"

minsky 1: Falling in Love

Overview of Chapter 1 of The Emotion Machine (summary, online draft, buy)

This chapter introduces a framework to think about the mind.

An attempt is going to be made to explain things that we take for granted, such as, perception, our comprehension of words, our preference for certain feelings.

Many words used to describe emotions and psychology are suitcase words, which have vague or multiple meanings. At strategic moments in this book Minsky introduces new words of his own because our current vocabulary often unintentionally serves to obscure the real workings of the mind

Some mind myths are critiqued. We don't have a single "logical" or "rational" Way to Think. Logic says nothing about which assumptions we begin with. There are dozens of different Ways to Think. We don't have a single Self but multiple models of Self.

The purpose of Minsky's lampooning of love is to point out that with love and some other emotions it is as though a switch has been thrown and a different program has started to run. It's an illustration of one of our many Ways to Think.

Quite a lot of infant behaviour can be explained by IF-then-DO reaction rules


With deliberate, calculated vagueness Minsky conceives of the mind as a cloud of resources. Different resources are activated for different Ways to Think and / or different emotional states.

During our childhood years our brains go through multiple stages of growth. Minsky conjectures that at least six levels of mental procedures will summarise his main ideas about how the human mind is organised

These ideas are explained in more detail in subsequent chapters

need to integrate different approaches to AI (Minsky)

Two different ways to represent an apple - a semantic network and a connectionist network

Minsky argues that to explain intelligence we need to integrate both of these approaches and not take an either / or attitude. The popularity of a connectionist only approach has retarded research into intelligence.

Connectionist networks (based on numbers showing strength of associations) can learn to recognise many important types of patterns - without any need for a person to program them. But number based networks have limitations. Every relationship is reduced to a number or strength so there remains almost no trace of the evidence that led to it, eg. the number 12 could represent all sorts of things

Minsky:

I see the popularity (of Connectionist Networks), in recent years, as having retarded the search for higher level ideas about human psychological machinery ... research on commonsense thinking kept advancing until about 1980, but then it was clearly recognised that further progress would need ways to acquire and organise millions of fragments of commonsense knowledge. That prospect seemed so daunting that most researchers decided to try, instead, to invent machines that could learn, by themselves, all the knowledge that they would need - in short, to invent new kinds of "baby machines" ...

Quite a few of these learning machines did indeed learn to do some useful things, but none of them went on to develop higher-level reflective Ways to Think - and I suspect that this was mainly because they tried to represent knowledge in numerical terms....

... I do not mean to suggest that such networks are not important ... it seems safe to assume that many of the low level processes in our brains must use some form of Connectionist Networks
- Minsky, pp. 289-91, The Emotion Machine

This helps me situate the work of Rodney Brooks (behavioural AI) as important but limited.

Logical vs.Analogical or Symbolic vs. Connectionist or Neat vs. Scruffy - this paper by Minsky (1990) has more detail

update: I'm still summarising minsky's book on the learning evolves wiki minsky page

mental modelling, all the way down

Some of the language of the following quote is mangled (bits missing) but the meaning is still clear:

Education is another area in which the computer scientist has confused form and content, but this time the confusion concerns his professional role. He perceives his principal function to provide programs and machines for use in old and new educational schemes. Well and good, but I believe he has a more complex responsibility–to work out and communicate models of the process of education itself.

In the discussion below, I sketch briefly the viewpoint (developed with Seymour Papert) from which this belief stems. The following statements are typical of our view:

– To help people learn is to help them heads, various kinds of computational models.
– This can best be done by a teacher who has, in his head, a reasonable model of what is in the pupil's head.
– For the same reason the student, when debugging his own models and procedures, should have a model of what he is doing, and must know good debugging techniques, such as how to formulate simple but critical test cases.
– It will help the student to know something about computational models and programming. The idea of debugging [note 2] itself, for example, is a very powerful concept-in contrast to the helplessness promoted by our cultural heritage about gifts, talents, and aptitudes. The latter encourages "I'm not good at this" instead of "How can I make myself better at it?"

These have the sound of common sense, yet they are not among the basic principles of any of the popular educational schemes such as "operant reinforcement," "discovery methods," audio-visual synergism, etc. This is not because educators have ignored the possibility of mental models, but because they simply had no effective way, before the beginning of work on simulation of thought processes, to describe, construct, and test such ideas
- Marvin Minsky, Turing Award Lecture, 1970

Teacher and student mental modelling are rather important, including debugging, and can be facilitated by computers properly used. But this requires a teacher who can both program the computer and understand the importance of mental modelling. If those prerequisites are missing then it's not all that surprising to discover that someone has done a research project showing that "it doesn't work".

reading Minsky

The Emotion Machine by Marvin Minsky

Minsky has studied many great writers who have thought deeply about the human mind. Not only contemporary thinkers but he ranges across the centuries (Aristotle, Augustine, Descarte, Darwin, Franklin, Poincare, Freud etc.). Many of the sections of his book begin with quotations and summaries from these writers and then proceed onto Minsky's own independent evaluation of them.

To provide just one example (there are many) in section 7-7 he uses quotations from a book written by Henri Poincare in 1913 as the basis for a discussion and presentation of his own views on a 4 stage model of unconscious processes (preparation, incubation, revelation and evaluation)

In reading Minsky, carefully, I obtain a strong feeling that I am receiving a distillation of some of the best thoughts from the best thinkers in human history from one of the current best thinkers who also happens to be a great writer

As well as that I'm discovering a very plausible view of what the research agenda for our understanding the mind ought to be.

I've been summarising some of it on the learning evolves wiki. In some ways it's a deceptively simple book but quite hard to hold all of it in your mind as an integrated whole.

the importance of and potential for the enhancement of mentoring

marvin minsky has recently written a great series of articles about the importance of cross age mentoring and how networks open up new opportunities for that - on the OLPC wiki

http://wiki.laptop.org/go/Marvin_Minsky_essays
Memo 3 essays (all four)
Memo 2 -> drawbacks of age based segregation

extract:

From where do our children’s self-images come? Of course, they copy a lot from their parents, siblings, teachers, and friends but (as noted in Memo 2) they also tend to emulate familiar public “celebrities,” so that many children come to know a lot about athletes, pop-stars and actors, but few can recognize the name of a single philosopher, scientist, or mathematician, because such achievers are rarely mentioned either in classrooms or media. The images of those celebrities must have substantial effects on our children’s goals—yet those descriptions are mainly fictitious, crafted by publicists to grip our children’s attentions for countless thousands of valuable hours. And even when those biographies are accurate, they don’t often demonstrate qualities that we should want our children to admire.

the teacher's union conservatism is just as bad or worse than the education departments conservatism on this issue - look at what DECS (Ed Department) and the AEU (Union) have done to Al Upton's students (update 3):

"Mentors/coaches – any communication between students and adults overseas was strongly advised against. DECS and AEU representatives agree on this"

study marvin minsky's work

It was a huge moment for me to receive a comment from marvin minsky on my blog recently

Maybe others would like to join me in studying his work?

Some things take a while to figure out. Papert and Minsky worked closely together at the MIT Media lab but Papert wrote about education of children and Minsky wrote about Artifical Intelligence, how to make machines think. Where did it meet? This is explained by Papert in his Afterword to Mindstorms:

For several years now Marvin Minsky and I have been working on a general theory of intelligence (called "The Society Theory of Mind") which has emerged from a strategy of thinking simultaneously about how children do and how computers might think ... the point of departure that separates us from most other members (of the AI community) is (that) ... seeing ideas from computer science not only as instruments of explanation of how learning and thinking in fact do work, but also as instruments of change that might alter, and possibly improve, the way people learn and think ... Marvin Minsky was the most important person in my intellectual life during the growth of the ideas in this book. It was from him that I first learned that computation could be more than a theoretical science and a practical art: It can also be the material from which to fashion a powerful and personal vision of the world" (pp. 208-210)

Society of Mind(1987) is a fascinating and brilliantly written book. Each page of the book presents a new idea, which piece by piece build to create a big picture of how parts of the mind might work. I read this book a long time ago but many of the ideas in it still seem fresh and relevant, eg. (why maths and science are hard)

Minsky's new book, The Emotion Machine, is available on line in draft form if you want to check it out before buying

Also check out these recent writings in support of the OLPC project

A lot of the research into the mind these days focuses on connectionism and neuroscience. With the noise and interest generated from those areas it is easy to get the impression that things have moved on and Minsky's ideas are out of date. However, it was recently pointed out to me that Minsky's ideas are very relevant to the notion of messy mind. It would be a huge mistake to not take a hard look at his latest contributions.

If you search this blog with the keyword 'minsky' you'll find several other relevant articles too.

why maths and science are hard

When we understand something well our cognitive structures are robust and cross linked. I can't prove that but it is a reasonable hypothesis

Whereas in maths and science work the preferred structures are often fragile and linear. So that if something goes wrong the whole thing collapses and we notice the error

So the dominant culture of maths / science (fragile linear) is at odds with our normal ways of learning something well (robust, cross linked)

In real life, our minds must always tolerate beliefs that later turn out to be wrong. It's also bad the way we let teachers shape our children's mathematics into slender, shaky chains instead of robust, cross-connected webs. A chain can break at any link, a tower can topple at the slightest shove. And that's what happens in a mathematics class to a child's mind whose attention turns just for a moment to watch a pretty cloud
- Marvin Minsky, Society of Mind, 18.8 Mathematics Made Hard, p 193

This is why we need Papert's turtle or Resnick's cat

building complexity

Introduction to LogoWorks by Marvin Minsky (1994)

I had a few LOLs and AHA moments whilst reading this article.The scratch program in conjunction with Barry Newell's Turtle Confusion booklet does provide us with the opportunity to teach the concept of state and how to build complex structures from simpler structures.

State is an important fundamental concept that has come into being as a "fundamental" following the invention of the computer, which Alan Turing ran in his head before it came into being as a physical thing. Which goes to show that the fundamentals change.

One possible reason why kids building things declined in popularity:

The golden age of construction-sets came to its end in the 1960's. Most newer sets have changed to using gross, shabby, plastic parts, too bulky to make fine machinery. Meccano went out of business. That made me very sad. You can still buy Erector, but insist on the metal versions. Today the most popular construction set seems to be LEGO -- a set of little plastic bricks that snap together. ... It is probably easier for children, at first, but it spans a less interesting universe, and doesn't quite give that sense of being able to build "anything." Another new construction toy is FischerTechnik, which has good strong parts and fasteners. It is so well made that engineers can use it. But because it has so many different kinds of parts, it doesn't quite give you that LOGO-like sense of being able to build your own imaginary world.

About the time that building-toys went out of style, so did many other things that clever kids could do. Cars got too hard to take apart -- and radios, impossible. No one learned to build much any more, except to snap-together useless plastic toys. And no one seemed to notice this, since sports and drugs and television-crime came just in time. Perhaps computers can help bring us back.

How not to explain to a Martian how things work:

A Martian szneech once mindlinked me; it wanted to know what literature was. I told it how we make sentences by putting words together, and words by putting letters together, and how we put bigger spaces between words so that you can tell where they start and stop. "Aha," it said, "but what about the letters?" I explained that all you need are little dots since, if you have enough of them, you can make anything.

The next time, it called to ask what tigers were. I explained that tigers were mostly composed of hydrogen and oxygen. "Aha," it said, "I wondered why they burned so bright." The last time it called, it had to know about computers. I told it all about bits and binary decisions. "Aha," it said, "I understand."

The importance of understanding state:

When Turing was quite young, he realized that what a computer does only depends on the States of its parts -- and on the laws that change their states. Except for that, it doesn't matter how the parts are made. Then Turing asked what programs are -- and realized that you could think of programs as just sets of states -- or rather, ways to pre-arrange how a computer will, later, change its States

Computer programs are societies and algorithmic processes work independently of what materials they are composed of:

This must be the secret of those magical experiences I had, first with those construction sets and, later, with languages like LOGO. There's something "universal" about the ways that big things don't depend so much on what's inside their little parts. What matters is more how the parts affect each other – and less about what they are, themselves. That's why it doesn't matter much if money's made of paper or of gold, or houses out of boards or bricks. Similarly, it probably won't matter much if aliens from outer space had golden bones instead of ones of stones, like ours. People are missing something important, who don't appreciate how simple things can grow into entire worlds. They find it hard to understand Science, because they find it hard to see how all the different things we know could be made of just a few kinds of atoms. They find it hard to understand Evolution because they find it hard to see how different things like birds and bees and bears could come from boring, lifeless chemicals -- by testing trillions of procedures. The trick, of course, is doing it by many steps, each using procedures which have been debugged already, in the same way, but on smaller scales