The Society of Mind

1. Prologue

"Much of the power of the mind seems to stem from just the messy ways its agents cross-connect. If so, that complication [of the structure of this book] can't be helped; it's only what we must expect from evolution's countless tricks."

• The Agents of the Mind - Minds are built from mindless agents, parts that are much smaller and simpler than anything we'd consider smart. Our theory must span three scales of time:
  • Slow - for the billion years in which our brains have evolved.
  • Fast - for the fleeting weeks and months of infancy and childhood
  • In-Between - for the centuries of growth of our ideas through history
• The Mind and the Brain - Psychologists, like Freud and Piaget, and mathematicians, like Kurt Gödel and Alan Turing contributed ideas that were brought together in the 1940s to show how machines might be made to see, reason, and remember
• The Society of Mind - Many many processes are going on in our minds and bodies all the time to allow us to walk, drink a cup of tea and hold conversations. These things seem so natural that we take them for granted, but they all take vasts amounts of machinery
• The World of Blocks - Though all adults know how to build a tower of blocks, no one understands how we learn to do them! This amnesia of infancy makes us think that all our abilities were always there inside our minds, and we don't take time to ask how they began and grew.
• Common Sense - Is not a simple thing. Instead, it is an immense society of hard-earned practical ideas - of multitudes of life-learned rules and exceptions, dispositions and tendencies, balances, and check
  • As each new group of skills matures, we build more layers on top of them. As time goes on, the layers below become increasingly remote until, when we try to speak of them in later life, we find ourselves with little more to say than "I don't know".
• Agents and Agencies - Block Builder and other agents have "agency" in that they seem to know how to do their jobs, but as "agents" cannot know anything at all. Every time we seem to find an agent with intelligence, we must look inside it to break it down smaller
  • When you drive a car, you don't care how it works, but when something goes wrong you have to look inside it to see. But you can't be thinking about the detailed interior when you are driving, or you will crash
  • Knowing how is not the same as knowing why
  • We'll constantly switch between the viewpoints of agents and agencies.

2. Wholes and Parts

• Components and Connections - First we must know how each separate part works. Second, we must know how each part interacts with those to which it is connected. And third, we have to understand how all these local interactions combine to accomplish what that system does - as seen from the outside.
• Novelists and Reductionists :
  • Reductionists - Are people who prefer to build on old ideas. They are usually right - at least at science's cautious core, where novelties rarely survive for long.
  • Novelists - are people who like to champion new hypotheses. Outside science's core, older ideas have had more time to show their flaws
  • We need to approach our descriptions at various different levels and each higher level of description must add to our knowledge about lower levels.
  • Physics has only a dozen basic principles that are combined into explanations, while psychology may need to combine hundreds of smaller theories.
• Parts and Wholes - It's hard to explain what it happening in our brains, but talking about "more than the sum of its parts" won't help us.
• Holes and Parts - We can't use words like life and mind to describe the smallest components of living things because these words were invented to describe how larger assemblies interact.
• Easy Things are Hard - In general, we're least aware of what our minds do best. It's mainly when our other systems start to fail that we engage the special agencies involved with what we call consciousness. We'"re more aware of simple processes that don't work well than of complex ones that work flawlessly.
• Are People Machines? - Let's put aside this argument for now. We're certainly not trivial machines, but we are getting better and better at making highly sophisticated machines with millions of parts.

3. Conflict and Compromise

• Conflict - Agencies like "Play" must compete with other agencies like "Eat" and "Sleep". Conflicts within agencies tend to migrate to higher levels.
• Noncompromise - The Principle of Noncompromise: The longer an internal conflict persists among an agent's subordinates, the weaker becomes that agent's status among its own competitors. If such internal problems aren't settles soon, other agents will take control and the agents formerly involved will be "dismissed".
  • We sometimes settle disputes by appealing to superiors, but other conflicts never end and never cease to trouble us.
  • Tiny mental agents don't know enough to negotiate with each other. Only larger agencies could be resourceful enough to do such things.
• Hierarchies - The relations between agents are hierarchical with "Builder" being like a high-level executive, far removed from those subordinates who actually produce the final product. But there is no real planning or assignments happening or ways to deal with unexpected events.
• Heterarchies - But there are also heterarchies where agents require cooperation and no one is legitimately in charge of the other.
• Destructiveness - Destructive acts can serve constructive goals by leaving fewer problems to be solved. There are no simple causes for destructive acts, and no need for zero-sum games. When Sleep starts, Play can still run, with the child building towers in its dreams.
• Pain and Pleasure Simplified - They both make it hard to think of other things, thus simplifying your point of view.

4. The Self

• The Self - We don't know what we mean by "self". We'll use the following terms:
  • Self-Images - Beliefs about what we are, are capable of, and may be disposed to do. We use these beliefs when we solve problems or make plans.
  • Self-Ideals - Ideas about what we'd like to be and what we ought to be, which have guided our growth from infancy. May be hard to express, because they are (can be?) inaccessible to consciousness.
• One Self or Many? - We all sometimes have feelings of disunity, conflicting motives, compulsions, internal tensions and dissensions. Perhaps, paradoxically, it is because there are no persons in our heads, that we construct the myth that we're inside ourselves.
• The Soul - Beliefs in souls are insinuations that we're helpless to improve ourselves. But the value of a human self is not in some small precious core, but in its vast, constructed crust.
• The Conservative Self - One function of the self is to keep us from changing too rapidly. If we changed our minds too recklessly, we could never know what we might want next. We'd never get much done because we could never depend on ourselves.
• Exploitation - If work could simply turn off sleep, we'd quickly wear our bodies out. If work could simply switch anger on, we'd be fighting all the time. Directness is too dangerous. We'd die. If self-control were easy to obtain, we'd end up accomplishing nothing at all.
• Self-Control - Willpower, activity, expression, chemistry, emotion, attachment - so many schemes for self-control! How do we choose which ones to use? There isn't any easy way. Self-discipline takes years to learn. It grows inside us stage by stage.
• Long-Range Plans - The easiest path to "self-control" is doing only what one is already disposed to do.
  • Which are our slowest-changing agencies of all? Later we'll see that these must include the silent, hidden agencies that shape what we call character. These are the systems that are concerned no merely with the things we want, but with what we want ourselves to be - that is the ideals that we set for ourselves.
• Ideals - Without enduring self-ideals, our lives would lack coherence. As individuals, we'd never be able to trust ourselves to carry out our personal plans. In a social group no one person would be able to trust the others. A working society must evolve mechanisms that stabilize ideals - and many of the social principles that each of us regards as personal are really "long-term memories" in which our cultures stores what they have learned across the centuries.

5. Individuality

• Circular Causality - We often speak of "straightening things out" when we're involved in situations that seem too complicated. It seems to me that this metaphor reflects how hard it is to find one's way through a maze that has complicated loops in it. In such a situation, we always try to find a path through it by seeking causal explanations that go in only one direction, and we can apply the vary same types of reasoning to everything that we can represent in terms of chains of causes and effects.
• Unanswerable Questions - All human cultures evolve institutions of law, religion, and philosophy, and these institutions both adopt specific answers to circular questions and establish authority-schemes to indoctrinate people with those beliefs. Does this to substitute dogma for reason and truth? Maybe, but in exchange, they spare whole populations from wasting time in fruitless reason loops. Minds can lead more productive lives when working on problems that can be solved.
• The Remote-Control Self - The idea of a single, central Self doesn't explain anything. Maybe we believe it because so much of what our minds do is hidden from the parts of us that are involved with verbal consciousness.
• Personal Identity - In order to keep control, we simplify how we represent what's happening and then, when that complicated mental scene is straightened out it seems as though a single pipeline of ideas were flowing through the mind. Thinking of ourselves as a single thing helps with:
  • The Physical World - We can base our plans on having a single body.
  • Personal Privacy - We must remember to whom we have told something, and individuals give us a sense of responsibility.
  • Mental Activity - Thinking two different thoughts from different agencies is confusing
• Fashion and Style - Fredkin's paradox: The more equally attractive two alternatives seem, the harder it can be to choose between them. Aesthetics are useful for:
  • Recognisibility - Familiar styles make it easier for us to recognize and classify the things we see.
  • Uniformity - Uniform styles protect us from useless distractions
  • Predictability - Societies need rules that make sense for individuals
• Traits - We try to be consistent and to think that others are consistent, because this is easier.
• Permanent Identity - We all experience that sense of changelessness in spite of change.

6. Insight and Introspection

• Consciousness - Turning our bodies and walking in a direction is much like turning a car and driving - in both cases we are aware only of a general intention and all the rest takes care of itself. Our conscious thoughts use signal-signs to steer the engines in our minds, controlling countless processes of which we're never much aware. Not understanding how it's done, we learn to gain our ends by sending signals to those great machines, much as the sorcerers of older times used rituals to cast spells.
• Signals and Signs - How do we understand anything? Almost always, I think, by using one or another kind of analogy - that is by representing each new thing as though it resembles something we already know. Whenever a new thing's internal workings are too strange or complicated to deal with directly, we represent whatever parts of it we can in terms of more familiar signs:
  • To overstate the case a bit, what we call consciousness consists of little more than menu lists that flash, from time to time, on mental screen displays that other systems use. Like computer game players using symbols to invoke complicated processes of which they know nothing.
  • You can scarcely see a hammer except as something to hit with, or see a ball except as something to throw and catch. Why do we see things less as they are and more in view of how they can be used? It is because our minds did not evolve to serve as instruments for science or philosophy, but to solve practical problems of nutrition, defense, procreation, and the like. We tend to think of knowledge as good in itself, but knowledge is useful only when we can exploit it to help us reach our goals.
• Thought Experiments - Why is it so hard to explain the results of experiments of imagining things in our minds? Because we get confused. Our thoughts about our mind-experiments are mind-experiments themselves - and therefore interfere with one another:
  • Thinking affects our thoughts.
• B-Brains - The only way to get a brain to keep track of itself is to split it into two parts, A and B. Connect A to the world and connect B only to A. Then A is the B-Brain's world.
• Frozen Reflection - When introspection seems to work, it's not because we've found a magic way to see inside ourselves. Instead, it means that we've done some well-designed experiment.
• Momentary Mental Time - No portion of a mind can ever know everything that is happening at the same time in all the other agencies. Because of this, each agency must have at least a slightly different sense both of what has happened in the past - and of what is happening "now". Each different agent of the mind lives in a slightly different world of time.
• The Causal Now - Our everyday ideas about the progression of mental time are wrong: they leave no room for the fact that every agent has a different causal history. To be sure, those different pasts are intermixed over longer spans of time, and every agent is eventually influenced by what has happened in the common, remote history of its society. But that's not one means by "now". The problem is with the connections between the moment-to-moment activities of largely separate agencies.
• Thinking Without Thinking - If we're aware of anything at all, it is that "I'm aware - hence I'm aware." yet what do such convictions really mean? If self-awareness means to know what's happening inside one's mind, no realist could maintain for long that people have much insight in the literal sense of seeing-in.
• Heads in the Clouds - Even in your own mind, you can never know precisely what you mean! How useless any thought would be if, afterward, your mind return to the selfsame state. But that never happens, because every time we think about a certain thing, our thoughts go off in different ways:
  • The secret of what anything means to us depends on how we've connected it to all the other things we know. It's almost always wrong to seek the "real meaning" of anything. A thing with just one meaning has scarcely any meaning at all.
  • An idea with a single sense can lead you along only one track. Then, if anything goes wrong, it just gets stuck - it sits in your mind with nowhere to go. When someone learns something by rote (ie with no sensible connections) we say they don't really understand. Rich meaning-networks, however give you many different ways to go: if you can't solve a problem one way, you can try another. Too many indiscriminate connections will turn a mind to mush. But well-connected meaning structures let you turn ideas around in your mind, to consider alternatives and envision things from many perspectives until you find one that works. And that's what we mean by thinking!
  • David Hume: "What we call a mind is nothing but a heap or collection of different perceptions, united together by certain relations and suppos'd, tho' falsely, to be endow'd with a perfect simplicity and identity."
• Worlds Out of Mind - There is no singularly real world of thought; each mind evolves its own internal universe.
  • We appear to like best worlds of thought where goals and actions mesh in regions large enough to spend our lives in - and become a Buddhist, Republican, pet, or topologist.
  • Some mental starting points grow into great, coherent continents. In certain parts of maths, science, and philosophy, a relatively few but clear ideas may lead into an endless realm of complex yet consistent new structures. Yet even in maths, a handful of seemingly innocent rules can lead to complications far beyond our grasp.
  • In mental realms we make up countless artificial schemes to force things to seem orderly, by specifying legal codes, grammar rules and traffic laws. When growing up in such a world, it all seems right and natural - and only scholars and historians recall the mass of precedents and failed experiments it took to make it work so well. These "natural" worlds are actually more complex than the technical worlds of philosophy. They're far too vast to comprehend - except where we impose on them the rules we make.
  • In some cases, an accident of mental stress has temporarily suppressed the capacity to question, doubt, or probe. The mind has found a way to simplify itself - this may lead to a sense of revelation, but perhaps no problem has been solved at all.
• In-Sight - Where do we get the ideas we need? Most of our concepts come from the communities in which we're raised. Even the ideas we "get" for ourselves come from communities - this time the ones in our heads. Brains don't manufacture thoughts in the direct ways that muscles exert forces or ovaries make estrogens; instead, to get a good idea, one must engage huge organizations of submachines that do a vast variety of jobs.
• Internal Communication - We overestimate how much we actually communicate. Instead, despite those seemingly important differences, much of what we do is based on common knowledge and experience. Although we can't express what we mean, we can often cite various example to indicate how to connect structures we're sure must already exist inside the listener's mind. In short we can often indicate which sorts of thoughts to think, even though we can't express how they operate.
  • We find it particularly hard to use our language skills to talk about the parts of the mind that learned such skills as balancing, seeing, and remembering, before we started to learn to speak.
• Self-Knowledge is Dangerous - Why do we become bored when doing the same thing over and over, even if that activity was pleasant at first? Without variety, our pleasure systems tend to satiate. Every learning system must have some such protective scheme, since otherwise it could get trapped into endlessly repeating the same activity. It's good that we have such mechanisms and that they are very hard to suppress.
• Confusion - It's mainly when our systems fail that consciousness becomes engaged. It is better to realize that one is confused as opposed to being confused without knowing it. Then we can apply our intellect to alter or repair the defective process.

7. Problems and Goals

• Intelligence - Our minds contain processes that enable us to solve problems we consider difficult. "Intelligence" is our name for whichever of those processes we don't yet understand.
• Uncommon Sense - Much of "expert" adult thinking is actually simpler than what is involved when ordinary children play!
  • What people call common sense is actually more intricate than most of the technical expertise we admire. Think of all the different kinds of things a child must know merely to build a house of blocks - shapes and colors, space and time, support and balance, and an ability to keep track of what one is doing.
  • To be considered an "expert" one needs a large amount of knowledge of only a relatively few varieties. In contrast, an ordinary person's "common sense" involves a much larger variety of different types of knowledge - and this requires more complicated management systems.
  • Each type of knowledge needs some form of "representation" and a body of skills adapted to using that style of representation. Once that investment has been made, it is relatively easy for a specialist to accumulate further knowledge, provided the additional expertise is uniform enough to suit the same style of representation. The greater variety of representations would make it much harder for a single person to learn to deal with a few diseases, law cases, architectural blueprints, and orchestral scores. It would be like learning many different languages, each with its own grammar, lexicon, and idioms.
• The Puzzle Principle - We can program a computer to solve any problem by trial and error, without knowing how to solve it in advance, provided only that we have a way to recognize when the problem is solved. Without some notion of progress toward a goal, it is hard to do better than mindless chance.
• Problem Solving - The most powerful way we know for discovering how to solve a hard problem is to find a method that splits it into several simpler ones, each of which can be solved separately.
  • The Progress Principle - Any process of exhaustive search can be greatly reduced if we possess some way to detect when "progress" has been made. Then we can trace a path toward a solution, just as a person can climb an unfamiliar hill in the dark - by feeling around, at every step, to find the direction of steepest ascent.
  • Many easy problems can be solved this way, but for a hard problem, it may be almost as difficult to recognize "progress" as to solve the problem itself. Without a larger overview, that "hill climber" may get stuck forever on some minor peak and never find the mountaintop. There is no foolproof way to avoid this.
  • The most efficient way to solve a problem is to already know how to solve it. Then one can avoid search entirely.
• Learning and Memory - Those twin ideas - reward/success and punish/failure - do not explain enough about how people learn to produce the new ideas that enable them to solve difficult problems that could not otherwise be solved without many lifetimes of ineffectual trial and error. The answer must lie in learning better ways to learn.
  • At each moment, we must keep track of what we've just done, we must somehow maintain our goals and, finally, once the problem is solved, we need access to records of how it was done, for use when similar problems arise in the future.
  • When a human brain solves a hard problem, many millions of agents and processes are involved. Which agents could be wise enough to guess what changes should then be made? Where in the mind are judgements made about which agents merit praise or blame?
• Reinforcement and Reward - We cannot learn to solve hard problems by indiscriminately reinforcing agents or their connections. Why is it that among all the animals, only the great-brained relatives of man can learn to solve problems that require many steps or involve using the same agencies for different purposes?
• Local Responsibility - Local schemes reward each agent that helps accomplish its supervisor's goal. Global schemes reward only agents that help accomplish top-level goals.
  • It is harder to implement a global learning scheme, which is much more parsimonious, and global policies lead to learning more slowly. We need to learn which learning strategies to use, depending on the circumstances.
• Difference-Engines - A goal-driven system does not seem to react directly to the stimuli or situations it encounters. Instead, it treats the things it finds as objects to exploit, avoid, or ignore, as though it were concerned with something else that doesn't yet exist. When any disturbance or obstacle diverts a goal-directed system from its course, that system seems to try to remove the interference, go around it, or turn it to some advantage.
  • A difference engine must contain a description of a desired situation.
  • It must have subagents that are aroused by various differences between the desired situation and the actual situation.
  • Each subagent must act in a way that tends to diminish the difference that aroused it.
• Intentions - The difference-engine scheme scheme remains the most useful conception of goal, purpose, or intention yet discovered. It embodies both a representation of some outcome and a mechanism to make it persist until that outcome is achieved.
• Genius - Most heroes are intensely motivated, proficient in some field, and stubborn. But genius needs unusually effective ways to learn. You must learn a lot and manage what you learn, using special knacks of higher-order expertise:
  • Such knacks could begin with early accidents when a child happens upon clever ways of arranging blocks, etc. But adults cannot necessarily see these internal strategies, which can lead to silent growth in which some better ways to learn may lead to better ways to learn to learn. Then later we'll observe an awesome, qualitative change, with no apparent cause and call it a talent, aptitude, or gift.

8. A Theory of Memory

Proust: "In truth, the person within me who was at this moment enjoying this impression enjoyed in it the qualities which it possessed that were common to both an earlier day and the present moment; and this person came into play only when, by this process of identifying past with present, he could find himself in the only environment in which he could live, that is to say, entirely outside of time."

• K-Lines: A Theory of Memory - We keep each thing we learn close to the agents that learn it in the first place, using a type of agent called a Knowledge-line or K-line. We memorize what we're thinking about by making a list of the agents involved in that activity.
  • Whenever you get a good idea, solve a problem, or have a memorable experience, you activate a K-line to represent it. A K-line is a wirelike structure that attaches itself to whichever mental agents are active when you solve a problem or have a good idea.
  • When you activate that K-line later, the agents attached to it are aroused, putting you into a mental state much like the one you were in when you solved that problem or got that idea. This should make it relatively easy for you to solve new, similar problems.
  • Each agent can become attached to many different K-lines
  • For each familiar kind of mental job, your K-lines can refill your mind with fragments of ideas you've used before on similar jobs. In such a moment, you become in those respects more like an earlier version of yourself.
• Re-membering - When facing a new problem which is similar to an old problem, you activate an old K-line, kP, alongside your recent thoughts, Q, and both sets of agents will work together to solve today's problem. This is the simplest concept of what memories are and how they are formed.
  • If we give too much priority to the K-line's agents, we risk re-arousing old states of mind so strongly that they overwhelm our present thoughts and lost track of what we're thinking now and wipe out all the work we've done. We only want some hints, suggestion, and ideas.
  • The ideal scheme would activate exactly those P's that would be most helpful in solving the present problem, but judging that is hard.
• Mental States and Dispositions - K-lines can easily record relatively widespread and diffuse activities and, later, reactivate them all at once.
  • The experiences we find easiest to recollect are often just the kinds we find the hardest to describe.
  • In order fot a word to have a predictable effect on other persons, we must maintain strict, public discipline on how it is used - whereas each person's private, internal signals need not be so constrained.
  • The traditional view, that it is easy to understand how minds can deal with facts and propositions but hard to see how minds could have diffuse, hard-to-express dispositions, must be upside-down
• Partial Mental States:
  • A total state of mind is a list that specifies which agents are active and which are quiet at a certain moment
  • A partial state of mind merely specifies that certain agents are active but does not say which other agents are quiet
  • The "entire system" can "think several thoughts at once" because each of these thoughts is contained in a partial state of mind just like a crowd of separate people can.
• Level Bands - Understanding never ends! - we can always find more to say about a situation. We learn by attaching agents to K-lines, but we don't attach them all with equal firmness. We make strong connections at a certain level of detail, but we make weaker connections at higher and lower levels.
  • The weakly attachments are assumptions by default, which will serve unless and until they must be overridden by a specificity.
• Levels - The sorts of knowledge in mid-level bands is most broadly and generally useful, whereas uppermost and lowest-level bands are more likely to be based on aspects of the problem that are specific to an older goal or to the particular details of the original problem.
  • It is no accident that level-related ideas play many different roles in how we think.
• Fringes - Suppose some memory were so complete that it made you relive, in every detail, some perfect moment of your past. That would erase your present you - and you'd forget what you had asked your memory to do! Fringing effects make our memories more relevant to our present purposes. In order to think, we need intimate connections between things and goals - between structures and their functions. What use would thinking be at all, unless we could relate each thing's details to our plans and intentions?
  • Lower Band - Beyond a certain level of detail, increasingly complete memories of previous situations are increasingly difficult to match to new situations. The lower fringe is commonly concerned with the structure of things, and the objective details of reality
  • Upper Band - Memories that arouse agents at too high a level would tend to provide us with goals that are not appropriate to the present situation. The upper fringe is commonly involved with the functions of things and our subjective concerns with goals and intentions
• Societies of Memories - As we make new memories, we prefer to attach to existing K-lines than to individual agents.
  • Jack to Male, Young:
  • Kite to Paper, String, Red
  • Fly to Outside, Wind
  • Connecting new K-lines to old ones will not recapture so many of the scene's precise, perceptual details. Instead, the kinds of mental states that this hierarchical type of memory produces will be based more on stereotypes and default assumptions than on actual perceptions. You will tend to remember only what you recognized at the time.
• Knowledge-Trees - When making a new K-line memory, do not connect it to all the K-lines active at the time but only to those that are active within a certain level-band. Eventually all of our knowledge-structures become entangled with various sorts of exceptions, shortcuts, and cross-connections. No matter: the level-band idea will still apply in general, since most of what we know will still be mainly hierarchical because of how our knowledge grows.
• Levels and Classifications - We tend to think that our hierarchies illustrate some kind of order that exists in the world but frequently they come from the mind and merely appear to belong to the world.
  • We frequently use two or more classifications at the same time. A child can play with a porcelain duck as though it were a pretend animal but still behave in an appropriate way for a delicate china object.
  • When attempting a new task, we never like to start anew: we try to use what has worked previously. So we search around inside our minds for old ideas to use. Then, when part of any hierarchy seems to work, we drag the rest along with it.
• Layers of Societies - We can imagine an endless sequence of societies or agencies in which each new one learns to exploit the last. This is how minds develop in infancy, as layers of societies.
  • Each new layer begins as a set of K-lines, which starts by learning to exploit whatever skills have been acquired by the previous layer. Whenever a layer acquires some useful and substantial skill, it tends to stop learning and changing - and then yet another new layer can begin to learn to exploit the capabilities of the last.
  • Each new layer begins as a student, learning new ways to use what older layers can already do. Then it slows its learning rate - and starts to serve both as subject and as teacher to the layers that form afterward.

9. Summaries

• Wanting and Liking - Our reactions of pleasure or disgust are only superficial summaries of pyramids of underlying processes.
  • The surer you are that you like what you are doing, the more completely your other ambitions are being suppressed.
  • The relation between wanting and liking is not simple at all, because our preferences are the end products of so many negotiations among our agencies. To accomplish any substantial goal, we must renounce the other possibilities and engage machinery to keep ourselves from succumbing to nostalgia or remorse. Then we use words like "liking" to express the operation of the mechanisms that hold us to our choice.
  • Liking's job is shutting off alternatives. It narrows down our choices and provides artificial clarity.
• Gerrymandering - What is the significance in complicated systems of those pleasant feelings of accomplishment and disagreeable sensations of defeat? They must be involved with how our higher-level agencies make summaries. No single sense of good or bad can reflect much of what went on inside all your agencies; too much information must be concealed, but there are many reasons for oversimplifying.
• Learning from Failure - Some parts of our minds learn from success, but other portions learn mainly when we make mistakes, by remembering the circumstances in which various methods failed to work. We can learn what not to do and what not to think, which permeates our minds with taboos and prohibitions of which we're entirely unaware.
  • It is no accident that there are no exceptions to the rules in mathematical worlds. There we start with the rules and imagine only objects that obey them. But perfect logic rarely works in the real worlds of people, thoughts, and things. We can't so willfully make up the rules for objects that already exist, so our only course is to begin with imperfect guesses - collections of rough and ready rules - and then to proceed to find our where they're wrong.
• Enjoying Discomfort - Nothing would get done if we succumbed to satisfaction. When doing maths, climbing freezing mountain peaks, or playing pipe organs with our feet: some parts of the mind find it horrible, while other parts enjoy forcing those first parts to work for them. We seem to have no names for processes like these, though they must be among our most important ways to grow.

10. Papert's Principle

• Piaget's Experiments - Each normal child eventually acquires an adult view of quantity - apparently without adult help!
• Reasoning About Amounts - We do not learn one single, underlying "concept of quantity". Instead, each person must construct a multilevel agency, the Society-of-More, that finds different ways to deal with quantities.
  • Younger children may possess the ideas they need, but don't know how to apply them! They lack adequate knowledge about their knowledge or have not acquired the checks and balances required to select or override their hordes of agents with different perceptions and priorities.
  • It is not enough to be able to use many kinds of reasoning; one also must know which to use in different circumstances! Learning is more than the accumulation of skills. Whatever we learn, there is always more to learn - about how to use what we already learned.
• Priorities - Young children may place their agents in some order of priority. Most people seem most sensitive to vertical extents. This may be built into our brains or learned, but more height often goes along with other sorts of largeness. No other agent seems so good as Tall for making everyday comparisons.
• Papert's Principle - Some of the most crucial steps in mental growth are based not simply on acquiring new skills, but on acquiring new administrative ways to use what one already knows.
  • The processes which assemble agents into groups must somehow exploit relationships among the skills of those agents. Because Tall and Thin are more similar in character to one another than to Confined, it makes sense to group them more closely together in the administrative hierarchy.
• The Society of More - Each higher-level agent embodies a form of higher-order knowledge that helps us organize ourselves by telling us when and how to use the things we know. Without a many layered management, we couldn't use the knowledge in our low-level agencies; they'd all keep gettin in one another's way.
• About Piaget's Experiments - Stage magicians find that making things disappear does not entertain the youngest children; presumably that are too used to encountering the unexplainable. What happens when More cannot decide what to do? That depends upon the states of other agencies - including those involved in dealing with frustration, restlessness, and boredom.
• The Concept of Concept - How do children accumulate and classify their many methods for comparing things? No child has the time to generate and test all possible combinations to find which ones are sensible. Instead, always try to combine related agents first.
• Education and Development - We can't force children to learn too quickly. There is constantly a tension between organising a hierarchy of concepts and managing the mass of exceptions and only the mature mind can combine the two.
• Learning a Hierarchy - The nerve cells in an animal's brain can't always move aside to make more room for extra ones. So these new layers might indeed have to be located elsewhere, attached by bundles of connection wires. No aspect of the brain's anatomy is more striking than its huge masses of connection bundles.

11. The Shape of Space

• Seeing Red -
• The Shape of Space -
• Nearnesses -
• Innate Geography -
• Sensing Similarities -
• The Centered Self -
• Predestined Learning -
• Half-Brains -
• Dumbbell Theories -

12. Learning Meaning

• A Block-Arch Scenario -
• Learning Meaning -
• Uniframes -
• Structure and Function -
• The Functions of Structures -
• Accumulation -
• Accumulation Strategies -
• Problems of Disunity -
• The Exception Principle -
• How Towers Work -
• How Causes Work -
• Meaning and Definition -
• Bridge-Definitions -

13. Seeing and Believing

• Reformulation -
• Boundaries -
• Seeing and Believing -
• Children's Drawing-Frames -
• Learning a Script -
• The Frontier Effect -
• Duplications -

14. Reformulation

• Using Reformulations -
• The Body-Support Concept -
• Means and Ends -
• Seeing Squares -
• Brainstorming -
• The Investment Principle -
• Parts and Holes -
• The Power of Negative Thinking -
• The Interaction-Square -

15. Consciousness and Memory

• Momentary Mental State -
• Self-Examination -
• Memory -
• Memories of Memories -
• The Immanence Illusion -
• Many Kinds of Memory -
• Memory Rearrangements -
• Anatomy of Memory -
• Interruption and Recovery -
• Losing Track -
• The Recursion Principle -