This is probably one of the most important things to think about.

There are two aspects of paedagogy: initial knowledge, and current affairs. Consider television news bulletins. They assume a certain amount of existing knowledge - what a country is, what money is, where the United States is, how to understand spoken English, and so on. This is all a base of knowledge needed to understand the rest. Children need to be taught all of this. The initial knowledge is constantly updated with new knowledge.

Paedagogy extends the human being. Current affairs extend the senses - as well as seeing what is going on in one's immediate environment, one knows what is going on all over the world. Initial knowledge extends the memory of one's own life - now one knows about the history of the world which is the background to current affairs.

We should give careful thought to what should be the substance of both forms of paedagogy. We would like to present to children an account of how they came to be, viewing the whole universe as an extension of their bodies. This would be an outlook passed on through the generations. The accuracy of the outlook would depend on how long it took to learn. At the moment, children spend about twelve years in school, so we should look for the best presentation of facts that would take twelve years. At the moment, school lessons are very divided into different subjects. They ought to support and reinforce each other, as part of a single presentation. The key word here is holism.


A lot of the time when someone is trying to learn about something by reading a text they are trying to get sparks of understanding to occur in their mind when they are doing it. To know what this means, these sparks of understanding are what you are missing when you have read too much and your brain is tired and you can't make sense of anything, even parse one sentence.

Presentation of knowledge should reflect an internal representation and be as compact as possible. Diagrams should be used when possible. Looking at a diagram one can directly see the fact and doesn't have to use mental effort in constructing one's own mental image.

We'd like a collection of such presentations, that could cover a wide variety of relations: such as sequences, family trees, saying that one thing is a special case of another, and so on

Wikipedia is probably the closest thing at the moment to something you can use to explore the totality of knowledge. Interactive computer programs are the future of paedagogy, I think. One will be able to sit back and browse a body of knowledge, looking at what is found immediately interesting and slowly soaking knowledge into the brain.

I would like to think that this is true of even complicated and difficult bodies of knowledge, like mathematics or foreign languages. In hindsight, looking back at lecture notes, a lot of it is wordier than it needs to be and there aren't actually that many basic ideas. A good project for me could be to try to produce some mathematical educational videos, and see how easy it could be to put across understanding. It is my opinion that anything should be easy to learn if it is learnt slowly enough. What's 'hello' in Turkish? Well gee, I don't know. I saw it yesterday but forgot it instantly. But that would be an interesting fact. After I knew that, what 'goodbye' and 'thank you' are would be the next most interesting facts. This could gradually segue into knowledge of orthography and grammar. Once a larger body of vocabulary is built up, it's easier to learn more vocabulary, because every word in the language balances against every word in the language that is known, in distinction to it. (There are potential connections here between each and every word, but I'm not sure what connections should be included in a formal, electronic representation. I'd have to try making a system and cross such bridges when I came to them.)

I should point out that a body of knowledge is a collection of related facts. If I think about the family tree of my extended family, I don't hold it all in my head at the same time. If I were to represent this knowledge visually, and it was inconvenient and messy to have one large diagram, with each person occurring exactly once in it, containing all the relevant information about the relations between people, then actually nothing would be lost by splitting it into smaller trees ('facts'). I could have my parents and any siblings in a two-level tree. Then the same could be done for each of my parents along with their parents. Any uncles or aunts with their children (my cousins) could occur similarly. The aim is to represent basic facts and basic relations between them, which are very simple. I can't quickly guess the number of a collection of objects if the number is more than three, so basic concepts can't be much more complicated than including three entities. I think some 'concept maps' or 'mind maps' have gone wrong here - massive, complicated diagrams full of overlapping arrows pointing in all directions that one can't make nor tail of.

Okay, I shrank this on purpose


It is a basic paedagogical principle that examples make learning easier. Consider the following sound changes that occured in Early Middle English, taken from Wikipedia's page on the phonological history of English:

  • /æː/ and /ɑː/ became /ɛː/ and /ɔː/
  • /æ/ and /ɑ/ merged into /a/
  • /ʏ/ and /yː/ were unrounded to /ɪ/ and /iː/
  • /ɣ/ became /w/ or /j/, depending on surrounding vowels

Umm… fascinating?! What is missing is examples and context. If I may make a diversion into the science of thought, I would say that interest is a biological property. One may wish to learn a body of language, and this is his broad, overriding wish, but still find it difficult to get individual facts into his head. The biological level of interest is immediately felt when one sees a fact, and this reflects that this fact is easily incorporated into his memory - his body of knowledge, thoughts, dreams and beliefs - by virtue of the relations it has with what is already known. In order to learn a large body of knowledge, it is necessary to jam in boring facts just to get the interest started. (In fact, disciplined learning and study remains important, as others in society are capable of doing the same, giving an extra edge to what can be learnt and understood.) These sound changes are only interesting if one knows what words they occurred in. If I knew what words today were descended from words that had [ʏ] at one point but later had [ɪ] then I might actually be able to remember that information. I might be able to build up a complete picture of the historical development of the English language. As it is, it is empty and meaningless information which I have no biological interest in obtaining. (For example, one fact which would make one of the above facts interesting is that the unrounding of /ʏ/ and /yː/ explains why "i" and "y" represent the same sound in English spelling. I'm not 100% sure but I think the merger of /æ/ and /ɑ/ is reflected in the fact that Modern English does not have a letter "æ" whereas Old English had both "æ" and "a". For the last one, I think "year" used to be spelled "gear" or something similar. I remember reading that we know that the word "get" comes from Old Norse because if it came from Old English it would be "yet". Also "warden" and "guardian" have a common root, they came from two different dialects of French. These are examples of "g" being replaced with "w" and "y" respectively, even if they aren't examples of the specific change above. So without being precise, you can relate these facts to things you already know.)

To learn a foreign language, first you learn a few words and phrases. Maybe later you learn about different noun declensions, different systems of making plurals, different systems for making sentences to talk about past time, and so on. You wouldn't start off by memorizing tables of verb endings, or different forms of the definite article.

Things affecting interest:

  • Relevance to facts already known
  • Length of exposition (the shorter the better), or how easy it is to understand
  • Whether it will complete a body of knowledge — is it the 'missing piece' in the jigsaw. This is one of the benefits of learning from a fixed, written exposition, such as a vocabulary list or a set of lecture notes — it is possible to learn the whole thing, and any parts of it which haven't been learned are interesting because they will complete the knowledge of the exposition.
  • Is it seen to help in the understanding of other things? If there is another system which uses some elements from a first, then reading about the second system, a learner will have his interest in the first system increase.
  • Does it bring painful or joyful thoughts to mind? Someone might find it hard to learn about spiders if they were terrified or disgusted by them.
  • There also has to be a motivation. I thought of learning the first 81 digits of $\pi$ by structuring it into 3 groups of 3 groups of 3 groups of 3, and learning each group as a block in relation to other blocks. I failed because I wasn't interested. As well as an accessible structure there has to be motivation. The greater the motivation the greater the information content can be. If you aren't very interested, a summary of the subject will suffice.
    • Of course this isn't a good example because you would tend to get the blocks confused with each other. A better example would be memorizing a street map - first memorizing the main streets, and then using that as a foundation for memorizing the side streets.

Interest is very related to the experience of finding something difficult. If you try to do something or learn something, you will find some parts easy, and some difficult. If you come back the next day, you will be interested or receptive to learning whatever it was you found difficult the previous day. It is like this for learning a language - if you read a lot of text in the language, and you encounter a word which gets in the way of understanding a lot, you will become receptive to the meaning of this word.

The occasions of learning

Learning is clearly a process we go through, but what does it consist of and what does it feel like? Here are some conscious phenomena which are part of learning:

  • Reading a fact for the first time.
  • Having a fact come to mind (spontaneously coming from the subconscious)
  • Reading a fact which has been read already
  • Asking oneself a question, being unable to remember the answer, and then looking up the answer

Types of exposition

  • Dictionary exposition — A methodical presentation of a body of knowledge. Has all the information, but is difficult to learn from. Examples are the dictionary — it is hard to learn new words by reading a dictionary, but easy to use it to look up information — and the Unix man page — it has all the information about the operation of the program and how it responds to different command line switches and options and environment variables, but it can be difficult to find out how to do a specific thing with them.
  • Course exposition — A cruise through the oceans of knowledge, always keeping the learner's attention on new, interesting information relevant to what has gone before.
  • Revision - Material can be revised in a different way from the way that it is learned initially. Notably, every fact is related to several other facts in the internal representation of knowledge. By revising one fact, the peripheral facts are revised as well. Additionally, a lot more material can be covered in revision. You could easily skim a list of a hundred words in a foreign language if you already knew them, but trying to memorize the same list would not be the most efficient way of learning them in the first place.

Self-paedagogy and the interpretive cycle

One problem with trying to learn about the world is that you use your prior knowledge in interpreting texts, for example in judging how trustworthy or insightful they are. Learning from these updates your knowledge which leads you on to interpret differently in the future.

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