Types of Knowledge and Connective Knowledge

This is a presentation for Week Two of the Connectivism and Connective Knowledge course. It expands on the ideas in Part a of my paper, An Introduction to Connective Knowledge.


What can we know about an object? Historically, we have had two types of knowledge:

First, 'qualitative' knowledge. What colour the object is, for example. What the object is shaped like. What sort of sound it makes. Qualitative knowledge is knowledge typically derived from the senses. The things we see, the things we feel, the things we hear: these are the qualities of the object.

Second, 'quantitative' knowledge. How many things do we see, for example. How much do they weigh? What are their dimensions? Quantitative knowledge is derived from the practices of counting and measuring. Quantitative knowledge gives us a knowledge that is deeper than that gained merely from the senses. It gives us an insight into the nature of the objects through concepts like mass, atomic number, equations and calculus.

These two types of knowledge account for most of what we know about things that there are out there in the world. These two types of knowledge combine the best of human capacities: our ability to perceive, to sense the world, and our ability to calculate, to think about the world. They form the foundation for language, the foundation for logic, and the foundation for all of the sciences we have had up to today.

Empiricism and rationalism: these are the two great schools of philosophy that have shaped the world in modern times. Empiricism, the philosophy that all knowledge is derived from the senses. Rationalism, the philosophy that all knowledge is derived from calculation and realism. the two great schools of thought in our time.

In the 20th century, things changed. On the one hand, the great philosophers of the Vienna circle and their allies in Great Britain founded a philosophy that joined empiricism and rationalism. This philosophy, known as logical positivism, held that we begin with observations, and then use logic and reason to derive statements about the nature of the world. Any statement not derived in this way, they argued, was literally nonsense. It made no sense.

On the other hand, there was an undercurrent of scepticism about that grand enterprise. The American pragmaticsts - William James, Charles Sanders Pierce and John Dewey, argued that there was a third, practical domain of knowledge. The test that something is known, they said, is that it works. In Europe, meanwhile, philosophers found it difficult to accept that all of religion, art and literature were reduced to nonsense.

There are different types of meaning, said some. Meaning is derived from the text, say people like Heidegger and Derrida. meaning is use, say people like Wittgenstein. And there are different types of knowing. The logical positivists describe only our knowledge about things. But, argues Michael Polanyi, there is also 'knowing how'.

It seems clear, at the beginning of the 21st century, that there is a third type of knowledge, a type of knowledge that exists above and beyond the knowledge derived from the senses, and that exists above and beyond the calculations of logic and mathematics.

But though the existence of this knowledge seems to be beyond dispute, the characterization of this knowledge has been elusive. What is 'practical'? What is 'use'? What is 'literature'? What is 'knowing how'? What is 'ineffable knowledge'?

What is this knowledge? We are subjected to all kinds of theories, some that seem reasonable, some that are patent nonsense. Biorhythms. Astrology. Harmonic convergence. The 100th Monkey phenomenon. The music of the spheres. Intuition.

More to the point, such descriptions were importantly empty. It's one thing to say we should do whatever is practical, but quite another to figure out what the most practical thing is. Or when you say something is 'practical', for example, that it 'works', your description depends on what it was you wanted to do all along. If I don't want to do what you want to do, then what you know isn't what I know.

Connectivism is a theory that described this third type of knowledge. It is a theory that tells us what this third type of knowledge is, where it is, what produces it, how we learn it, and how it can be used.

Summary: Three types of knowledge
- of the senses (empirical)
- of quantity (rationalist)
- of connections (connective)


As we have said earler, connectivism is the thesis that knowledge is distributed across a network of connections. Let me expand on that a bit.

Think about what we know about a simple object, say, a lump of coal.

When we look at it, we can see that it is black in colour, and a bit shiny. It is a rough shape. It isn't that heavy. It is hard to the touch, but we can break it. That's the qualitative knowledge we have of the coal.

When we begin to measure it we can say more. We can say that it has a mass of 500 grams, say. We can say that it has a certain density. Our lump of coal is composed of some billions of individual carbon atoms. Under certain conditions, it combines with oxygen, producing a certain amount of heat and releasing a certain amount of smoke. It is values at 23 cents on the international market. That's the quantitative knowledge we have about coal.

Yet there is a third type of knowledge we have about coal. We can know how many carbon atoms we have. But what makes coal, coal, is not just the fact that it is made up of carbon, but also of the way these carbon atoms are connected together. Take exactly the same atoms and connect them differently and you have graphite. Take the very same atoms and connect them differently again and you have diamonds.

This is a very simple example. Carbon atoms are very simple entities. The connections are simple, and they don't vary very much. They are stable, not changing a whole lot with time. So we can find out about how the atoms are connected indirectly: coal has a particular colour, diamonds have a particular hardness, graphite has a particular weight. Still, knowing about the connections is to know more than to know about the qualities and quantity of the material involved.

So, connective knowledge is knowledge OF the connections that exist in the world. It is knowledge about how such connections are created, and what impact, or effect, such a system of connections has. It is knowledge about how we see such connections, how we observe them, and how we observe their results. It is a theory, in addition, about how we measure such connections, how we count them, what sort of measurable properties they have. This is important: connectivism is a new type of knowledge, but it is not independent of other types of knowledge. We need to be able to see connections, and we need to be able to count them, in order to talk about them.

But I also want to introduce a second aspect of connective knowledge: the idea of connections as a WAY of knowing. This is a bit trickier, but is essential to our understanding of what we know and how we know it.

A network is a set of connections between a collection of things. A diamond, for example, is basically a network: it is a collection of carbon atoms that are very tightly connected to each other. But these connections don't appear out of nowhere; they are not created by magic. If we ask, how did these carbon atoms come to be connected *this* way, we learn something about the history of those carbon atoms, that they were subjected to intense heat and pressure. So information about what happened in the past has been stored in these carbon atoms, in the way they are connected.

With *any* set of connected objects, we can ask how the connections came to be that way. Which means that *any* set of connected objects can contain information. What happened to the individual entities in the network, what sort of *input* did they have, to become connected in this way?

A network, therefore, is like a sense organ. A network is stimulated, it takes a certain shape. Stimulate a network of carbon atoms with intense heat and pressure, and the carbon atoms reorganize; they take the form of a diamond. This is what can happen in any network of connected objects. When you impact that network in some way, the connections between the objects in the network change. And this results in the storage of information.

So we have two types of connective knowledge, the knowledge that we have OF networks, that we obtain by looking at networks, and knowledge that is created and stored BY networks in the world.

Summary: Connective knowledge is both:
- knowledge OF networks in the world
- knowledge obtained BY networks


There are many types of networks, and therefore, many types of connective knowledge. We will look at these in much more detail through this course. For now, though, it is important to identify some different ways of talking about networks.

As we discussed in the introduction to connectivism, there are several types of networks that involve humans. One network, for example, is the human brain. The brain is composed of a collection of neurons that are connected to each other. Another network is society itself. Society is composed of humans that are connected to each other.

Now when we are talking about connectivism it is pretty easy to slip back and forth between these networks without noticing. It's easy to get confused. So it is important to keep in mind one's perspective or point of view when talking about networks.

Let's take, as our starting point, a single person.

This person is a part of a network. He or she is what we would call a 'node' in that network. As a node, he or she is connected to other people; it is this set of connections that make up what we can call a 'social network'.

At the same time, the person in question *has* a network. Or we might even say that the person *is* a network. This person is composed, at least in part, of a neural network, a brain, a complex organ for perceiving the world and storing those perceptions in the form of connections in a network of interconnected neurons.

These make up what may be thought of the person's 'active' participation in the network: the actual interactions that take place, the actual interactions that happen between this person and other people, the actual perceptions that reshape the person's neural network.

There is also a set of what may be called 'passive' or 'reflective' participations in the network.

Consider society. Society is a network of collected individuals. A person can participate in society as a node within the network. But it is also possible, through a variety of mechanisms, to observe society as a whole. To, if you will, detach oneself from society and to study it as though it were an collection of objects out there in the world. The same way you might study a lump of coal.

Similarly, we can (with more or less precision) reflect on our own neural network with some degree of detachment. We can observe, and feel, our sensation and passions, our thoughts, our ideas. We can study our own mind, through introspection. This process of reflection is a way of learning about ourselves.

When we are talking about connectivism and connective knowledge, we are talking about all four of these activities. And it is very easy to get caught up and mistake one for the other, to get confused by them. We need to get into the practice right from the very beginning of being clear about what sort of thing we are doing.

Now connectivism is sometimes characterizes a theory that emphasizes 'knowing who' over 'knowing what' and 'knowing how'. This may be, but only from a particular perspective. Only from a particular point of view. When you are looking to become a part of the network, to be and act as a node in the network, then you are most interested in 'knowing who'. You are interested in creating connections and using connections.

But it would be a mistake to characterize connectivism as a theory that is *only* about 'knowing who'. Understanding how networks work will help support our participation in them, but it will also help use create better networks - *knowing* networks - in ourselves and in our society, and it will help us better understand what we see when we *look* at networks.


Active participation in the network:
- as a node in the network, by participating in society
- as a whole network, by perceiving with the brain (the neiural network)
Reflective participation in the network:
- by observing society as a whole
- by reflecting on our mental states and processes


  1. At the time I read this post I was discussing concerns with an individual within my network. After reading your post these concerns are still present.

    In your analogy you use coal (quite effectively) to provide a concrete example of connectivism. However you are using a non-living object to describe connections. Human beings are living organisms with thoughts and emotions that usually hamper our nobler endeavors.

    Most of us do not intentionally distort information or ignore people. However at times we can all fall prey to our weaknesses, especially when we are online. Can we truly trust our network for knowledge, when we know it can be biased by human emotion.

    However I feel that these minor concerns can be mediated by taking the broad look at our knowledge (like you mentioned with our society). However what tools are available at this time to quickly ask a question to a network, and still be able to control the human emotions within that network?

  2. An interesting read Stephen, and it has helped me to put this idea of 'connectivism' in perspective. A few questions remain though:

    The coal analogy: Sorry I don't think that works for me. Atoms don't have connections first of all, that is just a concept that stems from our popular beliefs dictionary, but has little grounding in any physical reality. Secondly, I'm not sure how these 'connections' aren't just another qualitative and quantitative property of coal. There is as much information in the weight of coal, as there is in it's connections isn't there? The fact that you can derive information from a connection, doesn't mean in actually acquires knowledge does it? that's a few steps for which I really missed the justification.

    Also, for connectivism to 'work' on the social scale, wouldn't that mean that societies, groups or networks know things that the individuals don't? Just like I know things that no single neuron doesn't know? I could possibly see some sort of long term evolutionary path in that direction, but to say that that is a current reality is a bridge too far for me I think. What's your opinion on that?

  3. > The coal analogy: Sorry I don't think that works for me. Atoms don't have connections first of all, that is just a concept that stems from our popular beliefs dictionary, but has little grounding in any physical reality.

    Atoms don't have little sticks joining them, true. But atoms in compounds have bonds, and these bonds can be thought of as connections.



    Carbon atoms admit of several types of bonds.


    > The fact that you can derive information from a connection, doesn't mean in actually acquires knowledge does it? that's a few steps for which I really missed the justification.

    That's fine, this is a very introductory set of remarks. If you allow a network to store information, that's good enough for me - we can get to sorting out what kind of information constitutes knowledge later.

    wouldn't that mean that societies, groups or networks know things that the individuals don't?

    Exactly right.

    Brains clearly know things that neurons don't. That's pretty easy for us to see.

    Societies can know things individuals don't. That's harder to see.

    One example I have used a lot (and it's imperfect,. but bear with me) is that of "how to fly a 747 from London to Toronto". no single individual knows all of this - it takes a collection of people, working together, to know this.

    Another example (and it is flawed in its own way) is Adam Smith's 'Invisible hand of the marketplace'.

  4. Hmm ... not so sure about the focus on Knowledge. To me that refers to facts, descriptors and remembering things. I know it maybe just semantics, but I align learning with understanding, competence, wisdom and mastery. Knowledge is just one small part of that.
    I do, however, agree with the network analogy. The key to this is its recursive nature. It holds the same appeal for me as the recursive framework of Stafforsd Beer's Viable Systems Model in a management context.
    In another, more apocryphal, account 'it's turtles all the way down ...'

  5. Now bear with me, because I've really only been reading about this stuff fairly recently, but I have an epistemological question:

    In your view, do the connections exist independently of the nodes, in some objective sense (i.e. metaphysical realism), or do they only exist in the context of the nodes (i.e. multiple realizability, "brain-in-a-vat")??

    And if the latter, you seem to say that the context of multiple nodes (as in your 747 example) can together form yet another context, like a meta-context, correct?

    So the number of contexts is not just: a) individual (i^1) or b) the whole group (G); it's actually: i^1, i^2, i^3... i^G, correct?

    I hope that made some kind of sense in the absence of a degree in math or philosophy.

  6. Eyal,

    That's kind of like asking someone who has just described a car whether he thinks that the car really exists.

    Within the context of this course, using ordinary language to speak with other people, I refer to networks the way I would any other object existing in thew world, as a real existing type of object.

    Adopting a more philosophical stance - I am (more of less) a phenomenalist and an idealist - I think that reality is a construct (of a sort - since it's mostly involuntary) created in an attempt to make sense of sensory input.

    At best, I hope with my theorizing to, as they say, "save the phenomena".

  7. Of course he thinks the car exists. But does it?

    This seems to be important, because one of your premises is that "knowledge exists outside of the learner." So, does that mean the knowledge exists outside of any learners, even "aggregate learners" (i.e. a network of learners)?

    Or is this irrelevant to the theory, because even if it exists, we can't observe it (i.e. Berkeley)?

    In any case, thank you Stephen. I'll have to do some more background reading before asking any more questions.

    Do you have any recommended links? Or do you intend to cover this stuff this week ("Rethinking Epistemology")?

  8. "knowledge exists outside of the learner" the way "a car exists outside the learner"

    A person can be a mechanic while at the same time being a solopsist and an anti-realist. I am evidence (at least to myself) of that.

    As for the rest - I think that by the time we're finished, the question of whether our experiences 'justify knowledge of the external world' will take on a different light.

    That said: I will not be addressing realism directly at all this week - this being more in the domain of ontology than epistemology. I do address scepticism, albeit briefly, at the end of 'An Introduction to Connective Knowledge' (see the wiki, week two, optional readings) and may develop that argument further, as needed.

  9. As some of the others have said, I think you lost me a little on the coal analogy. It seems to me that the connective nature of what I know about coal would have to do with what I have learned about coal from different avenues or networks - this shapes my individual overall view and identification of coal. For example, I know about how we get coal, coal mining, from what I learned in history books. I know the ecological implications of coal from a variety of media sources such as the web and the television. I know the humanistic side of coal from meeting people who were raised in areas where coal was a large part of their life. So, to me, these examples are all ways that impact how I know about and define "coal", and they have become part of my individual definition because of connective knowledge.

    This change to the analogy would also seem to fit with your two types of connective knowledge, and your discussion in section 3 of participation in networks - I know about the different networks of knowledge surrounding coal (ecological, humanistic, historic) and I have also obtained my knowledge about coal by accessing or participating in these networks, and then observing and reflecting on how this information meshes with or adds to my own knowledge of the topic.

    I hope that I am on the right track with this - if not, I would enjoy further explanation of your point!

  10. Heidi, nothing you're saying is wrong, but you are including the whole world in an example I wanted to keep nice and simple.

    If we have a lump of coal - and *only* a lump of coal, then there are three types of things to be known about it:
    - its colour and shape and other qualities
    - its mass and size and other quantities
    - the way its parts are connected

    And as a result, we have three types of knowledge about this particular lump of coal:
    - qualitative
    - quantitative
    - connective

    Yes, I know you actually get your knowledge from other sources, and that there are other ways to know about coal. But they are not relevant to this example.

  11. Hmmm, at least we did not descend to quarks and muons inside that lump of coal.

    Perhaps there is some difficulty leaping from the lump of coal, who's connections are properties of physical forces of heat, pressure, ane sub-atomic physics, to knowledge-- where connections are forces of what?

  12. Alan, you ask: "knowledge-- where connections are forces of what?"

    "Biorhythms. Astrology. Harmonic convergence. The 100th Monkey phenomenon. The music of the spheres. Intuition."

    Take your pick. Because, as far as what is scientifically observable or measurable, we have no idea (yet).

    Maybe there is some Force connecting us together in the physical world, but for now we'll have to settle for the virtual.

  13. Hmmm, I guess that my interpretation of connectivism and how it works is that it is bigger than just one small idea - like one particular lump of coal - and that it is a way to connect and combine the various relational aspects. Going by what you are saying, what we know is actually 3 things in general about all lumps of coal: "its colour and shape and other qualities,
    its mass and size and other quantities,the way its parts are connected." These reliable aspects that define "coal" connect each single lump to all other lumps of coal forming a network of "peers". In addition, the way the parts of coal connect to form a lump of coal are an intrinsic network, but they are only one particular network of connections that a lump of coal, or "coal" in general, is involved in. What we know about one example of one thing - coal - inevitably networks into what we know on a larger scale. Otherwise, it doesn't seem that there is a potential for learning.

  14. (sorry for the length, got it out of my blogpost, hence the more lengthy approach.

    First of all this evolution of many brains making knowledge seems very natural to me as the same thing happens in nature already (most quoted species: ants), so I am happy to read a simple framework to get to this point.

    Connective knowledge has gotten humanity to where it is today

    After reading this (accessible) article I did get visions of connective knowledge building throughout human history. In a way history has always used connective knowledge and has build upon it as soon as enough people were curious enough to take it into consideration and replicating it. It is only because Darwin’s knowledge got out, got discussed, was first accepted by a few and got picked up by a growing number of scientists, that Darwin’s theory on the Origin of Species began to be seen as common ground. So in a way, because of several networks and their dynamics knowledge was picked up, tested through discussions and taken in as ‘solid knowledge’.

    But not all knowledge gets appreciated from the beginning and sometimes very valuable knowledge gets overlooked thus stopping further evolution of that knowledge. (example: only a couple of years ago a lost (thought lost) manuscript of Archimedes (the so called Method) was found in Paris. The manuscript was overwritten by religious texts, just because at the time those religious texts seemed more important than Archimedes’s. After deciphering parts of the manuscript scientists found that Archimedes put down essential modern mathematical proves that are now at the basis of big inventions. Because Archimedes’s knowledge was ‘lost’ and history was focusing on different types of knowledge, mathematical (and scientific) knowledge was (temporarily stopped)).

    So although I think connective knowledge gathering seems to have been around forever, it does not persé solve the problem of knowledge being lost or not being valued to the potential it has.

    If you are interested in the Archimedes documentary regarding this manuscript (but beware there are almost no links to the actual text that Archimedes wrote down in his Method, look here)

    In an increasingly specialized world connective knowledge can keep humanity together
    As connectivity looks at society as a whole as well as connections between information, it can be holistic. In this capacity it can add to interdisciplinary understanding and find mutual evolutions or parallel discussions. This holistic and connected knowledge ability does speak to my imagination, because it could bring all the specialist domains together again (and I believe that building bridges between disciplines always results in new ideas).

    But could this result in the need for new professions? Not specialists in the classical sense, but specialists in superficial knowledge gathering. People that only know the basics, but of different disciplines and these people could than be knowledge bridge builders. I would like that type of profession :-)

  15. I find the attractor 'connectivism' interesting, but I am not yet sure of its limits and limitations. (Too many for me at the moment, but lets keep that one open for now).

    Just one addition to the 'carbon atoms can connect differently to yield different things' metaphor. I have to make a distinction between what I call (reasonably) 'predictable variables'(inorganic, in the scientific sense) and 'complex variables (or organic, ditto) - the latter I prefer to call 'variables with attitude' and they include anything from viruses upwards - one of their key characteristics is that they are self-reproducing, and self-organising (hence the attitude).

    Given this fundamentally dualistic ontology (and no, I am not in favour of dualism) has implications for how we approach the connectivism of coal (no attitude, unless its C14, radioactive, I suppose) and of humans (attitude in spades as they say - with a nice pun coming out there on spades and coal, no?)

  16. ...differently. (sorry, should have added it to the previous post!)

  17. > Just one addition to the 'carbon atoms can connect differently to yield different things' metaphor.

    There's value to that suggestion.

    In my own understanding of networks, we add to the (admittedly very simple and static) connection of the carbon atom in a variety of ways:

    - the entities are multi-state - unlike carbon atons, that just sit there, the connected entities can be off/on, can be multi-valued, can be analog (think, eg., electron potential, excess potassium, whatever - there's a variety of ways to have different states)
    - the connection is stateful - what I mean by that is that a change of state in one entity can result in a change of state in the second entity
    - the connection is communicative - that is, there is a way to interpret the connection as the transmission of a signal (sometimes, as in neurons, there is not a single thing sent from A to B... but you can see one thing cause another cause another, which could be interpreted as a signal)
    - the connections can have different 'strengths' or 'weights'
    - the set of connections between entities changes (this is known as neural 'plasticity) based on various factors such as input, proximity, back-propagation, thermodynamic (boltzmann) mechanisms

    These together may give the organic feel that you're after, or you may have yet another type of dynamism in mind...

  18. "these bonds can be thought of as connections" or not! They are bonds because the limitations of our knowledge currently require this metaphor in order for us to make sense of the world. An object has real mass but only has "connections" as a metaphor for the probability cloud that make up the individual electrons. -- Geoff

  19. > "these bonds can be thought of as connections" or not!

    Works for me. Think of them as connections.

  20. "These together may give the organic feel that you're after, or you may have yet another type of dynamism in mind..."

    -exactly. The network/ecology dynamism is the complex adaptive characteristic that I am after. Thanks for the rich description!

  21. Re: "Societies can know things individuals don't. That's harder to see."

    I'll say. Who gets to see this, Stepehn? and how is it determined to be just?

  22. "Societies can know things individuals don't. That's harder to see."

    A society is an abstraction. It is very real, but an abstraction. That is, I can't literally go to one thing we call "society" and ask for its opinion or feedback. Society as one voice can't talk to me, only those who constitute what we call society can do this. However, we can aggregate feedback from many individuals and call *that* a snapshot of societal knowledge. Within that snapshot could lay knowledge (via connections) that individuals at first are not aware of...it has yet to be discovered at that level. And once they look at the aggregation, they might be able to pull knowledge from it (by discovering connections) and make it their own.

    Is this sort of what you mean, Stephen? Or am I way off here?

  23. Peter, your interpretation is subtle, but it is correct.

    I have argued on numerous occasions that the patterns created by a network - such as those we see in society - are a matter of perception and interpretation. They must be recognized by a perceiver. They do not have some sort of inherent existence, and the only 'objective reality' about them describes the individual elements themselves, not the patterns.

    This is important from the perspective of agency. Such a pattern could be said to 'cause' some effect - for example, a wave of green-sentiments in society could be said to 'cause' a lowering of gas consumption - but only through intermediaries. The 'wave of green sentiment' does not itself cause anything - it only has an effect insofar as it is perceived as such by people who, as a consequence, lower their gasoline purchases.

  24. Yeah that makes sense. One might say the wave is then a condition. If that condition is present and then the other condition of perception takes place, then cause may occur.

    That's probably a little simplistic and in fact, other key conditions (e.g. the veracity of the wave to begin with) may be identified, but I think I see what you are saying.

    What is also interesting is that the cause can then become another effect.

  25. I am interested in your perspective in connectivism as a third type of knowledge. I've uploaded a comparison chart (http://spreadsheets.google.com/ccc?key=p0b8V3n8LND0a7Uj_ZTkaYg) on research methods and would appreciate any information you (or anyone else) can add to this table in facilitating my understanding of these differences.


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