Assembling the heterogeneous elements for (digital) learning

A question (or two) on the similarity of "neuronal" and "networked" knowledge

To some extent this post is a cop out. Rather than take the time to looking into what, is for me, an important and interesting question I am going to post this for two reasons. First, to remind myself to follow up later. But mostly and second, to see if someone within my PLN (why do I find the use of that term somewhat troubling?) can offer some suggestions.

It is a little sad/ironic/funny that the reason I don’t feel I can follow up on this directly by myself is that I feel I’m somewhat behind in my formal studies and that an investigation of the following is not directly related to the requirements of that study. Even though the question arises from work associated with that study and more importantly, a comment on that work by Charles Nelson.

I am now wishing that I had had the persistence and/or motivation to stick with or start the various MOOCs on connectivism.

The question

The question is about connectivism. “A theory of learning” which has as an important component the idea that “a network with nodes and connections as a central metaphor for learning”. The Wikipedia article suggests that in connectivism “learning (is) the process of creating connections and developing a network”. Stephen Downes has said it this way

At its heart, connectivism is the thesis that knowledge is distributed across a network of connections, and therefore that learning consists of the ability to construct and traverse those networks.

This metaphor/idea is attractive to me for at least two reasons:

  1. It has, what I understand to be, some significant coherence with what we know about the human brain and its network of neurons.
  2. It resonates quite strongly with my experience on the web, with social media, and also within organisations. i.e. that networks and connections offer a strong and useful insight into how folk/collections of folk learn.

A part of Charles’ comments include the following

Connections are being created at (least) two levels: in the brain of an individual and in the network of individual people. The knowledge that is in the brain (or body) is not the same as the knowledge distributed across people. The knowledge that is constructed, for radical constructivists (and Piaget), is in the brain.

One doesn’t traverse neurons of the brain, yet connectivists talk about the learning of the individual, which should refer to a neuronal network. Conversely, they don’t really talk about the knowledge of the network of individuals, but rather talk about the knowledge of a single individual as if it were at a network of individuals. Connectivists seem to conflate these two networks.

So, the questions to which I don’t know the answer to yet include

  • Does connectivism conflate or equate the knowledge/connections with these two levels (“neuronal” and “networked”)?
  • Regardless of whether the answer is yes or no, what are the implications that arise from that response?

There are probably a whole range of other questions embedded in these questions. Not to mention implications I’ve missed.


Pedagogical Content Knowledge: Week 1


A comparison of schools – enabled by MySchools v2.0


  1. Does connectivism conflate or equate the knowledge/connections with these two levels (“neuronal” and “networked”)?
    Regardless of whether the answer is yes or no, what are the implications that arise from that response?

    The answer to the first question is ‘yes’, but with some caveats.

    The first caveat is expressed in several of my papers. It is that historically we can describe three major types of knowledge:
    – qualitative – ie., knowledge of properties, relations, and other typically sensible features of entities
    – quantitative – ie., knowledge of number, area, mass, and other features derived by means of discernment or division of entities within sensory perception
    – connective – ie., knowledge of patterns, systems, ecologies, and other features that arise from the recognition of interactions of these entities with each other

    (There is an increasing effect of context-sensitivity across these three types of knowledge. Sensory information is in the first instance context-independent, as (if you will) raw sense data, but as we begin to discern and name properties, context-sensitivity increases. As we begin to discern entities in order to count them, context-sensitivity increases further. Connective knowledge is the most context-sensitive of all, as it arises only after the perceiver has learned to detect patterns in the input data.)

    The second caveat is that there is not one single domain, ‘knowledge’, and, correspondingly, not one single entity, the (typically undesignated) knower. Any entity or set of entities that can (a) receive raw sensory input, and (b) discern properties, quantities and connections within that input, can be a knowledge, and consequently, know.

    (Not that I do not say ‘possess knowledge’. To ‘know’ is to be in the state of perceiving, discerning and recognizing. It is the state itself that is knowledge; while there are numerous theories of ‘knowledge of’ or ‘knowledge that’, etc., these are meta-theories, intended to assess or verify the meaning, veracity, relevance, or some other relational property of knowledge with respect to some domain external to that knowledge.)

    Given these caveats, I can identify two major types of knowledge, specifically, two major entities that instantiate the states I have described above as ‘knowledge’. (There are many more than two, but these two are particularly relevant for the present discussion).

    1. The individual person, which senses, discerns and recognizes using the human brain.

    2. The human society, which senses, discerns and recognizes using its constituent humans.

    These are two separate (though obviously related) systems, and correspondingly, we have two distinct types of knowledge, what might be called ‘personal knowledge’ and ‘public knowledge’ (I sometimes also use the term ‘social knowledge’ to mean the same thing as ‘public knowledge’).

    Now, to return to the original question, “Does connectivism conflate or equate the knowledge/connections with these two levels (‘neuronal’ and ‘networked’)?”, I take it to *mean*, “Does connectionism conflate or equate personal knowledge and public knowledge.”

    Are they the same thing? No.

    Are they each instances of an underlying mechanism or process that can be called (for lack of a better term) ‘networked knowledge’? Yes.

    Is ‘networked knowledge’ the same as ‘public knowledge’? No. Nor is it the same as ‘personal knowledge’. By ‘networked knowledge’ I mean the properties and processes that underlie both personal knowledge and public knowledge.

    Now to be specific: the state we call ‘knowledge’ is produced in (complex) entities as a consequence of the connections between and interactions among the parts of that entity.

    This definition is significant because it makes it clear that:
    – ‘knowledge’ is not equivalent to, or derived from, the properties of those parts.
    – ‘knowledge’ is not equivalent to, or derived from, the numerical properities of those parts

    Knowledge is not compositional, in other words. This becomes most clear when we talk about personal knowledge. In a human, the parts are neurons, and the states or properties of those neurons are electro-chemical potentials, and the interactions between those neurons are electro-chemical signals. Yet a description of what a person ‘knows’ is not a tallying of descriptions of electro-chemical potentials and signals.

    Similarly, what makes a table ‘a table’ is not derivable merely by listing the atoms that compose the table, and there is no property, ‘tableness’, inherent in each of those atoms. What makes a table a ‘table’ is the organization and interactions (which produce ‘solidity’) between those atoms. But additionally, ascription of this property, being a ‘table’, is context-dependent; it depends on the viewer being able to recognzie that such-and-such an otganization constitutes a table.

    A lot follows from this, but I would like to focus here on what personal knowledge and public knowledge has in common. And, given that these two types of knowledge result from the connections between the parts of these entities, the question now arises, what are the mechanisms by which these connections form or arise?

    There are two ways to answer this:
    – the connections arise as a result of the actual physical properties of the parts, and are unique to each type of entity. Hence (for example) the connections between carbon atoms that arise to produce various organizations of carbon, such as ‘graphite’ or ‘diamond’, are unique to carbon, and do not arise elsewhere
    – the connections arise as a result of (or in a way that can be described as (depending on whether you’re a realist about connections)) a set of connection-forming mechanisms that are common to all types of knowledge

    Natural science is the domain of the former. Connective science (what we now call fields such as ‘economics’, ‘education’, ‘sociology’) is the domain of the latter.

    One proposition of connectivism (call it ‘strong connectivism’) is that what we call ‘knowledge’ is what connections are created solely as a result of the common connection-forming mechanisms, and not as a result of the particular physical constitution of the system involved. Weak connectivism, by contrast, will allow that the physical properties of the entities create connections, and hence knowledge, unique to those entities. Most people (including me) would, I suspect, support both strong and weak connectivism.

    The question “Does connectivism conflate or equate the knowledge/connections with these two levels” thus now resolves to the question of whether strong connectivism is (a) possible, and (b) part of the theory known as connectivism. I am unequivocal in answering ‘yes’ to both parts of the question, with the following caveat: the connection-forming mechanisms are, and are describably as, physical processes. I am not postulating some extra-worldly notion of ‘the connection’ in order to explain this commonality.

    These connection-forming mechanisms are well known and well udnerstood and are sometimes rolled up under the heading of ‘learning mechanisms’. I have at various points in my writing described four major types of learning mechanisms:

    – Hebbian associationism – what wires together, fires together
    – Contiguity – proximate entities will link together are form competitive pools
    – Back Propagation – feedback; sending signals back through a network
    – Settling – eg., conservation of energy or natural equilibrium

    There may be more. For example, Hebbian associationism may consist not only of ‘birds of a feather link together’ but also associationism of compatible types, as in ‘opposites attract’.

    What underlying mechanisms exist, what are the physical processes that realize these mechanisms, and what laws or principles describe these mechanisms, is an empirical question. And thus, it is also an empirical question as to *whether* there is a common underlying set of connection-forming mechanisms.

    But from what I can discern to date, the answer to this question is ‘yes’, which is why I am a strong connectivism. But note that it does place the onus on me to actually *describe* the physical processes that are instances of one of these four mechanisms (or at least, since I am limited to a single lifetime, to describe the conditions for the possibility of such a description).

    There is a separate and associated version of the question, “Does connectivism conflate or equate the knowledge/connections with these two levels,” and that is whether the principles of the *assessment* of knowledge are the same at both levels (and all levels generally).

    There are various ways to formulate that question. For example, “Is the reliability of knowledge-forming processes derived from the physical constitution of the entity, or is it an instance of an underlying general principle of reliability.” And, just as above, we can discern a weak theory, which would ground reliability in the physical constitution, and a strong theory, which grounds it in underlying mechanisms (I am aware of the various forms of ‘reliablism’ proposed by Goldman, Swain and Plantinga, and am not referring to their theory with this incidental use of the word ‘reliable’).

    As before, I am a proponent of both, which means there are some forms of underlying principles that I think inform the assessment of connection-forming mechanisms within collections of interacting entities. Some structures are more (for lack of a better word) ‘reliable’ than others.

    I class these generally as types of methodological principles (the exact designation is unimportant; Wittgenstein might call them ‘rules’ in a ‘game’). By analogy, I appear to the mechanisms we use to evaluate theories: simplicity, parsimony, testability, etc. These mechanisms do not guarantee the truth of theories (whatever that means) but have come to be accepted as generally (for lack of a better word) reliable means to select theories.

    In the case of networks, the mechanisms are grounded in a distinction I made above, that knowledge is not compositional. Mechanisms that can be seen as methods to define knowledge as compositional are detrimental to knowledge formation, while mechanisms that define knowledge as connective, are helpful to knowledge formation.

    I have attempted to characterize this distinction more generally under the heading of ‘groups’ and ‘networks’. In this line of argument, groups are defined compositionally – sameness of purpose, sameness of type of entity, etc., while networks are defined in terms of the interactions. This distinction between groups and networks has led me to identify four major methgodological principles”

    – autonomy – each entity in a network governs itself
    – diversity – entities in a network can have distinct, unique states
    – openness – membership in the network is fluid; the network receives external input
    – interactivity – ‘knowledge’ in the network is derived through a process of interactivity, rather than through a process of propagating the properties of one entity to other entities

    Again, as with the four learning mechanisms, it is an empirical question as to *whether* these processes create reliable network-forming networks (I believe they do, based on my own observations, but a more rigorous proof is desirable), and I am by this theory committed to a description of the *mechanisms* by which these principles engender the reliabiliuty of networks.

    In the case of the latter, the mechanism I describe is the prevention of ‘network death’. Network death occurs when all entities are of the same state, and hence all interaction between them has either stopped or entered into a static or stead state. Network death is the typical result of what are called ‘cascade phenomena’, whereby a process of spreading activation eliminates diversity in the network. The four principoles are mechanisms that govern, or regulate, spreading activation.

    So, the short answer to the first question is “yes”, but with the requirement that there be a clear description of exactly what it is that underlies public and personal knowledge, and with the requirement that it be clearly described and emprically observed.

    I will leave the answer to the second question as an exercise for another day.

  2. David, it helps me to think of connectivism as an approach to knowledge as complex, network phenomena. This approach has a range of results, some of which are enumerated by Olaf Sporns in his book Networks of the Brain (2011). Most pertinent to your questions, I think, are two statements: all complex systems display network patterns, which “are the outcome of highly structured and selective coupling between elements, achieved through an intricate web of connectivity” (1); and network patterns span multiple scales, “from the microscale of individual cells and synapses to the macroscale of cognitive systems and embodied organisms” (2).

    To my understanding, connectivism says that knowledge is a complex system and, therefore, at any level is a network, an intricate web of connectivity and selective coupling between elements. This is true if we look at a pattern of neurons firing at the sound of the word connectivism or if we examine a pattern of people in a MOOC all firing during a discussion of connectivism. The creation of knowledge at either scale is a self-similar function of the interconnectivity of individual elements.

    We can examine the knowledge on either the micro- or macro-scales apart from the other scale to achieve clarity and precision, but we must always keep in mind that networks span multiple scales. Thus, we can look at the single concept of connectivism in an individual brain, or we can look at the social concept of connectivism in a MOOC, but we must keep in mind that Connectivism as knowledge spans multiple scales, and that as Sporns says, “in multiscale systems, levels do not operate in isolation—instead, patterns at each level critically depend on processes unfolding on both lower and higher levels” (2).

    To my mind, then, connectivism is saying that knowledge at the brain scale is self-similar to knowledge at the social scale—a networked pattern of interconnected elements—and that the knowledge on either scale depends on the patterns emerging and functioning on the higher and lower scales. However, connectivism does not say that the knowledge at either scale is identical, but then the whole notion of identical chunks of knowledge is false anyway, and probably a result of a sensibility shaped by industrial manufacturing. Knowledge is not stamped out like identical soup cans.

    One of the key issues for Connectivists is to develop a language that allows us to move beyond either/or thinking to and/and/and (or complex) thinking. We like to think that we walking brains are either individuals or we are lost in the herd. We are reduced to either discrete entities or nameless parts of the Whole. Complex network thinking says that we are individuals in a system and that we have no meaning apart from the interactivity of our individualism with the system. Neurons are like this. By themselves, they create no meaning. Meaning emerges only within the interactions of the single neuron with many of the other neurons within the ecosystem, the brain. On the other hand, each neuron absolutely must maintain its own identity, its position and potency within the ecosystem. It cannot merge into the cosmic soup of the brain. Knowledge depends totally and absolutely on all the neurons both maintaining their independent individual functions and positions AND interacting harmoniously with the ecosystem.

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