Thinking of knowledge as a graph

This is a response to the E-Learning 3.0 task  for course participants created by Matthias Melcher. See https://x28newblog.wordpress.com/2018/11/09/el30-graph-task/

The task requires that we select from one of the topics of this course, and create a map from the list of keywords for the topic provided by Matthias. Matthias took the keywords from the synopsis for each topic written by Stephen Downes. The task is to connect and annotate the keywords.

Matthias provided links to two types of mapping tool – cmap.ihmc.us  and  a tool he has created himself – http://condensr.de/download-page/ . I have used both tools in the past, but I am more familiar with Matthias’ tool, so I used that.

I selected the ‘Cloud’ list of keywords, to create this map.

  • storage
  • electricity
  • server virtualization
  • vmware
  • docker
  • amazon web services
  • edx
  • coursera
  • yaml
  • vagrantfile
  • jupyter
  • redefine textbooks
  • experience
  • algorithm
  • containers
  • load-balancing

Creating the map

Since I have used this tool before (see A new mapping tool: useful for research purposes) I did not find it technically difficult.

Here is a screenshot of the map I created. Click on the image to enlarge it.

And here is a link to the interactive map, which is much more interesting, because by clicking on a node you can see the annotations – http://x28hd.de/tool/samples/JM%20Cloud%20Map.htm 

(I contacted Matthias to ask him to create this link for me. WordPress does not host .htm files; at least, as far as I am aware it does not)

Despite the lack of serious technical difficulties,  I did somehow manage to inadvertently make 4 copies of my map, one under the other. I found that it took a while to delete each node and link individually. And at another stage I managed to lose the map entirely (I think I swiped it off the screen). I have done this before, but I couldn’t remember how to get it back. I had saved the xml file though, so just uploaded it again. I know that Matthias is refining this tool all the time, so a block delete function sometime in the future would be great. (Update 13-11-18 – See http://condensr.de/2018/11/12/a-user-question/ for Matthias’s video explanation of how to overcome these minor difficulties that I had)

I created the map using the text from Stephen’s synopsis. This revealed the aspects of the topic that I still haven’t understood. I made a note of these in the text annotations (in italics). I did look up definitions and explanations of some terms and added text if an explanation wasn’t evident in Stephen’s text, e.g. algorithm. If I were to continue to develop the map, I would do more of this.

Thinking of knowledge as a graph

This is the real challenge, i.e. moving from thinking and seeing knowledge in a linear way to thinking and seeing knowledge as a network/graph.  I like lists, but in recent years I have come to appreciate that when you organise and categorise terms in lists you miss the richness of connections. Some terms need to be in more that one category. A map shows us how ideas are interconnected. A list cannot do this. Matthias explains this really well at the start of his video, which is posted on his website download page – http://condensr.de/download-page/

I know from my experience of using this tool, that my tendency is to use it as a repository for resources. It is actually great for this. I have used it for research purposes, as a place to store information and thoughts about related articles, but as Stephen writes

The graph, properly constructed, is not merely a knowledge repository, but a perceptual system that draws on the individual experiences and contributions of each node. This informs not only what we learn, but how we learn.

To develop my knowledge of the Cloud, to learn and understand more about it, I need to grow my connections and the links between them. The state of my knowledge can then be represented by the map. A  key affordance of Matthias’ Think Tool is that it is easy to ‘grow’ the map, adding nodes and links, and storing information about them, as this growth occurs.

A graph is a distributed representation of a state of affairs created by our interactions with each other. The graph is at once the ­outcome of these interactions and the source of truth about those states of affairs. The graph, properly constructed, is not merely a knowledge repository, but a perceptual system that draws on the individual experiences and contributions of each node. This informs not only what we learn, but how we learn. (Stephen Downes – https://el30.mooc.ca/cgi-bin/page.cgi?post=68472)

I do not yet fully understand the link that Stephen makes between graphs and the “source of truth”. I have yet to read the article he links to – Epistemology in the Cloud, which I think might help. Stephen has written

The source of truth, if there is any, lies in how those links are created and maintained ….. and that …. it’s not the individual idea that’s important, but rather how the entire graph grows and develops. It protects us from categorization errors and helps prevent things like confirmation bias.

This links to what Matthias says, at the beginning of his video, about the dangers of pigeon-holing things.

These ideas go beyond what Matthias asked for in his task, but I do see that in order to start thinking of knowledge as a graph, we probably need to start by creating graphs, and his Think Tool helps to make the shift from thinking of knowledge as a representational system to thinking of knowledge as a perceptual system.

And finally, I now realise, more than before, that I have already been thinking about this, implicitly, in my search for understanding what Iain McGilchrist means by ‘betweenness’, which I was writing about last month on this blog. See

‘Betweenness’ : a way of being in the world – https://jennymackness.wordpress.com/2018/10/02/betweenness-a-way-of-being-in-the-world/

Understanding ‘Betweenness’ – seeing beyond the parts – https://jennymackness.wordpress.com/2018/10/10/understanding-betweenness-seeing-beyond-the-parts/

Edusemiotics, the Divided Brain and Connectivism https://jennymackness.wordpress.com/2018/09/17/4436/

Resources

Matthias Melcher Thought Condensr website – http://condensr.de/

E-Learning 3.0, Part 3: Graph – https://el30.mooc.ca/cgi-bin/page.cgi?post=68472 and associated video https://youtu.be/WiaxHxiN_IA  (Stephen’s summary of the week)

Understanding ‘Betweenness’ – seeing beyond the parts

In a previous post, I began to explore and share my understanding of what Iain McGilchrist has written about and means by ‘betweenness’ as a way of being in the world.

I thought that maybe a ‘both/and’ view of the world, rather than ‘either/or’ might explain it, but this explanation feels over-simplistic and unsatisfactory. It seems to miss the depth that McGilchrist is exploring. Whilst more ‘both/and’ thinking might serve, at least in part, to  counter ‘either/or’ thinking, it wouldn’t get to the heart of the problem.

Gary Goldberg in commenting on my last post about ‘betweenness’, has written that he considers the issue of betweenness to be ‘ effectively addressed …. in the architectonic philosophical system of Charles Sanders Peirce…… the issue is a tolerance for ‘vagueness’ when one considers the universe as fundamentally relational and context-dependent.’

Martina Emke wrote ‘Betweenness’ is related to the concepts of ‘rhizome’ and ‘becoming’ (Deleuze & Guattari, 1987). ‘Betweenness’ is a counter-narrative to the idea of identity, a constant process of transitioning that pertains to humans and non-humans.

And Matthias Melcher in a private communication emphasised the similarities between the idea of ‘betweenness’ and connectivism. For example, in his article ‘An Introduction to Connective Knowledge’, Stephen Downes has written ‘Connective knowledge requires an interaction. More to the point, connective knowledge is knowledge of the connection.’

But McGilchrist’s idea of ‘betweenness’ as a way of being in the world, goes, I think, beyond all these three quests at seeking understanding of how we learn to understand and live with the uncertainty,  ambiguities and complexities of the world we live in. It even goes beyond language.

Any one thing can be understood only in terms of another thing, and ultimately that must come down to a something that is experienced, outside the system of signs (i.e. by the body). The very words which form the building blocks of explicit thought are themselves all originally metaphors, grounded in the human body and its experience.’ (p. 118. The Master and his Emissary: The Divided Brain and the Making of the Western World).

If this is the case – then how can we talk about ‘betweenness’ so that we can share an understanding of it and so that it can be applied as a way of learning and being? How can the idea of betweenness be made explicit without losing its meaning. This would mean ‘seeing’ the relationships between concepts as a whole, and avoiding separating concepts from experience? It would mean recognising ‘knowing’ as a reciprocal, reverberative process, a back and forth, reflecting the way in which neurones behave, which is not linear, sequential, unidirectional. As McGilchrist writes, p.194,

It seems that this reciprocity, this betweenness, goes to the core of our being. Further than even this, there is fascinating evidence that betweenness and reciprocity exist at the level of cell structure and function within the single neurone, even at the molecular level, as the brain comes to understand something and lay down memory traces.’

I suspect that any attempt to fully articulate and define what ‘betweenness’ might mean is going to fail, if only because, if it is embedded in experience, then it will necessarily be personal to each and every one of us. The nearest anyone I know has come to presenting a holistic view of ‘betweenness’ as expressed by McGilchrist is Matthias Melcher with this map, which he sent me in a personal communication and has given me permission to share in this blog post. (Clicking on the image will enlarge it).

To fully appreciate the power of this map in articulating the idea of ‘betweenness’, you will need to engage with the interactive version, which you can quickly see via this link – http://x28hd.de/tool/samples/betweenness.htm

The interactive map allows you to click on a node (as seen in the example below where the node ‘reciprocation’ has been clicked on, to reveal text from p.194 of Iain McGilchrist’s book – The Master and his Emissary: The Divided Brain and the Making of the Western World.)

This view of ‘betweenness’, a view resonant of the right hemisphere’s holistic approach (the view that McGilchrist has suggested is being lost in favour of the left hemipshere’s fragmented abstracted view of our world, in which we see things as parts rather than a whole), has been arrived at by reading through The Master and his Emissary’ to find everything that McGcilchrist has said about ‘betweenness’. There is no one section or chapter addressing this point. (It would be rather ironic if there were.) ‘Betweenness’ is a theme that runs through the book. Having collected all the ‘parts’, Matthias, using his Think Tool, has been able to look for relationships between the parts and create this ‘whole’. Someone else, of course, would have created a different set of connections, a different whole, but there would probably be enough similarity to come to some common understanding.

Is there then, some value to thinking not in terms of either/or, nor even in terms of ‘both/and’, but in terms of maps of relations? Would this be a better way to understand ‘betweenness’?

Further information about Matthias Melcher’s Think Tool

It may be that on viewing the map that you can see different or additional connections that you would like to make. If you would like to edit the map you can download Matthias Melcher’s Think Tool from his website – http://condensr.de/  and then upload his file, which is accessible via this link  http://x28hd.de/tool/samples/betweenness.xml by dragging and dropping it into the tool.

Many thanks to Matthias Melcher for creating this map which helped me better understand ‘betweenness’ and for sharing his open website and the file links.

‘Betweenness’ : a way of being in the world

At the beginning of this year my colleague Mariana Funes and I published a paper in which we argued for ‘both/and’ thinking, as opposed to ‘either/or’. We did this in the context of open, online education environments, which we suggested can be both inclusive and exclusive. This was our abstract:

Open education aspires to democratize education, promote inclusion and effect change through social justice. These aspirations are difficult to realise in open, online environments, which enable multiple, and often conflicting, perspectives. This paper proposes a counter-narrative that surfaces certain operational norms of the internet and foregrounds their exclusionary nature. We offer an illustrative inventory of some social media interactional patterns to examine communication used in open online education communities. This examination leads us to conclude that language online is subject to a dialectical tension that both includes and excludes. We conclude that a different language is needed in open online educational environments; one that embraces exclusionary structures and strategic ambiguity, as well as the aspirations to further democratise education via digital means.

Mariana Funes & Jenny Mackness (2018) When inclusion excludes: a counter narrative of open online education, Learning, Media and Technology, 43:2, 119 138, DOI: 10.1080/17439884.2018.1444638

(See also https://jennymackness.wordpress.com/2018/02/28/when-inclusion-excludes/)

In the paper, we examine online communication patterns in open education environments and find them to be subject to dialectical tensions. We quote Gibbs et al. (2013, 106) as saying that “dialectical tensions have been found to be productive in enabling the accomplishment of multiple goals since they enable organizational members to creatively attend to both poles of the opposition by transforming or transcending it and embracing both alternatives as ‘both-and’ options (Putnam & Boys 2006)”.

Whilst the idea of ‘both/and’ thinking is not new, it does seem particularly relevant in this post-truth age of intolerance for ambiguity and alternative perspectives, where ‘either/or’ thinking seems to dominate. Iain McGilchrist, author of ‘The Master and his Emissary: The Divided Brain and the Making of the Western World’, considers this to be one of the results of the increasing dominance of a left-hemisphere view of the world in our current civilisation. On p.137 of his book he writes:

‘If one had to characterise the left hemisphere by reference to one governing principle it would be that of division. Manipulation and use require clarity and fixity, and clarity and fixity require separation and division. What is moving and seamless, a process, becomes static and separate – things. It is the hemisphere of ‘either/or’: clarity yields sharp boundaries.’

By contrast a right-hemisphere view of the world is one which embraces, complexity, uncertainty, and  ambiguity.  (For an introduction, but necessarily over-simplistic description of the differences between right and left hemisphere views of the world, according to McGilchrist, see this blog post. Better still watch this video.)

‘Both/and’ thinking requires accepting that opposite poles might actually be complementary, interconnected and interdependent as suggested by Yin and Yang in Chinese philosophy, and embracing paradox as depicted by Escher in his Drawing Hands lithograph.

Escher’s lithograph is one that Iain McGilchrist often uses to discuss the paradox of linear analysis. He writes: (p.134, The Master and his Emissary). ‘The paradox applies to how we get to know anything, but is particularly problematic for the special case whereby we are seeking to approach the very process whereby knowledge itself comes into being.’

If it is difficult to determine how we know something, it’s interesting to consider how, when and why ‘either/or’ thinking would be appropriate.

Implicit in McGilchrist’s writing is the suggestion that ‘both/and’ thinking is characteristic of a view of the world in which opposite poles (where subjective and objective appear as fundamentally asymmetrical, separate ways of being), are held in suspension; a world where there is ‘betweenness’.

It is this idea of ‘betweenness’ that intrigues me. What does it mean? How can we recognise it? In talking about ‘betweenness’, McGilchrist seems to go beyond the complementarity of separate poles, to thinking about a world of ‘togetherness’ and intersubjectivity, rather than one of competition and bias; a world where we transcend the apparent duality of subjective and objective, of realism and idealism (p.144, The Master and his Emissary). This is a world which focusses on the relations between things, reciprocity and empathy, where knowledge comes through a relationship. From this perspective ‘belief is a matter of care: it describes a relationship, where there is a calling and an answering, the root concept of ‘responsibility’ (p.170, The Master and his Emissary).

Betweenness does not deny our distinctness as individuals. ‘Betweenness is being able to share in the character of the Other and feel separateness from it’ (p.363, The Master and his Emissary). My interpretation is that a world view that acknowledges ‘betweenness’ enables a ‘both/and’ sort of arrangement. For me, McGilchrist best describes ‘betweenness’ when writing about music.

‘Music consists entirely of relations, ‘betweenness’. The notes mean nothing in themselves: the tensions between the notes, and between notes and the silence with which they live in reciprocal indebtedness, are everything. Melody, harmony and rhythm each lie in the gaps, and yet the betweenness is only what it is because of the notes themselves. Actually the music is not just in the gaps any more than it is just in the notes: it is in the whole that the notes and the silence make together. Each note becomes transformed by the context in which it lies. What we mean by music is not just any agglomeration of notes, but one in which the whole created is powerful enough to make each note live in a new way, a way that it had never done before.’ (p.72, The Master and his Emissary).

It’s important to stress that I am not suggesting that there is never any need for ‘either/or’ thinking, nor that a right hemisphere view of the world, which seems to embrace a ‘both/and’ approach, is the only view. As McGilchrist stresses ‘Both hemispheres clearly play crucial roles in the experience of each human individual, and … both have contributed importantly to our culture. Each needs the other.’ (p.6, The Master and his Emissary).

We need  ‘either/or’ and ‘both/and’ thinking, but these are currently out of balance. We seem to live in a world dominated by ‘either/or’ thinking. The question is how to promote more ‘both/and’ thinking and how to acknowledge ‘betweenness’ as a way of being in the world.