Where do trees come from? Graphs!

TREES & GRAPHS

Trees start from a root node and might connect to other nodes, which means that could contain subtrees within them. Trees are defined by a certain set of rules: one root node may or may not connect to others, but ultimately, it all stems from one specific place. The tree follows one direction and cannot have loops or cyclical links.

Graphs are non linear structures: their data doesn’t follow an order. Trees will always be graphs, but not all graphs will be trees. Graphs do not have a concept of a root node. They can have a direction or not or they could have some links that have direction and others that don’t. Every graph must have at least one single node. (a graph with one node is called singleton).

Edges (sometimes referred to as links) can connect nodes in any way possible. Edges are what differentiates graphs. There are two types of edges: a edge that has a direction or flow, and an edge that has no direction or flow. We refer to these as directed and undirected edges, respectfully. In a directed edge, we can only travel from the origin to the destination, and never the other way around (digraph). However, it’s an entirely different story with undirected edges. In an undirected edge, the path that we can travel goes both ways. That is to say, the path between the two nodes is bidirectional, meaning that the origin and destination nodes are not fixed.

In mathematics, graphs are a way to formally represent a network, which is basically just a collection of objects that are all interconnected. For example, in mathematical terms, we describe graphs as ordered pairs. Remember high school algebra, when we learned about (x,y) ordered pair coordinates? Similar deal here, with one difference: instead of x and y, the parts of a graph instead are: v, for vertices, and e, for its edges. If our graph has more than one node and more than one edge that ordered pair — (V, E) — is actually made up of two objects: a set of vertices, and a set of edges. The “unordered” part is really important here, because remember, unlike trees, there is no hierarchy of nodes.

Facebook, a massive social network, is a type of graph. Twitter, on the other hand, works very differently from Facebook. I can follow you, but you might not follow me back.

References+Image

Vaidehi Joshi, A Gentle Introduction To Graph Theory. In Medium, Retrieved from here

Networks as predictive tools

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Networks play a key role when there is no objective way to determine performance, claims Barabasi in his new book called: “The Formula: The Universal Laws of Success.” Barabasi examined the career paths of scientists and artists both successful and less successful ones by tracing their networks.  While performance is about each individual, their success is about the people they connect to, therefore for Barabasi, success is a collective measure.

However appealing this research may be I resist the predictive character the author implies. I’d love to read the book eventually, but still, this bothers me. Networks are the very representation of complexity and it is inconsistent to consider them as normative tools where quantitative/statistical data can lead to predetermined results. Networks are all about emergence; thus the inability to predict how and when they will evolve. Sure, sometimes it could be that some patterns reappear, but just like the author says, networks are bigger than us or our ability to control them.

I also fail to see the relevance of the term success in this context. It looks so arbitrary and shallow. As much as I would love to see some professionals’ networks and the way they penetrate society, I’d rather the research focused on their ability to change the world for the better. If success is a collective measure, then it should be evaluated in regard to α collective benefit.

 

For more on this book and image, click here

Bruno Latour

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  • His early work had done more than that of any other living thinker to unsettle the traditional understanding of how we acquire knowledge of what’s real
  • In a series of controversial books in the 1970s and 1980s, he argued that scientific facts should instead be seen as a product of scientific inquiry. Facts, Latour said, were “networked”;  they stood or fell not on the strength of their inherent veracity but on the strength of the institutions and practices that produced them and made them intelligible. If this network broke down, the facts would go with them.
  • Founder of the new academic discipline of science and technology studies
  • The mid-1990s were the years of the so-called science wars, a series of heated public debates between “realists,” who held that facts were objective and free-standing, and “social constructionists,” like Latour. If scientific knowledge was socially produced — and thus partial, fallible, contingent — how could that not weaken its claims on reality?  Lately, however, these debates have begun to look more like a prelude to the post-truth era in which society as a whole is presently condemned to live.
  • By showing that scientific facts are the product of all-too-human procedures, these critics charge, Latour — whether he intended to or not — gave license to a pernicious anything-goes relativism that cynical conservatives were only too happy to appropriate for their own ends (…) But Latour believes that if the climate skeptics and other junk scientists have made anything clear, it’s that the traditional image of facts was never sustainable to begin with.
  • With the rise of alternative facts, it has become clear that whether or not a statement is believed depends far less on its veracity than on the conditions of its “construction” — that is, who is making it, to whom it’s being addressed and from which institutions it emerges and is made visible. 
  • In Abidjan, Latour began to wonder what it would look like to study scientific knowledge not as a cognitive process but as an embodied cultural practice enabled by instruments, machinery and specific historical conditions.
  • Day-to-day research — what he termed science in the making — appeared not so much as a stepwise progression toward rational truth as a disorderly mass of stray observations, inconclusive results and fledgling explanations (…) During the process of arguing over uncertain data, scientists foregrounded the reality that they were, in some essential sense, always speaking for the facts; and yet, as soon as their propositions were turned into indisputable statements and peer-reviewed papers — what Latour called ready-made science — they claimed that such facts had always spoken for themselves.
  • In the 1980s, Latour helped to develop and advocate for a new approach to sociological research called Actor-Network Theory (…) Latour had seen how an apparently weak and isolated item — a scientific instrument, a scrap of paper, a photograph, a bacterial culture — could acquire enormous power because of the complicated network of other items, known as actors, that were mobilized around it. The more socially “networked” a fact was (the more people and things involved in its production), the more effectively it could refute its less-plausible alternatives.
  • Latour believes that if scientists were transparent about how science really functions — as a process in which people, politics, institutions, peer review and so forth all play their parts — they would be in a stronger position to convince people of their claims
  • Whether they are conscious of this epistemological shift, it is becoming increasingly common to hear scientists characterize their discipline as a “social enterprise” and to point to the strength of their scientific track record, their labors of consensus building and the credible reputations of their researchers.

Excerpts from: Bruno Latour, the Post-Truth Philosopher, Mounts a Defense of Science, By Ava Kofman published in New York Times, full article available here

Image available here

Networked Learning

NETWORK LEARNING

The network is a network of people: networked learning aims to understand social learning processes by asking how people develop and maintain a ‘web’ of social relations used for their learning and development (de Laat)

Networked learning does not necessarily involve ICT, though in specific cases it may make use of technology. What makes learning networked is the connection to and engagement with other people across different social positions inside and outside of a given institution.  The network is supportive of a person’s learning through the access it provides to other people’s ideas and ways of participating in practice as well as of course through the opportunity to discuss these ideas and ways of participating and to potentially develop nuanced, common perspectives (Carvalho and Goodyear)

Networked learning may utilize ICT but it might me also supported by other means such as physical artefacts or artistic stimulation of senses and feelings while connections may also be drawn spontaneously by the learners themselves (Bober & Hynes)

The network is a network of situations or contexts: connections between the diverse contexts in which the learners participate as significant for understanding learning beyond online learning spaces, and, indeed, within them as well. This is the sense in which the network, under-stood as a network of situations, supports learning: by offering tacit knowledge, perspectives and ways of acting from known situations for re-situated use in new ones. Networked Learning’ on this under-standing is the learning arising from the connections drawn between situations and from the resituated use in new situations of knowledge, perspectives and ways of acting from known ones (Dohn)

The ‘network’ is one of ICT infrastructure, enabling connections across space and time: The support for learning provided by the network is one of infrastructure, i.e. the ease of saving, transporting and retrieving content for future use. Learning, it would seem, will be ‘networked’ whenever it is ICT-mediated, by that very fact; perhaps with the proviso that the situations of learning should indeed be separated in space and/or time so that the infrastructure (the ‘network’) is actually brought into play. This proviso would differentiate the field of networked learning somewhat from the field of Computer Supported Collaborative Learning (CSCL), where many studies concern ICT-facilitated group work between physically co-located students. The re-search field of Networked Learning is characterized, not only by focusing on ‘networks’, but also by taking a certain approach to learning, focusing critically on aspects of democratization and empowerment (Czerniewicz and Lee)

The ‘network’ is one of actants: consisting of both human and non-human agents in symmetrical relationship to each other. It is a systemic approach to learning, where individual learners’ interaction and learning may be analyzed as a result of socio-material entanglement with objects and other people. The network supports learning in the sense that any learning is in fact the result of concrete socio-material entanglement of physical, virtual, and human actants (Wright and Parchoma; Jones)

 

References

Bonderup Dohn, N., Sime, J-A., Cranmer, S., Ryberg, T., & de Laat, M. (2018). Reflections and challenges in Networked Learning. In N. Bonderup Dohn, S. Cranmer, J-A. Sime, M. de Laat, & T. Ryberg (Eds.), Networked Learning – reflections and challenges (pp. 187-212). Switzerland: Springer. Research in Networked Learning,
DOI: https://doi.org/10.1007/978-3-319-74857-3_11

Image available here