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

Downes-Siemens discussion (E-Learning 3.0) 17.10.2018

E-LEARNING 3.0_01

Just finished watching the conversation between Steven Downes and George Siemens in the framework of the E-Learning 3.0 course. Here is some of the key points I wrote down:

  • In the last five years we are kind of being in the wilderness/ now, there is an emergence of a more shared consistent narrative about AI and human intelligence and how these two intersect/ how we learn is structurally different way that predicted
  • The human equation in learning is critical to understanding/ Ai is influenced by human intelligence, one determines what the other does/ so the question is: what is uniquely human? Siemens advocated for an idea of beingness, who we are as people, kindness, compassion, emotion, maybe, he says, that’s our final domain of control. Machine learning model can be more accurate and effective that human intelligence, humans may slip through, computers always learn more/ So, if cognition isn’t our domain there are still areas where we are can prevail. Downes rejected the idea of being as fuzzy and suggested purpose and definition of goodness instead as more unique human qualities. However,  he said, that if we can come up with ethics, so can computers and that perhaps we are destined to be the voice in the computer’s head. 
  • What is learning? A persistent change in behavior or behavioral potential due to having undergone some type of experience, reflection or interaction with the environment/ the first part of learning is the capacity to choose what is important to you/ choosing-deciding that’s the skill in support we should be providing to students developmental attributes/
  • The things that are not being measured but end up to be more consequential
  • We can not not learn unless there is sth structurally wrong with us
  • So, why are we teaching in a way that is counter intuitive and not personally satisfying to students? Learning can be a bit of a struggle sometimes unless you are doing something that you absolutely love/ if we can have access to systems that can learn and out-learn us what should we be teaching? What’s the point of a formal system of learning when a student has an enormous disadvantage in relation to any type of technology agent? Maybe we should turn to the library of Alexandria, the lyceum or the academia for a model of more random exploration.
  • Siemens prediction for the next 50 years (short term) is that we are going to be working with technology, build knowledge and physically work in some in of relationship with technology. He quoted Andy Clark’s phrase about the mind being extended in the environment so our knowledge is not solely in our heads/ the ideas of connectivism seem all the more relevant as we proceed, he said.
  • Underlying layers of bitcoin and related technology reveal imply a significant change to the web itself (Downes)
  • The trustworthiness of the system is significant/ the places to hide are becoming minimum/ fragmenting the conversation has the same effect as denying a fact because people can’t get on the same page. Siemens used the word obfuscation: the conversation is not held long enough to have a shared opinion on that/ the strategies of dealing with is is fragmenting the main participants so that won’t be a coherent narrative
  • The joker problem: sometimes you just want to see the city burnt (Downes)
  • We are no longer engaging with information but with identities/ we only care about the info that validates our identity, the authenticity is secondary
  • Will to power (narcissistic) or will to control: I want to have control of what I do/ we often don’t see the long term impact-
  • What information abundance consumes is attention/ in the past we had more attention that information/ getting better for using our attention/ raising the IQ of individuals is important especially in an analytics world drives everything what happens

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You can watch the discussion here