Re:Graphical Linear Algebra
by hansvm on Wednesday August 19, 2020 @10:45AM
(#24210889)
With the caveat that I learned this material the old-fashioned way and probably can't adequately put myself in the shoes of a new learner, this feels overly pessimistic. A few general points come to mind:
(1) The human mind is pretty good at visual pattern recognition. For the same reason that people advocate for a big status monitor that every developer can see for your live service (since you can quickly spot anomalies your monitoring might miss) and for the same reason visualizing a data set is one of the first things you ought to do on your way to understanding it, creating a diagrammatic representation of linear algebra seems helpful for immediately getting a sense of where something feels "off" or for quickly grasping the intuition of a problem.
(2) The right notation (pictures in this case -- not that the idea I'm about to highlight couldn't be presented textually) can help highlight the portions of a problem that matter. Thinking about matrices as boxes of elements that you can individually manipulate is IMO actively harmful to understanding them and puts you in a situation where you miss the forest for the trees.
(2a) The matrix wiring diagram presented here naturally extends to higher order tensors, and for the life of me I can't find the source right now, but it was precisely that representation that made tensors click for me and gave me a foothold into other material about them.
(3) I think the current consensus is that multiple representations of a problem (via some mechanism -- call it "magic") are actively beneficial for learning a topic. From that point of view alone a diagrammatic representation doesn't seem especially bad.
(1) The human mind is pretty good at visual pattern recognition. For the same reason that people advocate for a big status monitor that every developer can see for your live service (since you can quickly spot anomalies your monitoring might miss) and for the same reason visualizing a data set is one of the first things you ought to do on your way to understanding it, creating a diagrammatic representation of linear algebra seems helpful for immediately getting a sense of where something feels "off" or for quickly grasping the intuition of a problem.
(2) The right notation (pictures in this case -- not that the idea I'm about to highlight couldn't be presented textually) can help highlight the portions of a problem that matter. Thinking about matrices as boxes of elements that you can individually manipulate is IMO actively harmful to understanding them and puts you in a situation where you miss the forest for the trees.
(2a) The matrix wiring diagram presented here naturally extends to higher order tensors, and for the life of me I can't find the source right now, but it was precisely that representation that made tensors click for me and gave me a foothold into other material about them.
(3) I think the current consensus is that multiple representations of a problem (via some mechanism -- call it "magic") are actively beneficial for learning a topic. From that point of view alone a diagrammatic representation doesn't seem especially bad.