Due to the heavy use of the calculus of variations in my image analysis class, I’m having to refresh some of my mathematical knowledge. Frankly, I’ve felt like an idiot at several times during the class, since, ya know, the phrase “as we all know” in the lectures was often followed by something that I, for one, didn’t really know.<\/p>\n
Part of it, though, is that my criterion for ‘to know’ has changed over time. Through grade school, high school and my early college years, I think the main thing I was trying to achieve in my mathematical learning was recognition by my teachers and peers. And, that I did accomplish. I was praised by teachers and somewhat respected by peers. But most of what they were seeing was a symbolic show, like the translator in Searle’s Chinese Room.<\/p>\n
Not that I had a complete lack of deeper understanding, just that I didn’t particularly care about a deeper understanding and was fine with being able to do the symbolic manipulation efficiently and ‘correctly’. Nor did I really have any basis for connecting the stuff to the real world: I didn’t have any applications in mind when learning a new concept, except for the sham applications that textbooks present (“you can use this to calculate the area under the graph of x^2”. BFD!).<\/p>\n
So now, when I remember the ‘rules’ of mathematics, I’m immediately stopped short by the fact that they don’t all really make _sense_ to me. And with my new criteria for an acceptable level of understanding, I now have to put my work in the class on hold for a while while I try to get the next level of understanding of, for example, what ‘dy\/dx’ means (hint: it’s not just an indivisible symbol for ‘derivative of y with respect to x’).<\/p>\n
Of course, I do know that in order to apply image processing techniques, I can get by without really understanding it very deeply, just like I can drive a car without being able to design an aerodynamically optimal intake manifold. So, I can still get through the applications by symbolic manipulation, but I’m going to be backfilling a lot of understanding of some basic mathematics at the same time.<\/p>\n
Huh.<\/p>\n","protected":false},"excerpt":{"rendered":"
Due to the heavy use of the calculus of variations in my image analysis class, I’m having to refresh some of my mathematical knowledge. Frankly, I’ve felt like an idiot at several times during the class, since, ya know, the phrase “as we all know” in the lectures was often followed by something that I, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-86","post","type-post","status-publish","format-standard","hentry","category-general","author-admin"],"_links":{"self":[{"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/posts\/86","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/comments?post=86"}],"version-history":[{"count":0,"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/posts\/86\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/media?parent=86"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/categories?post=86"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/tags?post=86"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}