{"id":698,"date":"2006-10-11T10:27:54","date_gmt":"2006-10-11T10:27:54","guid":{"rendered":"http:\/\/scienceblogs.com\/principles\/2006\/10\/11\/understanding-vs-mathematics\/"},"modified":"2006-10-11T10:27:54","modified_gmt":"2006-10-11T10:27:54","slug":"understanding-vs-mathematics","status":"publish","type":"post","link":"http:\/\/chadorzel.com\/principles\/2006\/10\/11\/understanding-vs-mathematics\/","title":{"rendered":"Understanding vs. Mathematics"},"content":{"rendered":"

Over at Crooked Timber, Daniel picks up the Harry Collins thing<\/a> I talked about last week, and asks an interesting question about the role of math<\/a>:<\/p>\n

\n

We don’t want to make “understanding the subject” mean “being able to do calculations about the subject”, unless we have some reason to believe that this is a necessary condition rather than a sufficient one (and to be frank, I don’t believe it’s a sufficient condition; I’ve spent enough time with economists to know that ability to do the maths does not mean that someone understands the economics). Is there anything? Or is Collins’ concept of “interactive expertise” really all there is, in terms of understanding?<\/p>\n<\/blockquote>\n

The question isn’t unique to Daniel, of course– physicists have come up with this one all on their own, and debated it in bars and at conferences for years. I’m not aware of any conclusive answer, but it’s occasionally fun to think about. Most of the usual arguments are reproduced in one form or another in the comments to that post.<\/p>\n

Personally, I tend to like the possibly apocryphal comment attributed to Feynman, to the effect of “if you really understand a subject, you ought to be able to explain it in terms that a college freshman can understand.” Mere facility with numbers doesn’t equal real understanding of a subject, and if the only way you can explain some result is by invoking higher math, there’s either a problem with your model, or your understanding of it.<\/p>\n

At the same time, though, I’m not entirely comfortable with saying that somebody who can’t interpret the equations of physics really understands the subject. It’s a tough problem.<\/p>\n","protected":false},"excerpt":{"rendered":"

Over at Crooked Timber, Daniel picks up the Harry Collins thing I talked about last week, and asks an interesting question about the role of math: We don’t want to make “understanding the subject” mean “being able to do calculations about the subject”, unless we have some reason to believe that this is a necessary… Continue reading Understanding vs. Mathematics<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"1","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-698","post","type-post","status-publish","format-standard","hentry","category-physics","entry"],"_links":{"self":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/698","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/comments?post=698"}],"version-history":[{"count":0,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/698\/revisions"}],"wp:attachment":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/media?parent=698"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/categories?post=698"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/tags?post=698"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}