{"id":1544,"date":"2010-01-23T04:30:00","date_gmt":"2010-01-22T17:30:00","guid":{"rendered":"https:\/\/www.homebrewradio.us\/blog\/2010\/01\/23\/does-math-lead-to-understanding\/"},"modified":"2025-07-21T11:42:50","modified_gmt":"2025-07-21T01:42:50","slug":"does-math-lead-to-understanding","status":"publish","type":"post","link":"https:\/\/www.homebrewradio.us\/blog\/2010\/01\/23\/does-math-lead-to-understanding\/","title":{"rendered":"Does Math Lead to Understanding?"},"content":{"rendered":"

\"\"<\/a>In “SolderSmoke — The Book” <\/a>I describe the quest for deep understanding of the circuits that we build and use. There is some discussion in the book of the role of mathematics in this quest. A while back a reader e-mailed me on this subject. In the hope of stimulating a discussion, I’ll present the key paragraph from that e-mail here (the author will, for now, remain anonymous):<\/span><\/p>\n

I appreciate your quotes from Feynman, Asimov, etc. about not
really being able<\/span> to fully understand everything. As a <\/span>math<\/span> teacher
I can say that one of the <\/span>biggest misunderstandings about <\/span>math<\/span>
is that it “explains” the phenomena of<\/span> physics and engineering.
(Science and <\/span>math<\/span> teachers are notorious for saying<\/span> to a student
who has just asked a “why” question things like, “well the <\/span>math<\/span> is<\/span>
a little bit more complicated than what you can handle right now.
Wait until<\/span>you have had a year or so of calculus.”) In reality it’s
the exact opposite!<\/span> The <\/span>math<\/span> equations actually hide the answers.
They are very good at accurately<\/span> describing phenomena, or at
predicting what will happen next, but they can never<\/span> answer the
question of why one equation works and another does not. We
get very <\/span>comfortable with allowing the familiar <\/span>math<\/span> equations
to hide our inability to<\/span> really answer the “whys.”<\/p>\n

This really resonated with me. In my effort to get a better grasp of mixer theoy a lot of people seemed to be simply pointing me to the trig equations, and equating a knowledge of those equations with an understanding of how the mixer circuits really work.<\/p>\n

Of course, I don’t mean to be anti-math here, but I thought the e-mail on the limits of mathematics was very interesting.<\/span> In “Empire of the Air” Tom Lewis wrote, “At Columbia, Edwin Howard Armstrong developed another trait that displeased some of the staff and would annoy others later in life: his distrust of mathematical explanations for phenomena of the physical world. All too often he found his professors taking refuge in such abstractions when faced with a difficult and seemingly intractable conundrum… Time and again as an undergraduate at Columbia, Armstrong had refused to seek in mathematics a refuge from physical realities.”<\/span>
<\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

In “SolderSmoke — The Book” I describe the quest for deep understanding of the circuits that we build and use. There is some discussion in the book of the role of mathematics in this quest. A while back a reader e-mailed me on this subject. In the hope of stimulating a discussion, I’ll present the … Continue reading “Does Math Lead to Understanding?”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":1545,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[224,282,34],"tags":[],"class_list":["post-1544","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-armstrong-e-howard","category-mathematics","category-mixer-theory"],"_links":{"self":[{"href":"https:\/\/www.homebrewradio.us\/blog\/wp-json\/wp\/v2\/posts\/1544","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.homebrewradio.us\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.homebrewradio.us\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.homebrewradio.us\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.homebrewradio.us\/blog\/wp-json\/wp\/v2\/comments?post=1544"}],"version-history":[{"count":1,"href":"https:\/\/www.homebrewradio.us\/blog\/wp-json\/wp\/v2\/posts\/1544\/revisions"}],"predecessor-version":[{"id":1546,"href":"https:\/\/www.homebrewradio.us\/blog\/wp-json\/wp\/v2\/posts\/1544\/revisions\/1546"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.homebrewradio.us\/blog\/wp-json\/wp\/v2\/media\/1545"}],"wp:attachment":[{"href":"https:\/\/www.homebrewradio.us\/blog\/wp-json\/wp\/v2\/media?parent=1544"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.homebrewradio.us\/blog\/wp-json\/wp\/v2\/categories?post=1544"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.homebrewradio.us\/blog\/wp-json\/wp\/v2\/tags?post=1544"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}