From time to time, I promise myself not to respond again to e-mails from strangers, asking me to comment on their research, view their paper, offer thoughts.<\/p>\n
Yet from time to time, when the person seems respectable, the research genuine, I do respond. Most of the time, in vain.<\/p>\n
Like the other day. Long story short, someone basically proved, as part of a lengthier derivation, that general relativity is always unimodular. This is of course manifestly untrue, but I was wondering where their seemingly reasonable derivation went awry.<\/p>\n
Eventually I spotted it. Without getting bogged down in the details, what they did was essentially equivalent to proving that second derivatives do not exist:<\/p>\n
$$\\frac{d^2f}{dx^2} = \\frac{d}{dx}\\frac{df}{dx} = \\frac{df}{dx}\\frac{d}{df}\\frac{df}{dx} = \\frac{df}{dx}\\frac{d}{dx}\\frac{df}{df} = \\frac{df}{dx}\\frac{d1}{dx} = 0.$$<\/p>\n
Of course second derivatives do exist, so you might wonder what’s happening here. The sleight of hand happens after the third equal sign: swapping differentiation with respect to two independent variables is permitted, but \\(x\\) and \\(f\\) are not independent and therefore, this step is illegal.<\/p>\n
I pointed this out, and received a mildly abusive comment in response questioning the quality of my mathematics education. Oh well. Maybe I will learn some wisdom and refrain from responding to strangers in the future.<\/p>\n From time to time, I promise myself not to respond again to e-mails from strangers, asking me to comment on their research, view their paper, offer thoughts. Yet from time to time, when the person seems respectable, the research genuine, I do respond. Most of the time, in vain. Like the other day. Long story […]<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[30,35,3],"tags":[],"class_list":["post-11224","post","type-post","status-publish","format-standard","hentry","category-mathematics","category-personal","category-physics","category-30-id","category-35-id","category-3-id","post-seq-1","post-parity-odd","meta-position-corners","fix"],"_links":{"self":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts\/11224","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=11224"}],"version-history":[{"count":5,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts\/11224\/revisions"}],"predecessor-version":[{"id":11229,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts\/11224\/revisions\/11229"}],"wp:attachment":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11224"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11224"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11224"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}