<\/p>\n\/\/
\n\/\/ Alan’s Editorializing: Here is YET ANOTHER place where the SI made a
\n\/\/ really stupid definition. Let’s follow their chain of definitions, shall
\n\/\/ we, and see how it leads to absolutely ridiculous results.<\/p>\n
\/\/ The Hz is currently defined simply as inverse seconds. (1\/s).
\n\/\/ See: http:\/\/physics.nist.gov\/cuu\/Units\/units.html
\n\/\/
\n\/\/ The base unit of frequency in the SI *used* to be “cycles per second”.
\n\/\/ This was fine and good. However, in 1960, the BIPM made the
\n\/\/ change to make the fundamental unit of frequency to
\n\/\/ be “Hz” which they defined as inverse seconds (without qualification.)
\n\/\/
\n\/\/ Then, in 1974, they changed the radian from its own base unit in the SI
\n\/\/ to be a dimensionless number, which it indeed is (it’s a length divided by
\n\/\/ a length.) That change was correct and good in itself.
\n\/\/
\n\/\/ However, the definition of the Hz was *not* corrected at the same
\n\/\/ time that the radian was changed. Thus, we have the conflicting SI
\n\/\/ definition of the radian as the dimensionless number 1 (without
\n\/\/ qualification) and Hz as 1\/s. (Without qualification.)
\n\/\/
\n\/\/ This means that, if you follow the rules of the SI,
\n\/\/ 1 Hz = 1\/s = 1 radian\/s which is simply inconsistent and violates basic
\n\/\/ ideas of sinusoidal motion, and is simply a stupid definition.
\n\/\/ The entire rest of the world, up until that point, knew that 1 Hz needs to
\n\/\/ be equal to *2 pi* radians\/s or be changed to mean *cycles\/second* for
\n\/\/ these to be reconcilable. If you use “Hz” to mean cycles\/second, say,
\n\/\/ in sinusoidal motion, as the world has done for a century, know that the SI
\n\/\/ made all your calculations wrong. A couple of times, in different ways.
\n\/\/
\n\/\/ This gives the wonderful situation that the SI’s Hz-vs-radian\/s definitions
\n\/\/ have meant completely different things in the timeperiods:
\n\/\/
\n\/\/ * pre-1960
\n\/\/ * 1960 to 1974
\n\/\/ * post-1974
\n\/\/
\n\/\/
\n\/\/ Thus, anyone trying to mix the SI definitions for Hz and angular
\n\/\/ frequencies (e.g. radians\/s) will get utterly wrong answers that don’t
\n\/\/ match basic mathematical reality, nor match any way that Hz was ever used
\n\/\/ for describing, say, sinusoidal motion.
\n\/\/
\n\/\/ Beware the SI’s broken definition
\n\/\/ of Hz. You should treat the radian as being correct, as a fundamental
\n\/\/ dimensionless property of the universe that falls out of pure math like
\n\/\/ the Taylor series for sin[x], and you should treat the Hz as being a
\n\/\/ fundamental property of incompetence by committee.
\n\/\/
\n\/\/ One could consider the CGPM in 1960 to have made the original mistake,
\n\/\/ re-defining Hz in a way that did not reflect its meaning up to that point,
\n\/\/ or the CGPM in 1974 to have made the absolutely huge mistake that made
\n\/\/ the whole system inconsistent and wrong, and clearly broke the definition
\n\/\/ of Hz-vs-radian\/s used everywhere in the world, turning it into a broken,
\n\/\/ self-contradictory mess that it is now.
\n\/\/
\n\/\/ Either way, if I ever develop a time machine, I’m going to go back and
\n\/\/ knock both groups’ heads together. At a frequency of about 1 Hz. Or
\n\/\/ better yet, strap them to a wheel and tell them I’m going to spin one group
\n\/\/ at a frequency of 1 Hz, and the other at 1 radian\/s and let them try to
\n\/\/ figure out which one of those stupid inconsistent definitions means what.
\n\/\/ Hint: It’ll depend on which time period I do it in, I guess, thanks to
\n\/\/ their useless inconsistent definition changes.
\n\/\/
\n\/\/ It’s as if this bunch of geniuses took a well-understood term like “day”
\n\/\/ and redefined it to mean “60 minutes”. It simply breaks every historical
\n\/\/ use, and present use, and just causes confusion and a blatant source of
\n\/\/ error.
\n\/\/
\n\/\/ In summary: Frink grudgingly follows the SI’s ridiculous, broken definition
\n\/\/ of “Hz”. You should not use “Hz”. The SI’s definition of Hz should be
\n\/\/ considered harmful and broken. Instead, if you’re talking about circular
\n\/\/ or sinusoidal motion, use terms like “cycles\/sec” “revolutions\/s”,
\n\/\/ “rpm”, “circle\/min”, etc. and Frink will do the right thing because it
\n\/\/ doesn’t involve the stupid SI definition that doesn’t match what any
\n\/\/ human knows about sinusoidal motion. Use of “Hz” will cause communication
\n\/\/ problems, errors, and make one party or another look insane in the eyes
\n\/\/ of the other.
\n<\/quote><\/p>\n","protected":false},"excerpt":{"rendered":"
One of the nice things about scmutils is that it tracks units, so you can’t accidentally add 10 seconds to 5 metres. (+ (& 10 &second) (& 5 &meter)) => Units do not match: + (*with-units* 10 (*unit* SI … 1)) (*with-units* 5 (*unit* SI … 1)) When dealing with angles, it initially seems to […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-947","post","type-post","status-publish","format-standard","hentry","category-general"],"_links":{"self":[{"href":"https:\/\/www.nobugs.org\/blog\/wp-json\/wp\/v2\/posts\/947","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.nobugs.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.nobugs.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.nobugs.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.nobugs.org\/blog\/wp-json\/wp\/v2\/comments?post=947"}],"version-history":[{"count":4,"href":"https:\/\/www.nobugs.org\/blog\/wp-json\/wp\/v2\/posts\/947\/revisions"}],"predecessor-version":[{"id":951,"href":"https:\/\/www.nobugs.org\/blog\/wp-json\/wp\/v2\/posts\/947\/revisions\/951"}],"wp:attachment":[{"href":"https:\/\/www.nobugs.org\/blog\/wp-json\/wp\/v2\/media?parent=947"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.nobugs.org\/blog\/wp-json\/wp\/v2\/categories?post=947"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.nobugs.org\/blog\/wp-json\/wp\/v2\/tags?post=947"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}