{"id":104,"date":"2003-08-11T16:49:27","date_gmt":"2003-08-11T20:49:27","guid":{"rendered":"http:\/\/blogs.law.harvard.edu\/desultor\/2003\/08\/11\/matrix-metrics\/"},"modified":"2003-08-11T16:49:27","modified_gmt":"2003-08-11T20:49:27","slug":"matrix-metrics","status":"publish","type":"post","link":"https:\/\/archive.blogs.harvard.edu\/desultor\/2003\/08\/11\/matrix-metrics\/","title":{"rendered":"Matrix, Metrics"},"content":{"rendered":"

<\/a><\/p>\n

After spewing four paragraphs of the following into Ez’s comments section re: this post<\/a>, I’ve decided to put it here instead. It is with reluctance that I forgo the advanced “strikethrough technology” that forum would offer, but the ability to save this and come back to it seems more valuable to me right now…<\/p>\n

Ovid uses “number” to refer to meter a couple of times. I wouldn’t be surprised if other Romans did so too. Nor if they bit the idea off the Greeks, from whom they swopped their prosody wholesale.<\/p>\n

Shakespeare was perhaps the earliest English user of “number” in this sense. He was by most accounts an Ovid fan, and a bit of a parrot — he’s been shown to be using some of Ovid’s words when he’s dealing with a theme or story lifted from that great author. It doesn’t seem ridiculous to suggest Ovid may have influenced his usage of “number”. OED’s first citation for the sense is from Love’s Labours Lost<\/i>. Here’s the section:<\/p>\n

\nLONGAVILLE. I fear these stubborn lines lack power to move.
\n  O sweet Maria, empress of my love!
\n  These numbers will I tear, and write in prose.
\nBEROWNE. O, rhymes are guards on wanton Cupid’s hose:
\n  Disfigure not his slop.\n<\/p><\/blockquote>\n

“Slop” is here in its old sense of “baggy sailor pants”. But onward… the giving up on one meter, and the presence of Cupid here, remind me tropically of the beginning of the Amores<\/i>:<\/p>\n

\nArma gravi numero violentaque bella parabam
\n  edere, materia conveniente modis.
\npar erat inferior versus—risisse Cupido
\n  dicitur atque unum surripuisse pedem.\n<\/p><\/blockquote>\n

I was going to publish about arms and violent wars using a heavy number, the matter matching the mode.
\nThe lower verse was equal – but they say Cupid laughed and stole a foot away.<\/p>\n

i.e. I wanted to write a big chest-thumping dactylic hexameter epic like Virgil, but that savage boy Cupid is messing up my concentration, and all I can do now is write these funny elegaic couplets (a hexameter followed by a pentameter – hence the innuendo of pedal-extremity abscondence).<\/p>\n

OK OK. Now about “matrix”. The basic meaning of this in earlier English is “womb”, as in Latin. The root is mater<\/i>, mother. This started to broaden in the 16c to figurative uses along the lines of, to borrow OED’s definition: “A place or medium in which something is originated, produced, or developed; the environment in which a particular activity or process begins; a point of origin and growth.”.<\/p>\n

So we see Darwin in Voyage of the Beagle<\/i>, using “matrix” to mean “the material by which fossils are surrounded” and to describe ore from which gold can be extracted. I haven’t read that book, but extracted the quote from a “Matrix Dictorum” which is itself part of The Matrix. The backend algorithms of this Matrix Dictorum use matrix algebra.<\/p>\n

The mathematical sense of “matrix” is actually amazingly new – OED’s first quotation follows:<\/p>\n

\n1850 J. J. SYLVESTER in Philos. Mag. 37 369 We..commence..with an oblong arrangement of terms consisting, suppose, of m lines and n columns. This will not in itself represent a determinant, but is, as it were, a Matrix out of which we may form various systems of determinants by fixing upon a number p, and selecting at will p lines and p columns, the squares corresponding to which may be termed determinants of the pth order.\n<\/p><\/blockquote>\n

In this quote, the original sense of “mother” or “womb” is apparent – a matrix is so called because it’s where determinants can be extracted from.<\/p>\n","protected":false},"excerpt":{"rendered":"

After spewing four paragraphs of the following into Ez’s comments section re: this post, I’ve decided to put it here instead. It is with reluctance that I forgo the advanced “strikethrough technology” that forum would offer, but the ability to save this and come back to it seems more valuable to me right now… Ovid […]<\/p>\n","protected":false},"author":25,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-104","post","type-post","status-publish","format-standard","hentry"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/archive.blogs.harvard.edu\/desultor\/wp-json\/wp\/v2\/posts\/104","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/archive.blogs.harvard.edu\/desultor\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/archive.blogs.harvard.edu\/desultor\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/desultor\/wp-json\/wp\/v2\/users\/25"}],"replies":[{"embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/desultor\/wp-json\/wp\/v2\/comments?post=104"}],"version-history":[{"count":0,"href":"https:\/\/archive.blogs.harvard.edu\/desultor\/wp-json\/wp\/v2\/posts\/104\/revisions"}],"wp:attachment":[{"href":"https:\/\/archive.blogs.harvard.edu\/desultor\/wp-json\/wp\/v2\/media?parent=104"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/desultor\/wp-json\/wp\/v2\/categories?post=104"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/desultor\/wp-json\/wp\/v2\/tags?post=104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}