From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on polar.synack.me X-Spam-Level: X-Spam-Status: No, score=-0.5 required=5.0 tests=BAYES_00,INVALID_MSGID, PP_MIME_FAKE_ASCII_TEXT autolearn=no autolearn_force=no version=3.4.4 X-Google-Language: ENGLISH,ASCII X-Google-Thread: 103376,a0ad312f61fa680d X-Google-Attributes: gid103376,public From: tmoran@bix.com Subject: RE: vectors, spacetime Date: 1999/11/19 Message-ID: <0Y6Z3.1773$602.64317@typhoon-sf.snfc21.pbi.net>#1/1 X-Deja-AN: 550441614 References: X-Complaints-To: abuse@pacbell.net X-Trace: typhoon-sf.snfc21.pbi.net 942996348 206.170.2.237 (Thu, 18 Nov 1999 23:25:48 PST) Organization: SBC Internet Services NNTP-Posting-Date: Thu, 18 Nov 1999 23:25:48 PST Newsgroups: comp.lang.ada Date: 1999-11-19T00:00:00+00:00 List-Id: >Mathematical vectors are a very general thing, they are just pairs, >triples, tuples of something. In physics they are used that way, >but in many cases vectors are homogeneous in physics. It�s very handy, To follow the weather map example, you could have wind velocity vectors, each with three components: the speed E-W, N-S and up-down. But you might alternatively choose to have vectors with 5 components: the three speed components and also the temperature and humidity at that point. Programming-wise, it just a question of what's more convenient. However, while it makes sense to talk about total wind speed as sqrt(vx**2+vy**2+vz**2), the quantity sqrt(vx**2+vy**2+vz**2+temperature**2+humidity**2) is surely a meaningless, useless number. > It has four real components, but a different metric etc. (the > fourth component behaves a little imaginary). The "different metric" is key. While the space-distance is sqrt(dx**2+dy**2+dz**2), the relativistic "distance" includes not "+t**2" but rather "-(ct)**2". But you can use regular componentwise addition and subtraction. Say baby Fred was born in a hospital. Baby Sam was born 20 feet to the east, 1 floor (10 feet) higher up, and 3 days later. Baby Charles was born 10 feet to the west of Sam, on the same floor, and 2 days earlier. Ordinary, componentwise arithmetic tells us Charles was born 10 feet to the East of Fred, 1 floor up, and 1 day later. But to calculate the relativistic "distance" between the births, you need to treat that time component differently. So if your program was using a generic package that does ordinary arithmetic on vectors with N components, you would have to overide its ordinary "distance" function with the relativistic one.