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=-1.9 required=5.0 tests=BAYES_00 autolearn=ham autolearn_force=no version=3.4.4 X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: 103376,cc4f25d878383cc X-Google-Attributes: gid103376,public X-Google-ArrivalTime: 2001-12-12 06:08:06 PST Path: archiver1.google.com!news1.google.com!newsfeed.stanford.edu!logbridge.uoregon.edu!hammer.uoregon.edu!skates!not-for-mail From: Stephen Leake Newsgroups: comp.lang.ada Subject: Re: Dimensionality Checking (Ada 20XX) Date: 12 Dec 2001 09:03:37 -0500 Organization: NASA Goddard Space Flight Center Message-ID: References: <11bf7180.0112070815.2625851b@posting.google.com> <9v0crt$bo2bi$1@ID-25716.news.dfncis.de> <9v37rs$cdmva$1@ID-25716.news.dfncis.de> <30wR7.37507$Yy.396223@rwcrnsc53> NNTP-Posting-Host: anarres.gsfc.nasa.gov Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: skates.gsfc.nasa.gov 1008166005 28954 128.183.220.71 (12 Dec 2001 14:06:45 GMT) X-Complaints-To: dscoggin@cne-odin.gsfc.nasa.gov NNTP-Posting-Date: 12 Dec 2001 14:06:45 GMT User-Agent: Gnus/5.0808 (Gnus v5.8.8) Emacs/20.7 Xref: archiver1.google.com comp.lang.ada:17830 Date: 2001-12-12T14:06:45+00:00 List-Id: "Mark Lundquist" writes: > "Stephen Leake" wrote in message > news:upu5ln22l.fsf@gsfc.nasa.gov... > > > > It is simply wrong to try to define units for trig and exponential > > functions. Remember the Taylor expansion for Sin: > > > > Sin (x) = x - 1/6 x**3 ... > > > > If x has dimensions of meters (shudder :), then what are the > > dimensions of Sin (x)? > > Hokey smokes, it's the ratio of two sides of a triangle, so its > dimensions are Distance/Distance! Forget the Taylor series! True. But Sin also appears in places that have nothing to do with triangles, and other functions in Ada.Numerics are also unrelated to geometry. So the point about Taylor expansions is more general, and I think makes it clearer about why it is simply wrong to try to define Sin (meters). > > This is why angles must be dimensionless, as > > radians are. > > Angles are not dimensionless. They are the ratio of distance around the > circumference to the radius. That's why for radian, there's 2 * Pi of 'em > in a circle. The SI defines the units of radians as (m * m**-1) ('m' stands > for 'meters'). I don't get why people keep saying radians are > dimensionless. Well, in my book m * m ** -1 == 1, so that's dimensionless. I think this SI definition is silly, but clearly we have to live with it. We are arguing over a minor point in the meaning of "dimensionless". The point is, to be meaningful for Sin, the argument x must have no dimensions. Another way to say this is that the dimensionality must resolve to 1 (as in m * m ** -1 == 1). Can we agree that any argument passed to Sin (or other transcendental functions) must have dimensionality that resolves to 1, in the above sense? Then I promise to not say "radians are dimensionless", instead I'll say "the dimensions of radians resolve to 1" :). -- -- Stephe