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: 2001-12-07 14:51:47 PST Path: archiver1.google.com!news1.google.com!newsfeed.stanford.edu!logbridge.uoregon.edu!arclight.uoregon.edu!wn4feed!worldnet.att.net!204.127.198.203!attbi_feed3!attbi.com!rwcrnsc51.POSTED!not-for-mail From: "Mark Lundquist" Newsgroups: comp.lang.ada References: <3C0F8E75.4F5CB3B8@amsjv.com> Subject: Re: Another Idea for Ada 20XX X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.50.4133.2400 X-MimeOLE: Produced By Microsoft MimeOLE V5.50.4133.2400 Message-ID: <7KbQ7.11747$wL4.10839@rwcrnsc51> Date: Fri, 07 Dec 2001 22:51:47 GMT NNTP-Posting-Host: 204.127.202.211 X-Complaints-To: abuse@attbi.com X-Trace: rwcrnsc51 1007765507 204.127.202.211 (Fri, 07 Dec 2001 22:51:47 GMT) NNTP-Posting-Date: Fri, 07 Dec 2001 22:51:47 GMT Organization: AT&T Broadband Xref: archiver1.google.com comp.lang.ada:17615 Date: 2001-12-07T22:51:47+00:00 List-Id: "Philip Anderson" wrote in message news:3C0F8E75.4F5CB3B8@amsjv.com... > Mark Lundquist wrote: > > > > > Units are unlike types in that they are optional (think about it, what units > > would you give for Pi?). > > > I don't think units are "optional", although they may be dimensionless, > ie just numbers like Pi. Eh? OK, so I'll ask again, what units would you give for Pi? > Note that radians, being a ratio, are actually > dimensionless. No, they are not! (BTW rate is also the ratio of distance/time, and of course rate isn't dimensionless -- any more than radians are!) The dimension of angle is distance/distance. (I'm not making this up -- the SI define radians in terms of meter*(meter**-1)). That's why when you multiply a distance by an angle, you get a distance. But if you were to multiply a mass by an angle, you do not get a mass (which would make it a unit conversion), but something whose units would be "kg-radians". (What use would that have? Beats me, for all I know there might be one... I'm a physics 'tard, my wise-ass PhD little brother got all the physics genes :-) :-) Dimensionless numbers do not change the units when you multiply them, that's the difference. No measurement is dimensionless. Cheers, Mark