"Strong typing vs. strong testing"

[RG]

In article <i930ek$uvp$1 at news.eternal-september.org>,
 "BartC" <bc at freeuk.com> wrote:

> "RG" <rNOSPAMon at flownet.com> wrote in message 
> news:rNOSPAMon-20651E.17410012102010 at news.albasani.net...
> > In article <i92dvd$ada$1 at news.eternal-september.org>,
> > "BartC" <bc at freeuk.com> wrote:
> >
> >> "Thomas A. Russ" <tar at sevak.isi.edu> wrote in message
> 
> >> > But radians are dimensionless.
> >>
> >> But they are still units
> >
> > No, they aren't.
> >
> >> so that you can choose to use radians, degrees or gradians
> >
> > Those aren't units either, any more than a percentage is a unit.  They
> > are just different ways of writing numbers.
> >
> > All of the following are the same number written in different notations:
> >
> > 0.5
> > 1/2
> > 50%
> >
> > Likewise, all of the following are the same number written in different
> > notations:
> >
> > pi/2
> > pi/2 radians
> > 90 degrees
> > 100 gradians
> > 1/4 circle
> > 0.25 circle
> > 25% of a circle
> > 25% of 2pi
> >
> > See?
> 
> But what exactly *is* this number? Is it 0.25, 1.57 or 90?

It's an irrational number, so it cannot be written out exactly.  But 
it's approximately 1.57.

> I can also write 12 inches, 1 foot, 1/3 yards, 1/5280 miles, 304.8 mm and so 
> on. They are all the same number, roughly 1/131000000 of the polar 
> circumference of the Earth.

These aren't numbers, these are lengths.  They correspond to a physical 
thing out there in the real world.  Numbers don't.

> This does depend on the actual size of an arbitrary circle, but that seems 
> little different from the choice of 0.25, 1.57 or 90 for your quarter 
> circle.

Why does it seem "little different"?  That is exactly the difference.  
What you're doing in your "1/131000000 of the polar circumference of the 
Earth" is taking the number 1/131000000 and using it to describe a 
length.  But what is 1/131000000?  Well, it's the ratio of one foot to 
the polar circumference of the earth.  It's also the ratio of one apple 
to 131000000 apples, or one sheep to 131000000 sheep, or one second to 
131000000 seconds.  It's the ratio of *anything* to 131000000 of the 
same thing.  (And, in case you're wondering, 131000000 is the 
131000000th successor of zero.)

rg