[Tutor] the binary math "wall"

[Lowell Tackett]

From the virtual desk of Lowell Tackett  



--- On Wed, 4/21/10, Dave Angel <davea at ieee.org> wrote:

> From: Dave Angel <davea at ieee.org>
> Subject: Re: [Tutor] the binary math "wall"
> To: "Lowell Tackett" <lowelltackett at yahoo.com>
> Cc: tutor at python.org, "Steven D'Aprano" <steve at pearwood.info>
> Date: Wednesday, April 21, 2010, 6:46 AM
> 
> 
> Lowell Tackett wrote:
> > --- On Tue, 4/20/10, Steven D'Aprano <steve at pearwood.info>
> wrote:
> > 
> >   
> >> From: Steven D'Aprano <steve at pearwood.info>
> >>     <snip>
> >> 
> >> The simplest, roughest way...hit them with a
> >> hammer:
> >>     
> >>>>> round(18.15*100) == 1815
> >>>>>       
>    
> >> True
> >>     
> > 
> > ...when I tried...:
> > 
> > Python 2.5.1 (r251:54863, Oct 14 2007, 12:51:35)
> > [GCC 3.4.1 (Mandrakelinux 10.1 3.4.1-4mdk)] on linux2
> > Type "help", "copyright", "credits" or "license" for
> more information.
> >   
> >>>> round(18.15)*100 == 1815
> >>>>         
> > False
> >   
> > <snip>
> But you typed it differently than Steven.  He
> had   round(18.15*100), and you used
> round(18.15)*100

As soon as I'd posted my answer I realized this mistake.

> 
> Very different.   His point boils down to
> comparing integers, and when you have dubious values, round
> them to an integer before comparing.  I have my doubts,
> since in this case it would lead to bigger sloppiness than
> necessary.
> 
> round(18.154 *100) == 1815
> 
> probably isn't what you'd want.
> 
> So let me ask again, are all angles a whole number of
> seconds?  Or can you make some assumption about how
> accurate they need to be when first input (like tenths of a
> second, or whatever)?  If so use an integer as
> follows:
> 
> val =  round((((degrees*60)+minutes)*60) +
> seconds)*10)
> 
> The 10 above is assuming that tenths of a second are your
> quantization.
> 
> HTH
> DaveA
> 
> 

Recalling (from a brief foray into college Chem.) that a result could not be displayed with precision greater than the least precise component that bore [the result].  So, yes, I could accept my input as the arbitrator of accuracy.

A scenario:

Calculating the coordinates of a forward station from a given base station would require [perhaps] the bearing (an angle from north, say) and distance from hither to there.  Calculating the north coordinate would set up this relationship, e.g.:

cos(3° 22' 49.6") x 415.9207'(Hyp) = adjacent side(North)

My first requirement, and this is the struggle I (we) are now engaged in, is to convert my bearing angle (3° 22' 49.6") to decimal degrees, such that I can assign its' proper cosine value.  Now, I am multiplying these two very refined values (yes, the distance really is honed down to 10,000'ths of a foot-that's normal in surveying data); within the bowels of the computer's blackboard scratch-pad, I cannot allow errors to evolve and emerge.

Were I to accumulate many of these "legs" into perhaps a 15 mile traverse-accumulating little computer errors along the way-the end result could be catastrophically wrong.

(Recall that in the great India Survey in the 1800's, Waugh got the elevation of Mt. Everest wrong by almost 30' feet for just this exact same reason.)  In surveying, we have a saying, "Measure with a micrometer, mark with chalk, cut with an axe".  Accuracy [in math] is a sacred tenet.

So, I am setting my self very high standards of accuracy, simply because those are the standards imposed by the project I am adapting, and I can require nothing less of my finished project.