From: Phillip Gawlowski <pg@...>
Date: 2009-12-23T23:03:00+09:00
Subject: Re: Trig value errors

On 23.12.2009 08:15, jzakiya wrote:

> This didn't nullify THE POINT I illustrated, which was
> using an increasingly smaller angle approaching zero as
> an argument, it eventually produced a value of '1' for
> cos, but not '0' for the same sin angle, as it should.

How many real world (as in, reality, out in the wild, where money and 
lives matter) cases do you know where a) Ruby is used for these 
calculations and b) these calculations matter?

> I feel I've made my points as clear as I think is needed.
> If it doesn't bother you that the present implementation produces
> incorrect results for clearly unambiguous
> situations then we just have different standards for the
> need to adhere to mathematical rigor and produce exact
> results. BUT THAT IS A CHOICE THAT HUMANS MAKE, AND IS
> NOT MANDATED BY NATURE.

A core tenent of mathematical rigor is consistency. Ruby *is* 
consistent. The results are, within the limitations already elaborated 
on earlier, correct, too.

If you need higher accuracy, you need a different tool.

Now to something no mathematician worth his or her salt likes to hear:
Math is *not* observed in nature. Math is a support science for physics, 
to help *describe* actual, observeable, phenomena, and express theories 
and formulae in an unambiguous manner, as well as in an abstract manner 
to allow the manipulation of said formulae.

--
Phillip Gawlowski