Re: Possreps and numeric types
Date: Tue, 27 Mar 2007 11:42:55 GMT
Message-ID: <3r7Oh.15895$PV3.164370_at_ursa-nb00s0.nbnet.nb.ca>
Marshall wrote:
> On Mar 26, 7:17 pm, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
>
>>Marshall wrote: >> >>>On Mar 26, 5:46 pm, Matthias Klaey <m..._at_hotmail.com> wrote: >> >>>>"Marshall" <marshall.spi..._at_gmail.com> wrote: >> >>[snip] >> >> >>>When approximation occurs, in all cases it occurs in the >>>operators and not in the numbers. >> >>When you read a volt meter and write down 12V, are you suggesting 12 is >>the exact value? Or is it really 12V +/- 0.5V or 12V +/- 1V ? Or some >>other range?
>
> Measurements are of course not exact values. However, when I
> tell my calculator that I have 12 volts running across a 3 ohm
> resistor, I wouldn't be happy if it told me that was 3.997 amperes,
> even though that answer is no less accurate that the measurements
> I took.
I don't recall ever recommending an epsilon as large as 0.1% so I am having difficulty understanding the point you were are trying to make.
> Furthermore, calculations on measurements are not the only
> thing numbers can do. I would also not be happy if it turned
> out my bank was using floating point math to calculate my
> interest, even if I could be assured that the overall error
> across all customers was small.
I have no problem with them using floating point as long as the error is a small fraction of a penny. In the end, everything gets rounded to the penny in any case.
> Suppose I am trying to calculate pi to some specific number
> of digits using some series. Suppose the series converges
> in the abstract, but the calculator I'm using introduces some
> modest amount of error with each operation. The series may
> not even converge any more.
This is why I said earlier that we ignore the nature of rational approximations at our peril.
> Approximations absolutely have their uses. So do exact calculations.
I don't recall suggesting that exact calculations have no utility. I merely acknowledged that representations of rationals are approximations representing very small ranges of values.
>>When the computer has 12 to operate on, how does the computer know the >>provenance and that it represented an exact value as opposed to some >>approximate measure?
>
> Ah! This is exactly the internal predicate/external predicate
> dichotomy!
> I have little to say on that specific topic.
>
> However, let us suppose that sometimes one is giving the computer
> approximate measurements, and other times exact numbers.
> Would you prefer the system to assume your numbers were
> always approximate and sometimes be wrong, or would you rather
> the system assume your numbers are always exact and sometimes
> be wrong?
>
> That is a false dichotomy, of course. The reality is that the
> programmer has full control over whether he is using
> exact or modular or approximate operations. Even in languages
> with automatic conversions such as C, a programmer rarely
> finds himself doing a floating point add when he meant to
> do a modular add.
None of which has anything to do with approximations of rational numbers. Received on Tue Mar 27 2007 - 13:42:55 CEST