Re: Re: power operator (again)

On Thu, Dec 19, 2013 at 4:27 PM, Tjerk Meesters <tjerk.meesters@gmail.com>wrote: > > > > On Fri, Dec 20, 2013 at 5:50 AM, Kris Craig <kris.craig@gmail.com> wrote: > >> On Thu, Dec 19, 2013 at 4:33 AM, Daniel Lowrey <rdlowrey@gmail.com> >> wrote: >> >> > > Thanks for all your effort! Unfortunately, since there's no option >> for >> > > negative numbers to intuitively square to positive outcomes, my vote >> is >> > > still No. I understand and respect your reasoning even though I do >> not >> > > agree with it. >> > > Intuition can (by definition) not coexist with mathematical reasoning, so > it seems that you're talking about experience here. > > Experience may come from: > > a) prior mathematical education > > Assuming a sane teacher, you would have been taught to write (-3) ^ 2 on > paper if you mean to square negative 3. > > > b) prior use of mathematical expressions in other programming languages > > 17 out of 22 programming languages that I have investigated are in favour > of a higher precedence for the power operation. > > > > >> > To me this is not a question of "intuitive" vs. "unintuitive" ... >> > -3^2 >> = -9 >> > is how the preponderance of credible resources evaluate the expression. >> As >> > far as I can tell voting "no" on this basis is equivalent to me claiming >> > the earth is flat because it better fits my world-view. >> >> >> That's a faulty analogy. In mathematics, the square of any number, >> positive or negative, yields a positive result. Any scientific or >> graphing >> calculator will match that behavior. I did sqr(-3) in the Windows >> Calculator just now and it outputted 9, not -9. >> > > Likewise, both pow(-3, 2) as well as (-3) ** > 2 yield 9. I'm not > arguing that an even power of a negative base should yield a negative > outcome; I'm arguing that what you deem to be intuitive is based on a > misconception. > > >> >> From http://en.wikipedia.org/wiki/Square_(algebra): >> >> "One of the important properties of squaring, for numbers as well as in >> many other mathematical systems, is that (for all numbers x), the square >> of >> x is the same as the square of its additive inverse -x. That is, the >> square >> function satisfies the identity x2 = (-x)2. This can also be expressed by >> saying that the squaring function is an even function." >> > > See what they're doing there? They disambiguate the expression to > (-x)2, > which is the same as (-3) ** 2 or (-$x) ** > 2. > > >> Now, I understand why some programming languages behave differently from >> the algebraic standard. I don't agree with it, but I understand their >> reasoning. Claiming that "the squaring function should always be an even >> function" is the equivalent of saying that the Earth is flat is faulty >> because it completely ignores the facts that support that argument, just >> as >> it would be faulty for me to ignore the facts that support yours. >> > > Not just some, more than 75% of the languages I've investigated do that. > Curiously, Visual Basic does it this way, whereas Excel doesn't :) I've > listed them here: > https://wiki.php.net/rfc/pow-operator#discussion > > >> I believe that, especially for a KISS language like PHP, our top priority >> with math operators should be to match arithmetic laws as closely and as >> intuitively as possible. The average PHP developer is going to do -3 ** 2 >> and expect a result of 9, not -9, and rightly so I think. >> > > And arithmetic law states that -3 ** 2 should be interpreted as > `-(3 ** > 2)`. See also: > > http://en.wikipedia.org/wiki/Order_of_operations#Exceptions_to_the_standard > > It's only in programming languages that this behaviour may be different > due to historical reasons or what not. > > >> >> You're free to disagree and you certainly have valid reasons for doing so, >> but please try to keep in mind that there is a valid argument on the other >> side of this, as well. >> > > Your case seems to promote following a minority of programming languages > that do this, though. > > >> >> --Kris >> > > > > -- > -- > Tjerk > So just to tie it all together (and please correct me if I'm mistaken), your argument is basically that: -x is actually -1 * x. Therefore, -3 ** 2 would actually be -1 * 3 ** 2. Due to order of operations, that comes out to -1 * 9 == -9. But now, let's look at another scenario: <?php $x = -3; // Or $x = -1 * 3, if you wish. $y = $x ** 2; ?> What would be the value of $y under this RFC? --Kris