Re: Math Skills? Message #18 Posted by Valentin Albillo on 24 Jan 2005, 9:56 a.m., in response to message #17 by Bram
Hi, Bram:
I'm probably wasting my time but I'll try anyway:
Bram posted: "It quickly appeared to me that he had typed in -5^2-2*-5-8 for the first value and he hadn't the foggiest that -5^2 came out -25."
Well, then an explanation of the rules of procedence would suffice. Something like
"a power takes precedence over a change of sign, so if
you type -5^2, the power will be executed first (5^2 =
25), then the sign will be changed (-25). If you want
the other way around, simply enclose in parentheses
what you would want to do first (-5)"
Instead of that, which is by no means complicated and that most 15-year old teens will have no problem understanding, specially since it's an universal rule ("whenever you want to force a particular order of operations, simply use parentheses"), you say this:
"Of course he should have typed (-5)^2 on the darn thing."
which immediately begs the question: Why "darn thing" ? The mere fact that it does things differently than what you consider "The Holy Bible of Calculating Expressions" is enough to belittle it and insult it ? Great ! Very rational ! Openmindedness at its best ! But wait, there's more:
"He obviously has to have an RPN calculator (an HP21 will do). One then cannot possibly make a mistake like this. "
Why "obviously" ? Because you like it to be so ? What may be so "obvious" to you, many other people can blatantly disagree with. I take it that you firmly believe that *only* RPN calculators can compute the coordinates of a parabolic curve, and "obviously" non-RPN models are grossly inadequate for such rocket-science applications !? C'mon !
Perhaps your rationale is that "One then cannot possibly make a mistake like this" in an RPN calculator, such as an HP-21. True, operators precedence is not an issue in RPN, the person will not make that particular mistake. But he/she can make many others.
For instance, the typical sequence to evaluate that expression for X=-5 in your HP-21 would be something like this:
5 [CHS][ENTER][X][LASTX][2][X][-][8][-]
As stated, there are other possibilities, but the above is typical. And, what's obvious about this sequence ? Do you think that having to press [CHS] instead of [-] is obvious ?
Or having to use [LASTX] to retrieve back the X value ? Or the "first enter the values into the stack, then perform the operations upon them" basic RPN rule itself ?
Of course this is obvious to *you* and to any other experienced RPN user, but not to anyone else !! The typical 15-year old, given an algebraic calculator might make the precedence error you mention, but if told the cause, he would understand it right away, and would use parentheses when necessary, or when wanting to make sure.
Same 15-year old, given an RPN calculator would do mistake after mistake, and throw the thing in despair, unable to even add two values. I've seen exactly this happen any number of times. And so do most of you.
Unless told how it all works. But the same applies to your "damned thing" and your "obvious" better way. All things are "obvious" once explained and understood, and algebraic calculators are just as able for computing expression as RPN ones are, even much better in many ways, we must not let RPN addiction to blind us to the objective facts.
Best regards from V.
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