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If RPN is less common in engineering schools these days, is this a reflection of the dumbing down of society? Or maybe they now need, and are required to use a computer for everything. I find both to be sad if true.
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I think the absence of RPN in general reflects two things. First and foremost, it's a result of the failure of HP in the calculator market. Fewer HP calculators means fewer RPN units in circulation. Second, it's a result of market research in the 1980s showing that RPN was a barrier to calculator sales. I don't know of any such studies specifically, but I infer their existence from two facts. First, that HP became more of a "market driven" as opposed to "engineering driven" company, and second, that they started to introduce algebraic models in the 1980s, gradually phasing out the RPN models. This may reflect the "dumbing down" of society, or it may just reflect the "dumbing down" of HP.
Of course, HP is still shipping an RPN calculator, and two models sporting the even more esoteric RPL operating and programming model. So their market research today must show there is a continuing, albeit small, market for smartypants calculators. Maybe their marketing department isn't so dumb after all?
Regards,
Howard
Edited: 29 Jan 2006, 2:24 p.m.
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Howard posted,
Quote:
First, that HP became more of a "market driven" as opposed to "engineering driven" company, and second, that they started to introduce algebraic models in the 1980s, gradually phasing out the RPN models.
There did seem to be a revised productdesign philosophy introduced with the Pioneer series in 1988. All mainstream calculator models preceding them  even the business models  were RPNbased. After the nonmainstream HP71B, HP75, and HP28C were introduced, the extensive set of original Pioneer models can be categorized as follows:
Scientific Business
Lowend 20S, 21S 10B
Midgrade 22S, 32S 14B
Highend 27S, 42S 17B
Only the 32S and 42S were RPNbased; all others were AOSbased. Clearly, RPN was now being reserved for only "upscale" scientific calculators, which had the highest model numbers. AOSbased scientifics had lower model numbers, and business calcs had the lowest model numbers.
RPN capability was restored to business models (by consumer demand?) with the introduction of the HP17BII. The convenient (but nonRPN) equation editor from the HP22S was ported to its "classmate" HP32SII in 1991, making it the undisputed leader of the midgrades. There was undeniably a "rhyme and reason" to the product design and positioning in that era.
NOTES:
 "lowend" models have 7segment displays
 "midgrade" models have lowresolution 1line dotmatrix displays
 "highend" models have highresolution 2line dotmatrix displays and IR tramsitters
As for "dumbing down", I did notice a decline in the quality of printing and verbiage in the Pioneerseries manuals, as opposed to the manuals for the Voyager series, HP41, and HP71B.
 KS
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In 1990 TI made a conscious business decision to pursue the student calculator market with graphing calculators. At the same time they stopped making the TI74 which used BASIC and the TI95 which used A.O.S. They mechanized what they dubbed the Equation Operating System (E.O.S.) with the graphing calculators. Educators liked it. I like E.O.S. because although it is a somewhat lower order methodology than BASIC or FORTRAN it is clearly a higher order methodology than A.O.S. or RPN. Some background follows:
As an undergraduate student in aeronautical engineering in the late 1940's I was exposed to the pencilandpaper equivalent of today's spread sheets. What we did was take manometer measurements at various points of the surface of an airfoil, enter the measurements in the left hand column of a large piece of paper and proceed to process the data by moving to the right as we processed the data by a sequence of mathematical operations listed across the top of the page. We used slide rules for multiplication and division, loglog slide rules if raising to a power was required, and pencilandpaper for addition and subtraction. One summer one of my friends worked as an intern at one of the large aircaft manufacturing firms. When he returned he told us that they had acres of junior engineers and technicians doing the same thing only they used log tables and mechanical calculators for increased precision. Don't try to tell me that the computerized spread sheet technology isn't a good thing.
After a tour in the Navy I returned to graduate school and took a computer programming course which used a RemRand 1103 which filled a whole building. We programmed in machine language. I left graduate school and worked as a field engineer in inertial navigation systems for seven years. We had miniaturized drum machines for airborne use. We programmed in machine language and did scaling in ones and zeroes. In the late 1960's I moved inhouse and took a course in BASIC which allowed me to use the company computer network and took a course in FORTRAN which allowed me to use a large numbercrunching company computer. No more messing around with ones and zeroes, or with octal and hexadecimal representations of machine language commands. I could enter equations just as I wrote them and didn't have to do my own scaling. With apologies to the memory of Martin Luther King, Jr. I found that I was "FREE AT LAST, FREE AT LAST, Thank God in Heaven, I was FREE AT LAST!"
A few years later someone tried to tell me that I needed to get an HP25 and learn to use it. I looked at the methodology and said "Good God, it's back to machine language! Why would I want to do that?"
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Well, I'm talking from Brazil, where things happen different way.
The vast majority of our public secondary schools don't have computers and, where I could see they have these machines, the teachers are not interested or prepared to use them.
About my life with calculators, I've started with one very simple 4 operations, used to help me with those long chemical calculations.
Since them I've been upgrading, but I have the luck to see a cousin of my friend using one HP41. Man, I was impressed with the power of that machine! He told me about cassettes, card readers, printers  a dream machine! So, I spent almost my mother's salary to buy my first HP: HP11C. I was starting in University, and it took to me less than 4 hours to make my first finite integral program.
Well, the rest of my time I've studying, I used one HP calculator. For me, RPN logic was almost natural, I don't know why. For my coleagues, usally afraid of HP calculators just because the RPN logic, just 15 to 30 minutes and they were proficient HP users.
I must agree with makority posts in this thread: the problem was the HP marketing, or the lack of it.
Also, removing models like 15C and not keeping the HP42S line was two great mistakes. Not I don't like the 48/49 series, but because the portability and quality of those machines.
About using calculators at University, I have to say that there was nothing I couldn't do with HP calculators. When 48 series arrived, so, really nothing! Even litteral calculus!
This bring to me a problem  let's take the Algebra course. I was always interested in the mechanic of things. After that, I implemented a program and, well, the problems were transformed in just typing numbers in the calculator  thanks to my devoted HP 15C or 48GX.
Now, I assume that it would be important to take more care about the principles, the math basis, the theorems around each problem. Even today, a decade after, I'm always interested in making programs and relegate to a second plane the mathematic basis.
When I discovered this gold mine called HPMuseum Forum and was prompted for some ardue mathematics problems proposed on the "challenges", I could see the brilliant brains working on both hands: the mathematics basis and the applied solution unsing 15C, 41C or other machines!
I believe that my choices were wrong: I am actually a programmer (calculator programmer ;>), not a proficient one, neither a mathematician, probably worst than the programmer.
Best ragards and forgive the grammar mistakes...
Artur
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Not ten minutes ago my wife and I were talking about this very subject. She is a middle school teacher and something of a math geek and I am sort of a jackofalltrades engineer/programmer.
I see some of the same problems with technical professionals my own age (I'm 38) as my wife does with her students: intellectual laziness, coupled with a lack of intimacy with (in this case) numbers. "Math" as taught these days is largely data entry into a TI CAS screen, with the natural effect is that the student/victims never develop that essential intimacy with numbers required to know, at a glance, the answers to most problems within an order of magnitide or less before doing any actual calculations.
I know, I know: every generation carps like this about the generations that come after. Caeser tells us in his Commentaries that the Gallic Druids frowned on writing  in part because they felt it was in intellectual crutch!
Still, I think anyone who can't function with what was available to the guys who ran the Manhattan Project (slipsticks, tables, pencils, paper) is nearly defenseless against the GIGO principle.
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Bah, sorry about the mutilated grammar above. The editing operation was successful, but the patient did not survive.
One thing that just occurred to me is that RPN is very similar to working through problems on paper ... which no one does anymore, hence the unpopularity of RPN.
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Quote:
"Math" as taught these days is largely data entry into a TI CAS screen
I know there are a lot of people who would agree with this assessment, and I am not naive enough to believe that it never happens. However, I have been observing in middle school math classrooms for the past two years (and student teaching currently) and my experience is that kids are allowed to use calculators only after they have demonstrated a mastery of the underlying mathematical procedures. That has been true in every math class I have observed, and this includes schools in both rich and poor communities.
Let's not be so quick to writeoff the kids and their teachers.
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Quote:
I know there are a lot of people who would agree with this assessment, and I am not naive enough to believe that it never happens. However, I have been observing in middle school math classrooms for the past two years (and student teaching currently) and my experience is that kids are allowed to use calculators only after they have demonstrated a mastery of the underlying mathematical procedures. That has been true in every math class I have observed, and this includes schools in both rich and poor communities.
If your observations are true, then you are working in an elightened school district. I hope they continue to actually teach concepts rather than procedures.
Quote:
Let's not be so quick to writeoff the kids and their teachers.
Far from it! As I mentioned, my wife is a teacher: BA in Human Development, MA in Special Education, and a growing list of credentials. I'm very proud of her and what she does, but she agrees with my assessment of public education as practiced here in sunny Southern California. It's not like she's in some benighted backwater, either: her school has been frequently presented as an educational technology leader by people like Bill Gates and newspapers like the Wall Street Journal.
As far as I can see, calculators/computers have no place in mathematics education, to limit to this one area. One needs nothing more than pencil, paper, a willing mind, and a good teacher to do everything from 2+2 to orbital mechanics. After someone has a good grounding in math ... well, computing devices are a godsend.
Good luck with your teaching career  it really takes a special kind of tenacity and concern for children to be a success in today's school system.
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Thanks John. I appreciate your feedback.
I don't know how enlightened the school system here in Louisville is. I have been lucky to have observed in the classrooms of some very sharp math teachers. I know all of them can't be that good. They probably pair us studentteachers up with the cream of the crop so we don't get so discouraged that we quit before we have even started!
I worked in the computer field for 28 years, and based upon how I have seen computers used in the schools so far, I tend to agree with you. I have not seen them used very effectively at all by the students. Some middle schools here even issue laptops (Apple iMacs) to each student, but 99% of the teachers do not even use them in their lessons, the kids just use them to play.
Regarding calculators in the classroom, I don't know. I can see them being of value in high school algebra, where a kid can do a graph of y=3x and see how it appears, then change it to y=.5x and see how the graph changes. But I agree, a kid would have to understand graphs and equations before being allowed to use them that way. I think they could help learning, but they could become a crutch too.
Ah, the challenges of education!
Don Shepherd
Louisville, KY
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My son is in the accelerated 5th grade math program at his school, and is not allowed to use a calculator, even though they are throwing some pretty tedious numbers at him. Having known nothing else, however, he whips through them with pencil and paper pretty handily. I was going to approach his teacher about when he can start using a calculator to spare him the drudgery of taking 12.369 into 3.587 longhand, but after reading this thread, I'll hold my horses. When that time does come, I'll send an HP rpn machine with him (maybe even a vintage one), and see what kind of reaction that evokes from his classmates. My son's favorite machine is my old 29C, but I DOUBT I'll be sending that to school with him... Best regards, Hal
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Feynman's talks about Los Alamos contain a lot of grist for that mill. His onesided competition with Hans Bethe over who could get an answer the fastest, Feynman with a Marchant calculator or Bethe in his head. Bethe won about 6 in 7 of these contests. He did it by knowing his logarithms, and by recognizing proportions and relations between various numeric values. Feynman got pretty good at doing the same thing, as he relates later in his talk about a contest with an abacus salseman.
The second point that relates to John's post was the use of IBM machines to do largescale computations at Los Alamos. Feynman was in charge of a group that took IBM machines that did discrete operations , such as addition, mechanically with punch cards, and ganged them together in an assembly line to do big problems very rapidly. It was a fascinating precursor to the digital computer. But the relevant bit is how Feynman got the job. The fellow who had the brainstorm of using the IBM machines fell victim to what Feynman called "the computer disease." This is probably well known to many on this list. I certainly recognize it. This fellow started designing clever programs to do things with his new "computer," like calculating tables of arctangents. He came up with very clever ways to do this after a lot of intense effort. Unfortunately, they already had completely fine tables of arctangents! He got lost in theoretically fascinating but completely useless activity, and neglected the problems he was supposed to try to solve with the machines.
So those certainly are cautionary tales for today's students. But they aren't the whole story. Doing number crunching on machines actually can free up your mind for higher level reasoning about mathematics, as long as you have obtained an appreciation for what the original meaning of the word "computation" was. Knowing the numeric shortcuts can help you reason about problems in applied math, as well, as it helped Bethe and Feynman think about Physics. But being able to get exact or approximate numeric results very quickly, or revealing symbolic transformations of a complicated expression must also be hugely helpful to that sort of effort too. (I don't do this sort of thing myself, but I watched the impact that Mathematica had on the Physics Department at UCSB where I ran the computing facilities. When Mathematica was released, the theoretical physicists burst into lyrical flights of praise for the software, and I was busy for weeks getting it on all their workstations.)
So computers obviously have great power to advance or retard learning, depending on how they are applied. Let's not throw the analytical baby out with the computational bathwater!
Regards,
Howard
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Quote:
Feynman's talks about Los Alamos contain a lot of grist for that mill. His onesided competition with Hans Bethe ...
Well, Bethe was a genius on several levels (his How a Supernova Explodes
is an amazing piece of science writing), as was Feynman (Surely You're Joking, Mr. Feynman, etc. are wonderful). I had Feynman in mind when I made my original post, so I'm pleased you brought him up.
Quote:
The second point that relates to John's post was the use of IBM machines to do largescale computations at Los Alamos. ...
I purposely ignored the use of computers at Los Alamos since the real issue is that the computers didn't do any calculations that Oppenheimer & Co. couldn't do backwards & forwards while standing on their heads in their sleep.
Quote:
So those certainly are cautionary tales for today's students. But they aren't the whole story. Doing number crunching on machines actually can free up your mind for higher level reasoning about mathematics, as long as you have obtained an appreciation for what the original meaning of the word "computation" was. Knowing the numeric shortcuts can help you reason about problems in applied math, as well, as it helped Bethe and Feynman think about Physics. But being able to get exact or approximate numeric results very quickly, or revealing symbolic transformations of a complicated expression must also be hugely helpful to that sort of effort too. (I don't do this sort of thing myself, but I watched the impact that Mathematica had on the Physics Department at UCSB where I ran the computing facilities. When Mathematica was released, the theoretical physicists burst into lyrical flights of praise for the software, and I was busy for weeks getting it on all their workstations.)
Spreadsheets were the original "killer app" for the personal computer, but I wonder if the net effect is positive or not after watching people fiddle them all day. There have been reports that over half of all "siginificant" spreadsheets used in business (i.e. they are used to justify financing or support significant business decisions) have "material" errors in them. I've witnessed a few instances of this, and I can't help but think their authors would be better off with a cocktail napkin and a pencil.
Quote:
So computers obviously have great power to advance or retard learning, depending on how they are applied. Let's not throw the analytical baby out with the computational bathwater!
Not a chance: I write software for a living and have been fascinated with computing devices ever since my uncle let me play Moon Lander on his shiny new HP97.
Thanks for the thoughtful response!
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Quote:
I had Feynman in mind when I made my original post, so I'm pleased you brought him up.
I'm reading "Classic Feynman" which is a new edition by Ralph Leighton combining Surely You're Joking, Mr. Feynman! and What do You Care What Other People Think?. Most of the stories are transcribed from taped interviews Leighton did with Feynman in the 1980s. But the classic Los Alamos From Below is from a talk Feynman gave at UCSB (where I used to work, alas more than ten years later) on the occasion of the 30th anniversary of the Los Alamos bomb. That talk is included with the book on a CD at the back of the volume, and it's a wonderful thing. Both the story of Bethe's facility with mental calculation and the tale of what may be the first "geek tragedy" of the modern era come from that talk. There is also The Value of Science in which Feynman propounds his idea that freedom of thought requires "a satisfactory philosophy of ignorance." Looking around now at those who are forcing their beliefs down others throats, some even resorting to murder and torture, all in the name of certainty, I can only add a reverent amen to that!
Quote:
Thanks for the thoughtful response!
You're welcome. Feynman is my hero. I'm only too glad to write about him! 8)
Regards,
Howard
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Quote:
I'm reading "Classic Feynman" which is a new edition by Ralph Leighton ...
I glanced at this in the bookstore the other day and dismissed it as a reissue of books I already have, which appears to be only partially true. Thanks for the tip!
To the original poster: sorry to have hijacked your thread. I'll desist now. :)
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I have relatives who are math teachers and they comment on how things are being dumbed down in educating students. When I was in school in the '80's, we couldn't have a calculator in math class. Only in physics and chemisty class. I know that some will say, "well that's because they didn't have graphing calculators back then". Well I'm glad they didn't have them because you were forced to do it the hard way. A lot of things may be tedious to do by hand, but they are also an excellent way to learn, and they also develop the muscle that resides between your ears. The automation should come later when you are a competent professional in you field.
I didn't get turned on to HP calculators in college through HP marketing, but by word of mouth. It seems there are fewer mouths spreading the word now. If calculators with RPN are less popular in college now, I question if it is just because HP does a bad job marketing or if it is because there is an overreliance on software solutions at the college level. It is not my goal to say that software should not be used in college, and that it is always inappropriate. No, not at all. It has a definite place and usefulness. But before you use it you should be able to do things by hand. You have to learn how to walk before you can run.
Being able to handle numbers with a pencil, paper, and calculator is a valuable skill. RPN is just better for this purpose than aos. One day, you might have to go into the field and do some calculating on the spot. I have. If you don't have a laptop, and can only solve problems using software, you are in trouble. Being able to solve a problem by hand, or at least being able to come up with a reasonable approximation by hand should be a pre=requisite for using software. Also, if you are weak in performing calcs by hand, how can you check your output?
My apologies for my spelling errors.
