The Dumbest Generation: AOS vs RPN



#34

This weekend I was reading both a book review:

The Dumbest Generation: How the Digital Age Stupefies Young Americans and Jeopardizes Our Future (Or, Don't Trust Anyone Under 30)

And a TI calculator brochure dated 1976:

Fast and easy. No calculator in its class is so easy to master.

The SR-50A lets you key the problem just as you would state it. A unique register system provides a sum-of-products capability directly at the keyboard. This ability to store the first product while the second is being calculated is in addition to the memory accessed by the memory keys. The efficiencies are suggested by this simple problem:

(2 x 3) + (4 x 5) = 26

TI’s Algebraic Entry Method:

2 [x] 3 [+] 4 [x] 5 [=] 26

Reverse Polish Entry Method

2 [^] 3 [x] 4 [^] 5 [x] [+] 26


It is easy to predict: "RPN is almost dead!"

Regards,
Joerg

BTW: My four kids use TI-84 Plus Silver Editions, a requirement of the local schools. And I sold my [ENTER] keys to db ;-))


#35

Quote:
The SR-50A lets you key the problem just as you would state it. A unique register system provides a sum-of-products capability directly at the keyboard. This ability to store the first product while the second is being calculated is in addition to the memory accessed by the memory keys. The efficiencies are suggested by this simple problem:

(2 x 3) + (4 x 5) = 2


I note that what TI omitted from the above was a methodology for handling the product of sums, or any other departure from mathematical hierarchy...as indeed there was virtually no such methodology on the SR-50A (apart from user ingenuity and it's lone memory register), it being an AOS machine with no parenthesis.

No wonder most TI engineers of that era used HP calculators.

...hal

#36

I find an equals key stupefies me :)

Trying to do any basic arithmetic on the 4-banger on my Blackberry is a torturous experience of clearing and reentering over and over again, given my automatic tendency to put the operands in the wrong place.

I am equally stupefied in a car with auto transmission. My unoccupied left foot just hovers around itching to get into trouble....

Les


#37

The only calculators I have more trouble with than algebraic calculators (or "algebraic" calculators) is trying to use the desktop printing calculators that use "adding machine logic".

In those, addition and subtraction are postfix, and multiplication and division are infix!


#38

And I bet the SR50A uses postfix for trigs and logs.

The first calcs I used were algebraic except for those functions so for example, the sqrt of sin 45 was done entirely RPN style: 45 sin sqrt.

Now we have more modern AOS calcs that prefix functions and force brackets round them - a system which completely throws me even if technically, it is more logical.

Yes, I prefer RPN but I still have a theory that the only reason HP selected the method was because it made writing the OS in the 9100 easier. It is obviously far easier to let the user deal with hierachy on a stack than have to write potentially awkward routines to sort it out.

Keystroke saving in RPN is slightly over-hyped. Its main benefit originally was ease of system programming.

Do I need a flame-proof suit for that?!

Mark


#39

Whatever the reason, everyone I know once got familiar with the RPN never went back. AOS makes me sick.

#40

Quote:
I am equally stupefied in a car with auto transmission. My unoccupied left foot just hovers around itching to get into trouble....

The first time I drove an automatic, I somehow managed to stall the engine while the car was already rolling. Intending to press the clutch in preparation for restarting the engine, my left foot pressed the leftmost pedal all the way to the floor, as it was trained to do. Burnt rubber ensued; fortunately no one was close behind me at the time.


My passenger (grandpa) was not amused. :-)

- Thomas

#41

Yes, but i just bought a "scientific" at the local 99 cent store for $2 + tax. How can RPN compete with $2? We are doomed.

Edited: 2 July 2009, 7:01 a.m.

#42

Quote:
It is easy to predict: "RPN is almost dead!"

From a marketing perspective, I'm sure TI wished this to be true. Has it happened, in 2009? Is RPN "almost dead?" By whatever indicator we attempt to evaluate this, if we're going to be honest, isn't the answer "yes?"

Indicators:

  • number of people who actually use (and understand) RPN
  • number of calculator manufacturers who build RPN machines
  • number of books describing how to use RPN
  • number of classes that teach RPN
  • sales of RPN calculators versus AOS and others

Now, members of this forum like RPN for many different reasons. Personally, I like it because it enables me to exercise my mind by writing programs for HP calculators to solve problems. I find RPN keystroke programming very similar to assembly language, which was the first programming language I learned way back in 1968 for the IBM 360. I loved assembly language because of its logic and because it required you to understand the actual hardware to a degree that higher-level languages did not. When I went to work in the industry, however, I never used assembly language; I used FORTRAN and COBOL. So my appreciation of RPN is based upon my affection for assembly language.

HP has always touted RPN as the "natural" way to do calculating, based upon how we do it manually and as we were taught in school. But I have always had a problem with that. We are taught to do pencil and paper math this way:

  12
+ 3
____
15

That is, we write down the first number, go down to the next line and write a +, write the second number on the same line as the +, then draw a line and do our actual work under that line. The operator doesn't come last, it actually comes before the second number. The last line we draw corresponds, essentially, to the = key. And that's how AOS calculators work, which is probably why they outnumber RPN calculators by a rather large factor.

I appreciate RPN because it provides a logic system that enables keystroke programming to work, and I enjoy keystroke programming. But if anyone actually believes that teaching RPN to school kids is what we need to do to save the newest generation from itself, I think that is wrong.

As a teacher for the past few years, I am keenly aware of how kids are more interested in their ipods than in learning long division. But when I was in junior high school, I was more interested in the Beatles than world history too. But most of us did OK in the world, and I believe that will happen to the current generation also.


#43

Quote:
But if anyone actually believes that teaching RPN to school kids is what we need to do to save the newest generation from itself, I think that is wrong.

And I completely agree with that. RPN seems totally counter-intuitive when you have only had exposure to traditional means of solving calculations, ie 1+2=3 etc..

My school era was when calculators were still quite exclusive and all without exception were algebraic. The only person in the entire school who had an HP was our computer science teacher. He was obviously very proud of it and showed and explained how it worked during one lesson (I think it was a Spice). None of us could understand the benefit of RPN even when the teacher kept trying to tell us how elegant it was.

None of us could remotely afford an HP anyway but coupled with the use of RPN, Casio mainly and TI ruled the roost as they worked the way we did.

If had we been taught RPN instead, would it have improved our understanding of maths? I seriously doubt it. My pride and joy - a Ti57 was stolen - so I had to borrow a Casio for my exams. In both O and A level, I hardly used it. At A level, I honestly don't think I touched it at all.

Nowadays, it seems that calculators are allowed at any level and all the time and by that, I would hunch that there is less attention to understanding methods and more emphasis on pure numeric results. Understanding RPN wouldn't change this for the better.

I often think back to that line from the Simpsons where Mrs. Krabappel asks her class, "now whose calculator can tell me what 2+2 is?" to which various comic answers are given.

If modern maths education is being reduced to a black-box process, it wont matter which method of calculation is used if people don't learn a basic feel for numbers.

Apologies for sounding like an old fogey.

Mark

#44

Quote:
I find RPN keystroke programming very similar to assembly language, which was the first programming language I learned way back in 1968 for the IBM 360.

Honk if you love JCL!

I grew up with Univac 1108 Exec 8 Level 27 OS and Fortran, and a little Bourroughs B6500 Algol (Now *that* was really a stack machine!)

Quote:
HP has always touted RPN as the "natural" way to do calculating, based upon how we do it manually and as we were taught in school. But I have always had a problem with that. We are taught to do pencil and paper math this way:

  12
+ 3
____
15

That is, we write down the first number, go down to the next line and write a +, write the second number on the same line as the +, then draw a line and do our actual work under that line. The operator doesn't come last, it actually comes before the second number. The last line we draw corresponds, essentially, to the = key.


When I manually add two numbers, I write down the first number, I write down the second number, then I perform the operation. That is exactly how the RPN stack works. I see the AOS sequence as an "un-natural" procedure, in comparison. I never start adding the second number to the first until both numbers are present in toto. To me, the "natural" claim some make for AOS fails completely, so AOS proponents must fall back on the claim that AOS is performed on an expression "just like it is written in a book." Weak!

Quote:
I appreciate RPN because it provides a logic system that enables keystroke programming to work, and I enjoy keystroke programming. But if anyone actually believes that teaching RPN to school kids is what we need to do to save the newest generation from itself, I think that is wrong.

No argument from me on any of that.

I appreciate RPN for its efficiency, and HP for its reliability.
In 1977, I bought an HP-67 and a TI-59. The TI-59 was actually quite a technical advance over the HP-67, with much greater memory, precision, speed, innovative solid-state software modules, and the PC-100C print cradle. But typically, programming a non-trivial function in the TI-59 took about 40 percent more memory steps than did the HP-67. The real problem was reliability. I used the HP-67 (and later an HP-97) for real-life professional needs in a submarine nuclear propulsion plant. I did not use the TI-59 because I couldn't keep the TI hardware working for more than about six months before it would fail.

I remember admiring the "technical" achievement of TI's AOS, even though it was a very real and significant impediment to effective and efficient program creation on the TI-59.


#45

My first calculator experience was with the first HP-35 so RPN was no problem for me. BUT, I quickly found the formulas written in books (and copied from book to book) were awkward in RPN, Indeed I think awkward with any calculator. I had to rewrite formulas to be handy for my calculator. I used keystroke sequences instead of formulas that were easy to remember and fast to do. some I wanted to do over and over at one frequency so having 2PiF in the repeating t register was my answer for easy usage. It wseemed important to do this when I saw people programming solutions that were rapid keystrokes for me.
Thus I ask, do we need to be tied to the past by awkward formulas "as written in texts? Or can we do it better today, I can. sam 80


#46

I will not advocate either RPN, AOS or EOS. For quick calculations (mostly additions, sometimes a few multiplications and/or divisions), I get used to the calculator a hand very quickly. When it comes to more elaborate formulas, EOS with a history has advantages over RPN/RPL and over AOS, because I keep my input while getting the result. A quick cursor up lets me check and or modify the formula and reexecute it. On my RPL machines, I've often the problem that is much less intuitive to back out from a mistake or to repeat a calculation: I see myself hitting ENTER a few times to save some copies of what is on the command line or in stack level 1.

#47

Quote:
Honk if you love JCL!

FORTH LOVE IF HONK THEN

(Are there people who love JCL? The mind boggles!)


#48

Quote:
(Are there people who love JCL? The mind boggles!)

I wouldn't exactly say I loved it, but since I had to read and write mag tapes (7 and 9 track for you afficionados) in all sorts of formats, I got pretty good at it!


#49

Yeah, I learned enough about JCL to do the task at hand. Like Mike Morrow above, my first real programming job was with a Univac 1108 using FORTRAN-V and the Exec 8 operating system, which was a lot more intuitive than JCL. The 1108 was a workhorse.

I always kind of wished that I had a chance to work for a company that used one of the smaller IBM systems, like the System 3. It would have been fun to use assembler with such a small system.

#50

Quote:
I appreciate RPN for its efficiency, and HP for its reliability.
My first HP machine was an HP-11C. My second was an HP-41C. After using those machines I was inclined to believe all the HP hoopla about quality and reliability. But then I started collecting and became acquainted with machines such as the HP-2X's and HP-3X's. When I couldn't get them to work the "old hands" gave me comments such as "twist the case and see if that helps" and "did you connect the charger without being sure that the battery pack was in place and making contact." I changed my impression of the HP. They have been as capable as everyone else of delivering inferior machinery to the customer, and not just recently.
#51

Quote:
I appreciate RPN because it provides a logic system that enables keystroke programming to work, and I enjoy keystroke programming. But if anyone actually believes that teaching RPN to school kids is what we need to do to save the newest generation from itself, I think that is wrong.

My experience in teaching my oldest kid calculators and math from he was 6 (he is now 10) is that it doesn't matter much which methodology I teach him. He picks 'em up with equal speed.

Teaching him programming, however... then it seemed very easy to teach him Raven, a stack based programming language, RPN-ish with a good set of math functions.

#52

Quote:
We are taught to do pencil and paper math this way:

  12
+ 3
____
15

Not all of us! I was taught to write it like this:

 12
3
——— +
15

-- I think that's the standard way in the Netherlands, maybe elsewhere in Europe as well.


Now to try to fit long division into this picture. :-)

- Thomas


#53

Wow! That's exactly RPN. So do schools in the Netherlands use HP RPN calculators, since kids are taught this way?


#54

Quote:
Wow! That's exactly RPN. So do schools in the Netherlands use HP RPN calculators, since kids are taught this way?

I wouldn't make too much of the notation -- we just put the "+" sign in a different location than they do in U.S. high schools, but the mechanics of addition on paper are the same regardless!

Regarding calculators in schools... I attended High School in the early 1980s, just as calculators were starting to be accepted for school use. There were some government guidelines on the issue, as I recall, but the details were left up to the schools themselves; my HS went from "disallowing calculators altogether" to "allowing" them; they recommended a small number, including some TI-30 model and some Casios; their main concern was that the calculators should have logarithmic and trigonometric functions, and, most importantly, be affordable, which the TIs and Casios were, but the HPs... not so much.



I had HP calculators back then, and I was allowed to use them during Math and Physics tests, but as far as I know, there were only 2 or 3 students using HP calculators in the entire school (about 600 students total, grades 7 through 12).


Apart from being easy to use, in my experience the other main advantage of RPN was that nobody would ask to borrow my calculator more than once; they'd go "where's the equals key" and zone out when I tried to explain how it did work...


#55

Quote:
Apart from being easy to use, in my experience the other main advantage of RPN was that nobody would ask to borrow my calculator more than once; they'd go "where's the equals key" and zone out when I tried to explain how it did work...

This matches my experience back in the seventies when I had the one time chance to carry a friend's HP-35 for one day at school:
The calc that always gave PI as the result.
#56

Quote:
...But if anyone actually believes that teaching RPN to school kids is what we need to do to save the newest generation from itself, I think that is wrong.

I would counter with an excerpt from Mark Edmonds response:

Quote:
...It is obviously far easier to let the user deal with hierachy on a stack than have to write potentially awkward routines to sort it out.

Indeed, while RPN may not save the latest generation from itself, it would at the very least force them to know and employ mathematical precedence, and in general be more involved in the calculation at hand. My 13 year old son, while compelled to use the school's TI84 classroom set from time to time, still prefers his HP 33s (in RPN mode). I really do think it's been of benefit to him to learn RPN.

Best regards, Hal

#57

Quote:
Indeed, while RPN may not save the latest generation from itself, it would at the very least force them to know and employ mathematical precedence, and in general be more involved in the calculation at hand.

This statement rings true to me. I do not know if it having to learn mathematics without the aid of symbolic calculators/computers or my choice to start using RPN in 1985, but I always break equations into parts and never just read from left to right. RPN is great training.

#58

Well, I am going to do a complete U-turn on my earlier comments when I said that teaching RPN wouldn't be any benefit.

If I think back to how I adjusted to RPN and what happened after that, it was obviously a benefit.

It was about 15 years after school that I got my first HP. I was expecting a real tussle with converting to RPN but much to my surprise, I found I adapted really quickly and then when I became fluent, I realised that I was approaching problems in a much more analytical manner than before. Rather than treating problems in a strictly linear left to right manner, I was breaking them down and thinking more about what exactly I was doing. It also made me appreciate precedence more so that in whatever high level language I was programming at the time, I started writing simpler more elegant expressions where use of brackets was rare.

Couple this with the unlimited stack in UserRPL and making efficient use of the stack rather than dumping values in variables as well as other programming benefits of a stack, RPN provides a programming solution that ticks all the right boxes; efficient, elegant, simple and fast.

So if I can be permitted to make this complete U-turn, I don't think RPN is going to save the educational system (!) but it should open up minds to its different approach which in turn should trigger more appreciation of number manipulation as well as important programming techniques.

Mark


#59

Quote:
Couple this with the unlimited stack in UserRPL and making efficient use of the stack rather than dumping values in variables as well as other programming benefits of a stack, RPN provides a programming solution that ticks all the right boxes; efficient, elegant, simple and fast.

I'd like to disagree. Having the stack as a means of transferring arguments and results back and forth between routines is a huge benefit over the way this had to be done with AOS TIs. It's just a clean interface.

But as soon as you start juggling the stack with OVERs, ROLLs and PICKs, your programs tend to become "write only".


#60

Quote:
But as soon as you start juggling the stack with OVERs, ROLLs and PICKs, your programs tend to become "write only".

Definitely! I find that I wind up drawing stack diagrams on scratch paper to untangle things. This is presumably why RPL introduced local variables. Sure, they have more run-time overhead, but I rarely use the calculator for such heavy-duty compute-bound tasks that it matters. In fact, since around 1984 or so, rarely in this case means never.


#61

Quote:
But as soon as you start juggling the stack with OVERs, ROLLs and PICKs, your programs tend to be "write only".

And, of course, messing with stores, recalls, rollups and rolldowns is exactly what one has to do if one writes any but the simplest kind of programs with the machines with a limited stack.
Quote:
Definitely! I find that I wind up drawing stack diagrams on scratch paper to untangle things. This is presumably why RPL introduced local variables. Sure, they have more run-time overhead, but I rarely use the calculator for such heavy-duty compute-bound tasks that it matters. In fact, since around 1984 or so, rarely in this case means never.

I also found that I needed to draw stack diagrams if I had the slightest suspicion that I might push data out the top of the stack. Working with stack diagrams is a real pain -- similar but not quite as bad as the pain with POS sheets that we had to live with when programming drum machines in the early 1960's.

The worst part for the novice RPNer was that there is no indication that pushout is occurring and the manuals aren't very good at warning the novice about that. By comparison the AOS machines all gave an error indication if the user exceeded the parentheses or pending operation limitations.

#62

Quote:
But as soon as you start juggling the stack with OVERs, ROLLs and PICKs, your programs tend to become "write only".
Extreme stack gymnastics does make things confusing, but a "write-only" result is still the programmer's fault. In those situations I like to put in the comment portion of each line what is on the stack after the line is executed, in addition to the normal comments. I still get more first-time-running success and fewer bugs with reverse polish than with algebraic languages.
#63

Joerg;
I agree that "the digital age stupefies Americans" but not just young ones. Don't underestimate the ability of one mediocre programmer to sell half baked programs to know-nothing middle managers so that their mathaphobe drinking buddies can almost do, sometimes, what real thinking humans used to do every day.
Trash like this is what makes people in general stupider each year. Neither AOS or RPN "Jeopardizes Our Future" (OK; AOS jeopardizes it just a little ;-) ).
Still; you would probably have made more money off me if you had figured the correct value of those beautiful calculators you sold me on an hp12c instead of one of the TI BA series. I practically stole them. Thanks. And BTW: why are you selling your Garrett RPN on ebaby? You might need to impress some nerd someday. What TI will do that? We're talking an enter key and cabinetry here. Get with it man, cancel that auction. Give that big German desk of yours some class.


#64

Dennis,

Oops - I sold the ITM2 already last week to a collector in France ;-))
(Here in Upstate New York we have Canadian neighbors and still talk to French people.)
But you mentioned on your website that you don't like the chicklet keyboard.

This week I have the Garrett 2000 on auction, nice Panaplex with ENTER key.

The real thing will be on auction next week, a wonderful operating Garrett 2002, this translates to 2 lbs american trees, the large Panaplex display glowing in warm orange, a full alarm clock and the ENTER key.

I have the auction pictures already on the server, view them here:

No, I won't cancel these auctions. I'm selling off some of my non- TI stuff, last inventory (after our minor flooding in the basement) revealed more than 3,500 calculators - time to say goodbye to at least 1,000 of them over the next years.

And, by the way, when we moved from Germany to Rochester, NY exactly 3 years and 1 day ago (we celebrated yesterday our 3rd year in this great country) it was a hot summer. Our 40-ft container was stored about 3 weeks w/o airconditioning in the full sun and most of the furniture didn't survive! The only THREE pieces that survived were the Garrett calculators ;-))

My nice desk is a piece of IKEA manufactured in China.

Greetings from Sunny-Rochester,

Joerg


PS: Thanks for your nice comments about the HP calcs - you don't have to feel guilty! I'm still figuring out what your TI-30 based terminal is doing - that was a great gift from you - worth at least my HP 21S ;-))

PSPS: Just browsed your pictures next to the software calculator, how is your Robotron baby doing? Still only used as a cup holder?


#65

Joerg; Yes, sadly, the Robotron is still just an RPN cup holder - but for fine California beer. Everything else runs, though my first 41 could use some work. Please let me know if you go to sell an RPN that i don't have. I'll bid like a maniac. But you should really keep a couple of them. You might have to do some engineering again someday ;-)
Took my first time off in eight months last weekend and walked up the Whitney glacier on Mt. Shasta - and met a German on the peak. You guys are everywhere. We didn't talk calculators but i did cut him a slice of watermelon. That surprised him so much he just about forgot his English. - db


#66

Dennis,

Keep in mind:

30 days vacation per year - and the Dollar is cheap for them (since one year we have the Greencard, otherwise I would write "for us") at an exchange rate of 1.40.

I compared last week the German vs US pricing of the Volkswagen Passat CC. There are different flavors in each regions, but I found one version (VW Passat CC - TSI, Tiptronic 2.0l, 200 PS) identical on both markets:

US / NY: $28,200 + Tax = $30,456

GERMANY: EUR 35,375 = $49,525

WOW - but know it from HP calculators ;-))

Regards,
Joerg

BTW: And NO - I didn't bought a Volkswagen.


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