I wouldn't take too seriously a 70s leaflet from HP trying to sell their calcs with a certain amount of charming bias. Let's go to 1974? and listen (again...) to a guy that worked there at the time and has "some" skill in technical matters.
Quote:Woz:
Infix to postfix was common to computer scientists in 1970. But this was back when very few colleges even had computer science programs for undergraduates. Postfix notation was not common to average people who use the infix written system. Computer scientists tend to find postfix to be more 'pure' than infix. It does have the qualities of left to right operation and no parentheses. But it requires a stack, which would translate to extra memory steps for a human if we wrote expressions in postfix. I'd guess that computer scientists would feel that early expression writers stuck us with a worse system, kind of like the QWERTY keyboard. The computer scientist view of postfix is similar to the scientists' view of the metric system.
At Hewlett Packard we were so proud that our calculators, the first scientific ones ever, were years ahead of competition. They used postfix partly because the least logic or ROM chips were quite expensive back then. It would have taken extra keys and an infix to postfix translator to use infix. Also, a larger and more expensive desktop HP machine from the division in Colorado Springs used postfix, for the same reasons. The HP-35 was an attempt to miniaturize this machine.
Our marketing department had a card with a monstrous formula to demonstrate how powerful our calculators were and what postfix calculation was capable of. They challenged people to solve it on a slide rule the normal way. Well, we could all solve it on our HP calculators but it took a few tries to get the steps accurate enough, there were so many of them.
Finally Texas Instruments introduced an infix 'algebraic entry' scientific calculator. The first one showed up in our lab one day. We were all pooh-poohing it and laughing at the arithmetic entry as being too weak for engineers. Someone pulled out our big formula challenge and we all laughed, sure that nobody could ever do it with the TI calculator. A challenge went up for someone to try. After a short silence I said that I'd try.
Well I started staring at the formula and looking at the keys and trying to decide which steps to calculate first, as you would do with an HP calculator. I finally realized that I'd never be able to solve the formula this way. With my fellow engineers watching I was very self conscious but I wanted to succeed. I managed to let go of my thinking and then came up with a very amazing concept. I just copied the formula from left to right! This was such an incredible concept that I pressed the keys as fast as I could on the TI calculator, risking a wrong press but impressing my colleagues. I had to guess whether this calculator used the square root button as prefix or postfix but I guessed right and got the proper answer the first time.
My colleagues couldn't believe it. I told them that you just copy the formula from left to right but not one of them could see through their postfix fog. After all, these were the calculator experts of the world. They are well accustomed to thinking ahead and analyzing an expression to come up with the order of steps to take on an HP postfix calculator, and they had to remember which sub-expressions were in what order on the calculator's stack. None of them could do what I had done, forget that they have to be smart.
I was strongly affected for life by this experience. There's a lot of rightness in using the same system on a calculator that we all learn to use on paper, a system that has been around for hundreds of years. My pure side prefers postfix but it's not what I'd recommend to others for a calculator. I also type on a Dvorak keyboard now, but I wouldn't recommend it.
http://archive.woz.org/letters/general/57.html
And he was using an awfully primitive algebraic system (for the Mach number chore I guess). Ten years later the modern expression entry calculators appeared and believe it or not, the war was over.
You can be smart with an expression calculator too. You don't have to copy formulas literally, there's room for technique there. A bit of planning before you write the expressions can make them shorter, some times much shorter. With expressions you can reuse code, which is faster than typing it again and in some cases faster than having to program a macro. If you're not using it again, you can perform interactive calculations by pivoting on a number as in RPN (or in old AOS), now instead of X you have Ans and instead of a fixed stack you store intermediate results in registers/variables, which are meant to be used BTW. You don't have to do that all the time because the precedence rules and the expression capabilities allow you to perform lots of steps in a single line and then store just that result... I wouldn't judge a system by looking at novices while being one myself.
And I think that RPN is great too. It's probably the more efficient way to perform one-time calculations with up to 3-4 levels of stack and then chain calculations. I also think that too much stack gymnastics blurs the original calculations in your mind and turns them into a juggling game, that's why I wouldn't recommend it to people who are still learning the basics.
There's no need to dismiss any tool in the box. Sometimes though, as some HP calculators have a complex design for the sake of it really, it's funny to see the amount of confusion generated by it and then how other systems are being discarded for being too simple and "for kids". Well, maybe you can have easy to understand calculators that work without friction. That's why there are not very interesting forums about them: they just work as expected and people get things done. I don't think that there are many things to write about how to use a Casio 115ES... Had the Prime worked as expected the Prime forum would be half the size (at least)
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