|Re: 35s complex-number functionality (& US $1 coin)|
Message #8 Posted by Karl Schneider on 29 July 2007, 6:56 p.m.,
in response to message #7 by Paul Dale
"x2, sqrt(x), and x-th root of y for complex-valued x and y were not provided because they were not absolutely necessary: yx can be used for those calculations."
Hi, Paul --
I really don't think this argument holds water. Following it merrily along, we also don't need any of the trig functions or even subtraction defined for complex arguments, they are available easily enough using other complex functionality.
Hey, don't blame the messenger! :-)
The HP-41 Math Pac was a "quick and dirty" 4 kB ROM released in 1980 or 1981, to provide some lacking functionality such as complex numbers and hyperbolics, as well as other useful applications such as triangle solutions and Fourier analyses. All functions were implemented as RPN keystroke programs. Sure, dedicated complex-valued functions for square root and square would have been useful on the Math Pac, but space limitations might have precluded that. (The Math Pac did provide real-integer and complex-valued powers and roots for complex-valued arguments as "Z^N", "Z^1/N", "Z^W", and "Z^1/W".
Certainly, complex-valued functions for square root and square, as a minimum, ought to have been implemented in microcode for the HP-32S, HP-32SII, HP-33s, and HP-35s, even if the original HP-41 Math Pac didn't have them as RPN routines. But, for whatever reason, they weren't.
A historical parallel: The misbegotten US $1 coins since 1971
Unfortunately, mistakes have a way of becoming immortal by perpetuation. Consider the US $1 coin. The old ones from the early 20th century were quite large, when a dollar was worth a lot and metals were less pricey by comparison. The 1971 Eisenhower dollar was the same size, but few people wanted to use it, and few vending machines accepted them. As a reaction to that, the next $1 coin -- the 1979 Susan B. Anthony dollar -- was barely larger than, or distinguishable from, a quarter-dollar. It was rejected by the public, minted only in 1979, 1980, and 1999 as a lead-in to -- the 2000 Sacagawea dollar coin. This new coin was made the same size as the Anthony dollar for compatibility with the machines that accepted it. However, the Sacajawea was goldtone, smooth-sided, and rimmed in order to distinguish it from quarters. It still failed to achieve public acceptance, as Americans preferred their beloved $1 paper "greenback".
Now, there's a new upcoming set of $1 coins that commemorate presidents. They look more like medallions, and yes, they will be the same size as Anthony and Sacagawea dollars. If that is true, I predict general failure once again to achieve widespread usage (as opposed to um, "seigniorage-producing collecting activity").
So, the bottom line of all that: If only the $1 coins from 1971 or 1979 had been made a reasonable and practical size -- not too big, but not just barely larger than a quarter -- and if the $1 paper bill had been politely but firmly phased out, we'd be using practical, long-lasting coins for small low-tech transactions, as most Western countries do. Instead, we use low-value coins and problematic paper currency -- all because of unsound thinking, perpetuation of mistakes, and an unwillingness to make unpopular decisions or expend the effort for progress.
So today, if the HP-35s doesn't have a mathematically-complete set of complex-valued functions, that can be traced back originally to the compromises made in the HP-41 Math Pac 27 years ago -- and the unwillingness to research the product history, and to make the effort to rectify shortcomings.
Edited: 30 July 2007, 9:56 p.m. after one or more responses were posted