Contributed Columns

Jim Davidson's awesome HP-25 Library and numerous articles about math and other heavy topics endeared thousands of his readers to his keen intellect, gentlemanly manner, and clear writing style.

The following 1977 article made a profound impact on my young mind, and led to a delightful correspondence with Jim Davidson until his tragic death a few years later. This classic essay surely belongs in some sort of place of honor in the annals of handheld computing.

Jim Davidson, this one's for you. 'Till I see you again, I remain

Your devoted student,
-Joe Horn-

James J. Davidson (547)

"65 Notes," July/August 1977
Volume 4, Number 6, Page 25

As an engineer married to an artist, I have had many occasions to reflect on two very different approaches to life. They have been noted often and given many names: humanities vs. science, arts vs. engineering, emotion vs. cognition, form vs. function. The terms I like best, because they are the most widely descriptive, are qualitative vs. quantitative.

On first encountering a pleasing new phenomenon, the quantitative mind asks "How does it work?" The qualitative mind declares "How nice!" The engineer questions; the artist responds. The difference is profound, in method, in conclusions, and in future implications.

The difference can be illustrated by a homely example. When my wife and I shop for an ashtray, I'm concerned with whether a lighted cigarette will fall out, whether the sides are high enough to keep ashes from blowing if the windows are open, whether it's large enough to hold a reasonable quantity of butts without frequent emptying, but not so big as to be a nuisance. Oh yes, it should look nice, too. Dotty is concerned with whether the color matches our drapes, whether the shape flows, whether it will look attractive on the coffee table. Will it hold cigarettes? The question doesn't arise. It's an ashtray, isn't it?

I love calculators. For Dotty they are an unnecessary evil, to be used solely for balancing the checkbook (a completely useless task imposed by her arbitrary husband. After all, the bank doesn't make mistakes.) Coincidence? No.

To the quantitative mind, numbers represent the very stuff of existence. Nobody has said this more clearly than William Thomson, Lord Kelvin (1824-1907):

When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science.

The qualitative mind, on the other hand, is often indifferent -- and sometimes openly hostile -- to numbers and all they stand for. Dostoevsky, in NOTES FROM UNDERGROUND vents the outrage of the "free soul" at the tyranny of numbers:

But yet mathematical certainty is, after all, something insufferable. Twice two makes four seems to me simply a piece of insolence. Twice two makes four is a pert coxcomb who stands with arms akimbo barring your path and spitting. I admit that twice two makes four is an excellent thing, but if we are to give everything its due, twice two makes five is sometimes a very charming thing too.

Dostoevsky would not have cared for calculators.

These, of course, are the extremes of the spectrum. Most people would not consider lack of numerical data "meager and unsatisfactory" (although in science it is), nor would they contend that twice two makes four is a piece of insolence. Nonetheless, most people do lean in one or the other of these directions; often quite strongly. I think it helps, in discussing calculators as recreation, to be aware of these inclinations. In oneself, it identifies the basis for the enjoyment of "number machines." In others, it explains those quizzical looks and pointed comments about an activity which they find literally incomprehensible.

Let's now assume that anyone reading this article is of a fundamentally quantitative turn of mind, and direct our attention specifically to calculator games and their popularity.

Games of all kinds, from solitaire to lions vs. Christians, have been a major preoccupation of human beings from the dawn of recorded history. We can define a game as an intelligently directed form of play, with the intelligence aspect most apparent in the existence of explicit rules. It is the acknowledgment and agreement on rules which distinguishes games from other forms of human recreation.

To be successful, a game must satisfy three main requirements:

  1. The rules must be fairly easy to learn and retain,
  2. Play must be sufficiently complex to present a challenge,
  3. Skill must have a discernable effect on the outcome. (In that last connection it's interesting to note that slot-machine play is not generally considered a game.)

Beyond that point it is the content of a particular game that will largely detemine whom it appeals to. There are physical games (tennis, football), intellectual games (chess, Scrabble), etc. And, of course, mathematical games, the general class in which we are interested. Even more specifically, there are number based games and a special category which might be called number-related games. These are the most likely candidates for calculator (or microcomputer) programming. Number-based games are those whose problem statement and solution are essentially numerical, such as Startrek, sub hunts, and many others. Number-related games depend on similarities or analogies to the number system and its laws for their operation.

Now consider the nature of a calculator. A calculator may be defined as a special-purpose computer whose primary intended function is the processing of numbers. There, by definition, is a device which would have enormous appeal to the quantitative mind. By performing the routine, boring and repetitive portions of number manipulation in a manner both rapid and infallible, a calculator permits its user to penetrate directly to the meaning of numbers (either in terms of answers or understanding) without getting bogged down in dogwork.

We need two more observations to complete the groundwork:

  1. The love of numbers is often quite independent of the level of mathematical training;
  2. Whatever one loves, one loves to play with. (That last statement may be interpreted as broadly as you choose.)

A calculator game, then, is a simple but challenging vehicle by which a quantitative mind can play directly with the objects of its affection -- numbers -- regardless of the amount of mathematical skill. Is it any wonder they're so popular?

James J. Davidson (547)

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