What Happened to Numbers?

From IEEE Spectrum Magazine, March 1994

In a recent trip to his alma mater, Purdue, the astronaut Neil Armstrong donated his old slide rule to the school. Several of us old alums looked wistfully at that aged wooden instrument, and it brought back shared memories of what it used to be like to be an engineering student.

Long before the word "nerd" was fashionable, engineers were maliciously identified by the long leather cases suspended from their belts. It was an "ever-ready" case, because you never knew when a number would be needed on the spur of the moment. A slide rule was my first purchase as a student, and at about $30 it was relatively expensive. Even though at first I had no idea how the thing worked, that slide rule was my most prized possession. In fact, unlike Armstrong, I still have mine. (Basically, there is no market for mine.)

I quickly realized that the key to being a good engineer was mastery of the slide rule. Thus I learned to carry temporary results from scale to scale on the rule, and how I strived get that not-quite-achievable third decimal place! After all, numbers were all-important; they were what engineering was all about. My slide rule was full of every number I could want, but of course not every number was a good one. Good numbers were the ones considered to be the correct answers to exam questions; the bad ones were everything else. It didn't matter how well you understood the subject matter -- if you slipped with your slide rule, you failed. This was so important that, like everyone else, I learned to work out a quick number by hand, just to check the slide rule and be sure the decimal place was correct.

How times have come and gone since then! Now slide rules are found only in museums, except museums don't care about them either. Electronic calculators came along and were exorbitantly expensive until something happened and they started appearing in cereal boxes. They didn't even make it to museums. Then personal computers conquered the universe, and now you can't exist as a student without a laptop. So what makes you think they're here to stay?

Meanwhile, Armstrong went to the moon, which is also hard to believe because that was back in 1969 before we had PCs. When you see the equipment that the astronauts used then, it looks hopelessly ancient. Armstrong's slide rule would not have been out of place. Today, of course, we have sophisticated computers, backed by millions of lines of mission software. We don't go to the moon anymore, though.

In fact, if I might digress for a moment, in these days of aborted countdowns, the moon landing was in retrospect an incredible feat. It is almost 25 years later, and it isn't clear to me that we could do it again. Moreover, the social impact of that event stands in contrast to the fractionalizing of television viewership that technology is inducing today. Science fiction writers had, of course, predicted a moon landing for decades, but none of them had foreseen that the landing would be on live, worldwide television. I often think that in these days where we are rushing towards thousand-channel television and individualized video-on-demand that the singular moment in the history of television was July 29, 1969, when it brought the world together for one glorious, shared event. In fact, I told Armstrong that he was the only one who missed out on it. It was thoughtless of him to have been away on a business trip.

But back to numbers... That old slide rule made me remember the forgotten primacy of numbers. Not only haven't I used the slide rule since I left school, but -- and I know this sounds perverted or impossible -- I've hardly needed a number in all these years. There, I've made a great confession! Of course, at income tax time I rummage around trying to find one of the calculators littering the backs of forgotten drawers, but other than that I seem to get along all right without them.

When I reflect on the improbability and unexpectedness of this numberless existence, I conclude that, as in many other matters, I was misled by the artificiality of the college classroom. Tests seem to beg for numbers, while life may not. But times have changed too; the world of engineering is now full of concepts, systems, and software. Numbers are kept somewhere in the backs of computers where people don't see them, and instead visualization programs display data and trends in an intuitive manner. I often think of Hamming's wonderful quote, "The purpose of computing is insight, not numbers."

I envy the students of today with computer simulations and tools like Mathematica. A focus on the numbers themselves often obscures conceptual intuition. And I imagine with jealously how it will be in the future, when students will use artificial reality to explore and experience "hands-on" the conceptual world of mathematics and engineering. At the same time I must admit that when you are asked to produce a number, you discover whether or not you really understand something. There is something hard-nosed and unequivocal about a number. "Put up or shut up," it says to you. Perhaps that is why numbers may be over-important in school.

In the numberless world of life-after-school I usually find out whether I know something when I have to give a talk about it. I can hardly confess the number of times I have been in the midst of explaining something to an audience when I suddenly discover that I don't know what I'm talking about! I often wonder whether this happens to anyone else. All I can tell you is that when this realization occurs, something goes fuzzy inside me, and I get the sensation of being in the audience watching this jerk -- me! -- loosing all powers of articulation. Maybe someone should have asked me to produce a number. I could have done that in secret!

The computer tells me that I have so far written 1012 words, which is just about my quota for this essay. So much for the thoughts and concepts -- in the end a number rules supreme!

Robert W. Lucky