by Bill Nye
There’s an art to having a productive scientific epiphany. Life delivers plenty of instructive experiences to all of us, but it’s up to us to figure out what to do with them. My recommendation is to internalize them as a real-world practice and not just as information on a page. We miss the opportunity way too often. I try to pay attention to everything around me but then apply a strong mental filter so I can focus on the things that really matter. I pay special attention to events that reveal new details about how the world around me works and about how I can make it work for us.
This is a stark difference between the religious and scientific viewpoints. If you depend on miracles to make great things happen, you rejoice in the moments when control is taken out of your hands. If you think like a nerd, you celebrate the moments when you are most in control—when you see a theoretical practice play out in a real way, in real time. It’s not that you take life’s marvels for granted; it’s that you work hard to understand them, to learn new things from them, and to add them to the storehouse of information in your brain. The more you learn, the more there is to enjoy about the world, and the more you can do to take control of it.
CHAPTER 4
When Slide Rules Ruled
Along with his many other remarkable contributions to the world of music, Sam Cooke recorded one of the greatest singles of the 1960s, the song “Wonderful World.” It’s a soulful pop song set to a chacha rhythm, at about 130 beats per minute. Sam sings:
Don’t know much about geography
Don’t know much trigonometry
Don’t know much about algebra
Don’t know what a slide rule is for
But I do know one and one is two
And if this one could be with you
What a wonderful world this would be
People of all ages love this song, not only for the memorable melody but also for the very relatable lyrics. I loved it as a kid, and I still do. Like Sam, I often feel I don’t know much about geography. (I’m pretty sure I could not locate Alexandria, Massilia, Syracuse, Antioch, Gades, Argo, and Carthage on the Mediterranean Sea’s coasts, as was required on the Cornell University admission examination in 1891. Although, come to think of it, I could find Alexandria.) However, I absolutely do know what a slide rule is for. I came of age with one of them hanging from my belt. If you want to understand where modern nerd culture came from—how we learned to see numbers and information everywhere we look—then consider learning about the slide rule. Swimming and paddling around gave me a feel for how science works, but slide rules introduced me to a lot of the subtleties of how to use the method of science for real. When you can decode the laws of nature through numbers . . . well, no offense to Sam Cooke, but that makes for a genuinely wonderful world.
A slide rule is a calculator, but it is not, absolutely not, electronic. It is just a set of beautifully machined wooden, plastic, or metal strips that have detailed sets of rule markings on them and that can slide past each other. Hence, slide rule. To understand how you can multiply and divide and find squares of numbers, square roots, cubes, cube roots, and several useful trigonometric functions in a flash using nothing more than a couple of sticks, start with this: Have you ever used a piece of paper or cardboard to figure out how wide something is? You put a pencil mark on the paper to note the dimension, then hold the paper against a ruler to read out the width. If a single piece of paper isn’t large enough, you put a second sheet next to it and put the mark on that second sheet instead, knowing you’ll add that partial dimension to the full dimension of the first sheet. Simple enough.
If you’re a more numbers-oriented sort, have you ever measured a length using two rulers? With two rulers and a little thought, you can add the full length of one ruler to the partial length of another. Here we go. A side table or an end table next to your bed might be 16 inches (40 centimeters) wide, for example. Set one 12-inch (30-centimeter) ruler on the table, and then set a second ruler next to it. Read that second ruler’s number. I’m confident you can find the 4-inch (10-centimeter) mark. Add 4 to 12 and you generally get 16 (inches). Add 10 to 30 and you’ll get 40 (centimeters). This approach works fine for round or even fractional numbers, with just a little adding-in-your-head work. (From here on out, I am going to use metric units. They are the very essence of the everything-all-at-once universal data conversion system. Our hands nominally have 10 fingers, so we use 10 digits, 0 through 9, with which we express any number in nature.)
A slide rule does the same basic thing, but it adds and subtracts using specialized scales marked on lengths of bamboo, magnesium, plastic, or even ivory. There are generally two main pieces: the “slide” and the “body.” Both have scales precisely engraved or printed on them, but instead of demarcating regular lengths, those scales are marked to indicate a number’s logarithm. By the way, slide rules are fitted with a crosshair—a thin wire or length of real hair embedded in plastic or glass to keep the all-important numbers on the slide scale and the body properly lined up. Gentle reader, do you know what that crosshair carriage is called? The “cursor.” This term was coined centuries before computers had cursors. People everywhere use the word today without knowing that it emerged from the early history of my fellow nerds. That secret connection fills me with pride.
If you don’t happen to remember logarithms, really, there’s nothing especially complicated or terrifying about them. They go like this: 100 is 10 squared, or 102. The logarithm of 100 is just 2. The number 2 is written above and to the right, and it’s called an “exponent,” from the Latin for “placed away.” The exponent describes the logarithm. The number 1,000 is the same as 103, and the logarithm of 103 is 3. If you multiply 100 times 1,000, you get 100,000. I suspect you already got that. The number 100,000 is 105, which is another way of saying that the logarithm of 100,000 is 5. It’s lovely. It’s 102 times 103, which equals 105. You don’t need to multiply the numbers. Just add the logarithms (2 + 3 = 5). Logarithms make life easier in a nerd-loving way. Exponentially easier, you might say. And there’s more, much more: You can have logarithms that are in between the round numbers. The logarithm of 10 is 1 (101 = 10), and the logarithm of 100 is 2. You can intuitively see that the logarithm of 50 is going to have to be between 1 and 2. In fact, it’s very nearly 1.70. Now here comes another dose of numerical beauty. The logarithm of 1 is zero (100 = 1), so the logarithm of 5 is very nearly 0.70; it’s just the logarithm of 50 minus the logarithm of 10. Can’t believe a number raised to the zeroth power is 1? It is, and I’ll prove it to you in one sentence: Anything multiplied by 1 is just that same anything, so anything raised to the zeroth power has to be 1 to make the multiplication work. Cue the spooky music.
Logarithms are an essential part of the language of science because they provide a convenient way to write down the staggeringly large and small quantities you encounter when you stretch beyond human-scale perceptions. How many stars are there in the observable universe? Oh, about 1023. How many atoms are there on Earth? About 1050. Logarithms are what make slide rules so delightful to use, too, once you get familiar with them. When you slide one logarithmic scale alongside another logarithmic scale and read the added-up sum, the way you did when we were measuring the end table, you are no longer getting the arithmetic or 2 + 2 kinda number. You are now getting the added-up logarithms. In other words, we are multiplying by adding. When we move the slide the other way, we are dividing numbers by subtracting logarithms. Whoa . . . Cue more spooky music.
When I was in high school and college, we used to have races to see who could multiply, divide, multiply by the number π (pi), and then find the square root of the resulting number the fastest, or similar festivities. It was a standard competitive sport among the nerds. I was pretty good at it. But Ken Severin was the major league. He got a perfect 800 on the SAT Level 2, back when that was the highest score you could achieve. He went on to the California Institute of Technology (Caltech) and became an expert on using electrons to take pictures of tiny things, with a now-s
tandard tool called a scanning electron microscope. Later, as Dr. Severin, he joined the faculty of the University of Alaska and established its Advanced Instrumentation Lab for geology. He was my best high school buddy. We had nerd adventures together, tinkering with resistors, transistors, capacitors, and the like.
Don’t worry if the specific details of the slide rule still sound a mite confusing. Learning to keep all the numerical patterns in your head takes practice, and that’s kind of the point. Mastering math, science, and any other advanced skill is hard work. A slide rule was therefore a badge of intellectual pride. No, more than just a stinkin’ badge. It was a giant airport runway beacon alerting others that you were part of the world of the nerds. We loved it. Our slide rules were objects of devotion. We lubricated the slide scale with talcum powder. We adjusted the clamping screws to get the slide scale to move with just the right amount of friction to maximize speed while minimizing misalignment errors. And there was a reason they were so precious, beyond just bragging rights: Using a slide rule imbued a sense of the size of just about anything relative to anything else. My slide rule changed my life. Just by moving the slide against the body, I could quickly navigate the scale of physics, from atoms to the whole universe. It was all at my fingertips.
One memorable day in high school, back in 1972, a kid from a technical family came in with a newfangled Hewlett-Packard 35, the very first pocket calculator. The “35” derived from it having 35 keys. It didn’t just multiply and divide; it could also find sines and cosines and square roots. It could find the elusive “natural logarithms” of numbers. Wow. This was the precursor of all the other pocket calculators that followed. It was also the beginning of the personal electronics revolution that eventually led to home computers, laptops, and smartphones.
Now, we nerds took, and still do take, great pride in having a deep, personal feel for numbers. We have a sense of how big a number is supposed to be. By this I mean, when we are working numbers—even really big or small ones—we have an immediate sense in our heads where the decimal point should fall. In my day, we believed it was because of our use of slide rules. On a slide rule, 1.7 looks exactly the same as 17, 0.17, 170, or 1.7 million. So “slide rulists” like us had to keep careful track of the powers of 10 when figuring out how big the answer would be. We had to feel the numbers in our bones. With electronic calculators, you don’t have to do that. At the time, letting a small box of circuits do the work felt a little bit like cheating to us. And get this: If you multiplied 9 times 9 on the HP 35, you got 81 (all good), but if you did 92, or 9 squared, you got 80.999999. Somewhere there was a tiny rounding error in the electronic logic. Ooooh, I thought . . . I’m keeping my slide rule.
The upshot is that my pals and I were not particularly impressed with modern calculators, at least not at first. We thought they were unnecessarily expensive and obviously fraught with shortcomings. The original HP 35 cost $395, roughly $2,300 in today’s dollars. Ouch. I took my trusty Pickett model N3-ES slide rule from high school to college. When I started engineering school, everyone still had a slide rule; most of us treasured them. My magnesium metal Pickett was said to be the same design that the Apollo 11 astronauts took with them to the Moon, just in case they had to check some numbers along the way. I found out later that my model is actually a little more capable than the one NASA provided. It has a few more scales than the ones that went into space and back, meaning that it could perform a wider range of calculations. See? I could have been an astronaut!
When change finally came to the nerd world, it arrived fast and hard. By my recollection, it was the winter of 1975, when everyone went home for the holidays and everyone came back to school with an electronic calculator. Whether it was Christmas, Hanukkah, or just winter break, everyone had parents who saw what was coming and decided that holiday gift giving was the perfect opportunity to get their kids up to date. My first machine was a Texas Instruments SR-50. And do you know what “SR” stood for? “Slide rule.” The manufacturer was practically shouting, “This thing is as good as a slide rule!”
If this is the point where you are waiting for me to wax nostalgic about the good old days, well, I’m about to disappoint you, dear reader. I can admit it now. The SR-50 was not just as good as a slide rule; it was better. It could do hyperbolic sines and cosines, for crying out loud! And there was something else important about the electronic calculator: It was more democratic than the slide rule. Making it easier for people to work with numbers and grasp scientific concepts was fundamentally a victory for knowledge and information, which in turn was fundamentally good for nerds. On the surface, sure, my buddies and I resented that it let more people into the nerd club without their having to learn the intricacies of the slide rule. Deep down, we understood that having more people in the nerd club was a good thing. We didn’t see ourselves as outsiders; we thought we were the ones who had the best, most honest way of looking at the world (I still think so).
Pretty soon there were plenty of people who didn’t know what a slide rule was for, even among the nerds. Human-built technology had delivered a more efficient way to crunch the numbers that define the results of scientific study that guide engineering solutions. By the way, I don’t have my Pickett N3-ES anymore: It’s in the Smithsonian Institution’s collection. Archivists came and “collected me,” and now my slide rule is preserved for future generations in some safe place somewhere. That’s the perfect place for a device that helped get us where we are now but was not a final step. The slide rule naturally joins the astrolabe, sextant, and other tools that advanced the cause of science until science outgrew them.
Today it can be hard to comprehend how engineers ever did their jobs without computers and electronic calculators. I often joke about the black-and-white footage of early rockets falling over and exploding—that it happened because the only thing the rocket scientists had to work with back then were slide rules. But the truth is, they did do their jobs. Not just the NASA engineers; I’m talking about everyone in the pre-electronic era who found effective ways to expand the range of human comprehension by manipulating numbers in ways that the brain alone cannot do. I’m looking all the way back to the Sumerians who developed the abacus something like 4,500 years ago. Or William Oughtred, the Anglican cleric and nerd cult hero who invented the very first slide rule in 1622.
Throughout history, scientists and engineers (whether or not they called themselves those things) used the newest available technology to quantify their world. So despite my deep affection for my old devices, I feel more than fine about the near-extinction of the slide rule. It disappeared from the classrooms and the math clubs not because science doesn’t matter to us anymore, but because it matters so much. We have vastly better, more powerful ways of manipulating numbers these days; it would be a little weird if we didn’t use them.
Anyone in the world with an Internet connection can now get access to countless advanced math programs and easy-to-use software. You type in something like y = ln(78) and instantly out pops y = 4.35671 (and lots more digits, if you want ’em). Many of them are free, or at least a lot cheaper than my old Pickett N3-ES slide rule, and they can do things that would have blown the bow tie right off my youthful neck. Any time calculations become easier, scientific investigations become easier, too. The implications are both practical and cosmic. Medical studies will be increasingly reliable because the statistics will be more comprehensive, for instance. At the other end, astronomers may soon figure out the nature of dark matter because they will have access to zettabytes of data on the motions of stars.
The passion I tapped into back in high school was all about grasping toward those kinds of possibilities. The slide rule was merely a means to an end: an end in which a group of 10 numbers and a few dozen mathematical operations can let the human mind wander across space and time, to commune mathematically with everything in nature. These days that passion is more accessible than ever. Citizen science projects let anyone participate in climate research, scan
distant galaxies, study the microbes in your gut, or listen for possible signals from alien civilizations. Free online courses teach advanced number theory. This is part of what I referred to earlier as the age of unprecedented access to information.
The slide rule provided a tangible bond for me with my fellow nerds, and that particular experience is sadly lost. Sure, I wax nostalgic about it from time to time. But I’m glad that there is one fewer barrier standing between us and a deep understanding of the world around us. My challenge to you now is not to fixate on the iconography of the slide rule (and all the other things like it that have become geek chic) but to look forward and, as Sam Cooke sang, “know what a slide rule is for.” Play with numbers. Notice patterns. Apply what you know about the world in all sorts of places. Feel your place in the universe, and feel the universe that is inside you. Contribute to the scientific process if you can, or simply read and listen and revel in it. If more people engage in the deep comprehension that comes with mathematical thinking—what a wonderful world that will be.
CHAPTER 5
The First Earth Day and National Service
On April 22, 1970, I rode my bicycle to the very first Earth Day on the National Mall in Washington, DC. To anyone full of nostalgia for the disco era, I must remind you: Those were not really the good old days. In many ways Washington was a city divided, even more so than it is today. The 1968 riots following the death of Martin Luther King, Jr. left sizable parts of the city center physically and economically devastated; an unofficial but very visible boundary separated the relatively wealthy, white part of town from the relatively poor, minority-dominated one. The United States as a whole was mired in the behated and increasingly deadly war in Vietnam. Young people like me lived in fear of receiving a low draft number. Yet when I arrived for the Earth Day celebration, I felt a hopeful sense of unity.