Letters to a Young Scientist (2 page)
Merit badge symbol for “Zoology” in 1940.
Boy Scout
Handbook
, Boy Scouts of America, fourth edition (1940).
I
BELIEVE IT WILL HELP
for me to start with this letter by telling you who I really am. This requires your going back with me to the summer of 1943, in the midst of the Second World War. I had just turned fourteen, and my hometown, the little city of Mobile, Alabama, had been largely taken over by the buildup of a wartime shipbuilding industry and military air base. Although I rode my bicycle around the streets of Mobile a couple of times as a potential emergency messenger, I remained oblivious to the great events occurring in the city and world. Instead, I spent a lot of my spare time—not required to be at school—earning merit badges in my quest to reach the Eagle rank in the Boy Scouts of America. Mostly, however, I explored nearby swamps and forests, collecting ants and butterflies. At home I attended to my menagerie of snakes and black widow spiders.
Global war meant that very few young men were available to serve as counselors at nearby Boy Scout Camp Pushmataha. The recruiters, having heard of my extracurricular activities, had asked me, I assume in desperation, to serve as the nature counselor. I was, of course, delighted with the prospect of a free summer camp experience doing approximately what I most wanted to do anyway. But I arrived at Pushmataha woefully underaged and underprepared in much of anything but ants and butterflies. I was nervous. Would the other scouts, some older than I, laugh at what I had to offer? Then I had an inspiration:
snakes
. Most people are simultaneously frightened, riveted, and instinctively interested in snakes. It’s in the genes. I didn’t realize it at the time, but the south-central Gulf coast is home to the largest variety of snakes in North America, upward of forty species. So upon arrival I got some of the other campers to help me build some cages from wooden crates and window screen. Then I directed all residents of the camp to join me in a summer-long hunt for snakes whenever their regular schedules allowed.
Thereafter, on an average of several times a day, the cry rang out from somewhere in the woods: Snake! Snake! All within hearing distance would rush to the spot, calling to others, while I, snake-wrangler-in-chief, was fetched.
If nonvenomous, I would simply grab it. If venomous, I would first press it down just behind the head with a stick, roll the stick forward until its head was immobile, then grasp it by the neck and lift it up. I’d then identify it for the gathering circle of scouts and deliver what little I knew about the species (usually very little, but they knew less). Then we would walk to headquarters and deposit it in a cage for a residence of a week or so. I’d deliver short talks at our zoo, throw in something new I learned about local insects and other animals. (I scored zero on plants.) The summer rolled by pleasantly for me and my small army.
The only thing that could interrupt this happy career was, of course, a snake. I have since learned that all snake specialists, scientists and amateurs alike, apparently get bitten at least once by a venomous snake. I was not to be an exception. Halfway through the summer I was cleaning out a cage that contained several pygmy rattlesnakes, a venomous but not deadly species. One coiled closer to my hand than I’d realized, suddenly uncoiled, and struck me on the left index finger. After first aid in a doctor’s office near the camp, which was too late to do any good, I was sent home to rest my swollen left hand and arm. Upon returning to Pushmataha a week later, I was instructed by the adult director of the camp, as I already had been by my parents, that I was to catch no more venomous snakes.
At the end of the season, as we all prepared to leave, the director held a popularity poll. The campers, most of whom were assistant snake hunters, placed me second, just behind the chief counselor. I had found my life’s work. Although the goal was not yet clearly defined then in my adolescent mind, I was going to be a scientist—and a professor.
Through high school I paid very little attention to my classes. Thanks to the relatively relaxed school systems of south Alabama in wartime, with overworked and distracted teachers, I got away with it. One memorable day at Mobile’s Murphy High School, I captured with a sweep of my hand and killed twenty houseflies, then lined them up on my desk for the next hour’s class to find. The following day the teacher, a young lady with considerable aplomb, congratulated me but kept a closer eye on me thereafter. That is all I remember, I am embarrassed to say, about my first year in high school.
I arrived at the University of Alabama shortly after my seventeenth birthday, the first member of my family on either side to attend college. I had by this time shifted from snakes and flies to ants. Now determined to be an entomologist and work in the outdoors as much as possible, I kept up enough effort to make A’s. I found that not very difficult (it is, I’m told,
very
different today), but soaked up all the elementary and intermediate chemistry and biology available.
Harvard University was similarly tolerant when I arrived as a Ph.D. student in 1951. I was considered a prodigy in field biology and entomology, and was allowed to make up the many gaps in general biology left from my happy days in Alabama. The momentum I built up in my southern childhood and at Harvard carried through to an appointment at Harvard as assistant professor. There followed more than six decades of fruitful work at this great university.
I’ve told you my Pushmataha-to-Harvard story not to recommend my kind of eccentricity (although in the right circumstances it could be of advantage); and I disavow my casual approach to early formal education. I grew up in a different age. You, in contrast, are well into a different era, where opportunity is broader but more demanding.
My confessional instead is intended to illustrate an important principle I’ve seen unfold in the careers of many successful scientists. It is quite simple: put passion ahead of training. Feel out in any way you can what you most want to do in science, or technology, or some other science-related profession. Obey that passion as long as it lasts. Feed it with the knowledge the mind needs to grow. Sample other subjects, acquire a general education in science, and be smart enough to switch to a greater love if one appears. But don’t just drift through courses in science hoping that love will come to you. Maybe it will, but don’t take the chance. As in other big choices in your life, there is too much at stake. Decision and hard work based on enduring passion will never fail you.
Reconstructed path of the “Trojan” asteroid 2010 TK
7
, during 165 years, seen from outside Earth’s orbit. Modified from drawing. © Paul Wiegert, University of Western Ontario.
L
ET ME MOVE ON
quickly, and before everything else remaining, to a subject that is both a vital asset for and a potential barrier to your career: mathematics, the great bugbear for many would-be scientists. I mention this not to nag but to encourage and help. I mean in this letter to put you at ease. If you’re already well prepared—let us say you’ve picked up calculus and analytic geometry—if you like to solve puzzles, and if you think logarithms are a neat way to express variables across orders of magnitude, then good for you; your capability is a comfort to me. I won’t worry so much about you, at least not right away. But keep in mind that a strong mathematical background does not—I repeat, does not—guarantee success in science. I will return to this caveat later, so please stay focused. Actually, I have a lot more to say to math lovers in particular.
If, on the other hand, you are a bit short in mathematical training, even very short, relax. You are far from alone in the community of scientists, and here is a professional secret to encourage you: many of the most successful scientists in the world today are mathematically no more than semiliterate. A metaphor will clarify the paradox in this statement. Where elite mathematicians often serve as architects of theory in the expanding realm of science, the remaining large majority of basic and applied scientists map the terrain, scout the frontier, cut the pathways, and raise the first buildings along the way. They define the problems that mathematicians, on occasion, may help solve. They think primarily in images and facts, and only marginally in mathematics.
You may think me foolhardy, but it’s been my habit to brush aside the fear of mathematics when talking to candidate scientists. During my decades of teaching biology at Harvard, I watched sadly as bright undergraduates turned away from the possibility of a scientific career, or even from nonrequired courses in the sciences, because they were afraid of failure in the math that might be required. Why should I care? Because such math-phobes deprive science of an immeasurable amount of sorely needed talent and deprive the many scientific disciplines of some of their most creative young people. This is a hemorrhage of brainpower we need to stanch.
Now I will tell you how to ease your anxieties. Understand that mathematics is a language, ruled like verbal languages by its own grammar and system of logic. Any person with average quantitative intelligence who learns to read and write mathematics at an elementary level will have little difficulty understanding math-speak.
Let me give you an example of the interplay of visual images and simple mathematical statements. I’ve chosen to reveal the undergirding of two relatively advanced disciplines in biology: population genetics and population ecology.
Consider this interesting fact. You have (or had) 2 parents, 4 grandparents, 8 great-grandparents, and 16 great-great-grandparents. In other words, since each person has to have two parents, the number of your direct forebears doubles every generation. The mathematical summary is
N
= 2
x
. The parameter
N
is the number of a person’s ancestors
x
generations back in time. How many of your ancestors existed 10 generations ago? We don’t have to write out each generation in turn. Instead you can use
N
= 2
x
= 2
10
, or, put the other way, 2
10
=
N
. So the answer is when
x
= 10 generations, you have
N
= 1,024 ancestors. Now reverse the timeline to forward and ask how many descendants you can expect to have 10 generations from now. The whole thing gets much more complicated in the case of descendants—we don’t really know how many children we will have—but to state the basic idea, it is all right to specify, in a way mathematicians often do, that each couple will have two surviving children and the length of the generations will be constant from one generation to the next. (Two children on average is not far from the actual rate in the United States today, and is close to the number 2.1, or 21 children for every 100 couples, needed to maintain a constant population size of native-born.) Then in 10 generations you will have 1,024 descendants.
What are we to make of this? For one thing, it is a humbling picture of the origin and the fate of one person’s genes. The fact is that sexual reproduction chops apart the combinations that prescribe each person’s traits and recombines half of them with somebody else’s genes to make the next generation. Over a very few generations, each parent’s combination will be dissolved in the gene pool of the population as a whole. Suppose you have a distinguished forebear who fought in the American Revolution, during which another roughly 250 of your other direct ancestors lived, including possibly a horse thief or two or three. (One of my 8 great-great-grandfathers, a confederate veteran of the Civil War, was a notoriously tricky horse trader, if not quite a thief.)
Mathematicians like to take the measurement of exponential growth from just counting jumps from one generation to the next, to the much more general state to fit a large population over a particular moment in time (to the hour, minute, or shorter interval as they choose). This is done with calculus, which expresses the growth of population in the form
dN/dt
=
rN
, which says in any very short interval of time,
dt
, the population is growing a certain amount,
dN
, and the rate is the differential
dN/dt
. In the case of exponential growth,
N
, the number of individuals in the population at the instant is multiplied by
r
, a constant that depends on the nature of the population and the circumstances in which it lives.
You can pick any
N
and
r
that interests you, and run with these two parameters for as long as you choose. If the differential
dN/dt
is larger than zero and the population (say, of bacteria or mice or humans) is allowed in theory to increase at the same rate indefinitely, in a surprising few years the population would weigh more than Earth, than the solar system, and finally than the entire known universe.
It is easy to produce fantastical results with mathematically correct theory. There are a lot of models that fit reality and produce factual implications that can jolt us into a new way of thinking. A famous one learned from exponential growth of the kind I’ve just described is the following. Suppose there is a pond, and a lily pad is put in the pond. This first pad doubles into two pads, each of which also doubles. The pond will fill and no more pads can double at the end of thirty days. When is the pond half full? On the twenty-ninth day. This elementary bit of mathematics, obvious upon commonsense reflection, is one of many ways to emphasize the risks of excessive population growth. For two centuries the global human population has been doubling every several generations. Most demographers and economists agree that a global population of more than ten billion would make it very difficult to sustain the planet. We recently shot past seven billion. When was the Earth half full? Decades ago, say the experts. Humanity is racing toward the wall.
The longer you wait to become at least semiliterate in math, the harder the language of mathematics will be to master—again the same as in verbal languages. But it can be done, and at any age. I speak as an authority on this subject, because I am an extreme case. Having spent my pre-college years in relatively poor southern schools, I didn’t take algebra until my freshman year at the University of Alabama. My student days being at the end of the Depression, algebra just wasn’t offered. I finally got around to calculus as a thirty-two-year-old tenured professor at Harvard, where I sat uncomfortably in classes with undergraduate students only a bit more than half my age. A couple of them were students in a course on evolutionary biology I was teaching. I swallowed my pride and learned calculus.
Admittedly, I was never more than a C student while catching up, but I was reassured somewhat by the discovery that superior mathematical ability is similar to fluency in foreign languages. I might have become fluent with more effort and sessions talking with the natives, but, being swept up with field and laboratory research, I advanced only by a small amount.
A true gift in mathematics is probably hereditary in part. What this means is that variation within a group in ability is due in some measurable degree to differences in genes among the group members rather than entirely just to the environment in which they grew up. There is nothing that you and I can do about hereditary differences, but it is possible to greatly reduce the part of the variation due to the environment simply by raising our ability through education and practice. Mathematics is convenient in that it can be achieved by self-instruction.
Having gone this far, I believe I should go on a bit further, and explain how fluency is achieved by those who wish to attain it. Practice allows elementary operations (such as, “If
y
=
x
+ 2, then
x
=
y
- 2”) to be effortlessly retrieved in memory, much like words and phrases (such as “effortlessly retrieved in memory”). Then, in the way verbal phrases are almost unconsciously put together in sentences and sentences are built into paragraphs, mathematical operations can be put together with ease in ever more complex sequences and structures. There is, of course, much more to mathematical reasoning. There are, for example, the positioning and proving of theorems, the exploration of series, and the invention of new modes of geometry. But short of these adventures of advanced pure mathematics, the language of mathematicians can be learned well enough to understand the majority of mathematical statements made in scientific publications.
Exceptional mathematical fluency is required in only a few disciplines. Particle physics, astrophysics, and information theory come to mind. Far more important throughout the rest of science and its applications, however, is the ability to form concepts, during which the researcher conjures images and processes in visual images by intuition. It’s something everyone already does to some degree.
In your imagination, be the great eighteenth century physicist Isaac Newton. Think of an object falling through space. (In the legend, he was attracted to an apple falling from the tree to the ground.) Make it from high up, like a package dropped from an airplane. The object accelerates to about 120 miles an hour, then holds that velocity until it hits the ground. How can you account for this acceleration up to but not beyond terminal velocity? By Newton’s laws of motion, plus the existence of air pressure, the kind used to propel a sailboat.
Stay as Newton a moment longer. Notice as he did how light passing through curved glass sometimes comes out as a rainbow of colors, always ranging from red to yellow to green to blue to violet. Newton thought that white light is just a mix of the colored lights. He proved it by passing the same array of colors back through a prism, turning the mix back into white light. Scientists were later to understand, from other experiments and mathematics, that the colors are radiations differing in wavelength. The longest we are able to see creates the sensation of red, and the shortest the sensation of blue.
You likely knew all that already. Whether you did or not, let’s go on to Darwin. As a young man in the 1830s, he made a five-year voyage on a British government vessel, the HMS
Beagle
, around the coast of South America. He took that long period to explore and think broadly and deeply about the natural world. He found, for example, a lot of fossils, some of extinct large animals similar to modern species like horses, tigers, and rhinoceroses—yet different in many important ways than these modern equivalents. Were they just victims of the biblical flood that Noah failed to save? But that couldn’t be, Darwin must have realized; Noah saved all the kinds of animals. The South American species were obviously not among them.