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What are the worlds of knowledge inside a bio-acoustic, spectrogram, a mathematical diagram, or an illustrated equation? 

 is a column in which scientists describe the power of drawings.

“After a certain high level of technical skill is achieved,” Albert Einstein famously remarked, “science and art tend to coalesce in aesthetics, plasticity, and form.”

I’ve long believed he was right. I can point to many moments in my career as a theoretical physicist when I’ve been guided as much by aesthetic intuition in engaging our deepest dilemmas about the behavior of subatomic particles, space, time, and the nature of reality, as I have been by mathematical logic. Aesthetics is always present in theoretical physics, in sometimes inarticulable and undepictable ways. But never have the mathematical and aesthetic aspects of my work found such striking synthesis as in the geometric objects that my colleagues and I came to call “adinkras.”

Adinkras are geometric objects whose underlying principles, and forms, have bolstered our understanding of the mathematical description of physical law. Lending visual form to some of the hardest problems in mathematical and theoretical physics, they’ve proved hugely useful in helping us understand relationships in the microscopic world according to the precepts of quantum theory and “supersymmetry,” the aspect of string theory to which I’ve devoted most of my career (and about which, more in a moment). But more than that, adinkras have shaped an understanding of subatomic physics in ways that transcend the specific questions they were created to help us see.

Human brains, as neuroscientists tell us, are often better at understanding problems we can visualize. And so it has proven to be the case with these adinkras. The laws of physics are typically represented in equations that are opaque to anyone who has not devoted their life to their interpretation. Adinkras are visualizations that represent the language of mathematics in a geometric object. The story of adinkras and of our discovery of them earlier this century, like many advances in mathematics, reaches back decades—and runs, for me, back to my first days as a student at MIT, where I arrived as an undergraduate in 1969.

As the first member of my family to attend college, I was what you could call a DEI kid from the wrong side of the tracks. As a teenager, I’d grown up in Orlando, Florida, in an area of that southern city—the so-called Parramore District—which from the 1890s was designated as the place where “colored people” were permitted to live, west of downtown and across a set of north-south railroad tracks that bisect the city. Jones High School, then the only secondary school in Orlando that Black students could attend, wasn’t a well-funded or well-supported institution. But I had some wonderfully committed and capable teachers. And at age 14, I learned from a TV program about the existence of the Massachusetts Institute of Technology. It became my dream to go there—a dream that came true when M.I.T. decided to let in 50 African American students in the fall of 1969, the first time the university admitted more than a handful of students from outside its traditional feeder schools and elite networks worldwide.

I was fortunate to be one of those students, and gratified to thrive so much as an undergrad that I earned two B.S. degrees in four years, one in mathematics and one in physics. I stayed in Cambridge for graduate school. As a PhD student, I undertook and then defended M.I.T.’s first-ever thesis on the topic of “supersymmetry.” In 1977, this wasn’t a topic that anyone else—faculty, researchers, graduate students––knew anything about. Through my sense of aesthetics, I was convinced that it represented a vital new strain of inquiry in theoretical physics. I was proven right in the decades that followed, and we’re still wrestling with the profound possible implications of supersymmetry today.

The putative discovery of antimatter, which dates from the 1920s, revealed a world of opposites. For almost every kind of particle, there exists an antiparticle: its exact, perfect opposite. If an electron spirals to the left, in a magnetic field, a positron will spiral to the right. If an electron is repelled from a source, a positron is attracted to it. This wasn’t science fiction. Antimatter could be created, and annihilated in the laboratory, and in nature. Supersymmetry took this deeper. It posits that for every particle, there is also a supersymmetric partner that interchanges the most inviolable quantum characteristics of matter—that for every boson, as one fundamental kind of subatomic particle is called, there exists a partner particle, a fermion, with different spin properties.

Supersymmetry is also known by the sobriquet SUSY; it grew from what was, in the 1970s, the still-novel field of string theory, which suggests that the subatomic world is composed of vibrating loops. This idea was profoundly unifying. There wasn’t a zoo of disconnected particles—just different notes on the same kind of fundamental string. In the unification was a hope for a theory of everything. Supersymmetry, by positing how elementary particles correspond and relate, suggested how such theories could be shaped.

By 1995, when I began working with a graduate student named Lubna Rana, many more people in our field were thinking about supersymmetry. Lubna, with whom I went on to publish several papers in this field, also happened to be my first female grad student in physics. I began our work together, as one does with any tyro student, by giving her a sort of starter problem—a task to test a student’s preparation and will to be successful in the difficult field of mathematical and theoretical physics. And so it was in Lubna’s case that I gave her a problem relating to the history and implications of various supersymmetric field theories.

What if reality itself is a computer simulation? 

One of the most beautiful things about mathematical-enabled research is that one can arrive at conclusions without knowing others have done the same beforehand. And in looking into the origins of supersymmetric field theories, we were struck to discover precursors to these theories in the work of mathematicians working on both sides of the divide between the Soviet Union and Western Europe during the Cold War. Though separated by the Iron Curtain, we could share ideas. We built on theirs to explore the mathematical structures undergirding supersymmetry. As I guided Lubna’s thesis to its completion, we wrote a series of papers about these mathematical models. We uncovered more and more interesting properties about the subatomic realm. Without quite realizing it, I had taken a giant step to realize my unexpressed dream––to find an intricate piece of hidden mathematics that accurately described something equally hidden in nature.

Expressing the mathematical structures and making them useful, however, involved a further step—as I found at a conference in France, at Luminy outside Marseille, in 2006. At that gathering of mathematicians, the nearby Calanques National Park was magnificent, but my presentation was not. The talk was a total failure that left me with a sharp sense that I needed a better way to communicate what we already knew across the language gap separating mathematics and physics. Luckily, by then I had begun to develop a way to bridge this gap.

A couple of summers before, I was in the republic of Georgia, visiting that nation's capital of Tbilisi, when I engaged in a typical morning habit of theoretical physicists around the world: I opened my laptop and looked at the website called “

,” a digital portal that chronicles evolving innovations across many scientific fields in near real-time—including physics, biology, economics, computer science, electrical engineering, quantitative finance, mathematics, and statistics. There, I happened upon an interesting paper on supersymmetry, whose authors included a researcher in New York named Michael Faux, to whom I wrote an email which commenced several weeks of intense correspondence. This correspondence quickly morphed, as I continued my travels, into elaborating diagrams for which we realized we needed a name. As we rushed to finish a research paper on these symbols, I was in the West African country of Benin. Perhaps inspired by my location at the time, Michael suggested the name “adinkra,” which he explained originated among the Akan peoples of West Africa, who have long used similarly-named symbols to convey abstract and weighty concepts with beautiful designs, like learning from the past, the omnipotence of God, and unity of life. The name “adinkras,” to me, seemed apt. Thus was born the name for our paper, "Adinkras: A Graphical Technology for Supersymmetric Representation Theory." And thus began our adventures with these symbols, which were technically graphs in the realm of mathematics that encoded data in two-dimensional systems about the behavior of equations in higher dimensions. Like the sublime insights described by the same title, and as I found when I began discussing adinkra diagrams at gatherings like that conference near Marseille, our findings proved even more useful and revelatory than I hoped.

Adinkras choreograph the relationships between particles and make it possible to bring our visual and geometric intuitions to bear on the domain of supersymmetry. But more than that, by translating the essence of our discoveries into other realms of mathematics, they widen the net of mathematicians and scientists who can readily appreciate their findings and potentially contribute to them. These diagrams are more than mere pictures: they can lead to new understandings of what is being studied.

I had taken a giant step to realize my unexpressed dream––to find an intricate piece of hidden mathematics that accurately described something equally hidden in nature. 

For example, we found that some adinkras could be broken up into two smaller parts, both of which were also adinkras—and that by folding, compressing, and coalescing the dots and links of one adinkra, another adinkra could be formed. Though not all such manipulations of adinkra result in new adinkra, by assigning binary words to the dots in an adinkra and following a specific process of transformation, its SUSY properties can be reliably preserved. From this discovery, we noted that the equations which adinkras represent exhibit properties held by a specific class of error-correcting codes used in computer communications.

About the latter mind-blowing idea, I’ve been asked often to speak in public, over the past couple of decades and especially after 

 films came out: What if reality itself is a computer simulation? It should be noted that this question itself is not a scientific one—and it is prompted not from studying equations directly, but from exploring their representations as adinkras, visual objects that continue to yield unexpected payoffs.

Now 20 years after their discovery, I’m only more convinced that when we found these adinkras, we stepped onto a new mathematical continent. The verification of supersymmetry in nature remains on the proverbial bucket list for theoretical physicists, who were thrilled by the once-unthinkable discovery, a decade ago and at the Large Hadron Collider in Switzerland, of the Higgs boson. The discovery of supersymmetry may occur decades or centuries from now. That is how progress, and our understanding of the nature of reality, works: Mother nature doesn’t care if I’m alive or dead when supersymmetry is found. But there’s great satisfaction in being part of the process we call progress. And I take great pleasure in being tagged to find, with the help of these adinkras, truths no one else has. ♦

Sylvester James Gates, Jr. is an American theoretical physicist who works on supersymmetry, supergravity, and superstring theory.

A computer-generated Adinkra, drawn by Gregory D. Landweber.

Picture This: Adinkras

Dogs’ reputation as super smellers is overrated, while ours is underrated. Olfaction, or the sense of smell, is thought to be reduced in humans compared to other animals—but in fact there is little to support this notion. In truth, the evidence points to humans possessing a rather refined sense of smell compared to other mammals. I am often asked, as an olfactory scientist, if the reputation dogs have as superior smellers is true. This question, and the conventional wisdom behind it, has always puzzled me. It seems to me that if dogs had such a miraculously good sense of smell then they could perform their customary method of greeting—sticking their noses quite directly into the private parts of some other unknown dog—from a greater distance, like at least a foot or two.

There is actually a perfectly good reason for this friendly if invasive practice. Dogs, and other animals, are simply willing to put their noses where the odors are. The single greatest challenge to our sense of smell is that we stand upright—an anatomical fact that places our noses some five feet or so in the air. Odor molecules have some weight and tend to accumulate near the ground. This is why, when dogs catch some interesting scent, they put their noses directly on the ground to follow where the smell is coming from. When we humans meet a stranger, we may shake hands. Social decorum (thankfully) prevents us from sniffing each other’s armpits, where there is much more olfactory information to be found. Even canine breeds that have been bred for a more refined sense of smell and to detect some scents at greater distances, like bloodhounds, need to put their nose to the ground and will sniff very close to an object or trail.

If dogs had such a miraculously good sense of smell then they could perform their customary method of greeting—sticking their noses directly into the private parts of some other unknown dog—from a greater distance.

There is one other interesting example that demonstrates our refined sense of smell, and that is flavor. Not taste, which refers only to sweet, sour, salty, bitter, and savory (or umami, as it was named in Japan). Flavor, on the other hand, is a blend of these tastes with smells, and is the result of an evolutionary adaptation specific to humans. An estimated 80–90% of flavor is determined by olfaction. When our jaws became shorter and our faces flatter, a change in the pharyngeal bones led to an opening between our oral cavity and our nasal organ. This conduit, known as the retronasal pathway, is how odor molecules released by chewing food find their way to the olfactory epithelium, the thin tissue at the very top of our nasal cavity where the cells that detect odors are located. When we eat, stimuli from food—odor molecules—and the nasal organ are in close proximity, facilitating the olfactory sense. Humans possess what is likely the most discriminating palette of any animal on the planet. Not to pick on our poor canine companions again, but as any dog owner knows, they will eat just about anything.

Our sense of smell, compared to our dogs’, is actually quite good. Scientists working in this area tend to place humans right about in the middle of the pack of terrestrial animals. Not as good as some, but not as bad as many.

But what exactly are we smelling? What are we detecting? Or more simply put, what is an odor? The answer is also not as simple as it seems.

Almost all odors are organic molecules, which means they are combinations, sometimes very complex combinations, of just three atoms: carbon, oxygen and hydrogen. Occasionally among the fouler odors there may be a bit of nitrogen or sulphur, but that’s about it. You wouldn’t think just three to five atoms could be put together in so many varied ways, but theoretical models show that there are likely to be trillions of organic molecules. We ourselves are mostly made up of organic molecules, often quite large ones. DNA, RNA and proteins are all organic molecules with nothing but chains of these five atoms strung together, by the thousands, in incredibly complex ways. An entire branch of chemistry, organic chemistry, is devoted to molecules made up of these five atoms. Carbon is the linchpin of sorts because a single carbon atom is able to form bonds, stable connections, to as many as four other atoms, the most of any atom in the entire periodic table. An oxygen atom can form two bonds and a hydrogen atom just one. This is why organic chemistry is often called the chemistry of carbon—and why scientists looking for signs of extraterrestrial life elsewhere in our galaxy do so by searching for complex carbon chemistry.

Odor molecules are on the simpler side of organic chemistry, typically consisting of between three and 50 atoms of carbon, oxygen, and hydrogen. Even with this number of atoms, it is possible to construct many millions of complicated molecules. And your nose can detect and discriminate between several thousands of these molecules. One could make the case, in fact, that your nose is the best chemical detector on the planet.

The nose’s receptors are proteins embedded in the surface membrane of the cells that live in your nasal epithelium (that aforementioned tissue that lines the upper nasal cavity). They are called olfactory neurons because they are actually brain cells that have evolved to detect odors and send signals back to the rest of the brain. Each protein receptor has a differently shaped pocket that is capable of capturing differently shaped odor molecules—a kind of lock-and-key arrangement where the receptors are the locks and the odor molecules are the keys. If the key (odor) fits into the lock (receptor) then it will activate the olfactory neuron and send a signal to the brain that such and such a molecule must be in the area. It’s not quite that simple, because most of the things we smell are actually mixtures of many different molecules, but that’s pretty close to the general idea.

I doubt you would ever mistake a banana for a pear. This means that you can smell the difference of one carbon atom! 

When molecules activate many different receptors at once, complications arise. For example, coffee is known to contain 780 odorous molecules. Some of them will activate the same receptor because they have similar shapes or properties, but it is still likely that sniffing coffee grounds will activate a fair number of the receptors in your nose.

One might wonder how different two molecules have to be in order for our olfactory system to register their smells as distinct. The answer lies in the diagram above, which details one way chemists show the structure of a molecule. Each of the little balls represents an atom—gray for carbon, red for oxygen and white for hydrogen. They are connected by bars that represent the bonds between them. In this case, the two molecules consist of a chain of carbon atoms with some hydrogens attached to them and what is known as a “functional group” at one end where the red oxygens are. The functional group shown here is called an ester. Among the sorts of organic molecules that make up odors there are about 25 different types of functional groups. Esters are among the most common of odor molecules.

If you count the number of carbon atoms in the two chains (from the red oxygens to the left) you will see that one of them has six carbons attached to the ester group and the other has seven. In other words, they are identical except for this difference in one carbon atom. Now here’s the kicker. The 6-carbon molecule (known as hexyl acetate) smells like bananas, while the 7-carbon molecule (known as heptyl acetate) smells like pears. While both are fruity smells, I doubt you would ever mistake a banana for a pear. This means that you can smell the difference of one carbon atom! And you aren’t even a trained perfumer.

Our noses can make a discrimination that only the most sophisticated chemistry equipment can make—a single carbon atom in a chain of only six or seven atoms. Your remarkable nose performs many feats like this dozens of times a day: at every meal, when you enter a room, when you take a walk in the park or down a narrow street on garbage day in the summer. It tells you what to avoid and what to seek out, bringing sensual pleasure to many simple activities. And all this without requiring you to think much about it at all. Next time you’re at the grocery store, go to the fruit section and close your eyes. Smell the bananas and the pears, and impress yourself with the amazing power of your olfactory sense. ♦

Stuart Firestein is a neuroscientist studying the vertebrate olfactory receptor neuron.

A standard ball and stick model of two odorous chemicals composed of carbon (gray), oxygen (red), and hydrogen (white) atoms.

Picture This: Atoms of Aroma

It has now been more than 160 years since Charles Darwin and Alfred Russell Wallace laid the keystone of modern biology with the theory of evolution. But geology—Darwin’s original field of study—would wait almost another full century, until the 1950s, for the first light of its new dawn. As evolutionary theory revolutionized biology, the theory of plate tectonics brought geology into the modern era and did away with the comforting fiction of the eternal, unchanging Earth once and for all. From then on, everything—from the distribution of earthquakes and volcanoes around the globe to the heights of the Himalayas and parallel peaks and valleys of the American Basin and Range—could be explained as facets of the same underlying theory. The planet finally began to 

: the Earth’s outermost rocky layer, the lithosphere, is not a solid shell, but a jigsaw of rocky plates adrift over an ocean of hot rock with the consistency of silly putty. Where warm material rises from this viscous part of the mantle, plates tear apart, and new land forms as lava pours forth from the ruptured crust. Where plates collide, they thrust up new mountain ranges and drive cold, dense oceanic crust back down into the mantle. It is a ceaseless cycle of creation and destruction; every few hundred million years, each rock on the seafloor will have been replaced and the contours of the continents redrawn.

Geology waited a long time for its revolution. But if not for one map—and the remarkable woman who created it—earth science would have had to wait even longer still.

Oceanographer Marie Tharp’s 1957 map of the North Atlantic turned geology upside down by revealing the topography of the seafloor, which until then scientists had largely assumed was a flat, featureless abyss. Tharp’s survey is cut through by twin chains of drowned volcanoes that rise along the banks of a rift valley rivaling the Grand Canyon in width and depth, but that stretches from Greenland to the edge of the Antarctic. This is the Mid-Atlantic Ridge, a long mountain range and rift valley that we now understand as the violent border marches of the great tectonic plates on either side of the Atlantic.

Tharp’s first map revealed only one section of this underwater topography, which she and her colleagues discovered was just one part of a larger system of mid-ocean ridges encircling the globe. Between 1952 and 1977, Tharp and her colleague Bruce Heezen would go on to chart the entire seafloor, revealing this world-spanning ridge in its entirety for the first time and connecting it to rift valleys on land like the East African Rift. However, the 1957 North Atlantic section was enough, eventually, to convince geologists to entertain the possibility that the continents were 

—a controversial idea that for decades had been widely dismissed as scientific hocus pocus. The Plate Tectonic Revolution had begun.

The theory of plate tectonics brought geology into the modern era and did away with the comforting fiction of the eternal, unchanging Earth once and for all. 

The polymath skillset that made Tharp such a unique and important mapmaker was very much a product of her place and time. Had she been born a few decades later, she might have gone directly into science. She grew up following her father, a soil surveyor for the USDA, across the country and developed an early interest in geology. But in college, she studied fine arts; women were not welcome in technical fields. Intellectually restless, she flitted between majors and ended up graduating with degrees in English and Music and four minors, including one in geology. She also learned technical drawing. Tharp thought she’d ultimately become a teacher, like her mother. But in 1941, Japan bombed American ships at Pearl Harbor and the US declared war in return. With so many young men gone to fight in World War II, institutions that had previously shunned women suddenly competed to recruit them. The University of Michigan, which had previously only admitted men to its geology program, put up flyers at other colleges advertising a geology master’s degree program for women, and Tharp applied. She graduated in 1944 and earned another bachelor’s degree in mathematics in 1948.

That year, she moved to New York and went looking for work. After the tedium of cleaning fossils dissuaded her from applying to jobs at the American Museum of Natural History, Tharp decided to try Columbia. Her math degree earned her an introduction to Maurice Ewing, a geophysicist and founder of Columbia’s fledgling Lamont-Doherty Earth Observatory. But it was her drafting skills that got her the job. Ewing—who colleagues at Lamont just called “Doc”—was gearing up to chart the Mid-Atlantic Ridge, and he needed a cartographer.

A mysterious underwater rise had been discovered halfway across the North Atlantic in the 1850s when sailors aboard the 

 dropped cannon balls tied to ropes overboard to sound the depths. In 1872, the 