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"The good life is one inspired by love and guided by knowledge."

-Bertrand Russell

Chapter 3.

“The Map of Eratosthenes”

 

“The world is all that is the case.”

-Wittgenstein 

 

Outside of Athens, Alexandria was perhaps the most important city in the Ancient Greek world. It was a port city in northeastern Egypt, founded by Alexander the Great in 331 BCE. Alexandria was known for its splendor. The greater part of the city was covered with beautiful public precincts, much like the Tuileries Garden in Paris, or magnificent royal buildings, like Blenheim Palace in England. Throughout the history of Alexandria, each king would erect his own fleet of monuments and ornaments scattered among those erected by his predecessors. Those features which we celebrate still today include the Temple of Serapis and the great lighthouse Pharos, considered one of the Seven Wonders of the Ancient World.

Undoubtedly, the most impressive feature of ancient Alexandria was its library. The library would have been housed in vast, grand building meant to be the centerpiece of the city. Its shelves housed all of the greatest works of the ancient world, many of which were permanently lost when the library was destroyed in a fire, ignited by the armies of Julius Caesar in 48 BCE. We don't know exactly how many books the library held, but historians' estimates go as high as five hundred thousand. It attracted scholars such as Euclid, Aristarchus, and Archimedes. For three hundred years, the library was the intellectual center of the Mediterranean. 

The most distinguished post in the Library of Alexandria was the head librarian. The head librarian was the foremost scholar of the library and also acted as royal tutor. The library was founded by Demetrios of Phaleron, who acted as its first head. Demetrios was a renown scholar and had enjoyed a successful political career until it ended in his exile, making him available for the new endeavor taking place in Alexandria. He was succeeded by Zenodotos of Ephesos, who was likely the first to hold the actual title of head librarian. Zenodotos was known for his Homeric scholarship. He was followed Apollonios of Rhodes, who was forced into an early retirement by a political regime change. The new regime appointed a new head librarian. His name was Eratosthenes.

Eratosthenes wasn't famous for his philosophy. His contemporaries considered his work adequate but rather derivative. He wasn't famous for his mathematical work, either, though he had spent considerable time on it. He was most famous for his poetry. Even so, he was by no means the most reknown poet of his generation. His friends called him 'Beta' because he was, according to them, second best in everything. He dedicated time to many different disciplines, excelling in each of them but never becoming the authority on any particular one. Eratosthenes was the original jack of all trades, master of none.

Today, we best remember Eratosthenes as founder of the field of geography. The Geographika, in which he was the first to coin the term, was Eratosthenes' magnum opus. He published it during his tenure at Alexandria, sometime between 240 and 220 BCE. It is three books in length. It covers topics ranging from climate zones to the geological history of earth to the customs of different populations. But what is perhaps most interesting about the Geographika is that it contains instructions for a map. We don’t actually have a copy of Eratosthenes' original map (it probably burned down with the Library of Alexandria). But we can reconstruct it from his detailed description. Eratosthenes' map was the first recorded attempt to chart the entire known world. Before Eratosthenes, the closest thing was a schematic depicting the world's landmass as a perfect circle, divided into three roughly equal parts, with Europe to the west, Asia to the east, and Africa to the south. In Eratosthenes’ map, the world's landmass looks like a parallelogram. It is divided into four quadrants. They are, roughly, Africa, Europe, Russia, and India—or at least that’s what we’d call them today.

 

Eratosthenes’ map was the first ambitious attempt to render the world as it actually appears from above. Of course, having seen the real thing in satellite images, the first thing we notice about Eratosthenes’ rendering is that it is way off. 

As far as maps of the world go, it features—to make the point gently—some peculiar omissions. The Americas, Australia, and East Asia come to mind. And even in what Eratosthenes does try to depict, he fails to grasp how expansive the earth’s landmasses really are. He insists that if you started at the Strait of Gibraltar at the southwest tip of Europe and sailed around Libya (Africa) then India then Scythia (Russia) then Britannica that you could make it back to Spain with relative ease. He writes, ”Those who attempted to sail around but turned back say that it was not because they came upon some continent and were prevented from sailing beyond, reversing their direction, but because of difficulties and isolation, not because of a lessening of the sea, which was still passable.” He is confident that the only reason that no one had yet to do this was because of unfavorable tides, and not for more consequential reasons—like the existence of the rest of Africa, China, and Russia.

Eratosthenes also divides the map according to parallels and meridians. He was the first to do this, and it was a huge innovation in cartography. You could now relate two different points on the map with precise reference to lines of latitude and longitude rather than other landmarks. But the way he chooses to do it is curious. He places cities on the same parallel that were known even in his day not to be aligned along the same axis. And the parallels are not evenly spaced. They go through his favorite landmarks—like Alexandria—rather than giving a sense of even proportion to the map. 

 

But what is most interesting to note about the map of Eratosthenes is not that it is off, but precisely how it is off. Upon seeing the map, our first impression is to note everything he missed and smirk because it’s so egregiously incorrect. The issue, we assume, is technical. If Eratosthenes had access to the same satellite images that we have, he would’ve known just how misinformed he really was. And that’s true. If he had pictures of the real thing, his map wouldn’t be as inaccurate. But it’s also the case that his map isn’t wholly off, either. He also gets a lot right. The area around the Mediterranean, especially North Africa, is rendered with fine detail. Eratosthenes’ map isn’t just roundly incorrect but contains very specific kinds of errors. The errors are there because he couldn’t use technology as a guideline. But the reason for the particular faults of his map aren’t technological. They’re psychological. In a very real sense, Eratosethenes’ map shows us the way he viewed the world. 

 

2.

 

Edward Tolman was a psychologist who conducted research during the first half of the twentieth century, primarily in the late 1940s. He was known for his work on rodent behavior. His studies on learning in rats continue to be influential to this day. In a typical rat experiment, Tolman would set the animal in a maze. One of the paths in the maze leads to the food. The others are dead ends. The experiment is to see how long it takes the rat to find the food. The first time the rat goes through the maze, she meanders, takes paths that lead to dead ends, and will be in the maze far longer than necessary if she took the quickest route to get the food. The second time she goes through it, she’ll be a little quicker. Then after, say, ten trials in the maze she more or less goes straight to the food. The way to interpret these results is to plot the trial number on the horizontal axis, and the time it took the rat to get the food on the vertical axis. For the first few trials, the response time is relatively long. Then the response times go down as the rat becomes a more efficient navigator. If you put a line through all of the data points, it would start in the top left and drop to the bottom right. This is a learning curve. 

In one experiment, Tolman tested a group of rats on the usual set up, but with one minor alteration. Instead of ten trials with food, Tolman administered the first half of the trials without the food at the end. The rat just wandered around the maze until, by chance, she happened upon the appointed path, at which point Tolman took her out of the maze. After a few of these non-food trials, Tolman returned to administering the normal trials ending when the rat finds the food. 

In the normal case, the reason that the rats got quicker at completing the maze was because they wanted to get the food as quickly as possible. Over time, they got better at doing so. What you might expect, then, from the rats who had five trials without food is that they show the same learning curve as the original rats, but shifted over the right. The rats wouldn’t have learned anything, because there was no incentive to do so. 

But that’s not what Tolman found. Instead what he observed was that as soon as he introduced the food after the fifth trial, the rats knew how to get to it on the next trial just as efficiently as the rats who had five rounds of practice. The learning curve wasn’t a straight line from top left to bottom right. It was flat for the first five trials (the rats were just wandering around randomly), then it plummeted to the same point that the normal rats were at after the same number of trials. The rats were learning something, even when there was no incentive to do so. 

“It appeared,” wrote Tolman, “that during the non-rewarded trials these animals had been learning much more than exhibited.” He continues, “Interpreting these results anthropomorphically, we would say that as long as the animals were not getting any food at the end of the maze they continued to take their time in going through it—they continued to enter many blinds. Once, however, they knew they were to get food, they demonstrated that during these preceding non-rewarded trials they had learned where many of the blinds were. They had been building up a ‘map,’ and could utilize the latter as soon as they were motivated to do so.” The rats, in short, had constructed a psychological map of the maze. And once they knew where on the map they could obtain food, they went straight there.

 

3.

 

Eratosthenes was born in Cyrene, in the modern day country of Libya, along the Mediterranean coast of northern Africa. Cyrene is due west of Alexandria and Cairo and directly south of Greece. It was the largest ancient Greek state and the main hub connecting the Mediterranean with the rest of Africa. Cyrene was cosmopolitan, economically crucial, and culturally diverse. We don't know much about Eratosthenes' childhood in the middle of the third century BCE, but he surely would have been exposed to many different kinds of people from many different backgrounds in Cyrene.

When he was twenty Eratosthenes moved to Athens to study. He became acquainted with many scholars in Athens. He met the architect and sculptor Callimachus, a fellow Cyrenian. Callimachus would later be a proponent of Eratosthenes' appointment as head librarian at Alexandria. For a brief period Eratosthenes was a follower of Zenon, the founder of the Stoic school of philosophy. Stoicism was influential in that time, and Zenon was much revered. The later Greek geographer Strabo criticized Eratosthenes because he did not show Zenon what Strabo considered to be an appropriate amount of respect. Eratosthenes, it seems, had a bit of an independent streak.

In Athens Eratosthenes would have had broad exposure to many influential schools of thought. Aristotle died in 322 BCE, about seventy-five years before Eratosthenes arrived in Athens, but the intellectual climate would still have been permeated with his philosophy, as well as that of Plato and Socrates. Eratosthenes would have studied mathematics in the tradition of Euclid. He would have studied the histories of Herodotus and had broad exposure to literature and language, like the tragedies of Euripides and the epics of Homer.

During his younger years Eratosthenes worked on mathematics, with a particular interest in prime numbers. His most celebrated mathematical invention is known today as the Sieve of Eratosthenes. The Sieve—which rhymes with 'give’—is an algorithm for generating a list of all the primes up to a chosen number. Eratosthenes didn't necessarily think of it as an algorithm, because that was a concept that was developed with the advent of the modern computer. He thought of it as a well-defined set of instructions that would reliably have the desired effect if you did it right. To this day, it's still the most efficient way for a computer to generate all the primes up through about one hundred thousand, and his algorithm is still relevant two thousand years later in contemporary fields like number theory and cryptography.

The calculation that garnered Eratosthenes the most fame in his own lifetime was his estimate of the earth's circumference. Using only basic Euclidean geometry and a few available measurements, he estimated the circumference of the earth to within a tenth of a percent of the modern calculation. The Nile river runs from Alexandria to Syene for about one thousand kilometers. It runs mostly north and south, with less than two hundred kilometers of east-west deviation at any point. The Nile had recently been surveyed by Ptolemy II, son and successor to the original Egyptian king Ptolemy. So its length was well documented in Eratosthenes' time. It was also known in the ancient world that the sun on the summer solstice was directly over the city of Syene, because there was a deep well in the city which cast no shadow on the solstice. This means that if you drew a straight line from the center of the sun to the center of the earth, the intersection of the line and the surface of the earth would be perpendicular, forming a right angle.

Eratosthenes, knowing all this, went to Alexandria on the solstice and measured the shadow of a tall building. He calculated the degree at which the shadow was being cast, which was angled at 7.2 degrees. It turns out that if you take 7.2 degrees and multiply it by 50 you get exactly 360 degrees. That's a full circle. So in order to figure out the circumference of the earth, all you have to do is take the length of the Nile from Syene to Alexandria and multiply it by fifty. His estimate was 252,000 stadia, which is roughly 40,074 kilometers. That's sixty-six kilometers off our modern calculation—the distance between John F. Kennedy airport in New York and Newark airport in New Jersey along i-95. In other words, you could walk Eratosthenes' margin of error in about nine hours. One historian calls Eratosthenes' estimate "a feat so profound yet so simple that it remains today one of the most amazing pieces of ancient scholarship, treated as such since antiquity."

There's a Greek word, philologos. Literally it means "lover of reason," but at its heart it means a learned person, an academic. It was a somewhat pejorative term. An ancient Greek might use it in the same way we might say that someone is a thinker, as opposed to a doer. Eratosthenes, allegedly, was the first to use the word to describe himself. That's sort of like someone today being declared the first “thought leader.” Not necessarily by anyone else, but according to their own estimation.

Of course, he was probably correct. 

 

4.

 

The first person in ancient Greece to come up with the idea of a map of the world was Anaximander of Miletus in the first half of the sixth century BCE, three hundred years before Eratosthenes. Anaximander, to be sure, had no idea what the world looked like from above. But that wasn't the point. The point was that he represented the world in a way that no single person had ever viewed it before. Unless you have access to satellite images or a hot air balloon, there's no way for an individual to view the world in the way it's depicted on a map. We don't see the world from a bird's eye view. We see it from our own perspective, on the ground. Anaximander's map was an entirely new way of making sense of the world. 

Anaximander thought the earth was shaped like a column, following the architectural sensibilities of the day. The earth's landmass then sat on the top of the column, like a drum head. Even in the sixth century BCE sailors knew that the surface of the earth was curved, not flat, so the column idea was soon discredited. But it opened up a question: What form does the earth really take? Not just the way we perceive it, but as a whole. Plato was the first to give a full account of the earth as a sphere. Plato didn't seem to have any good, principled reason for believing this. The guy just liked spheres. 

The person in the ancient world who took the question of the form of the earth most seriously was Aristotle. He documented it in his Meteorologika. (Aristotle is credited with inventing meteorology, but not geography). He was the first one to provide an estimate of the circumference of the earth—it was way off. He also proposed that if you start at the Strait of Gibraltar and sail due west, then you would eventually end up in India. This is where the term West Indies comes from. Columbus sailed west from Spain and thought that he had ended up in India, just as Aristotle suggested. Aristotle's students took his geographical speculation even further. They refined Aristotle's calculations of the earth's circumference. They refined notions of climate zones and estimates of the ratio of earth lengths on the east-west axis versus the north-south axis. They gathered information about the arctic and posed questions about the formation of the seas. But most of their work ultimately didn’t go much further than speculation. After all, how could they possibly know what the rest of the world was like when they’d never seen it?

So when Aristotle began tutoring Alexander the Great around 340 BCE, there were many questions about what the earth looked like but not many answers. These questions of what the earth looked like were of interest to Alexander if for no other reason than because he would, over the next couple decades, go on to conquer most of it. Alexander's campaigns went throughout most of Asia minor—northeastern Africa, Macedonia and the Hellenic peninsula, the eastern Mediterranean, Arabia, and into India, just north of Bombay. These campaigns started in 336 BCE and continued until 323 BCE, the year of Alexander's death. Eratosthenes was born about four decades later in 276 BCE and became head librarian in Alexandria at the age of forty. 

By the time Eratosthenes took his station at Alexandria, all of Alexander's military personnel had returned from their travels, compared notes with one another, and had written up reports about what they had seen. And where do you think they kept those reports once they’d been filed away? The Library of Alexandria, naturally. Eratosthenes had what Anaximander, Plato, and Aristotle did not. He had data. 

Aristotle was interested in the form of the earth, but had no systematic way of knowing what it actually looked like beyond the modest section of the Mediterranean with which he was familiar. For the first time in history, there was an opportunity to ask the question of what the world looked like and have actual information to answer it. And who did that opportunity fall to? Beta, the guy who was broadly exposed to many disciplines but didn't fit squarely in any single one. So he invented his own.

 

5.

 

In 1977, the psychologists Sarah Lichtenstein and Baruch Fischoff ran a series of experiments. They were interested in something they called “hindsight bias.” The premise of hindsight bias is straightforward: when we already know the solution to a problem, we overestimate how easy the problem is to solve. Knowledge, once earned, seems obvious in retrospect.

 

To demonstrate hindsight bias in action, they gave a group of participants a simple questionnaire. Each question had two possible answers. The used this questionnaire to gauge the average rate at which people get a question correct. Some of the questions were hard. For example, “Adaptive radiation refers to (a) evolutionary changes in animal life toward increased specialization, or (b) the movement of animals to a more suitable environment for survival.” Participants selected the correct answer (a) only half of the time. In other words, they were just guessing. Some of the questions were easier. For example, “Who was the first president of the US?” Participants, unsurprisingly, did well on these. Then there was also a category of deceptive questions, which participant got right less than half the time. For example, “Aladdin’s nationality was (a) Persian or, (b) Chinese.” The way the story is told in One Thousand and One Arabian Nights, Aladdin is actually from “one of the cities in China,” so the answer is (b) Chinese. 

Lichenstein and Fischoff then gave a different group of participants the same questionnaire. But this time the correct answer was already circled. Instead of choosing the correct answer, they were told to judge how likely they would be to choose the correct answer if it wasn’t already circled. For example, here’s an answer to a question: Philo Farnsworth invented the television. Now, how confident are you that you would be able to pick out the name of the inventor of the TV if I didn’t just tell you? What Lichtenstein and Fischoff found is that participants consistently overestimated the probability that they would get the correct answer for all three categories of questions, based on their baseline results from the first version of the experiment. That’s hindsight bias in action: it’s easier to answer a question in retrospect than it is in prospect. 

 

About a decade later, the economist Colin Camerer and his colleagues took Lichenstein and Fischoff’s work on hindsight bias and thought about it as an economic problem. Suppose you’re a used car salesperson, and you have a lemon to sell. You know that the car doesn’t run well, but a potential customer doesn’t. Since the customer doesn’t know it’s a lemon, you could sell the car for its usual market value. The customer would be willing to pay it, because they don’t know the difference. But that’s not usually what happens. The salesperson marks the cars down anyway. This comes at an unnecessary cost to them. They do this, Camerer argues, because they can’t help but incorporate the knowledge they already have. In other words, they have a hard time pretending not to know what they already know. Camerer and his colleagues called this the curse of knowledge. 

 

Of course, this is the kind of problem that only an economist could come up with. If you can’t think of any legitimate reasons not to sell a lemon for full market value, then it’s probably better that you’re an economist and not a salesperson. There is, however, a much more interesting application of the idea. 

"The curse of knowledge," says cognitive scientist Steven Pinker, "is the single best explanation I know of why good people write bad prose." When writing is unclear, it’s not because the author is deliberately trying to obfuscate their ideas. Rather, they’re saying something that makes plenty of sense in their own mind, but doesn’t transfer well to another person’s. They don’t know what it’s like not to know what they know. Clear writing is not about describing something that makes sense in your own head, but in someone else’s. "The curse of knowledge," says Pinker, "means that we're more likely to overestimate the average reader's familiarity with our little world than to underestimate it." 

Suppose a writer has a certain thought in mind she wants to communicate. She comes up with a candidate sentence to express the idea. Then she asks herself, “Does the sentence accurately describe what I have in mind?” She then inspects the idea she’s thinking about and determines whether or not the sentence accurately describes it. But that’s a much different problem than what the reader faces. She has to figure out, from an infinite set of possibilities, what exactly the writer means by a term. Imagine, for instance, that a psychologist is trying to describe something that happens at the end of her experiment. She alights upon the term, to use Pinker’s example, “post-stimulus response.” Does this term accurately describe what she has in mind? Sure. The thing she is thinking of most certainly does come after stimulus, whatever she first showed the participant. But then you, as the reader, have to transform that term into something concrete. You have to infer what she has in mind based on the description. The problem is that almost anything could be a post-stimulus event. It could be a tap on the arm, or the experimenter asking you for your phone number after the study, or being hit upside the head with a castiron frying pan. The term “post-stimulus event” is not helpful when in actuality, all she means is whether the participant circled (a) or (b) for a given problem in the questionnaire. If you’ve ever read a piece of technical writing, you know this kind of thing happens all the time. 

The curse of knowledge, however, is not specific to writing. It is a problem for the whole of human communication. Successful communication happens when a person has an idea in their head, sends out a signal that other people can observe (such as language), and causes another person to have the same idea in their head as well. Think back to Freshman year calculus. The professor begins the lecture, and immediately launches into something that is way over your head (at least that’s how I remember it). The professor has an idea in her head that she wants to communicate. She attempts to get other people to have the same idea. But it’s not successful communication unless she causes the students sitting in the hall to have the same idea about mathematics that she has. The reason communication breaks down isn’t because she doesn’t understand introductory calculus or is intentionally resisting clarity. She simply can’t bring herself back from the frontier of mathematical knowledge to remember what it’s like to learn calculus. "The better you know something,” says Pinker, “the less you remember about how hard it was to learn."

 

6.

 

When psychologists saw Tolman’s work on psychological maps in rats, they began to think about how to apply it in humans. For rats in a maze, a psychological map is relatively a straightforward concept. They either know how to navigate through it or they don’t. But what exactly does a psychological map mean for humans? A human’s natural environment is much more complex than a maze. Does it mean that she can navigate from point A to point B? Does it mean she can describe those directions to someone else? Does it mean that they’d recognize the true map if they saw it?

 

In 1976, the psychologist Stanley Milgram ran a study on psychological maps in humans. He had recently moved to Paris, and he was particularly interested in people’s psychological maps of the city. “It is not,” he wrote, “an examination of Paris as a geographic reality, but rather of the way that reality is mirrored in the minds of its inhabitants.” How, in other words, do people’s psychological maps differ from the way Paris actually looks? “The first principle,” as Milgram puts it, “is that reality and image are imperfectly linked.” 

Here is a typical tourist map of Paris:

X.

 

It has all the major landmarks—the Eiffel Tower, Notre Dame, the Arc de Triomphe. This kind of map is posted all around the city. And even if you live in Paris—perhaps especially if you live in Paris—you’ve seen this map many times. Even without the map, this is the city in which these people live; they’re going to be familiar with the way it’s laid out. There is, to be sure, a common basis for what the real thing looks like.

In order to get at people’s private psychological maps, Milgram simply had his participants draw them. It’s not a test of cartographic skill, per se, but of spatial, nonverbal concepts. What do they leave out of their map? What do they include? What do they misremember or place inaccurately? You might expect that these maps will be like the tourist maps, but slightly less accurate and with less detail. These people are not, after all, professional map makers. They don’t have the real thing in front of them to use as a guideline, either. So we wouldn’t expect them to draw a perfect map from memory. 

 

But that’s not exactly what Milgram found. For instance, here’s a map from one of his participants:

X.

 

This was drawn by a fifty year old woman, who at the time of the interview lived in the twelfth arrondissement (one of the twenty municipalities into which Paris is divided). However, she lived for fifteen years in arrondissement number four. I bet you can guess which one that is. Just above the bend in the Seine River, she maps it in scrupulous detail, all the way down to the one way streets. And do you notice what’s missing in her map? The Eiffel Tower! It should be south of the river, just up and to the left from Montparnasse, the only landmark she includes south of the Seine. As a tourist map, this isn’t just under detailed. It’s totally useless. But if you live in the fourth arrondissement? It’s all you need. 

In this respect, her map is representative of what Milgram found overall. “She centers her map not on Paris as a whole,” writes Milgram, “but on a segment of it that has special meaning to her.”

The implication for psychological maps more generally is that our conception of reality, in part, is not just a reflection of the geographic reality. There is a social component to it. It depends, in part, on where we live and who we live with. A person’s psychological map represents their perspective. In a real sense, it how they see the world. And that perspective, that worldview is a influenced by associations with factions. 

For Milgram’s subjects, the neighborhood in which they lived was a pertinent faction that influenced the way they conceptualized Paris. This is, in some respects, a surprising assertion. I think for most of us, if we thought about drawing a map of the city with which we’re most familiar, we imagine that it would be a slightly less detailed version of the real thing, like a tourist map that’s just a little off. We don’t imagine that our picture of reality would be outrageously biased by social considerations like where we live and who we spend our time with. The fact of the matter is that the factions we’re a part of exert a dramatic influence over the way we see the world. Our psychological maps are more similar to the maps of members of the same factions than they are to those of other factions.

 

7.

 

One of the most famous proofs of mathematician Carl Friedrich Gauss is called the Theorema Egregium (meaning incredible theorem). What it says is quite simple. In mathematical terms, it says you can’t project a 3D surface onto a 2D surface without distortion. For us, what that means is you can’t take a globe and turn it into a flat, 2D map without getting something wrong. In other words, whenever we’re looking at a 2D map, no matter how technologically sophisticated, something is guaranteed to be misrepresented. Distortion in how we render the world is inevitable.

What this suggests is that we have to make choices about what we distort. For example, the Mercator projection—perhaps the most famous map projection, at least through the early twenty-first century—was developed by a Belgian in the sixteenth century. Mercator had to choose how he was going to distort his 2D rendering of the world. He chose to magnify the northern hemisphere at the expense of the southern hemisphere. In the Mercator projection, Greenland looks huge. It appears to be the size of Africa. But that’s nowhere near the reality. Africa is fourteen times larger than Greenland. But if you’re a sixteenth century Belgian, you don’t care about the relative size of Greenland and Africa. Like the Parisians drawing their psychological maps, you only really care about rendering the world in detail in the part that’s relevant to your faction.

When we consider Eratosthenes with this in mind, I think we get a very different how to interpret his map. It’s not just that Eratosthenes constructed an inaccurate map because of technological limitations. He rendered reality as he saw it, and in the process creating a psychological map that represents the point of view of his faction. Since Eratosthenes’ time our technological capabilities have changed. We have access to high fidelity images of what the world really looks like. What hasn’t changed is the way we render our own version of the world. We inevitably view reality—like Eratosthenes and the Parisians—through the lens of factions.

This is why it’s so much harder to understand the perspective of someone in another faction than it is to understand someone in our own. The curse of knowledge suggests that we assume other people’s maps look like our own than they actually are. When our maps are in fact similar—when we come from the same factions—then that doesn’t present a problem. But when there are big discrepancies in the map, as there are for people from different faction, the curse of knowledge becomes a big problem. 

Just take Eratosthenes. He rendered what was important to him in fine-grained detail and only vaguely described what he knew was out there, but wasn’t intimately familiar with. How else could he have done it? But this suggests that a different person, living in a different place—someone from a different faction—would have drawn a different map. But does Eratosthenes allow for that in his rendering? Absolutely not. He’s confident that he’s right. He admits there might be some things he doesn’t know. Sure, he isn’t exactly certain what’s in the far reaches of India. But he’s positive the map is, on the whole, correct. 

Understanding someone’s perspective is like being able to draw their map. It’s a hard problem. This is why perspective-taking is so difficult. How are you supposed to know what their map looks like? You can only really assume that it looks like your own, with some modest deviations. Instead, what you need is perspective-getting. If you want to get at their perspective, the only way is to get them to draw the map for you.

There is an outstanding question here. Given that trying to reconstruct someone else’s psychological map is so difficult, how are we able to do it at all? Perspective-taking is a crucial process in how human beings relate to one another. The idea of a psychological map gives us a framing for the problem—seeing things from their perspective is like drawing your map. But it doesn’t tell us how to solve it. In order to understand that, we need to go deeper in to the mechanisms behind empathy and theory of mind. 

draft 25/08/2018

Next: Chapter 4. A Natural History of Empathy.