In parts 1 and 2 of the “even oddness” tale, I introduced prototypes and idealized cognitive models (ICMs). The goal? To lay the groundwork for explaining the mysterious experimental results of a 1983 study which showed that people judge some even numbers as “better” than others. Today we tie it all together.

How does George Lakoff’s theory of ICMs explain the results of Armstrong, Gleitman and Gleitman’s experiment? In order to understand, we first need to draw a clear distinction between “folk” and “expert” models.

“Folk models” — also called “folk theories” — are mental models held by “regular old folks.” These are the models that make up almost all of Otto’s interpretations of events around us. “Expert models,” or “expert theories,” are Ralph’s consciously-constructed models of how the world works. For instance, the “camcorder” model of vision — the idea that they eyes are like camcorders, recording what is “actually out there” — is a commonly held folk model of how vision works. Expert models of vision are created by neuroscientists who understand how the eyes and brain work together to generate the images we perceive as “real.”

In the case of even number, the definition we learn in school is an expert definition: an even number is a multiple of 2. It is consciously accessible, and we know, via Ralph, that any given number either is or isn’t even. There is no gray at all.

At the same time, though, Otto, unbeknownst to us, has created folk models of numbers, including even numbers, which affect our judgments unconsciously.^[1] The first model, underlying all others, is what we might call the “name equals number” model. Most people who aren’t mathematicians don’t normally distinguish between numbers and their names. Take the number 26: in our familiar base-10 system, 26 is both a number and a name. However, the number 26 can be represented by many different names: 11010 in binary, 1A in hexadecimal, and so on. It just happens that the base-10 system is what we have all grown up with, and is the one we use unconsciously to understand numbers — so much so that we equate numbers with their base-10 names.

Another folk model is the “single-digit numbers are primary” model. Because numbers are infinite, but systems of representing numbers are finite, we have to start somewhere. Our folk starting point is the positive numbers near zero, which in base 10 are represented with single numerals: 1 through 9. Every number in base 10 is represented using some combination of these numerals, plus 0. This gives 0–9 a privileged cognitive status: we view any number, no matter how large, in terms of these numerals.

Consider 106, which was one of the stimuli in the experiment. The name-equals-number model equates the quantity “one hundred six” with the string of numerals, 1 — 0 — 6. This string, three digits long, is more complex than any single numeral. So, via the single-digit-numbers-are-primary model, we understand 106/“one hundred six” in terms of the numbers/digits it’s made up of.

These two models are in us so deeply that it can be hard to see that they’re completely made up. For name-equals-number, it just seems so obvious that the quantity denoted by “106” just is 106. Its hexadecimal name, 6A, or its binary name, 1101010, seem fanciful, false — but 106 seems real.

As for the single-digit-numbers-are-primary model, this stems from the fact that we can imagine numbers much larger than we can count on our ten fingers and ten toes. Human creativity and imagination have outstripped our limited bodies, so we have invented a system of representation that starts with something basic and easy to understand — quantities less than ten — and we’ve figured out a way to represent everything else in terms of this simple concept.

Given these two models, it’s no longer surprising that Armstrong, Gleitman and Gleitman’s experiments gave the results they did. Subjects were asked to make rapid, unconscious  judgments about some even numbers. Given the rapidity, Otto was in charge, and drew on the only models it could draw on under such stress: the folk models just discussed. This is what yielded the strange experimental results.

Importantly, when asked explicitly whether even number is a graded category, they said no. Able to draw on Ralph to answer the question, they gave the logically obvious and truthful response. Otto, though, left to his own automated, time-pressured devices, begged to differ.

The two models discussed here suffice to explain Armstrong, Gleitman and Gleitman’s results. We also use many other simplifying models to help us understand numbers. For example, multiples of 10, 100, 1,000, etc., are more cognitively basic and provide key reference points. We could expect that the same kinds of experiments Armstrong, Gleitman and Gleitman did would show 1,001 to be more prototypical than 1,173.

George Lakoff’s contributions to category theory have been immense, and aren’t limited to prototype theory. Just within this sub-field, though, he accomplished what many who went before him had tried but failed to accomplish: he provided a highly plausible theory of human cognition that offered to explain the origins of prototype effects, while being completely in line with how psychologists and neuroscientists understand the brain and body to work.

Last post I introduced some research results showing that people judge certain numbers (e.g., 4) to be “better” examples of “even number” than others (e.g., 106). This posed a challenge to Rosch’s prototype theory, because how could any even number be “better” than any other? Critics of prototype theory said, well, obviously prototype theory can’t be right.

First we have to remember that Rosch didn’t claim that the prototype effects — that is, the ways in which people rated some category members (like robins and swallows) as “better birds” than others (like ostriches and penguins) — had anything to do with how the category is “really” structured. Instead, Rosch said that any future theory of categories had to account for prototype effects. Any theory of categories that didn’t predict prototype effects would be a bad theory.

The question then becomes: where do prototype effects come from?

We can only begin to look seriously at the question if we keep reminding ourselves that categories are a human phenomenon through and through: categories only appear to exist in the world, independent of human categorizers. As we’ve seen, Otto is masterful at making up a story, in an instant, completely outside of our conscious control, convincing us that everything is just “out there,” and that we are passive observers of a pre-existing reality. The story is so convincing that few of us ever call it into question at all.

If we do keep in mind the human-made nature of categories, then we can begin to understand where prototype effects come from. This was one of the major tasks George Lakoff set for himself in his seminal work, Women, Fire and Dangerous Things (1987)^[1].

The basic idea Lakoff proposes is that prototype effects result from imperfect, simplified mental “models” that we have of the world. A “model” is basically an idea or “best guess” about how something works. A model tells us what to expect and what to do.

Lakoff coined a term: Idealized Cognitive Model, or ICM. The “idealized” part is key. The world is complex, and to function in the world we need ways of idealizing, or simplifying. This gives us reference points to compare actual events to.

Lakoff offers the example of the category mother. In a standard, idealized notion of motherhood, a mother is all of the following:

• the person who gave birth to the child
• the primary female nurturer of the child
• the female provider of half the child’s genetic material
• the person who is married to the genetic father of the child

The world often doesn’t match our idealizations. Imagine the following cases:

1. The primary female nurturer did not give birth to the child or provide any of the child’s genetic material, but is married to the child’s genetic father.
2. The primary female nurturer of the child did not give birth to the child or provide any of the child’s genetic material, and is not married to the genetic father of the child.
3. The female provider of half the child’s genetic material also gave birth to the child, but is neither married to the child’s genetic father nor is the child’s primary female nurturer.
4. The female provider of half the child’s genetic material did not give birth to the child, is not married to the child’s genetic father, and is not the child’s primary female nurturer.

Some of these cases are more common than others, but they are all familiar, and we have names for all these sub-types of mothers. #1 probably describes a stepmother, but could also describe an adoptive mother if the father donated sperm to fertilize the egg. #2 describes an adoptive mother or a foster mother. #3 could describe either a birth mother or a surrogate mother. #4 describes a donor mother.

Usually we don’t need to worry about disentangling all these attributes from one another. Typically all four attributes converge. When they don’t converge, questions arise. And in the case of motherhood, how we answer these questions can have dire consequences for people’s lives.

Here’s a bizarre story, in three parts, about just how strangely Otto can behave, and just how clueless we are about what Otto is doing.

It starts with a technical debate in psychology. When Eleanor Rosch and colleagues were discovering prototypes, they were also making a lot of people nervous. For over 2,000 years (since Aristotle) the dominant view of how categories worked was that they were objective (i.e., existed in the world, independent of human categorizers) and organized into a hierarchy (like animal -> mammal -> primate -> human). Crucially, categories were seen as “in or out”: either something is or isn’t a [you name it: mammal, bird, chair, etc.].

Prototype theory threatened to turn all this on its head — especially the last part about in-or-out membership. How could a robin could be a “better bird” than a penguin? Psychologists raised in the Aristotelian tradition couldn’t wrap their heads around it. So they tried to disprove it.

The most famous attempt came from Armstrong, Gleitman and Gleitman, in a 1983 paper entitled, “What Some Concepts Might Not Be.” (Armstrong, Sharon Lee, Gleitman, Lila R. and Gleitman, Henry. 1983. What some concepts might not be. Cognition, 13. 263-308.) The paper is a classic reductio ad absurdum: take something to its logical extreme, show that the extreme is invalid, and claim that the entire theory is bogus.

They took a category that couldn’t possibly show prototype effects and replicated some of Rosch’s experiments to see if prototype effects showed up. (“Prototype effects” refers to all the ways in which people saw robins and swallows as “better birds” than ostriches and penguins.) The category they chose was even number. The category has a clear, precise mathematical definition: an even number is a multiple of 2. Any number that is a multiple of 2 is an even number; any number that isn’t, isn’t. No even number is any “better” than any other, so prototype effects can’t show up. That is, no even number could possibly be rated as “better” than any other even number.

But prototype effects did show up. Of the six examples of even number on offer — 4, 8, 10, 18, 34, 106 — 4 was judged to be the “best example” of an even number, followed by the others in rank order.

The authors argue that since even numbers don’t have prototypes, and since prototype effects show up anyway, then prototype effects can’t say anything about how categories are “really” structured.

It’s a seductive argument. The problem is that the authors are comparing two completely different notions of what categories “are.” They’re confusing Otto and Ralph. Prototype effects result from human beings making judgments under time pressure. Anthropologists call these “folk” judgments: they aren’t scientific, and they aren’t generated by rules; they are intuitive — products of Otto. Even number is an “expert” category: rule-bound, binary, black-and-white. It’s also a category human beings designed as binary: even numbers couldn’t do what they do if they weren’t defined in such a clear way. The category “even number” is something Ralph came up with.

Rosch’s studies were of human beings making judgments of category membership. She did not make any strong claims about how or why these judgments were made — that is, she did not present a theory of where prototype effects come from. What Armstrong, Gleitman and Gleitman did was rebut a claim that Rosch never made: that prototype effects somehow reveal the “actual structure” of a category (whatever that means).

In the end what their paper really did was, ironically, to provide even stronger evidence for prototype theory than Rosch’s experiments had: with natural categories like bird or tree we feel intuitively that there are “better” examples than others. With “even number” we don’t expect it, and yet the prototype effects show up anyway. How could this be? There must be something powerful about human categorization that could take a crisp, simple category like even number and turn it into something fuzzy. It seems Otto must be up to something. But what?

This is worth thinking about for a moment. How could there possibly be one even number that is “better” than another? If we believe that numbers exist in an objective world outside of human experience, and that all we’re doing as humans is putting pre-existing categories into boxes, then the finding is complete nonsense. It’s an easy trap to fall into: the objectivist trap of believing that categories exist before a human being does some categorizing.

This is when we have to use discipline and remind ourselves that even our very perception of what is “out there” is a fiction created by Otto. He’s doing a lot behind the scenes. Armstrong, Gleitman and Gleitman’s findings, because they seem so strange, urge us to press forward for an explanation. How does the human categorization system work, such that a perfectly “objective” category like even number can be judged by humans to have “better” and “worse” exemplars?

What exactly is Otto up to?

I’ve never seen a statement about the business value of intercultural skills as clear and concise as this:

More and more business leaders are identifying real business value in employing staff with intercultural skills. These skills are vital, not just in smoothing international business transactions, but also in developing long term relationships with customers and suppliers. Increasingly they also play a key role within the workplace, enhancing team working, fostering creativity, improving communication and reducing conflict. All this translates into greater efficiency, stronger brand identity, enhanced reputation and ultimately impact on the bottom line.

This is in the foreword of a new report from the British Council, in association with Ipsos and Booz Allen Hamilton. The report is called “Culture at Work,” and it reads like a manifesto.

It’s music to the ears of interculturalists, who struggle with old stereotypes that “communication” is somehow “soft” and lacks “hard” business value. (See also an earlier post about a similar report from the Economist Intelligence Unit.)

The study surveyed HR managers at 367 large employers located in nine countries: Brazil, China, India, Indonesia, Jordan, South Africa, the UAE, the UK and the US.

The report is packed with good data. A few highlights:

• An overwhelming majority of employers view intercultural skills as important or very important. China brings up the rear at 70%; the US is in the middle at 88%; and Indonesia and Jordan lead with 100%.
• The three skills most valued by employers are, in order: “demonstrates respect for others,” “builds trust,” “works effectively in diverse teams.” “Qualifications related to job” is tied for fourth place with “open to new ideas / ways of thinking.”
• Skills which have hard business value include “good for reputation,” “bringing in new clients,” “building trust with clients.”
• Skills which help mitigate risk include preventing damage to reputation and loss of clients.
• In several of the countries there is a belief that the education system isn’t providing the needed set of intercultural skills. In the US, for instance, 70% say the education system meets these needs “somewhat” or “not at all.”
• Interestingly, though maybe not surprisingly, the US is by far the most insular of the nine countries represented: only 28% of employees have frequent contact with customers or partners in other countries, and 26% with colleagues in other countries. The next lowest is Brazil, with 56% and 54%. The highest is Indonesia, with 83% and 100%.

We’ve got some distance to go yet, but we’re on a long, one-way road toward greater valuing of intercultural skills in the global workplace.

In the last post we looked at how Otto simplifies the world for us through metaphor. How does this work? How do we come to see something abstract in terms of something concrete?

Humans are amazing learning organisms, and it turns out that metaphor is with us from our earliest days as toddlers, and maybe even before.

In 1980, when they published Metaphors We Live By, George Lakoff and Mark Johnson had an intuitive sense that metaphor was tied to the body, but it wasn’t until 1997 that it became clear exactly how. That year Lakoff’s student Joe Grady completed his U.C. Berkeley dissertation, “Foundations of Meaning: Primary Metaphors and Primary Scenes.”[1] In his thesis Grady explained how our bodily experiences as toddlers create the conceptual mappings between source and target domains.

Consider a simple and intuitive example: walking towards and arriving at a destination. Imagine a toddler toddling across the floor towards her dad. She’s wobbling here and there, probably unsure whether she’ll make it. She has to stay focused, constantly rebalancing herself to avoid falling. Finally, she makes it, joyously hugging daddy’s legs. Daddy and all spectators immediately shout praise, and the toddler smiles a big smile of accomplishment.

At that moment, Grady argues, a binding in the brain/body is established (or reinforced, since this scene and scenes like it are repeated hundreds or thousands of times throughout childhood). The binding is between the physical experience of arriving at a destination and the emotional sense of accomplishment. This binding is so strong that we begin to think about accomplishments generally in terms of arrivals: the subjective sense of accomplishment reminds us of that earliest type of accomplishment called “arriving.”

The binding isn’t limited just to the moment of arrival. The entire journey can be thought of as a set of correlations — mappings — between physical experiences and our associated assessments of those experiences. Swift, unimpeded motion feels hopeful, exciting, easy. Halting, interrupted motion feels frustrating and discouraging. Physical obstacles in our path become metaphorical “obstacles” to the good feelings we are seeking in our purposeful motion. And so on.

This is reflected in our language and its staggering abundance of expressions that describe purposeful actions generally in terms of purposeful motion specifically. Just a few off the top of my head:

• Pat’s new job has been smooth sailing so far. (Nothing interfering with swift forward motion = nothing interfering with goal-directed actions)
• There’s no getting around it. You’ve got a lot of revising to do before the report is ready. (Obstacle = difficulty in accomplishing a goal)
• Chris has been in a rut. (Lack of ability to change direction = lack of ability to change goals and/or actions)

Languages the world over have this metaphor, which Lakoff and Johnson dubbed Life Is a Journey. The specific linguistic expressions used in each language are unique, as are broader social meanings around purposeful action. But the fact that the metaphor is so common around the world — quite possibly a linguistic universal — shows how fundamental the body is to how people think and talk.

Grady called this kind of correlation between sensory experience and subjective assessment “primary metaphor.” His research showed definitively that we can’t understand the mind without understanding the body. Grady brought metaphor down out of the ether and into the world of the body, providing a rigorous account of how exactly the body constrains and influences human thought and language — including even that most special, “high,” uniquely human faculty: reason.

Another early experience children have is of accumulating quantities of stuff and things. Milk goes from the carton to the glass, and the level goes up. The more blocks there are, the higher the tower is. A robust correlation forms between quantity and verticality: the more stuff there is, the higher it goes.

This correlation is so strong that we easily forget that it is metaphorical. In the introductory metaphor course at U.C. Berkeley, the More Is Up metaphor is one of the first examples given. Invariably a skeptical student will say something like this: “C’mon, this is isn’t a metaphor. Look at the stock chart in the newspaper. The line goes up and down for higher and lower prices. That’s it.” When asked why the line does what it does, the student goes silent, and then they see: the line does what it does because of the More Is Up metaphor. The line is an instance of the metaphor par excellence.

Verticality is associated with much more than just greater quantities. A lot of “good” things about verticality contrast with a lot of “bad” things about non-verticality. When people are vertical, we are alive, awake and functional. When we are non-vertical, we might be dead, asleep, sick or injured. Across all sorts of life forms and inanimate objects, vertical means functional and non-vertical means non-functional: animals, trees, buildings, and on and on. This creates a metaphorical mapping between verticality and positivity generally. Feeling “up” means feeling good; feeling “low” or “down” means feeling bad. Being in “top” shape means being healthy. Moving “up” the “career ladder” means gaining influence and autonomy. And so on.

Consider now the meaning of the following sentence: “It’s all downhill from here.” What does it mean? It has two very different meanings. We could paraphrase the sentence in two ways:

1. Starting now, everything gets worse.
2. Starting now, everything gets easier.

This simple English expression, in its ambiguity, makes a crucial point about metaphor: how we reason about the world depends on which set of metaphorical mappings is active at any given moment. One set of mappings is active in #1; a separate, almost opposite set of mappings is active in #2.[2]

As usual Otto does all of this simplifying for us behind the scenes. We’re completely unaware. He takes something abstract and more difficult to understand, and puts in simple, physical, sensory terms. It’s handy. But we need to know it’s another way Otto is constantly tricking us.

Last post I showed how prototypes are one way in which Otto simplifies the world for us. Metaphor is another of Otto’s tricks.

More than anyone else, linguist George Lakoff and philosopher Mark Johnson are responsible for revealing how metaphor pervades everyday thinking. For over 2,000 years metaphor was thought of as a fancy rhetorical flourish — a kind of linguistic window-dressing. In their 1980 classic, Metaphors We Live By, Lakoff and Johnson defined metaphor not in linguistic terms but in conceptual terms. And they showed how metaphor pervades “normal,” everyday experience.

Take the following set of statements:

Where is Pat’s life headed?

I’m worried that my new job will be a step backwards.

Her latest hurdle cleared, Kim felt she could finally move forward.

These examples took me about ten seconds to come up with, and we could easily keep going. It’s easy because there is a common metaphor that generates the statements. Lakoff and Johnson call the metaphor Life Is a Journey.

What does it mean to say that metaphor is conceptual rather than linguistic? What Lakoff and Johnson mean is that language is just one of many ways to express something that is happening at the conceptual level. We could, for instance, imagine pictures portraying each of the above statements. When we’re struggling with accomplishing our goals we might have dreams of obstacles blocking our path. And so on.

To get just a bit more technical, Lakoff and Johnson say that metaphor is a set of “conceptual mappings” between two “domains”: a source domain and a target domain. The source domain (in this case forward motion) provides the conceptual structure that we use for reasoning about the target domain (in this case accomplishing things in our lives).

Metaphor is one of Otto’s chief ways of simplifying the world for us. Just as we need prototypes, without metaphor the complexity of the world would overwhelm us.

As human society has become more intricate over the centuries, the need for metaphor has grown. There’s just so much more that needs to be simplified for us. Otto does this without us knowing. And, per usual, if Otto is running the show without Ralph’s awareness, problems can result.

In the mid-1990s in California, where I was attending graduate school, affirmative action was attracting a lot of legislative skepticism. As a general supporter of affirmative action, I was alarmed at how rhetorically challenging I was finding it to defend affirmative action. I did some research and discovered a gigantic metaphor that Otto had created.

Essentially, to Americans life is one big competition. Sometimes it’s a game, sometimes a sport or a race, but always a competition. From our youngest days we are taught, through games and sports, about “fair play,” “good sportsmanship,” and, above all, “playing by the rules.” It is good and right, even beautiful, to play hard, to sacrifice for our team, and to do our very best to win. It is also good and right to accept defeat with grace, and to understand that, though we desperately wanted to win, we are greater for playing by the rules and accepting the result, whatever it is.

In order for play to be meaningful, it must be fair. And in order for play to be fair, everyone has to play by the same rules. No exceptions. If you make an exception for even one player, a Pandora’s box of horrors awaits. The entire system becomes meaningless. Can you imagine if we let Johnny have four strikes instead of three, just because some committee decided that something about his life to that point had put him at a disadvantage?

At root this last question is how opponents feel about affirmative action. And they feel that way because the structure of the metaphor dictates it. Reasoning about affirmative action strictly in terms of sports inevitably leads to opposition to affirmative action.

In the technical terms of metaphor analysis, we say that the “inferential structure” of the source domain gets mapped onto the target domain. In other words, we reason about the target domain (school admissions, hiring, etc.) in terms of the source domain (sports). The source domain contains certain logical if-then statements, and all of these are used for reasoning in the target domain. In this case, the source domain follows this reasoning pattern:

1. There is a set of rules.
2. Each competitor knows the rules equally well, or at least has a responsibility to know the rules well.
3. The rules apply equally to all competitors.
4. We can objectively measure skill by numbers: the fastest time, or the most points, wins.
5. Given (1) – (4), it would be nonsensical and absolutely unfair to change the rules so that, for instance, a person or team could win by scoring fewer points.

When we import this structure into the target domain — let’s call it “public life” — the details change but the reasoning structure doesn’t:

1. There is a set of laws, or at least codified procedures, for admissions, hiring, etc.
2. Each citizen/applicant knows the rules equally well, which are spelled out on application forms, in accompanying booklets, or elsewhere.
3. The rules apply equally to all applicants.
4. We can objectively measure ability by numbers: grades and test scores.
5. Given (1) – (4), it would be nonsensical and absolutely unfair to change the rules so that, for instance, a person could win (i.e., be admitted or hired) with lower grades and test scores than the competition.

As a social scientist I was excited by these findings, because they seemed to explain my difficulties in debating affirmative action. As an affirmative action supporter, though, I was discouraged: The source domain logic is so tight, and the mapping is so natural in American culture, that affirmative action is extremely difficult to defend.

And it was now clear to me that it wasn’t difficult to defend because of any inherent flaw in the policy, but because the metaphor simplifies the world in a specific way. The metaphor has no room for the complexity of human society, such as: How do people learn “the rules”? What if some people have more access than others to this information? What about all the other factors in preparing people for school and for the workplace? And so on.

The metaphor can’t address these issues. The source domain just doesn’t have room.

Lest we blame poor Otto again, it helps to remember that we need to simplify in order to survive. Otto is doing the best he can. As always, Ralph being aware of Otto’s tricks is what gives us the best chance to consciously create the world we want.

Otto does so much work for us behind the scenes that we can scarcely imagine the complexity. It starts with moment-to-moment categorization of the world around us.

Categorization plays the vital role of simplifying an otherwise impossibly complex mass of sensory data. Whenever we perceive, we categorize. Every split second. We can’t help it. Categorization is the foundation of human cognition. Without the ability to simplify our environment into identifiable, individuated things, the world would appear to us as one big blur of light and sound and smell and taste and touch.

Categorization has been debated for over 2,000 years. Yet until recently it was mostly philosophers doing the debating. Only in the 1970s did scientists get seriously involved: psychologists began performing experiments that provided evidence of how human categorization actually works. These experiments led to an approach called “embodied realism,” which is a compromise between “objectivists” and “subjectivists”: yes, there is a world out there, but how we perceive it is a function of our brains and bodies. Categories don’t exist “in the world”; they are human inventions. And, crucially, they serve to simplify the world for us.

One set of experimental findings that rocked the study of categories to its core involves something called “prototypes.”

Prototypes are exemplars, or reference points — simplified conceptual anchors. When we see something new, we compare the new thing to these exemplars. If we see an object with four legs, a flat surface and a straight back, and it looks like a human could sit in it, we’ll call it a chair. We recognize the shape immediately, and we would all agree that it’s a chair. But what if a chair happened to have only three legs? Or no legs at all, as is the case with some types of modular furniture? What about beanbag chairs? Until Eleanor Rosch and colleagues discovered prototypes in the 1970s, no theorist could make a serious attempt at answering these questions.

Rosch and colleagues conducted dozens of rounds of studies asking subjects a variety of questions about categories and their members. They discovered what they called “prototype effects.” Take the category bird. Certain birds — especially robins and swallows — were rated “better” birds than, say, ostriches and penguins. Robins and swallows were listed first, recognized as birds first, explicitly rated as better examples of birds, and so on.

Strangest of all, even categories with crisp boundaries showed prototype effects. Take the category “even number”: 4 is judged to be a “better” even number than 8, 8 is better than 10, 10 is better than 34, and 34 is better than 106. How could this be?

It could only be true if categories are human inventions — specifically, simplifications carried out by Otto. The category judgments in the experiments were made under time pressure, when only Otto could operate. When asked explicitly, and able to draw on Ralph’s insights, subjects were clear that all even numbers are equally valid. Most cognition, though, is carried out by Otto, and we are at his mercy.

What can we expect for humanity when our lives are run by a lizard who thinks that 4 is a better even number than 106?

Most importantly for the human condition, prototypes can take on a sinister form: the stereotype. They are sinister for two reasons. First, they reduce entire groups, in all their complexity and diversity, to a single, fictitious, usually negative exemplar. This fundamentally limits our ability to appreciate diversity and uniqueness. Second, stereotypes, as products of Otto, do their work in the shadows. Each of us has countless stereotypes, and we reason and act based on these stereotypes, without even knowing that we’re doing it.

This is a real conundrum. On the one hand, the complexity of human cognition guarantees diversity: each of us holds a dizzyingly complex and unique set of truths, as does each culture. On the other hand, Otto is programmed to simplify this diversity into stereotypes. It’s no wonder people have trouble getting along.

Oliver Sacks has made a brilliant career of introducing readers to people who, because of abnormalities in their brains, perceive “reality” in ways that seem strange to “normal” people. In his book The Mind’s Eye, though, he becomes one of his own case studies: he developed melanoma in his right eye, and various surgeries and treatments left him with a large “scotoma”: a degenerated portion of his right eye’s field of vision.

Ever the unflappable observer, Dr. Sacks shares with us some fascinating observations about the blind spot / “filling in” phenomenon discussed in the previous blog post:

I knew that the normal blind spot, which we all have, where the optic nerve enters the eye, is automatically filled in, so we are unaware of its existence. But the normal blind spot is tiny, whereas my own scotoma was huge, blotting out more than half of the entire visual field of the right eye. And yet, within a second or two of looking at a white surface, it could completely fill in, becoming white instead of black. The next day I tested this with a blue sky and found the same result. The scotoma became as blue as the sky, but this time I had no need to plot its margins with my finger, for when a flock of birds flew by, they suddenly disappeared into my scotoma, emerging on the other side a few seconds later — as if they had been cloaked in invisibility like a Klingon warship.

This filling in, I discovered, was strictly local, depending on a steady fixation of gaze. If there was a slight movement of the eye, the filling in dissipated, and the ugly black amoeba was back. Local, but persistent, for if I looked at a red surface for a few minutes and then at a white wall, I would see a large red amoeba (or Australia) on the wall, which would last about ten seconds before it turned white.

The blind spot, so called, does not just fill in color, it fills in patterns too, and I enjoyed experimenting with my own scotoma, testing its powers and limitations. It was easy to fill in a simple repetitive pattern — I started with the carpet in my office — though a pattern took a bit longer than a color, perhaps needing ten or fifteen seconds to duplicate. It would fill in from the edges, like ice crystallizing on a pond.…

I started to think of my visual cortex not just as a rigid duplicating device, but as an averaging device, capable of sampling what was presented to it and making a statistically plausible (if not photographically accurate) representation of it. [1]

Sacks’s injury pulled back the curtain on his brain’s inner workings in a way that most of us hope we never experience. The image of the scotoma filling in “from the edges, like ice crystallizing on a pond” — is extraordinary. You can almost feel the brain straining to create some kind of coherence in Sacks’s visual world. In the end, though, it’s complete and utter fiction.

In the same book Sacks also tells of a man named Howard Engle, who, one normal-seeming morning, went to fetch his newspaper:

The July 31, 2001, Globe and Mail looked the way it always did in its make-up, pictures, assorted headlines and smaller captions. The only difference was that I could no longer read what they said. The letters, I could tell, were the familiar twenty-six I had grown up with. Only now, when I brought them into focus, they looked like Cyrillic one moment and Korean the next. Was this a Serbo-Croatian version of the Globe, made for export?…Was I the victim of a practical joke? I have friends who are capable of such things….I wondered what I might do to them that would improve on this piece of foolery. Then, I considered the alternative possibility. I checked the Globe’s inside pages to see if they looked as strange as the front page. I checked the want ads and the comics. I couldn’t read them either….

Panic should have hit me like the proverbial ton of bricks. But instead I was suffused with a reasonable, business-as-usual calm. “Since this isn’t somebody’s idea of a joke, then, it follows, I have suffered a stroke.” [2]

Indeed he had suffered a stroke, a minor one, in a part of the brain that handles vision. A few other parts of his world were a bit out of whack as well — he had some trouble recalling the names of everyday objects, and some difficulty recognizing colors and faces — but most everything else was normal. And maybe strangest of all, he had no trouble with writing: he could write as fluidly as ever. He couldn’t, though, read what he had written.

What makes the case of Howard Engel so fascinating is its subtlety. If a major brain injury causes big vision problems, that’s not surprising: if you do massive damage to the brain, of course you won’t be able to see properly. In the case of Mr. Engel, though, “the world” is still so obviously “out there” — and yet it can’t be, for why else would this one little piece of “the world” be so…off? Why would almost everything look normal except for letters? Somehow the “off-ness” of this one small portion of vision makes us question how “real” everything else is.

The fact that vision is affected makes it even more unsettling. We rely more on vision than on any other sense for our feeling that the world is real. Yet Howard Engle’s case forces us to ask: Can I trust what I see?

“Seeing is believing” is one of our deepest articles of faith. It is, though, faith, and it’s not supported by science.

Neuroscientist David Eagleman describes how most of us think of perception:

Intuition suggests that you open your eyes and voilà: there’s the world, with all its beautiful reds and golds, dogs and taxicabs, bustling cities and floriferous landscapes. Vision appears effortless and, with minor exceptions, accurate. There is little important difference, it might seem, between your eyes and a high-resolution digital video camera. For that matter, your ears seem like compact microphones that accurately record the sounds of the world, and your fingertips appear to detect the three-dimensional shape of objects in the outside world. What intuition suggests is dead wrong.[1]

If we think of our eyes as video cameras, then logically we would expect that light hits our retinas, and that the retinas pass on this information to the rest of the brain for processing. In their classic book The Tree of Knowledge, Humberto Maturana and Francisco Varela explain that this is not how vision works in the brain: they estimate that only 20% of what we see comes from information passed along by the retinas. The key part of the brain here is the lateral geniculate nucleus, or LGN. Maturana and Varela write:

This nucleus is the most prominent region of connections between the retina and the central nervous system.…As is clear, the retina does not affect the brain like a telephone line that encounters a relay station at the LGN, since more than 80 percent of the interconnections come together at the LGN at the same time. Consequently, the retina can modulate — but not specify — the state of the neurons in the geniculate nucleus, whose state will be given by all the connections it receives from many different parts of the brain.[2]

In other words: your brain is inventing 80% of what you see — just making it up, based on what it already believes to be true about the world.

Take a look at the figure below, which is similar to an example given by Maturana and Varela (p. 20). Position your face about 12 inches from the screen. Now, while keeping your left eye closed and your right eye fixed on the plus sign, slowly — very slowly — move your face closer to the screen. As your face moves, keep your right eye laser-focused on the plus sign. Don’t waver. You’ll see that at one point the image to the right just…disappears. Keep moving closer and it appears again. What happened?

David Eagleman, who also uses this example in Incognito, explains:

How could brilliant minds like Michelangelo, Shakespeare, and Galileo have lived and died without ever detecting this basic fact of vision? One reason is because there are two eyes and the blind spots are in different, nonoverlapping locations; this means that with both eyes open you have full coverage of the scene. But more significantly, no one had noticed because the brain “fills in” the missing information from the blind spot. Notice what you see in the location of the dot when it’s in your blind spot. When the dot disappears, you do not perceive a hole of whiteness or blackness in its place; instead your brain invents a patch of the background pattern. Your brain, with no information from that particular spot in visual space, fills in with the patterns around it.[3]

In fact, the sense that the dot has disappeared could only result from the brain filling in the background pattern: “disappearing” means the same thing as “looking exactly the same as the background.”

I invite you to do this a few times. Try keeping the face invisible for as long as you can. Remember to stay focused on the plus sign. As you stare at the lonely plus sign, think about what’s going on. You know the face is right there, waiting to be seen. Can you feel it taunting you? Resist the temptation to shift your gaze. Keep focusing and contemplating. What is going on here? You just saw it. Why can’t you see it? And how did that background pattern sneak into its place?

Next, flick your right eye’s gaze to the face. There it is! Then, flick back. Gone again. Do this a few times.

It’s such a simple little experiment, yet it offers a profound opportunity to start to get, in a meaningful way, what a gigantic, fantastic illusion our brains and bodies have created for us.

Building on this interview the gritty startup ATLAS did with me several months ago, they recently interviewed me again as part of the “meet the board” series. You can link to it here or read the full text below.

Meet the Board: Jason Patent

Dr. Jason Patent, American Co-Director of the Hopkins-Nanjing Center, has forged his own path to the forefront of the conversation about international China education.  Jason’s pioneering work in intercultural training over the past two decades makes him uniquely qualified to identify the areas in which cross-culturally competent professionals can contribute to companies’ success internationally.

Jason’s current role at the HNC puts him at the intersection of the classroom and the workforce.  Read on for his advice on how to get the best out of both:

In your China career you’ve been a business consultant, educator, and author. Is there a unifying theme that you can draw out of your diverse experience?

What unifies all these experiences is a commitment to understanding, both ourselves and those who are different from us. If you look at the state of humanity, it’s not pretty. Despite all the technological advances that have the potential to connect us, we’re still killing one another.

Decades of findings in psychology, linguistics and neuroscience have shown that almost all of what we believe has been programmed into us by our perceptual systems, languages and cultures. We’re not rational beings, despite what our minds may tell us. If we want a better future for the species we have to start by looking at our unconscious assumptions. Only then can we choose what to keep and what to reexamine.

Could you say a little bit about your vision for the Hopkins-Nanjing Center as it prepares students to get meaningfully engaged in building the US-China relationship?

I see HNC headed in a more global direction, so that it’s about more than the U.S. and China. What would the Center look like if we had, say, a few students from Japan each year? From India? From Russia? The list goes on.

Also, with the addition of a full-time career services professional to our Nanjing staff, we’re in a great position to help our students find careers where their talents are maximally leveraged. When combined with our intensified efforts to build an active community of alumni, we’re putting in place an infrastructure for our graduates to have the maximum possible impact on the world using the utterly unique skill set they’ve built at the HNC.

What are the most important skills and attitudes that you encourage international students at the HNC to acquire?

It’s the same for both international and Chinese students, and relates to question #1: be skeptical of your own truths and be open to other truths.

What roles do you see international HNC graduates playing in China business?

Translated into the business world, the seemingly high-minded ideas I’ve been talking about translate into efficiency and endurance: HNC grads, armed with these skills, will help businesses operate with lower costs in the short and long term, and with smoother cooperation with Chinese partners. Things will move more quickly, and turnover will go down. This builds strengths for long-term success.

Where do you see the most room for improvement in the way international students are educated about China?

The sorts of skills I’ve been talking about building — doggedly questioning our own truths and laying the groundwork for other truths — are best learned in a structured environment, with skilled facilitators, over the course of months and years. I’m teaching a course at HNC that helps build these skills, but there is still a structural problem that the world at large views these issues as “soft” and peripheral, rather than as the most hardcore learning issues there are. More courses on China should begin with questioning ourselves, rather than with treating “China,” whatever we take China to be, as “out there,” as something independent of our perceptions and biases.

How do you advise HNC students and other young professionals developing China-focused careers?

Two things. First, I tell them they need to do the work of translating their skill set into something a hiring manager can understand. “Cross-cultural” and “bilingual” just don’t cut it. What do these skills mean for any given job description?

Second, I urge students to get whatever experience they can working in an actual company. Future employers will want to know what specific experience students have had in this or that industry and function. Knowledge of China and Chinese by itself is not that valuable in the eyes of most companies. It has to be supplemented with actual experience.

Why did you join ATLAS’ Board of Advisors?

ATLAS is on the cutting edge of China business and of global business. They are actively demonstrating, and advocating for, the value of the sort of talent developed at HNC. They are doing the hard work of translating the abstract “language” and “culture” skills into terms that matter for companies. As ATLAS grows and becomes more successful, there will be more and more happy companies who owe their success to these types of talented people. More and more people and organizations will begin to see how crucial these once-“soft” skills are to success.

The ultimate result is more global interconnection and more understanding, which is good for humanity.

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To share in more of Jason’s insights, follow his active personal blog at Jasonpatent.com.  I would also encourage anyone who likes what they hear to check out the Hopkins-Nanjing Center, a unique graduate program.  Thanks for reading and stay tuned for the next post in the series soon. In the meantime, please register online with ATLAS-China to receive updates on exclusive job listings and new career development resources.