Making a lemon battery is the staple of middle school science activities. The experiment involves jamming two dissimilar metals into a lemon; copper and zinc are the usual picks. If you connect a voltmeter to the electrodes, it should read about 1 V. String two or three lemons in series and you can even light up a small LED.

The chemistry of the lemon cell appears simple, up to a point. Lemon juice is essentially a 5% solution of citric acid in water. Water is a small and strongly polar molecule, so it can cleave the ionic bonds of many substances that were formed by the exchange of electrons and that are held together by the resulting electrostatic field.

This process — known as dissociation — produces electrically-charged halves that lead independent lives in the solution, but revert back to complete molecules once the solvent is removed. In the case of citric acid, we end up with some modest number of positively-charged hydronium cations and negatively-charged citrate anions floating around.

Dude, where’s my hydrogen?

Past this point, introductory texts get hand-wavy. Many metals react with acids in a redox reaction. Conceptually, the reaction involves hydronium ions snagging electrons from the metal and then turning into hydrogen gas; in parallel, electron-deficient atoms of metal turn into positive ions. The high-school explanation is that the hydronium ion “want” the electron more, and when they come across each other in a dark alley, the metal doesn’t put up a fight.

Phrased this way, it’s an electrically-neutral exchange, so it doesn’t quite explain the generation of electricity. Just as important, the story doesn’t add up for zinc in dilute citric acid: the metal starts dissolving into Zn²⁺ cations at an appreciable rate only after an electrical connection is made. Even more confusingly, when the electrodes are connected together, the bulk of the hydrogen is evolving on the copper electrode, not on the zinc one.

In other words, it appears that zinc atoms are spontaneously falling off the electrode, leaving two electrons behind; there are no hydronium ions nearby holding a knife to their throats. After that, the electrons start moving toward the copper electrode, where the reduction of the hydronium ion occurs. Why?

The first half of the answer is that is the reduction of the hydronium ion doesn’t happen easily on the surface of zinc. The actual reaction is a multi-step process that involves atomic hydrogen absorbing into the metal; zinc is a poor substrate for that. In electrochemistry, we have the concept of overpotential — the excess voltage that would need to be applied to carry out the reaction, compared to what’s predicted by simple thermodynamics. The bottom line is that the reduction to atomic hydrogen can proceed at lower voltages on the copper side.

The crooked equilibrium

A more fundamental question is why do these reactions start happening in the first place. Electrostatic fields are quite powerful; why would an atom ever part with its electrons if it’s not being persuaded to do? Doesn’t that add energy to the system? Why zinc and not copper? How can mirrors be real if our eyes aren't real?!

All good questions! If you’re familiar with electronics, a good analogy might be the p-n junction in semiconductors. If you’re new to the concept, I recommend starting with this article. Otherwise, in brief: we start by manufacturing an “n-type” material that has some energetic, mobile electrons in a high-energy conduction band. We bring it in contact with a “p-type” material, where electrons occupy a lower-energy valence band, and where there are some available vacancies (holes) in that band.

Both of the materials are electrically-neutral, but when we bring them together, something interesting happens: a number of the higher-energy electrons from the n-side falls into the lower-energy vacancies on the p-side. This is somewhat akin to a billiard ball falling into a pocket. The result is a region with an unbalanced distribution of charges and a built-in electrostatic field:

The effect is self-limiting: eventually, the field grows strong enough that the net inflow of electrons must stop. But the bottom line is that despite the presence of a field, the situation at the junction is a lower-energy state. If you connect a voltmeter across, it will read zero volts: there are no electrons trying to go back where they used to be.

Semiconductor junctions are not special. Quantum-mechanical properties of molecules and crystal lattices often result in energetically-favorable spots that can be taken up by electrons “belonging” to some other substance. This usually doesn’t result in macroscopic voltages or currents because of the self-limiting nature of the process. That said, in the case of batteries, lower-energy products are continuously removed (as gas or ions), and higher-energy reagents are continuously exposed. This continues until the entire electrode or the electrolyte is spent.

In fact, a migration of charges happens if you simply bring together two dissimilar metals; no electrolyte is needed at all. The resulting field — known as the Volta potential — can be measured in a vacuum with sufficiently precise instruments. The importance of this field in guiding electrochemical reactions is apparently not a settled matter in battery science. Some think it’s the key factor; others arrive at similar results from more abstract principles.

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There is something unique about the color purple: Our brain makes it up. So you might just call purple a pigment of our imagination.

It’s also a fascinating example of how the brain creates something beautiful when faced with a systems error.

To understand where purple comes from, we need to know how our eyes and brain work together to perceive color. And that all begins with light.

Light is another term for electromagnetic radiation. Most comes from the sun and travels to Earth in waves. There are many different types of light, which scientists group based on the lengths of those waves. (The wavelength is the distance between one wave peak and the next.) Together, all of those wavelengths make up the electromagnetic spectrum.

Our eyes can’t see most wavelengths, such as the microwaves used to cook food or the ultraviolet light that can burn our skin when we don’t wear sunscreen. We can directly see only a teeny, tiny sliver of the spectrum — just 0.0035 percent! This slice is known as the visible-light spectrum. It spans wavelengths between roughly 350 and 700 nanometers.

The acronym ROYGBIV (pronounced Roy-gee-biv) can be used to remember the order of colors in that visible spectrum: red, orange, yellow, green, blue, indigo and violet. You can see these colors in a rainbow stretching across the sky after a rainstorm or when light shines through a prism. In the visible spectrum, red light has the longest wavelength. Blue and violet are the shortest. Green and yellow sit toward the middle.

Although violet is in the visible spectrum, purple is not. Indeed, violet and purple are not the same color. They look similar, but the way our brain perceives them is very different.

How we see color

Color perception starts in our eyes. The backs of our eyes contain light-sensitive cells called cones. Most people have three types. They’re sometimes called red, green and blue cones because each is most sensitive to one of those colors.

But cones don’t “see” color, notes Zab Johnson. Instead, they detect certain wavelengths of light.

Johnson works at the University of Pennsylvania in Philadelphia. She and other scientists who study how we perceive color prefer to classify cones based on the range of wavelengths they detect: long, mid or short.

So-called red cones detect long wavelengths of light. Green cones respond most strongly to light in the middle of the visible spectrum. Blue cones best detect wavelengths toward the shorter end of the visible spectrum.

When light enters our eyes, the specific combination of cones it activates is like a code. Our brain deciphers that code and then translates it into a color.

Consider light that stimulates long- and mid-wavelength cones but few, if any, short-wavelength cones. Our brain interprets this as orange. When light triggers mostly short-wavelength cones, we see blue or violet. A combination of mid- and short-wavelength cones looks green. Any color within the visible rainbow can be created by a single wavelength of light stimulating a specific combination of cones.

Notice that the visible spectrum is a gradient. One color gradually shifts into the next. The activity of cones activated by the light also gradually shifts from one type to the next. At the red end of the spectrum, for instance, long-wavelength cones do most of the work. As you move from red to orange, the mid-wavelength cones help more and the long-wavelength cones do less.

In the middle of the rainbow — colors like green and yellow — the mid-wavelength cones are busiest, with help from both long- and short-wavelength cones. At the blue end of the spectrum, short-wavelength cones do most of the work.

But there is no color on the spectrum that’s created by combining long- and short-wavelength cones.

So where does purple come from?

This makes purple a puzzle.

Purple is a mix of red (long) and blue (short) wavelengths. Seeing something that’s purple, such as eggplants or lilacs, stimulates both short- and long-wavelength cones. This confuses the brain. If long-wavelength cones are excited, the color should be red or near to that. If short-wavelength cones are excited, the color should be near to blue.

The problem: Those colors are on opposite ends of the spectrum. How can a color be close to both ends at once?

To cope, the brain improvises. It takes the visible spectrum — usually a straight line — and bends it into a circle. This puts blue and red next to each other.

“Blue and red should be on opposite ends of that linear scale,” Johnson explains. “Yet at some point, blue and red start to come together. And that coming-together point is called purple.”

Our brain now remodels the visible spectrum into a color wheel and pops in a palette of purples — which don’t exist — as a solution to why it’s receiving information from opposite ends of the visible spectrum.

Colors that are part of the visible spectrum are known as spectral colors. It only takes one wavelength of light for our brain to perceive shades of each color. Purple, however, is a nonspectral color. That means it’s made of two wavelengths of light (one long and one short).

This is the difference between violet and purple. Violet is a spectral color — part of the visible spectrum. Purple is a nonspectral color that the brain creates to make sense of confusing information.

Purple thus arises from a unique quirk of how we process light. And it’s a beautiful example of how our brains respond when faced with something out of the norm. But it’s not the only color that deserves our admiration, says Anya Hurlbert.

“All colors are made up by the brain. Full stop,” says this visual scientist at Newcastle University in England. They’re our brain’s way of interpreting signals from our eyes. And they add so much meaning to things we perceive, she says.

“The color of a bruise tells me how old it is. The color of a fruit tells me how ripe it is. The color of a piece of fabric tells me whether it’s been washed many times or it’s fresh off the factory line,” she says. “There’s almost nothing else that starts with something so simple [like a wavelength of light] and ends with something so deep and rich.”

Every semester, college students are given the chance to evaluate their professors. Their evaluations, like ratings of workers in other fields, show persistent gender gaps. The underlying biases are not easily defeated, but research by management scholars Lauren Rivera and András Tilcsik finds that there is a startlingly simple way to reduce inequality in evaluation systems: change the top rating from ten to six.

Rivera and Tilcsik’s findings draw on two sets of data. When one large university professional school changed its top rating from ten to six, it set up a quasi-natural experiment, allowing the researchers to draw on 105,034 student ratings of 369 different instructors from before and after the change. Additionally, to establish how much of the gender inequality in evaluations came from bias as opposed to gendered differences in teaching effectiveness, they administered a survey showing students identical course transcripts but randomly varied the gender attributed to the instructor and the number of choices in the rating system.

The results were striking. When the real-life university evaluations used a ten-point scale, women teaching in the most male-dominated fields were significantly less likely than men to get the highest rating on the scale. Their average ratings were half a point lower than men. On a six-point scale, “differences largely disappeared,” they write.

Rivera and Tilcsik note that this is partly because more options allow for more subtle distinctions, but they also argue that the shift goes beyond that. The “perfect 10” has a deeper cultural resonance and is associated with qualities like brilliance—qualities that are more often attributed to men.

The survey supports this argument. In addition to that gender gap of about two-thirds of a point on a ten-point scale almost disappearing on the six-point scale, a shift was also detected in qualitative data. When the participants responded to the transcripts, they were significantly more likely to use words like “brilliant,” “genius,” and “perfect” when they believed the lecture to have been delivered by a man. Finally, when asked specifically if they agreed that the instructor was brilliant, participants were significantly more likely to strongly agree if they believed the instructor to be a man.

Taken together, the two data sources show that a move from a ten-point scale to a six-point one can reduce the gender gap in performance evaluations even as underlying biases, as revealed by qualitative descriptions, remain. The use of random gender attribution for the survey experiment, meanwhile, shows that bias is verifiably a factor in gender gaps.

Numerical evaluations are often used to validate the existence of a pure meritocracy, in which people are judged by the quality of their work rather than their identities. However, Rivera and Tilcsik write, “Evaluative tools are not neutral instruments: their precise design—even factors as seemingly small as the number of categories available in a performance rating system—can have major effects on how female and male workers are evaluated.”

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A few days ago, an 18-year-old by the name of Zach Yadegari publicly shared his impressive accomplishments—and the disappointing outcome of his attempt to get into an elite college. Zach had a GPA of 4.0. He had a score of 34 (out of 36) on the ACT, a standardized test applicants sometimes take in lieu of the SAT. Perhaps most impressively, he is an accomplished coder who has built a genuinely successful business: an app that allows users to count calories by submitting photographs of their food, and which he claims already earns $30 million in annual recurring revenue.

Despite this impressive record, most schools weren’t interested in Zach. According to his post, he was roundly rejected by every Ivy League school (except for Dartmouth, to which he didn’t apply). Nor did he fare any better at other top colleges, such as MIT and Stanford. Even some comparatively less selective schools such as UVA and Washington University did not take any interest in him.

At first, the ensuing debate on social media focused on the disadvantages many impressive white and Asian applicants face in college admissions. After all, an anonymous hacker had recently published the latest admissions data from NYU, another school that rejected Zach, and the leak strongly suggested that many American universities are effectively defying a recent Supreme Court order to end affirmative action. The average test scores for white students admitted to NYU are lower than Zach’s; but the average test scores for Hispanic and especially black students admitted to NYU are far lower. This leaked data suggests that Zach would have been highly likely to gain admission to NYU—and perhaps many of the other schools he applied to—if he wasn’t white.

Then someone on X asked Zach to share his admissions essay, and the conversation quickly took a turn. As soon as he did, dozens or hundreds of large accounts explained to him—some in a paternalistic, others in a sneering tone—why his essay likely tanked his application. The essay was undone by “a general sense of fakeness,” one social media account with a big following judged. “For every student with perfect scores like Zach, there’s a student with near perfect scores and more humility who’s overcome terrible circumstances and does not seem entitled,” a condescending professor tweeted. “Whenever people complain about not getting in despite good grades/scores the essay is almost always garbage,” a former admissions director concluded.

And that gave me a long-awaited opportunity to pen a rant I had been saving up for a rainy day. For every aspect of this saga, from the fact that a misguided admissions essay really may have tanked Zach’s chances for admission to the way in which commentators across the political spectrum accept this exercise as a natural part of the selection process, reminds me of one of the most pernicious aspects of higher education in America.

The college essay is a deeply unfair way to select students for top colleges, one that is much more biased against the poor than standardized tests. The college essay wrongly encourages students to cast themselves as victims, to exaggerate the adversity they’ve faced, and to turn genuinely upsetting experiences into the focal point of their self-understanding. The college essay, dear reader, should be banned and banished and burned to the ground.

There are many tangible, “objective” reasons to oppose making personal statements a key part of the admissions process. Perhaps the most obvious is that they have always been the easiest part of the system to game. While rich parents can hire SAT tutors they can’t sit the standardized test in the stead of their offspring; they can, however, easily write the admissions essay for their kid or hire a “college consultant” who “works with” the applicant to “improve” that essay.

Even if rich parents don’t cheat in those ways, their class position gives rich kids a huge advantage in the exercise. As the responses to Zach’s essay show, writing a good admissions essay is to a large extent an exercise in demonstrating one’s good taste—and the ability to do so has always depended on being fluent in the unspoken norms of an elite community. Legions of commentators scolded Zach for such sins as touting his accomplishments too aggressively or sounding too much like other applicants. But like avoiding the fate of the ambitious Asian immigrant parents who encourage their child to excel at the piano, only for her to be reduced to a file dismissively set aside by an admissions officer who sneers at “yet another nerdy Asian kid who plays the piano,” the ability to highlight your accomplishments in an appropriately roundabout way depends on cultural knowledge. If you come from a background in which your parents and grandparents went to college and many family friends have recently gone through the Kafkaesque process of gaining admission to an elite institution and you are friends with a person or two who teaches at such a university, then you obviously have a giant advantage.

This is all borne out by the data. Many on the left oppose standardized tests on the grounds that they have a class bias, and that hiring a tutor can make you perform better at them. But studies on the subject consistently suggest that the class bias of personal essays is far stronger than the class bias of standardized tests; notably, standardized tests can, as Rob Henderson movingly recounts in his memoir, show that kids from disadvantaged backgrounds have hidden talents to a far greater extent than college essays.

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But the thing I truly hate about the college essay is not that it is part of a system that keeps deserving kids out of top colleges while rewarding privileged kids who (to add insult to injury) get to flatter themselves that they have been selected for showcasing such superior personality in their 750-word statements composed by their college consultant or ghostwritten by ChatGPT. In the end, truly talented kids like Zach are going to be just fine; he’ll still have plenty of educational opportunities at the less prestigious schools to which he was admitted, or he can keep pursuing a career in Silicon Valley without a college degree. Rather, what I truly hate about the college essay is the way in which it shapes the lives of high school students and encourages the whole elite stratum of society—including some of its most affluent, privileged and sheltered members—to conceive of themselves in terms of the hardships they have supposedly suffered.

For obvious reasons, this is especially true for members of ethnic minority groups. A big proportion of black students admitted to the most elite colleges in America are the children or grandchildren of relatively recent immigrants from countries such as Kenya and Nigeria, many of them doctors or other professionals from elite families who came to America on H-1B visas; many of the rest come from families that have been middle- or upper-middle class for multiple generations. This suggests a mismatch between the most intuitive moral justification for the affirmative action policies which colleges like NYU are evidently continuing to pursue (to provide some form of reparation for the grave ill of slavery) and the actual beneficiaries of these practices (who rarely include those from communities like Central L.A. or the South Side of Chicago, whose lives remain most obviously shaped by such historical injustices). Whatever this mismatch may imply about the moral status of affirmative action, it is the bizarre spectacle of those kids from comparatively privileged backgrounds being effectively coerced by the admissions system to self-exoticize as products of great hardship which I find to be truly unseemly.

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But this game is by no means restricted to applicants from minority groups. The true art—the highest display of “good taste”—consists in transforming an applicant who is “privileged” in every dimension, including the ones particularly salient to admissions officers steeped in identity politics, into the kind of unique individual who appears to have triumphed over great adversity. Perhaps the best example of the genre I can think of is an acquaintance from college who won a prestigious fellowship to study in America based on a sob story about having his house bombed during the “troubles” in Northern Ireland; his essay left unstated that he had spent his high school years at Eton College, and that said house was one of the family’s many estates.

It’s bad enough that jostling for membership in the elite now requires ambitious Americans to turn themselves into essay-length avatars demonstrating their good taste or showcasing their resilience or performatively celebrating their quirkiness. It is worse that the prospect of having to do so now helps to shape how they spend their teenage years.

The truly ambitious kid doesn’t just sit down at the age of 16 or 17 to reflect about what element of their lives they can highlight to reveal their personality; they begin, at the age of 14 or 12 or even earlier, to lead their lives with an eye to preparing the ground for the perfect college application. (Or, worse, their parents do so for them.) This leads to all the cynical activities which pretend to showcase some intrinsic motivation but are actually covert exercises in getting ahead—witness the countless “nonprofits” now started by high schoolers on a mission to get into Yale.

The British philosopher Bernard Williams once complained that the utilitarian justification for why a man might choose to save his drowning wife rather than three similarly imperilled strangers would require him to have “one thought too many.” On the face of it, Williams pointed out, the utilitarian emphasis on maximizing the balance of happiness over pain would seem to suggest that he has to save the strangers. Utilitarian philosophers may be able to avoid this counterintuitive conclusion, for example by claiming that over the long run the balance of happiness over pain would improve if we give people some leeway to act on their special attachments. But even that, Williams insisted, wouldn’t capture the real reason why the man would and should want to save his wife: that he loves her, has vowed to protect her, and must place her interests over those of others.

Something similar holds true for the manner in which the self-marketization of college applicants transforms their attitude towards the world. Many teenagers no doubt genuinely enjoy sports or playing the violin or participating in the math Olympiad or helping little old ladies cross the street. But the admissions system makes it impossible for them not to pursue those activities with one eye to their future advancement. The central role the college essay plays in admissions forces even genuine and well-meaning kids to have “one thought too many” as they go about activities they might otherwise undertake for the pure pleasure of it. It is the first of many steps in shaping a social elite that is willing to put its own advancement ahead of any authentic engagement with the world—a social elite that has proven to be so unpopular and dysfunctional in part because those over whom it reigns smell its inauthenticity from a mile away.

And this is why I suspect that the seemingly innocuous institution of the college essay is more deeply damaging—to the high school experience, to the self-conception of millions of Americans, and even to the country’s ability to sustain a trusted elite—than it appears. The fundamental problem with it isn’t that it arbitrarily excludes some highly talented individuals like Zach from positions of power and privilege; it’s that it drains the souls of teenagers and encourages a deeply pernicious brand of fakery and breeds widespread mistrust in social elites.

The college essay is absurd and unfair and—ironically—unforgivably cringe. It’s time to put an end to its strange hold over American society, and liberate us all from its tyranny.

• Mouseover a puck to select it
• Click in a direction to slide
• Pucks stop at walls or other pucks
• Get the matching puck to the colored X
• This game is obviously inspired by Ricochet Robots which is the best nerd party game that you should buy a copy of immediately