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Color is a mathematical nightmare

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Breaking down the confusing world of color spaces.

The best method that we have for defining color is by using math. Specifically, mind-boggling mathematical models called color spaces that use geometry to assign colors as a fixed point that we can reference, ensuring the blue that I see is the same blue you see. As a creative-leaning person who can barely split a bill without a calculator app, all that math is extremely daunting.

The good news is that computing software will do all these complicated calculations for us, allowing us to rely on our eyeballs to pick whatever colors look best. The bad news is that there’s an equally daunting number of color spaces to choose from, and they’re all optimized for different tasks across web design, photography, video editing, physical printing, and more. And if you select the wrong one at any point between creating, editing, and viewing something, it can really mess with what colors are supposed to look like.

It’s a lot to absorb. Thankfully, most of us will only ever need to understand the basics, and that knowledge can be useful to everyone — not just creative professionals. Learning about it can help you buy your next phone, TV, laptop, or computer monitor, and get the most o …

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Your Phone Should Be Distributed, Not Centralized

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This is something that I realized this week after leaving for work but having to turn back because I forgot my phone. That phone hosts an app containing my train tickets: without it, I wouldn’t be able to commute to work—unless we do it the YOLO way, of course. I despise apps and have expressed my dislike for them at many occasions here on Brain Baking (see for example Smartphone Pervasiveness). Registering an account took 10 attempts and 3 browsers.

But we’re not here to diss on one particular app, but on the very dangerous services centralization movement. That same software as a (centralized cloud) service movement that we as privacy-aware tech nerds do identify as a real threat. As a response, we search and find alternative software that doesn’t rely on just one Silicon Valley tech giant, we self-host software, we turn to distributed social media services backed by ActivityPub. And by “we” I mean the 1% that is technically capable to do so and that cares enough to do it.

Yet it seems that we forget to critically evaluate that thing we carry with us all the time (and is connected to god-knows-what all the time): our phone. Ads happily announce yet another handy new app that provides convenience for the end user, having “everything in one place”. Well, I’m here to tell you that having everything in one place is a bug, not a feature. Instead, I think we should aim to distribute, not centralize.

I don’t want to be dependent on my phone to:

  • Buy groceries in the supermarket as a credit card replacement;
  • Store and validate train tickets as a railway subscription card replacement;
  • Receive & reply to emails, read news, use a spreadsheet editor, … as a computer replacement;
  • Play games as a dedicated handheld gaming replacement;
  • Scan QR codes and have to surf the web just to be able to read what’s on the menu as a proper printed restaurant menu replacement;
  • Read & write notes as a pen & paper/notebook replacement;
  • Read eBooks as a book replacement;
  • Identify myself using an app that gobbles up my data as a identity card replacement that suddenly drops off the radar two years later only to then have to repeat this procedure with another shady vendor;
  • Take mindless snapshots instead of real photos as a dedicated camera replacement;

The more dependent we become on this one device, the worse it becomes: big tech bros will love having more access to our data, and decision makers will find even more creative ways to have “everything in one place”. Speaking of data, I have never encountered a service that is fully transparent as to (1) what data is exactly used for what, (2) where it is stored, and (3) how they secure and eventually delete it.

The worst thing, however, is that I fear it is too late to stop this. That 1% critical mass like this rant here is not going to change anything. We can urge people to be more mindful when it comes to phone and services-on-phone usage, but we cannot turn the tide thanks to, among many other factors, the way capitalism seems to work. Judging from the way most people use their phone, it seems that either they don’t care or they’re in too deep.

Even the critical-minded folks will have gradually less and less options to bow out. The particular kind of flexible train ride subscription I wanted was for some unknown reason “only available using the app”. There was no way around it: more and more I am being forced to centralize services on my phone. And I fucking hate it.

Opening up a professional bank account was a nightmare because I was running a phone without Google Play Services. The bank employees were flabbergasted and had “never experienced this kind of failure” when attempting to create an account. Previously, this could be done with just a few clicks with their software and a few print-outs of various forms. Now, it requires a smartphone and their dedicated app on the client’s phone to sign the paperworks. The fallback in case that doesn’t work simply was scratched. When I ask them how they handle opening up accounts for older people without smartphone knowledge, they simply replied “old people don’t open professional accounts sir”. Are you kidding me?

They were not. So now I am a very unsatisfied customer who still found a loophole and it’s just a matter of time before that’s closed too and I’m out of options to decentralize my own stuff.

So what can we do to help combat this centralization movement?

  • Complain! If there would be enough people with “broken phones”, the bank institution would have no choice but to provide alternatives. But it seems that I was the only curious case they’ve had in years. I also complain when restaurants are too lazy to print their menus: I don’t want to bring a smartphone to a social dinner, and I certainly don’t want to pay for the internet connection just to download a .PDF. This is called off-loading costs and you won’t see me there ever again.
  • Be mindful! Ask and look for alternatives. Don’t just mindlessly install that app.
  • Distribute the services you can. Don’t connect your email to your smartphone. Buy a book or dedicated e-reader. If you’re into gaming, get yourself a retro gaming portable.
  • Disable as much as you can. Don’t rely on NFC to pay.

This is very obvious but deservers to be mentioned time and time again: get rid of your Google account. Find other ways to host your photos and contact information. I know this sounds easy but in practice can be a real pain, especially if you’re not very technical. And that is exactly why all this makes me very mad: if I as dabbler in technical things can’t even get all this done, then how are we supposed to protect everyone else who also deserve privacy and security?

Related topics: / phone /

By Wouter Groeneveld on 6 April 2025.  Reply via email.

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Why do lemon batteries work?

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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.

A scientific diagram of the experiment. By author.

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:

A basic illustration of a p-n junction.

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.


I write well-researched, original articles about geek culture, electronic circuit design, and more. If you like the content, please subscribe. It’s increasingly difficult to stay in touch with readers via social media; my typical post on X is shown to less than 5% of my followers and gets a ~0.2% clickthrough rate.

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The 7 writing apps I used to start and finish my book

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There’s a famous two-decade-old Paris Review interview with Haruki Murakami in which he, one of the world’s most celebrated novelists, details his daily routine. He wakes up at 4AM, works for five hours, goes for a run, reads, goes to bed, and then repeats it all over again. The rigor and repetition are the point.

I am not Haruki Murakami.

In addition to my work at The Verge, I write novels — my second one is out today — and while I admire Murakami’s commitment to an immovable schedule, I’ve found that I produce my best work when I’m constantly rethinking routines, processes, and, mostly, how I’m writing. In the modern age, that means what software I’m using.

What I am about to describe will be a nightmare to anyone who likes all of their tools to work harmoniously. All of these apps are disconnected and do not interoperate with each other in any way. Many of the things they do are redundant and overlap. I suppose this process is quite the opposite of frictionless — but that’s precisely the point. I’m not sure I believe that ambitious creative work is borne from a perfectly efficient workflow.

This is, instead, a journey of moving the work through diffe …

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Purple exists only in our brains

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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.

an illustration showing wavelength, crest and trough of a wave
Light moves its energy in waves (illustrated by blue line) that move up and down. This creates high points called crests and low points called troughs. Light varies in terms of the length of its waves (called wavelength), which is measured as the distance from one crest to another or one trough to another.J. LOOK

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.

a visualization showing the electromagnetic spectrum from least to most intense
The electromagnetic spectrum contains all the types of light that exist. Our eyes can only see a tiny portion of this broad spectrum, labeled here as visible light.ttsz/iStock/Getty Images Plus

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.

a diagram of the eye's photoreceptors
This is an illustration of the back of the retina, filled with rods and cones. The rods are long and straight. Very sensitive to light, they help us see when it’s dark. Our eyes have fewer cones, which are sensitive to color. The pigment epithelium is a layer of dark cells under the photoreceptors. They absorb excess light.ttsz/iStock/Getty Images

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.

a representation of the wavelengths of light (and their colors) visible to humans
The visible spectrum is the range of wavelengths of light our eyes can detect. Olena Poliakevych/iStock/Getty Images Plus

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.

What do we mean when we say purple doesn’t really exist?

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.”

Do you have a science question? We can help!

Submit your question here, and we might answer it an upcoming issue of Science News Explores



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This One Number on a Form Can Reduce Gender Inequality

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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.

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From the Mixed-Up History of Mrs., Miss, and Ms.

Language can reveal power dynamics, as in the terms of address, or honorifics, are used to refer to a woman's social status: Mrs., Miss, and Ms.

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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The post This One Number on a Form Can Reduce Gender Inequality appeared first on JSTOR Daily.

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