Naismith's Rule provides a quick estimate for hiking time in the mountains, intended for "easy expeditions." It suggests:

+1 hour for every 2,000 ft (600m) of ascent

For example, suppose your hike covers 6 miles with 2,000 ft of ascent. In that case, Naismith's Rule suggests allowing 3 hours total—2 hours for distance and 1 hour for elevation.

(Here's a metric sketch of Naismith's Rule)

William Naismith was a Scottish Mountaineer born in 1856. He spent years trekking in the Highlands and was, to be fair, probably made of nails. In the Scottish Mountaineering Club Journal in 1893, he wrote:

"...a simple formula, that may be found useful in estimating what time men in fair condition should allow for easy expeditions, namely, an hour for every three miles on the map, with an additional hour for every 2,000 feet of ascent."

The Scottish Mountaineering Club Journal, Vol. II, September 1892, No.3, p.136 (pdf)

A figure I learned that's stuck with me is that a brisk walk is around 4 mph. But that's actually pretty fast and wouldn't apply on a mountain trail and certainly not hiking up a mountain. So I've run into the challenge myself when planning a trip in the mountains of how to guess how long a hike will likely take.

From a recent hike—where I made sure to run through the full kitchen table survival skills and 10 essentials before leaving—limited daylight was a safety consideration. So knowing how long the hike might take was really important. Incidentally, there's a rule of thumb, literally, for estimating remaining daylight.

Lots of people have put Naismith's Rule to the test, including me, and though it's a slightly optimistic metric, it's a starting point. On my recent hike, we were slightly over, but not by much.

To adjust for your circumstances, add time for:

Tricky or technical terrain and trail condition

Not being "in fair [physical] condition" in the view of a rugged mountaineer from Scotland in the 1890s

Photography, bird watching, animal spotting

The size of your group—I have heard the rule of thumb to add 15 mins for each person in your group

Presumably, if the hike was really long, you'd slow down

So, there are many reasons why Naismith's Rule may be on the light side. But it's a decent place to start from.

Killian Jornet Laughs in the Face of Naismith's Rule

Someone for whom Naismith's Rule definitely doesn't apply is the incredible Killian Jornet, whom I watched in the beautiful documentary Déjame Vivir on Netflix. Footage of him running along knife-edge ridges at the top of the Alps is breathtaking. In 2024, he hiked all 82 peaks above 4,000m in the Alps in 19 days without using motorized vehicles between them 🤯.

I was told about the term lock-miles, a kind of Naismith's Rule but for canal journeys rather than hikes. To estimate the journey time, you'd first calculate the lock-miles with the idea that it takes as long to travel through a lock as it does to travel a mile.

A journey of 10 miles with 5 locks would be 15 lock-miles. For experienced boaters, a typical speed might be 3 lock-miles an hour, so the journey of 15 lock-miles would take 5 hours.

Let me know if you give Naismith's Rule a try!

Prefer metric? So do I. Here's a metric Naismith's rule (with the approximate rounding)

Kaffikok — the time you can travel before needing another cup of coffee

I made some prints and products with and without the text in case, like me, you like a peaceful mountain ridge without any rules

Naismith's Rule for mountain hiking time

An eponym is a word named after somebody or someplace.

An eponym, almost by definition, comes with a story, making them some of the most intriguing words. Knowing what an eponym is also allows you to use the word eponymous, which is always a good way to sound smart.

Some of my favourite eponyms are now commonplace products that took the inventor's name. Some examples:

The Rubik's cube is an invention by Hungarian architecture professor Ernő Rubik. The cube has the fascinating property of being a solid object that's also fluid.

This year (2024), the Rubik's Cube turned 50, celebrating around half a billion cube sales, scores of speed-cubing championships, and documentaries. When Rubik first invented the cube, he wasn't sure it was solvable and only managed it for the first time several months after creating it.

In 2020, Rubik told the story of the cube in his book, Cubed: The Puzzle of Us All.

The fabulously named jacuzzi, or more generally the hot tub, is named after the Italian Jacuzzi family. The seven brothers of the family—there were also six daughters—trained to become engineers, making plane propellers, irrigation systems and pumps before one of the brothers created a homemade bath to help his two-year-old son who was suffering from rheumatoid arthritis. The rest, as they say, is history.

Saskia Solomon tells some of the brothers' story, which includes the court case Jacuzzi vs Jacuzzi, and the invention of the jacuzzi in the 2023 New York Times article, The Frothy Saga of the Jacuzzi Family.

After so long as what seems the most basic of foods, it was remarkable for me to learn that the humble sandwich was named after a person: John Montague, the 4th Earl of Sandwich. Though he probably spent most of his time in London, the title itself is associated with the small town of Sandwich in Kent, in Southeast England.

The story goes that the Earl liked playing cards and wanted food he could eat without having to leave his game and that wouldn't give him sticky fingers that would damage the cards. Incarnations of open sandwiches appeared much earlier elsewhere. For example, the trencher—something I had to look up when reading Game of Thrones—involved serving food on top of old bread as a sort of plate. But it took the Earl's dedication to card playing, or at least desk work, to take the next step many years later.

László Bíró was a Hungarian-Argentine inventor who created the first truly successful ballpoint pen. In the US, the BiC is more common, an eponym this time from Marcel Bich.

It's said that Lázló experienced his fountain pen leaking from heat—fountain pens being very common before the ballpoint—and was inspired by a printing press that used a cylinder to spread the ink. All it needed was to go in all directions. Enter the ballpoint.

While the invention seems obvious in hindsight, perfecting it for robust, commercial use was challenging. For example, finding suitable ink for the tiny ball bearing to spread, which doesn't leak or clog and isn't overly affected by heat. Lázló teamed up with an aviation company—who use a lot of ball bearings—which also provided a great use case of finding a pen that wouldn't leak from the air pressure changes in planes. Later, BiC licenced the technology from Biro. A Bic Cristal® Ballpoint pen is part of the collection at the MoMA.

I only learned that silhouette was an eponym while preparing this sketch, but it's perhaps the best of all.

Étienne de Silhouette, a French government finance official tasked with curbing a French deficit in the 1700s, unwittingly gave his name to the classic black-on-white simple outline image of a person. His severe frugal policies of taxes, curbing royal spending and even melting down gold and silverware earned him the reputation of doing things cheaply. Hence, a cheap method of creating a portrait, cutting out black paper and laying it on a white background, became known as a silhouette.

Nearly everyone will recognise the fuel that Rudolf Diesel gave his name to and his diesel engine. Diesel created a breakthrough engine that was more efficient than typical steam engines while being smaller and weighing less.

Curiously, I learned that Diesel died in mysterious circumstances, disappearing on a journey across the English Channel in 1913.

An excellent episode of the 99% Invisible podcast featuring Helen Zaltzman of the Allusionist raised several interesting questions about eponyms I hadn't considered. Here are a few to think about:

Eponyms are common in medicine, for example, when we name a disease or condition after those playing a part in the discovery. However, the name, for example, Creutzfeldt-Jakob disease, tells a medical practitioner very little about the disease compared to a name that relates to the symptoms of the sufferer or the cause. Should examples like these be replaced with more practical names?

Eponyms almost always have a way of oversimplifying a story, often wrapping up complex histories with the names of white males. For example, rarely are products invented or diseases identified solely through the actions of one person. Yet an eponym chooses one, or some people, at the expense of others.

Eponyms may be the name of someone later discredited or who develops a tarnished reputation from other actions in their lives. Should someone who did evil deeds be remembered in an eponym or should it be changed?

Who knew eponyms could be so interesting?

Know some good eponyms with fun stories? I'd love to hear them.

Eponyms are distinct from the fun concept of Nominative determinism—an aptronym—where someone's name seemingly influenced their future actions or career choices (for example, Les McBurney — Volunteer firefighter).

I've covered a lot of eponyms over the years, far more than I realised. Using the handy list page on the site, I've collected some other eponym examples, which include a lot of my favourites:

Eponym

Hanlon's Razor is the adage: "Never attribute to malice that which is adequately explained by stupidity."

Or sometimes, "Never attribute to malice what can be attributed to incompetence."

It appears in a similar form by the inimitable Johann Wolfgang von Goethe as, "And I have again observed, my dear friend, in this trifling affair, that misunderstandings and neglect occasion more mischief in the world than even malice and wickedness. At all events, the two latter are of less frequent occurrence," in The Sorrows of Young Werther. The same sentiments are also shared by William James, Churchill, and H.G. Wells. More recently, Douglas Hubbard gave a more modern version in his book The Failure of Risk Management: Why It's Broken and How to Fix It: "Never attribute to malice or stupidity that which can be explained by moderately rational individuals following incentives in a complex system."

The mistake of assuming bad intentions was brought home to me when puzzling why people kept leaving paper towels in the sinks of the bathrooms at university. How hard is it to put them in the bin?? A year after assuming my fellow students were either lazy or inconsiderate or both, I was washing my hands when another student dried his hands on the towel, walked to the door, opened it by covering the handle with the paper towel — presumably to avoid the germs — and then aimed his paper towel at the bin which was between the sinks. He missed, and it landed in the sink as he walked off down the corridor. Suddenly, it was clear to me that the hygiene of the door handle was higher in consideration of towel-in-the-sink people than whether or not their towel hit their target (and whether it was worth checking if their towel had hit the bin). It made sense. Someone later moved the bin next to the door, and it didn't happen again.

Besides towels in sinks, I've seen people get mad at others pushing in line when the pushers-in didn't realise other people were queuing. I've seen drivers shouting at another driver who's in blissful ignorance of the trouble they've caused. I've seen agents blamed for terrible customer service when the system is at fault, and customer service blame users when the product is at fault. I've seen people despairing at others leaving litter in the park or on the street when animals had dragged out the mess overnight. I've seen people vilified for not moving down on a train when they weren't aware of the squeeze at the other end. And, usually, I think people aren't smart or capable enough, or in fact wicked enough, to carry out the conspiracies that people credit them for. Very often it's the person assuming bad intentions and getting mad who suffers the most.

To be sure, there are different degrees of negligence. We can all make mistakes, but if you're doing your taxes, it's not okay to make a mistake because you didn't read the instructions. If you're standing on a busy train, you owe it to others to be aware that you may be blocking an aisle, and we should do our best to make sure our rubbish stays where we put it. But none of us are perfect and so often I think Hanlon's Razor has some truth to it.

Perhaps a better formulation of Hanlon's Razor would be, "Before attributing to malice, try attributing to incompetence." But I'm not a fan of the wording with 'stupidity' or 'incompetence'. Awareness is so often the necessary start and what's missing.

Since posting this, a few people also shared with me Clarke's Corollary:  "Any sufficiently advanced incompetence is indistinguishable from malice." And another relevant name for a similar situation is Cock-up Over Conspiracy.

Hanlon's Razor, which encourages us first to consider innocent mistakes rather than assuming ill will, was a submission to Murphy's Law, book two: more reasons why things go wrong, by Arthur Bloch (p52). Murphy's Law is "If anything can go wrong, it will." I've also previously covered Muphry's Law, where, when criticising spelling or grammar, you will make a spelling or grammar mistake yourself.

Fundamental Attribution Error (someone shared Hanlon's Razor with me on posting this)

More conjectures and thinking named after people:

Hanlon's Razor

The Barnum effect is our tendency to apply personal meaning to statements that could apply to many people.

For statements such as the results of a personality test, the effect is stronger if:

they are sufficiently vague — handy phrases include "at times," "a tendency to," "some of," etc.

they are mostly positive — we're more inclined to accept positive evaluations of ourselves than critical ones

You may recognise these tricks from a horoscope or your star sign, magicians, fortune-tellers, fortune cookies, con artists and, perhaps, marketing. There's a fascinating magician's technique you may have seen called cold reading that uses the Barnum effect with other tricks ("I see someone with heart pain in your family.") to make it seem like they know a lot of personal details about someone at a first meeting.

Originally from Bertram Forer, who called it "the fallacy of personal validation," it was later known as the Forer effect until Paul Meehl suggested it should be named the Barnum effect after P. T. Barnum (now of The Greatest Showman fame) for the way he could easily fool an audience with these techniques and to emphasize that we should all know and be on the lookout for being fooled. For that reason, I called it the same here.

Bertram Forer ran an experiment with his students (pdf), giving everyone the same results for their individual personality assessment. Generally, the students all thought the same description applied very well to themselves. He used these statements taken "largely from a newsstand astrology book":

You have a great need for other people to like and admire you.

You have a tendency to be critical of yourself.

You have a great deal of unused capacity which you have not turned to your advantage.

While you have some personality weaknesses, you are generally able to compensate for them.

Your sexual adjustment has presented problems for you.

Disciplined and self-controlled outside, you tend to be worrisome and insecure inside.

At times you have serious doubts as to whether you have made the right decision or done the right thing.

You prefer a certain amount of change and variety and become dissatisfied when hemmed in by restrictions and limitations.

You pride yourself as an independent thinker and do not accept others' statements without satisfactory proof.

You have found it unwise to be too frank in revealing yourself to others.

At times you are extroverted, affable, sociable, while at other times you are introverted, wary, reserved.

Some of your aspirations tend to be pretty unrealistic.

Security is one of your major goals in life.

I learned about it from a discussion of the Meyers-Briggs test (I'm an ENTP btw).

Here's Paul Meehl advocating for the Barnum effect:

"Many psychometric reports bear a disconcerting resemblance to what my colleague Donald G. Paterson calls “personality description after the manner of P. T. Barnum” ... I suggest—and I am quite serious—that we adopt the phrase Barnum effect to stigmatize those pseudo-successful clinical procedures in which personality descriptions from tests are made to fit the patient largely or wholly by virtue of their triviality; and in which any nontrivial, but perhaps erroneous, inferences are hidden in a context of assertions or denials which carry high confidence simply because of the population base rates, regardless of the test’s validity. I think this fallacy is at least as important and frequent as others for which we have familiar labels (halo effect, leniency error, contamination, etc.). One of the best ways to increase the general sensitivity to such fallacies is to give them a name. We ought to make our clinical students as acutely aware of the Barnum effect as they are of the dangers of countertransference or the standard error of r."

Meehl, P. E. (1956). Wanted—a good cook-book. American Psychologist, 11(6), 263–272. https://doi.org/10.1037/h0044164

The Barnum effect

The Overton window is a simple device to consider the full spectrum of policy ideas and identify the range of politically acceptable ones.

Attitudes generally change slowly, as does policy to support them—with exceptions. Ideas that seemed radical or unthinkable at one time may gradually become plausible and popular. As this happens, the Overton Window shifts or expands.

Consider how attitudes have changed towards slavery, segregation, women's rights, animal welfare or gay marriage. Or consider policies made alongside the development of driverless cars or supporting sustainable energy. At one time, prohibition—banning the production and sale of alcohol—was popular enough to become policy in the US, though it would be unlikely to be proposed now.

Generally, the public is unlikely to elect politicians if they stand on policies too far outside the Overton window. And elected politicians will have difficulty enacting policies outside the window.

Named after Joseph Overton of the Mackinac Center for Public Policy, the original model was a cardboard window that could slide over paper, and looking through the window, you could see policy options in one direction towards more government control and in the other towards less government control. He called it the window of political possibilities. The Centre named it after him after his death. He made the slider vertical to avoid associations with the political left or right.

The Overton Window

The Droste effect is an endless picture-in-picture—a part of the picture contains the whole picture, which contains the picture, which contains the picture, and on.

Most of us are likely familiar with it from the fun visual effect you often see when sharing your screen on a video call, which contains the video call where you're sharing your screen, on which is the video call where... Always entertaining. Google calls it an infinity mirror.

The name derives from a Dutch brand of cocoa powder, Droste, where the classic advert was a picture of a nurse carrying a tray with a box of the cocoa powder, with the picture of the woman on it carrying the tray with a box of the cocoa...

Articles about the Droste effect often mention the amazing M.C. Escher's Print gallery, a picture without beginning or end.

The Droste effect

Richard Feynman was one of the great scientists of the 20th century, making significant contributions to physics and other related fields. Part of what made him stand out was his gift for teaching. He had a remarkable knack for explaining some of the most complex things in ways anyone could understand. He was also a model of the desire to deeply understand how things worked, often deriving a result in several ways to be more confident he was right.

The Feynman learning technique is typical of how he approached understanding something deeply and helps explain some of his teaching skills.

Spend time writing about a topic as if explaining it to someone.

Then practice explaining it, speaking and drawing as if you were a teacher at the front of the class. You may figure out some other aspect wasn't as clear as you thought and need to look into something.

Refine any gaps you reveal until you can share the topic fluently and clearly.

Then, simplify your language by replacing complex words and ideas with simpler ones and considering analogies to help people relate.

Now, you can explain it because you deeply understand it, too.

"You can know the name of that bird in all the languages of the world, but when you're finished, you'll know absolutely nothing whatever about the bird."

— Feynman's father, from Surely You're Joking Mr Feynman?

I loved the Fun to Imagine interviews to experience some of Feynman's joy and skill for teaching.

The sketch was inspired by this excellent animated video of the Feynman Learning Technique.

Though he was primarily a theoretical physicist, Feynman also made lasting contributions to the field of computation. If you want to get into those, you might enjoy the Feynman Lectures on Computation from the last course he taught at Caltech, edited, no less, by my Dad.

The Feynman Learning Technique

A Pyrrhic victory is one where your own losses or damage make it nearly as costly as defeat.

Perhaps that business rival finally went out of business after you lowered prices so much that you can now barely get by. Maybe you managed to prove you were right at the cost of ruining a relationship. Or it could be that the kids did in fact get in the car and go out on that blasted walk only for everyone to have a miserable time, angry at each other for the rest of the day.

Or maybe, as King Pyrrhus of Epirus found in 279 BCE, you won several battles against the Romans while losing so many of your best warriors as to make you wonder at the worth of the whole campaign.

Pyrrhic victory

Braille is a tactile writing and reading system for the blind and visually impaired. It was invented by Louis Braille when just 15 in 1824. Respect! I don't know about you, but when I've tried braille on signs occasionally, it's always seemed difficult to train my fingers to differentiate the shapes and the dots. Perhaps it would have helped if I'd known how it worked.

Braille is based on a pattern of 6 dots, like a 6 on dice, with different letters, numerals, or sounds being different combinations. It doesn't match the shapes of written letters though, instead breaking the alphabet up into groups of 10. The first 10 letters are combinations of the top 4 dots. The following 10 letters repeat the combinations and add dot 3 in the bottom-left. Then the remaining letters, except w start again adding with dot 6 added. W wasn't in Louis Braille's original French alphabet so appears tacked on at the end.

Since its invention, it's gone through multiple iterations and languages, and there are combinations for punctuation (some common ones formed by shifting down the original 10 combinations), numbers, accented letters, maths symbols, and more. There is also agreed-upon shorthand where a letter may mean a common word eg l for like, and there are contractions where a symbol may mean a sound or set of letters like 'ch'.

The sketch shows the Latin alphabet for modern English braille.

Braille

The two most commonly used temperature scales are Celsius and Fahrenheit. The Celsius scale, named after Swedish astronomer Anders Celsius, sets 0C at the freezing point of water and 100C as the boiling point of water at 1 atmosphere of pressure — normal air pressure at sea level. The Fahrenheit scale has 32F as the freezing point of water and 212F as the boiling point. With 180F between freezing and boiling that means each degree Celsius is 1.8 degrees Fahrenheit.

Several accounts of the creation of the Fahrenheit scale exist but the general gist is that Daniel Fahrenheit set 0F at the freezing point of a brine mixture, 32F at the freezing point of water, and another point at body temperature around 96F (now 98.6F). He divided up the scale between these points giving a scale with helpful resolution.

It's interesting to think that for most of history, there was no comparable way to say how hot or cold something was.

Having spent time on both sides of the Atlantic I've tried to get at least somewhat familiar with both of them. To convert between them in my head, at least around most air temperatures, I use a quick approximation. As 32F is 0C, and for each one Celsius you move almost two Fahrenheit, you can roughly go from Fahrenheit to Celsius by subtracting 32 and dividing by 2 (or a little less to be closer). So 50F is approximately 9C (actually 10C), or 86F is approximately 27C (actually 29.4C). It's not perfect, but it's often good enough if you're trying to work out if it'll be hot out. To go from Celsius to Fahrenheit, it's the reverse, times by 2 and add 32.

There are also at least two simple anchor points that can help just by swapping the digits around:

Both scales are now defined relative to the Kelvin scale, which sets the lowest point of 0K at absolute zero, where basically all movement stops. Zero on the Kelvin scale is around -273C. As such, the Kelvin scale, though helpful for scientists, is not very practical for discussing the weather.

Fahrenheit and Celsius

Most things increase in demand as they get cheaper — as the price of electric cars comes down we can expect more people to buy more of them. Veblen goods are the opposite. They thrive on exclusivity. Veblen goods are more desirable exactly because they are more expensive. If everyone could buy a Rolex, the vintage whisky, or that supercar, then they wouldn't seem so super anymore. Many luxury items are veblen goods.

The I Am Rich iPhone app briefly sold for $999.99 and displayed only a glowing red gem and a mantra about being rich. Genius/madness.

Veblen goods are named after Thorstein Veblen, coiner of the concept of conspicuous consumption.

Veblen goods

Maslow's hierarchy of needs, or Maslow's pyramid of needs, was created as the basis for a theory of human motivation by the psychologist Abraham Maslow shared in a 1943 paper. He was interested in what gives our lives meaning and what makes people happy — particularly in the context of a world increasingly driven by consumerism.

He suggested there were our basic needs and our higher level needs — psychological, spiritual, and growth.

In the basic needs you have physiological needs such as not being hungry, thirsty, or cold. Then we have our safety needs such as being free from the threat of violence, or being healthy.

Then we have the higher-level needs of love and belonging including friendship, connection, family. Then esteem needs such as self-respect and self-esteem. And finally our need for self-actualization — reaching our potential, achieving mastery, or being the best we can be.

Maslow continued to refine his original framework. For all its flaws — it always provokes discussion and counter-arguments in my experience — it's remained a clarifying and remarkably enduring model.

If you're designing for needs I prefer Patnaik's hierarchy of needs.

Maslow's hierarchy of needs

Chesterton's fence put simply is: Don't take a fence down unless you know why it was put up.

It is tempting, in a spirit of progress, to want to do away with old designs, laws, policies, or institutions that no longer help. To think, perhaps, that the people that made them weren't maybe as smart as we are, or seeing things in the right way. Yet institutions, policies, or fences, weren't usually made by accident — they require effort and action, even putting up a fence. Chesterton's fence, after GK Chesterton, is a reminder that before we remove the old and perhaps replace it with the new we would do well to at least understand why the original was put in place.

Once we understand why the fence was there in the first place if we still think it's of no use, then by all means pull it down.

Read more on Chesterton's fence, including its origins.

Chesterton's fence

Möbius strip: the mindbending shape with only one side.

It's very simple to create: take a long piece of paper, give one end a 180-degree twist and then stick the ends together. The simple shape just created has only one side. What??

You can test this by running your finger over the surface and you'll cover the entire shape and end up back where you started.

Try to follow the red ball in the animation as it follows the surface over the entire loop.

Möbius strips have a couple of other interesting properties including how cutting them in half down the middle simply makes a longer loop, and cutting a third of the way in over the full length will reveal two distinct yet interconnected loops. Fun to try!

I once spent a memorable evening with a friend trying to feed a Möbius strip through a regular printer to see if we could print on both sides in one go.

SP 759 - Möbius strip - single.png

In case it's handy, here's a static Möbius strip sketch

Möbius strip

Sankey diagrams are handy ways to visualise material or energy flows through usage and time. They are excellent for displaying energy source and usage, for example the UK government publishes a Sankey diagram of UK energy each year (pdf).

Perhaps the most famous example is Charles Joseph Minard's remarkable visual showing Napoleon's invasion of and retreat from Russia in the Winter of 1812–13. In that chilling example the thickness of the lines represent the remaining size of Napoleon's army.

I learned about Sankey diagrams from Edward Tufte but perhaps people see them most commonly today in Google Analytics showing the different paths visitors take on a website before leaving.

Sankey diagram

Russell's teapot is a memorable example illustrating how, if you are going to make claims that are difficult to verify, the burden of proof lies on the one making a claim — not on any skeptics to disprove it.

The example he gave was claiming there's a china teapot in elliptical orbit somewhere between Earth and Mars that's too small to spot with a telescope. He suggests it would be unreasonable to expect anyone to believe such a patently unfalsifiable claim.

Bertrand Russell original invoked the teapot in the context of religion and the existence of an unverifiable God, in a similar vein to the Flying Spaghetti Monster and Carl Sagan's invisible dragon. It can however be applied much wider than that.

I learned about it from a helpful commenter on the BS Asymmetry Principle, also known as Brandolini's Law.

Russell's Teapot

Bloom's taxonomy has 6 levels of increasingly sophisticated thinking skills.

It was originally developed in a slightly different form to here for classifying educational objectives and with additional variations, dimensions and sub-levels in the full models, it is useful for informing teaching and learning.

The hierarchy reflects, among other things, that a strong foundation for learning is knowledge.

The 6 levels in the revised Bloom's Taxonomy for learning are:

Bloom's Taxonomy

The Gini coefficient, or Gini index, is a common way to gauge income or wealth inequality within a population.

The coefficient gives a single number showing how equal a distribution is. For example, in a population where everyone earns the same amount the Gini coefficient would be 0 — total equality — and in a population where one person earned all of the population's money, the Gini coefficient would be 1 (sometimes expressed as 100%) — maximum inequality. In practice all countries' Gini coefficients are somewhere in between, at around 0.25 to 0.5 after taxes.

Like any simple measure the Gini has its difficulties, like being easily misinterpreted when compared, but is still widely used. The BBC has a short piece on its history and an alternative measure called the Palma ratio.

Of course, we have some high profile zillionaires at the moment. You might like this old sketch of wealth inequality in America.

The Gini coefficient

Perhaps the most important curve of our times, Charles Keeling’s  curve shows the change in concentration of CO2 in the air with measurements taken every year for over 60 years. Taken at the top of Mauna Loa volcano in Hawaii because of its high altitude and relative isolation in the Pacific, Charles Keeling’s measurements show that the monthly average CO2 concentration in the air has risen from around 310 ppm (parts per million) to around 410 ppm in 2020. As a greenhouse gas this change in CO2 concentration is one of the critical causes of climate change.

The concentration varies seasonally as plants bloom in Spring and Summer reducing the concentration from its high around May as the CO2 has built up over the Norhern Hemisphere Winter.

The Scripps CO2 program is now overseen by Charles’ son Ralph Keeling.

The Keeling curve

In 2016 the British Government had plans to launch a new polar research vessel. To decide on a name for it, they put it out to a public vote. Despite a number of serious, meaningful or historic names suggested, like Shackleton and Endeavour, one name put forward, Boaty McBoatface, quickly overwhelmed all the other options put together.

It turns out this is not limited to the British sense of humour, and people will vote for a joke candidate because it’s fun and subversive, and people want to see what will happen if it wins. This NYT article by Katie Rogers has some other fun examples of competitions going ‘wrong’, such as an attempt to name a bridge 'Chuck Norris’ and selecting a school for the deaf as a concert location: What you get when you let the Internet decide.

I learned about the Boaty McBoatface effect from Dr Roger Miles on the Human Risk podcast. Also see Conduct Risk Management: A behavioural approach by Dr Roger Miles.

The Boaty McBoatface effect

The Peter Principle is that “every employee tends to rise to his level of incompetence.”

The logic of the Peter Principle of management

Someone good at their job is likely to get promoted. However, the promoted position will likely require different skills. If they’re good, they may get promoted again, but if not, they will stay. At some point, each employee in an organisation will be incompetent in their position.

The Peter Principle was an observation originally meant as satire. Laurence Peter later wrote a book called The Peter Principle: Why things always go wrong.

I like this short take on the Peter Principle by Tim Harford.

We discussed the Peter Principle in the Sketchplanations podcast. During the podcast, I learned about a counterpoint to the Peter Principle called the Paula Principle.

In his book, The Paula Principle: why women lose out at work ― and what needs to be done about it, Tom Shuller explains that the Paula Principle is "most women work below their level of competence."

Tom explains that the Paula Principle is caused by at least five factors: Discrimination, Caring responsibilities, Self-confidence, Lack of vertical networks, and what Tom calls Positive choice. Read more about the Gender, competence and the Paula Principle in the workplace.

The Peter Principle is a specific case, the case of people, of the Generalised Peter Principle which states that "Anything that works will be used in progressively more challenging situations until it fails." See rule number 1 of indoor games.

Keeping the Peter Principle in mind might help be more tolerant of mistakes from higher-ups—they may be out of their depth.

The Peter Principle is different from the Peter Parker Principle, which is: "With great power comes great responsibility." Though Spider-Man popularized this wise proverb, many precursors of the sentiment exist.

The Peter Principle

The Doppler effect is the change in frequency of a wave as its source moves relative to the observer. 

The same effect that causes a siren's pitch to change as it drives past is also used to estimate blood flow with ultrasound, measure the speed of a passing car, and even determine the motion of the stars. Doppler shift-based satellite navigation was also the first operational use of a system that eventually led to GPS.

When a siren or similar sounds approach, I try to imagine the crunching of the sound waves—the vehicle seemingly chasing after its own sound—and the stretching out of the waves as it heads past and into the distance. At least it makes it less painful on the ears.

Here's an excerpt from my Dad's book, Einstein's Mirror, in a fascinating chapter discussing the speed of light:

"In 1845 in Utrecht, a troupe of trumpeters played their instruments while being transported by a train. Another group of musicians arrayed alongside the railway track were paid to listen carefully as the train and the trumpeters went by. This seemingly bizarre experiment was the invention of the Austrian physicist Johann Christian Doppler. Most readers will have noticed the drop in pitch of a whistle as a train goes by, or of a siren as an ambulance or police car passes. It was precisely this same change in pitch with motion that Doppler was investigating with his entertaining train and trumpet experiment."

A polished version of this sketch appears in my book Big Ideas Little Pictures

The Doppler Effect

Named after the brilliant Clay Shirky his principle broadly states that:

Eponym sketches