Sketchplanations
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Explaining the world one sketch at a time

Have great conversations about ideas through simple and insightful sketches.

In a Book: Big Ideas Little Pictures

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Absorb big ideas with crystal-clear understanding through this collection of 135 visual explanations. Including 24 exclusive new sketches and enhanced versions of classic favourites, each page shares life-improving ideas through beautifully simple illustrations.

Perfect for curious minds and visual learners alike.

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Hi, I'm Jono 👋

I'm an author and illustrator creating one of the world's largest libraries of hand-drawn sketches explaining the world—sketch-by-sketch.

Sketchplanations have been shared millions of times and used in books, articles, classrooms, and more. Learn more about the project, search for a sketch you like, or see recent sketches below.

Recent sketches

The Mathematics of Everyday Life showing everyday maths examples including budgeting, shopping, splitting a bill, travel planning, buying a house, voting statistics, baking measurements and fitting furniture, created for the VERDI inclusive mathematics project.

Mathematics in Everyday Life

At school, it’s easy to think that mathematics is a somewhat arcane and abstract subject and that we don’t need to learn it. But I was surprised when I thought about all the times that knowing maths helps us in our everyday lives. Examples of everyday mathematics Here are some scenarios I noted over a few weeks, both where I personally ran into everyday maths challenges and where I noticed how much it matters: Travel and time Comparing the relative costs of holidays Deciding the cheapest or best way to get somewhere, balancing journey time, ease, cost, and comfort Estimating travel times to know when you can meet someone Converting between units when travelling (for example, miles and kilometres) Manipulating dates and shifting between time zones Homes and DIY Fitting furniture in a room, or checking whether a sofa will go up the stairs Estimating how many tiles you need for a bathroom Working out how much paint you need for a fence or wall Food and sharing Estimating the cost of your shopping and comparing value (this one’s buy one, get one half-price, but that one’s cheaper per 100g…) Splitting a bill at a restaurant Adapting recipes for different numbers of people Estimating food quantities for a party or a camping trip Converting weights and measures—oz to g, Fahrenheit and Celsius What I like to call “baguette maths”: dividing three baguettes between five people while keeping the largest intact sections Money and finances Understanding interest and return rates for savings and investments Comparing insurance policies Working out interest rates and monthly payments for a mortgage Financing a car and comparing deals Calculating tips Media and society Interpreting statistics in headlines, advertising claims, or medicines Understanding the maths behind political claims, arguments, and elections I’m sure you could add to the list—I didn’t even start on the sorts of metrics and measurements you might need at work. Thinking about these everyday moments matters. Difficulty with basic, practical maths doesn’t just affect school performance—it affects independence, confidence, and daily life. You might not need a Fourier transform or integration by parts for most of these. But facility with numbers, fractions and ratios, plus a little algebra and geometry, will go a long way toward making your life easier. In the case of the big financial decisions, like buying a house and deciding on your mortgage, just a little maths could make the difference of ten years of saving. And a little understanding of statistics can help temper wild advertising claims and misleading headlines. The VERDI Project I tried to capture a few of these in this sketch for Francesca Granone, Associate Professor at the University of Stavanger, and her co-researchers Glenn, Mia, Adam, Fionn and Mariagrazia who work on the project VERDI. The project is funded by Stiftelsen Dam and developed in cooperation with The Norwegian Association for Persons with Intellectual Disabilities (NFU) and aims to develop learning resources for everyday mathematics as a route to inclusion, particularly for people with Intellectual and Developmental Disabilities (IDD) such as autism or Down Syndrome. Traditional approaches to teaching mathematics don’t work for everyone, which can create challenges not just in learning environments but also in everyday life. An aim is to reduce unnecessary barriers to confidence and independence and improve the quality of life for a large group of people. Read more about the VERDI project or get in touch with Francesca. Mathematics isn’t all abstract theory; it’s also vital to making everyday life a little easier, fairer, and more enjoyable. Related Ideas to the Mathematics of Everyday Life Also see: Temperature Scales: Fahrenheit and Celsius Naismith’s Rule for estimating walking time in the mountains Sneaky averages Sampling Bias Parts of a circle The 9 times table on your fingers Asymmetry of returns BODMAS - order of operations
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When there’s a gold rush, sell shovels and picks, a classic business and entrepreneurship quote with prospectors chasing gold and suppliers lining the road

When there's a gold rush, sell shovels

I love this age-old wisdom. It may be about the gold rush, but I see it everywhere to this day. When everyone is trying to get rich in the sensational way, the people who reliably do well are those who sell to the people trying to get rich. In the gold rush, prospectors and miners seeking their fortunes headed up to the hills to find gold. A few of them found it. But, like all get-rich-quick schemes, the vast majority of them found no gold claims that made their fortune. Whether they got lucky or not, they needed tools—shovels, picks, buckets, pans. They also might have purchased mules, food, lodging, supplies, guidance, and maybe they bought whiskey to drown their sorrows. Famously, they might have needed hardwearing work clothes, of which denim was the perfect solution. And the interesting thing about all the people who sold to the prospectors is that they could make money whether their customers found gold or not. They can sell to the people winning and the people losing. The saying has at least a few different forms: The secret to getting rich in a gold rush is selling picks. When Everybody Is Digging for Gold, It’s Good To Be in the Pick and Shovel Business Don’t dig for gold, sell shovels. Some Modern Examples Selling shovels in the gold rush is the classic example, but modern-day examples abound. It often looks like selling access, tools, platforms or advice to people chasing a quick buck. Investment brokers and platforms that charge for trading. Brokers and platforms make a profit when the market dives and when it soars. The more activity there is, the better they do. Exchanges and marketplaces. Where the trading happens, whether it’s stocks and shares, second-hand goods, or vintage furniture. Tooling and platforms. YouTube, AWS, Domain providers profit the more people try to seek their fortune. “How to make money doing X” courses and education. Looking to make money doing X? Buy the course, and you’ll get the exact steps to replicate the winning strategies. Earn on YouTube. Monetise your newsletter. Publish your book. And some slightly more oblique examples: Transformation industries. Gyms and supplements sell the promise of transformation, regardless of whether people achieve their goals. Self-help and productivity. Just implement this new productivity tip, and you’ll transform your prospects. In each case, millions of people purchase without achieving the ends they were hoping for. But the shovel-sellers do well either way. A Simple Formula It’s seductive because, in classic survivorship bias, we see the people who’ve made it: the YouTubers with millions of followers, the crypto early adopters who didn’t sell in a crash, the property flippers who bought at the right place and time. But sometimes the people doing best seem to be those promising to teach you how to get rich that way In most of these cases there’s: A new way of making money High-visibility successes A self-reinforcing loop: the more people follow or buy your course, program, or product promising success, the more successful you look, and the more legitimate your service seems. Try Selling Shovels I share this because I regularly reflect on it as a lens for my own activity. Am I trying to follow the herd and the gold rush? Maybe I would be better off helping others in their journey for gold? How could I support them instead of rushing myself? It’s tempting to imagine yourself as one of the winners of the gold rush. But all that activity creates opportunities to support the prospectors. Selling shovels means your future is less dependent on being lucky, early, or exceptional and hitting a gold seam. Or maybe I'm just jealous ;o) -- As usual, if you’re looking for the origins of the phrase selling shovels in a gold rush, Quote Investigator has done the work for you. Related Ideas to Selling Shovels in a Gold Rush More business and entrepreneurship advice and ideas in sketches: Sell painkillers, not vitamins To scale, do things that don’t scale Starting a company is like jumping off a cliff The Butcher, the Brewer, the Baker The twin engines of altruism and ambition Don’t ask the barber if you need a haircut The Big Ideal TM The Golden Circle—People don’t buy what you do, they buy why you do it Survivorship Bias Optimism Bias Contentment: what you have, relative to what you want
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Front-load key words in lists and when writing for the web for clearer communication with a conference features example

Front-load Key Words

People don’t usually want to read online—they want to get something done. This means that when deciding whether a service is worth subscribing to, figuring out which plan is better, trying to understand a set of features, or determining whether you need this product or that, people mostly just want to skim through. So the easier you can make this for them as a writer and designer, the better. One simple tweak I use regularly when writing or editing is to front-load the meaningful words in lists. What Is Front-Loading Meaningful Words? Front-loading means placing the words that signal most—those that convey meaning or make the point—right at the start, not buried in the middle or end. I learned this lesson through many painful examples of people not reading what we’d written on a page and then complaining that we never told them. Here’s a list I worked on from the welcome email to the newsletter. This was my first draft: Explore the sketch archive on sketchplanations.com Dig in more with the Sketchplanations podcast. At 50+ episodes and counting. Fun, lighthearted and thought-provoking, my co-hosts and I take a sketch each week and dive in, sometimes with an expert guest to help us out. Prefer reading off devices? Me too. You can catch up on past sketches with my book Big Ideas Little Pictures Revision: More to explore 🔍 The full archive on sketchplanations.com 🎙️ Sketchplanations podcast—50+ lighthearted episodes diving into one sketch a week, often with expert guests 📔 Big Ideas Little Pictures—Prefer reading off devices? Me too. A collection of nearly 150 of my favourite sketches in a book (emojis optional, but in this case, they perhaps are an even better scanning tool. Or not.) Now, you may prefer the first one, but if you’re in a hurry or still undecided about whether this is worth reading, the second is more likely to convey the key points I wanted to share. No doubt more improvements are still possible. Because links have formatting that draws attention, it also helps to have each of those at the start, or at least in a consistent place, to aid scanning and skimming—as in the revision where your eyes can scan straight down the key information. This supports the F-Shaped Reading pattern, in which people often scan pages in an F shape. The revision is also shorter, so it’s more likely to be read. This is not a tip for writing novels. Nor, perhaps, for your email newsletter. But in situations where people are skimming—often not even sure they want to read your writing—it helps a lot. That includes almost everything on the web except long-form essays, but also plenty that’s off the web too: Safety notices Public transport information Shop signage Job descriptions Menus Instruction manuals Onboarding checklists Property listings Event schedules And more. Front-Loading to Refine your Link Text The same front-loading principle applies to the words you use within link text, for example, take this sentence and link: For another use case, see the F-Shaped Reading pattern For scanning, this is generally better as: For another use case, see the F-Shaped Reading pattern. ...because scanning the text of the link itself immediately tells me “F-Shaped Reading” rather than “see the...” Link text is one of those places I always want to improve. I made a ‘click here‘ category of sketches to get across this idea: Rewrite to avoid click here. For another post. When time is short, attention is limited, or people just want the next step. So, start with the most useful words. Related Ideas to Front-Load Meaningful Words in Bullets Also see: Front-load names to cue attention F-Shaped Reading Cognitive Overhead Micro-editing Redundant Words By Monkeys — Write actively The First Draft is Always Perfect Happy talk must die
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Laplace's Demon thought experiment quote by Pierre-Simon Laplace about determinism and predictability

Laplace's Demon

For an all-seeing, all-knowing being, the future is as clear as the past Perhaps you, like me, have once considered a thought experiment: Given all the laws of nature and given the current state of everything in the universe, in principle, you could figure out exactly what was going to happen. The laws of nature would just keep things moving as expected, and events in the universe would unfold predictably and imperturbably. What about free will and all that? This idea of a being that knew all the laws and the current states of everything, and therefore how everything would play out, is called Laplace’s Demon. It was named after an extremely smart French mathematician and polymath, Pierre-Simon Laplace, who once wrote (translations vary a little): “We ought then to regard the present state of the universe as the effect of its anterior state and as the cause of the one which is to follow. Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it—an intelligence sufficiently vast to submit these data to analysis—it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes.” — Pierre-Simon Laplace, A Philosophical Essay on Probabilities Determinism is the idea that everything is pre-determined and nothing is left to chance. Laplace’s Demon thought experiment represents the extreme side of that. There are a few challenges to this idea since then, including the practical unpredictability of chaotic systems, quantum mechanics, the difficulty of measuring without disturbing, as well as philosophical and religious ideas about free will. Even if the future did follow perfectly from the past, in practice we couldn’t work it out. Notes on Laplace’s Demon I learned about Laplace’s Demon in David Spiegelhalter’s The Art of Uncertainty after he joined us on the podcast about microlives. Laplace’s Demon is less well-known than Maxwell’s demon — a teeny being that appears to violate the second law of thermodynamics. More generally, Laplace’s Demon is a thought experiment—a hypothetical scenario that helps stress-test and illuminate ideas. Related Ideas to Laplace’s Demon Also see: Laplace’s Demon is an eponym Russell’s Teapot Chesterton’s Fence Black Swan events The Lucretius Problem Hanlon’s Razor The Monty Hall Problem More eponyms You can read a translation of Laplace’s words in his article A Philosophical Essay on Probabilities on Project Gutenberg (this appears near the beginning).
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Common dune types showing how different wind patterns and sand availability shape transverse dunes, linear dunes, barchan dunes and star dunes.

Dune Types: Transverse, Linear, Barchan, Star Dunes

Sand dunes can be beautiful and awe-inspiring. And, though they come in infinite shapes and sizes, specific combinations of winds and sand together create common dune types. I find it interesting to try to recognise the basic types and why they form in the way they do. Here are some of the most common dune types. Transverse Dunes Transverse dunes form, somewhat counterintuitively for me, perpendicular to the wind direction. It’s rather like how a dirt road washboards perpendicular to the direction of traffic, and ripples on the beach will often form at right angles to the wash of the waves. When there’s plenty of sand and the wind is predominantly from one direction, sand begins to pile up and creates sheltered depressions on the other side of growing dunes. The sheltered zones help set up fairly consistent spacing between dunes. It’s fascinating to observe both at a tiny scale on the beach and flying over a vast desert. Transverse dunes typically have a shallower up slope in the direction the wind arrives from and a steeper slip slope on the sheltered side. I learned that the shallower upface is called the stoss side, and the steeper slipface is called the lee face. Linear Dunes When wind blows from two directions, dunes can be pulled into long, linear ridges, forming longitudinal dunes or linear dunes. The ridges align with the average direction of the wind. Some ridges can run for a hundred miles. In contrast to transverse dunes, wind from both directions creates slip faces on both sides, often forming sharp edges along the dune ridges. This leads to the more poetic name of seif dunes, meaning sword in Arabic. Barchan Dunes When the prevailing wind is from one direction and sand is less plentiful, crescent-shaped barchan dunes form. They have characteristic horns extending in the direction the wind blows. Sands are always shifting, and barchan dunes can move relatively quickly along the desert floor compared to other large dunes. Star Dunes When winds blow from many directions, sand can get blown into dunes that grow vertically in a star or pyramid shape. Remarkably, they can reach up to 500m tall. In some areas, star dunes form along longitudinal ridges. Other Dune Types The interactions of sand and wind are endlessly complex, and other types of dunes exist. These include: Dome dunes, without prominent ridges, as you might imagine Parabolic dunes, which look like barchan but face the opposite way. Look out for these near the coast. Reversing dunes, which have a sort of mini-dune facing the opposite way at the top of the ridge. Draas: mega-dunes sometimes made up of other dune forms. Related Ideas to Common Dune Types Also see: The 3 Tallest Mountains Tectonic Plate Interaction Boundaries Settlement Patterns Shapes of Valleys One hump or two hump camel? Topography - Bathymetry Rain Shadow Types of Surf Break Strand line Point Nemo — the remotest place in the oceans
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What is contentment? Happiness, wellbeing and contentment is what you have relative to what you want, from Morgan Housel’s The Art of Spending Money.

Contentment: What you Have Relative to What you Want

Morgan Housel, in his book The Art of Spending Money, says that contentment is what you have relative to what you want. If you have money for a life full of comforts but envy a more glamorous one, you will make yourself unhappy. If you have a simple life with friends, family, health, and interests, and don’t want anything more, then you will be happy as you are. Money makes this visible, but the same rule applies to almost everything: time, relationships, status, health, and freedom. Being content with what you have is a counter to the hedonic treadmill: how people can easily get used to a better situation and start longing for the next thing (been on the list to sketch for a long time!). As Morgan says, “If your expectations grow faster than your income, you will never be happy with your money.” It’s funny how knowing that someone or something has something better can affect your own satisfaction with what you have. “If I hadn’t seen such riches, I could live with being poor.” — from Sit Down by James (video) I think about this song line quite often. One of my favourite perspective shifts on this is comedian Louis C.K.’s Everything is Amazing, and Nobody is Happy clip with Conan O’Brien. He captures brilliantly how quickly our sense of what is normal inflates, even as life objectively improves. Low expectations? In a class on utility theory long ago, I remember mathematically seeing that if you expect little value, then you’ll be satisfied with whatever you get. And I’ve heard it said that the secret to happiness is low expectations. There’s something in it for sure, but it always seems like a double-edged sword to me. Sure, if you expect your team to lose every time, you might not be bothered when they do. But if you hope that they’ll win, you can get some happiness from that excitement, too. It’s always intriguing how supporters of better teams get more frustrated when they do slightly worse than usual, even while they are still doing much better than my team. Expectations are tricky. It’s so easy to recalibrate what counts as normal. You can skip the ups and downs of supporting a team by not supporting one and not caring what happens. You avoid the downs, but you miss the ups, too. (see The Supporter’s Paradox in Big Ideas Little Pictures) The late Queen Elizabeth II said it beautifully: "Grief is the price we pay for love." — Queen Elizabeth II You can skip the grief by not loving, but that seems a shame. How life feels depends on what we expect as much as what we get. Related quotes "Annual income twenty pounds, annual expenditure nineteen nineteen and six , result happiness. Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery." ― Mr. Micawber in David Copperfield by Charles Dickens "Comparison is the thief of joy" — Often attributed to Theodore Roosevelt, but from various sources Related Ideas to Contentment Also see: Five Ways to Wellbeing Spend better: If money doesn’t make you happy, you’re not spending it right “If this isn’t nice, I don’t know what is.” Flow: state of total focus and joy Prospect Theory Languishing The irresistible power of variable rewards The Overview Effect Don’t compare your back of house with other’s front of house
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