It’s always been mind-boggling to me how some of the largest and heaviest things we build on Earth are ships that float on water. Cruise ships are like floating towns, some able to accommodate over 5,000 people. How can it be that these gigantic, impossibly heavy objects made of steel can float on water? The key is displacement and realising the considerable weight that the water already supports.

In a lake or ocean, each drop of water is supported by the water around it. 1m³ of fresh water weighs 1 metric tonne, which is 1,000 kg. If a ship displaces 1m³ of water, the buoyant force of the surrounding water supports 1 tonne of the ship’s weight. Therefore, a ship weighing 50,000 tonnes will just float if it displaces 50,000m³ of water.

Sea water contains salt, which makes it denser than freshwater. As the denser water supports a greater weight, a ship will float slightly higher in salt water than in fresh. The International Load Line, previously called the Plimsoll line, shows how deep a boat sits in the water.

To realise the immense power of water, you can try submerging a biscuit tin in a bath. It’ll put up quite a fight.

Buoyancy

Nearly every iceberg you see in a picture or diagram is probably floating the wrong way. This was what I learned (from Megan Thompson-Munson) after sketching Biz Stone's brilliant saying about the myth of overnight success.

With some approximation, the density of ice is around 900 kg/m3, and seawater is around 1,000 kg/m3. Therefore, the fraction of an iceberg that's submerged is around ~900/1000 or 0.9. So, about 90% of an iceberg is below the surface and 10% above, which is partly why they can be so dangerous. While most iceberg pictures get this part more or less correct, most of these icebergs will be floating vertically. In reality, a tall, thin iceberg will likely topple, so most icebergs end up floating on their side, not their tips, even though we rarely draw them this way.

I remember learning about a fascinating experiment with children of different ages estimating which glass holds more water: a tall, slender one filled high or a wider glass filled to a lower level. Younger children almost always chose the glass with the higher water level as the most water, even when it was significantly less than the shorter and wider glass. I wonder if it's part of why we draw icebergs vertically, at least when we're using them as a metaphor. It's easier to grasp quantities vertically, and we commonly underestimate volume spread over a wider area.

We may still want to draw our icebergs tall and deep to make our point, but now, at least, we can do so with the knowledge that they're not like the real ones.

If you want to see it yourself, Joshua Tauberer made a brilliant draw-an-iceberg-and-see-how-it-will-float game. I recommend you give it a go so it sinks in forever (sorry).

Know your poles: penguins or polar bears, frozen ice or land

Iceberg orientation

Parallax is the change in the apparent position of objects from different viewpoints. For example, from one viewpoint, a nearby house may appear in front of a hill, and from another, it may be in front of a lake. Objects at different distances appear to move by different amounts. As you move between viewpoints, say when driving along a road, nearby objects move past you quickly, while distant objects appear to move by slowly. This difference in motion from near to far objects helps us determine how far objects are away.

I remember learning parallax from video games, like playing Sonic the Hedgehog on the old Sega Mega Drive. As the character moves in the foreground, elements at different distances in the background move progressively slower, creating a sense of depth. Saturation and contrast change at with distance also, known as atmospheric perspective.

I also enjoy observing parallax while looking out of a train window; nearby hedges and trees race by, buildings in the middle distance move more slowly, and distant hills or mountains barely seem to change. It's fascinating how our brains interpret this relative movement to judge distances.

One of the more intriguing applications of parallax is stellar parallax in astronomy. The basic geometry of parallax allows us to measure the distance of (relatively) nearby stars by observing relative shifts against the background of distant stars. Here's how it works: we observe the stars from different points in our orbit around the Sun. As a result, the stars appear to move relative to each other. By measuring this apparent shift, we can calculate the distance of the stars.

Parallax

It's mindblowing to me to think at any moment, over 6,000 satellites are whipping around the Earth at terrific speeds and somehow not drifting off into space or crashing into Earth. How does this work?

An orbit around Earth is a delicate balance between the momentum of a satellite traveling at speed parallel to the Earth's surface and the constant tug of gravity towards the Earth.

If the satellite travels too slowly, gravity wins, eventually pulling the satellite back to Earth. If it travels too fast, gravity isn't strong enough to hold it, and the satellite will shoot off into space. But at just the right speed—which depends on its distance from Earth—gravity will pull the satellite towards Earth, but the satellite's speed ensures it will keep missing and instead continue its journey orbiting around Earth. In this case, gravity acts as a centripetal force, a force acting towards the centre, enabling satellites to stay in orbit.

Newton had a thought experiment known as Newton's Cannon where he imagined firing a cannonball off a high mountain at different velocities and what the resultant trajectories would be.

Most orbits are slightly elliptical or oval-shaped. For example, the elliptical nature of the Moon's orbit gives us the joys of things like supermoons.

Orbit

Redshift refers to light being 'shifted' towards the redder end of the spectrum — longer wavelengths — as objects move away from each other. If a light source is moving towards us then light is blueshifted, shifting towards the bluer end of the spectrum, shorter wavelengths.

Imagine waving a spring back and forth to create a wave and then starting to run away – the waves would be stretched longer. Because the universe is expanding 🤯 distant galaxies are moving away from us faster than nearer ones — imagine how the chocolate chips in a cookie move away from each other as the cookie bakes and grows in an oven. By comparing the redshift of light seen from distant galaxies with what we would expect to see it's possible to use redshift to determine how far they are away.

Redshift is an example of the Doppler effect, or Doppler shift, in action. It's more commonly known by the stretching or compressing of soundwaves as, say, an ambulance moves towards or away from you, or how the sound in front of a moving aircraft eventually can produce a sonic boom.

Redshift

Physics envy refers to the wish that a field of study would turn out to be as precise, as predictable, as repeatable, and as amenable to modeling and theory that replicates practice as physics is.

As it turns out, most fields that involve people — such as economics and the social sciences — are rarely so tidy and orderly and neatly mathematically modeled. They are instead usually messy, uncertain, and filled with context, nuance, history and confounding factors such that making sense of them in broadly applicable ways is rather difficult. And while we do our best to quantify and identify effects, or cleanly isolate our cognitive biases or our quirks of behavioural psychology, rarely are they able to live up to the purest standards of physics. It's enough to turn one green with envy.

It reminded me of the best laid plans of our Saturday sports coaches turning for their substitutes to execute their plans, only to find the players climbing trees in the adjacent field.

Physics Envy

Brilliance bias is the tendency for people to think of 'brilliance' as generally a male trait. With fewer women generally recorded in the history books, the brilliant people that come to mind from a young age tend to be men.

Underrepresentation has consequences. Careers that are generally understood to require 'brilliance' to succeed, such as maths, physics, or philosophy, are likely to have fewer women working in them. Even at school age, attitudes start to shift in both girls and boys. For example, having an interest in games that require you to be 'really smart' or whether, when asked to draw a scientist, we draw a woman or a man. We need to stop teaching brilliance bias, and we need to celebrate the many female role models we have.

My sister shared with me a page on drawing famous faces that showed 49 men to draw, and an example of the board game Guess Who having as many women to guess as it has men with facial hair as an attribute.

Caroline Criado Perez's eye-opening book Invisible Women taught me about brilliance bias, including the examples here.

Brilliance bias

If you wanted to know who would win an election, then the only reliable (most of the time) way to do that is to ask everyone to vote for real and count them all. Short of doing that, if you want to get an idea who would win you can pick a group that you hope is representative of the whole of the voting population, ask them what they plan to vote instead, and then multiply up to the full group. But it turns out, whenever you ask people things, it's jolly hard to really have confidence in what you're extrapolating up to as all sorts of bias can creep into your sample.

If you ask people what they plan to vote they may lie, they may tell you what they plan to do then change their mind, they may tell you what they think you want to hear depending on who's asking, they may say the first option because it's easiest, and you may ask in the places where it's easy or cheap to do so, or hear from only the people who are happy and not too busy to talk with you.

In the example in the sketch, if you hope to receive responses to your questions by surveys then you get responses from people who happen to not mind doing surveys — from anyone who throws them in the bin you won't receive a single data point.

All of these, and others, can lead to a bias in your sample and, at times, to drawing wholly inaccurate conclusions.

Extreme example from How to Lie with Statistics by Darrell Huff.

Sampling bias

Sir Arthur Eddington, an English astrophysicist, told a short story involving a scientist studying fish by pulling them up with nets. After checking all the fish hauled up, the scientist concludes that there is a minimum size of fish in the sea. But the fish seen were determined by the size of the holes in the net, the smaller ones having slipped through, unmeasurable. The instrument you use affects what you see. Or as Richard Hamming puts it: "You get what you measure."

This analogy provides a nice concrete example of a phenomena that affects us routinely in more subtle ways. What and how we choose to measure affects the conclusions we draw. So, a website may easily measure sales and bounce rate for its pages, while things like trust, authority or satisfaction, which may be more significant longer-term metrics, go unmeasured.

"There is always a tendency to grab the hard, firm measurement, though it may be quite irrelevant as compared to the soft one which in the long run may be much more relevant to your goals. Accuracy of measurement tends to get confused with relevance of measurement, much more than most people believe. That a measurement is accurate, reproducible, and easy to make does not mean it should be done, instead a much poorer one which is more closely related to your goals may be much more preferable. For example, in school it is easy to measure training and hard to measure education, and hence you tend to see on final exams an emphasis on the training part and a great neglect of the education part."

What gets measured gets better (an earlier take on this)

Quote from Chapter 29, You get what you measure, of Richard Hamming's, The Art of Doing Science and Engineering: Learning to Learn.

If you happen to be in the business of doing research or science Richard Hamming's Bell Lab's talk, You and Your Research (pdf), is an excellent read.

You get what you measure

A school science refresher: the 3 primary states of matter, solids, liquids and gases and the transitions between each one. If you’re like me you probably forget about the more obscure sublimation and deposition directly between solids and gases. And vaporisation of a liquid is evaporation, occurring at the surface, if it is below boiling point, otherwise it’s boiling.

There are some more unusual states including plasma — seen in lightning and fluorescent lights — and Bose-Einstein condensates, but mostly we’re familiar with ice cubes, water and steam.

States of matter

Also known as Brandolini’s Law, this is the simple observation that it’s far easier to produce and spread BS, misinformation and nonsense than it is to refute it.

In fact, the iSchool at University of Washington launched a course on Calling Bullshit with the first class being booked up within one-minute of registration. The professors, Carl Bergstrom and Jevin West have since written a book: Calling Bullshit: The Art of Skepticism in a Data-Driven World.

Phil Williamson in Nature also wrote a nice article emphasizing that we should take the time and effort to correct misinformation where we can. In it, he proposed the idea that “The global scientific community could…set up its own, moderated, rating system for websites that claim to report on science. We could call it the Scientific Honesty and Integrity Tracker, and give online nonsense the SHAIT rating it deserves.”

The BS asymmetry principle

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

It’s pretty hard to get to grips with the scale of the solar system. It's really, really, really big.

To help process the vast distances within our system, astronomers use Astronomical Units where 1 AU is the distance of Earth from the Sun. If you see Venus in the night sky, our closest neighbour just 0.7 AU from the sun, it looks impossibly far away. But the further out you go, the more the distances multiply.

Earth and Venus are practically on top of each other compared to Uranus and Neptune. Neptune is a full 30 times the distance between Earth and the Sun.

Now think about the fact that our little solar system is over 250,000 AUs from our nearest star, which is, in turn, just one of many tucked away in a small corner of the Milky Way, which is only one of many galaxies that make up the known universe.

James O'Donoghue has made some brilliant videos about the solar system that explain this and more.

This sketch, and plenty more in the Starry-eyed Surprises section, features in my book Big Ideas Little Pictures

The original sketch of solar system sizes is on a paper background.

Paper background solar system sizes sketch

Dark sky background solar system sizes sketch

Solar system planets: how big is the solar system?

What is a blue moon? A blue moon is a full moon that hits twice in a calendar month.

Given the cycle from full moon to full moon is about 29.5 days and months are generally 30 or 31 days a full moon appearing twice in a month doesn’t happen very often. And February never has a blue moon.

I like this definition, but it is apparently a modification of the original definition which is a little more complicated. The original blue moon definition is explained like this. Given the 29.5 day cycle, most seasons of 3 months have 3 full moons. But every now and then, a season would come by, like Sep, Oct, Nov in the sketch, where there would be 4 full moons. The 3rd of these was known as a blue moon, or a seasonal blue moon. See why I like the modern definition?

Here’s a good article that explains the subtleties and history of blue moons.

Check out more moon or astronomy explanations

What is a blue moon?

These days beards are in. There will come a day when beards are out. And a day when beards are back in again. That’s how it seems to go.

Turns out there is a name for this kind of thing: negative frequency-dependent selection. Essentially, the less common it is, the more useful a trait it is. As opposed to positive frequency-dependent selection which, as you can imagine, is the reverse.

According to this study, for example, when there are fewer men with beards in a population, they are judged as more attractive than when there are more of them. Hence they become gradually more popular until the effect starts to wear off and the clean-shaven look starts to appeal again. And round the cycle we go.

The beard cycle

Moon pools are protected entrances to water that can even give the remarkable ability to enter from under the water.

First created to support drilling operations on offshore platforms, moon pools can include entrances on the decks or undersides of ships or an entry and exit for divers from permanent underwater research bases.

For underwater entrances, also known as wet porches, the trick is to pressurize the air around the pool to the same pressure as the surrounding water. The raised pressure keeps the water from gushing in and enables a swimming pool-like entrance even though you’re already below the surface.

I've never used one, but I'd absolutely love to. One of my earliest memories of a moon pool and corresponding bafflement and wonder was in James Cameron's 1989 film The Abyss. A moon pool features in the recent trailer for the remastered version of The Abyss

Moon pool

Which is kind of amazing. The magnetic field is produced by some remarkable result of the convection of molten hot iron alloys in the core of the Earth. Kind of hard to really get your head round if you’re sitting calmly at your desk or walking on a nice stable surface. Periodically, the poles switch round it seems but at the moment the magnetic South pole is actually near the point we’d normally call the geographical North pole. They’re pretty close, but the geographic axis doesn’t exactly coincide along the geographic axis of rotation of Earth. And the lines of force go from magnetic North to magnetic South so your compass needle is actually pointing towards magnetic South. Remember iron filings and bar magnets from physics class?

Earth is a big magnet.

Asteroids are often considered irregular, lumpy, potato-shaped rocks, while planets seem smooth and spherical. The “potato radius” is the fascinating threshold where this transformation begins—a concept that illustrates how gravity shapes celestial bodies.

When a space rock’s radius (the distance from its centre to its edge) grows to around 200–300 kilometres, its own gravity becomes powerful enough to reshape it. At this size, gravity pulls the rock’s mass inward toward its centre, overcoming its irregular structure and creating a more spherical shape. Think of it like compressing a crumpled ball of paper into something rounder and smoother.

Rocks smaller than this threshold retain their irregular, asteroid-like shapes, while larger bodies transition into planet-like spheres due to self-gravity. This natural process highlights the profound role gravity plays in shaping the universe.

Potatoes as Asteroids in The Empire Strikes Back

Our image of asteroids is so closely linked to potatoes that they have even served as asteroid doubles in movies. In a brilliant example of creative special effects, The Empire Strikes Back used potatoes as some of the asteroids in the famous scene where the Millennium Falcon flies through an asteroid field.

The potato radius and other remarkable natural phenomena feature in Professor Brian Cox in the BBC series Forces of Nature.

Not sure about Asteroids, meteors and meteorites?

The potato radius features, along with many other fun, spacey-sketches in my book Big Ideas Little Pictures

The Potato Radius: When Asteroids Turn Spherical

How do you remember the difference between stalactites and stalagmites in a cave? And how do you spell them?

A simple mnemonic that’s helped me is this:

For Stalactite, the "-tite" and "tight" remind you of the ceiling connection, and the letter “C” in stalactite fits perfectly with “ceiling.”

For Stalagmite, once you’ve got stalactite, stalagmites naturally become the ones that grow up from the ground, with their cheeky “G” matching “ground.” Easy, right?

With this trick, you’ll never mix them up again, whether you’re exploring caves or acing a quiz. Sorted.

Stalactites, Stalagmites

The clarity of the night sky. A low number means clear, black and amazing stars. Higher numbers mean gradually more urban environments with increasing light pollution. At 9 you’ll barely spot a star being pretty much in Piccadilly Circus or Times Square.

More detail needed? John Bortle, Light Pollution And Astronomy: The Bortle Dark-Sky Scale, Sky and Telescope, July 18 2006.

Bortle Scale

All of these guys can grow back major parts of their body, even limbs, and in the case of the flatworm a new head. Crazy.

Animals that regenerate

When it comes to the phases of the moon, it’s good to know your waxing (growing) from your waning (shrinking), and that a gibbous is the shape of the moon when you take a crescent of shadow from a circle of light, and that the hardest moon to see is a new one.

Or, as a reader passed on: If it’s light on the right, it’s gonna get bright. If it’s light on the left, it ain’t.

Like the moon? Apparently, so do I. Also see:

Phases of the moon

This chart is from the original he published - just the five data points. Pretty simple huh? The “observation, originally made in 1965, that the number of transistors on an integrated circuit would continue to double every year. Although this increase has slowed to a doubling in eighteen to twenty four months, Moore’s law has held true for nearly fifty years and is the foundation for the astounding Information Technology revolution we see around us.”

For those interested in Moore’s law, remarkably, I think the best information is my Dad’s book, The Computing Universe, which is also the source of the quote.

Moore’s Law

A centipede has 1 pair of legs on each body ring, and a millipede has two on most body segments. Hence millipedes will generally have plenty more legs to go round. As far as I know this is fairly foolproof. Though generally speaking there are more obvious ways to tell, such as millipedes looking more like long armoured nice round worms and usually moving slowly, and centipedes zipping around while generally seeming more long-legged and insecty, with longer antennae at the front and longer angled back legs, sometimes with hooks for defence.

If you were offered to pick one of them up, you’d probably pick the millipede.

Also, in case you were tempted to think they are insects, they’re not because insects have six legs. They are arthropods (loosely meaning jointed feet) along with insects, spiders, scorpions and crustaceans, but in their own subphylum of, aptly named, myriapoda (loosely meaning many legs).

Check out core insect anatomy for a sketchplanation insect refresher.

How to tell a centipede from a millipede

Meteor: A rock burning up as it enters the atmosphere. Also known as a shooting star.

Meteorite: Parts of a meteor that made it all the way to the ground. Look out!

It was a long time before I really knew the difference between these things.

Asteroids, meteors and meteorites

Turns out a bunch of substances have the power to make you sleepy - tryptophan, vitamin B6, calcium, glycine, lactucarium and carbohydrates are some of the major ones. Some even interact with each other for maximum sleepiness. A few common foods with these compounds in good measure include:

turkey, walnuts - tryptophan
tuna, pistachios - vitamin B6
dairy - calcium
chamomile - glycine
lettuce - lactucarium

So an evening turkey or tuna, walnut, cheese and lettuce sandwich with a glass of milk and a side of pistachios or walnuts and you’ll be set for a good night.

Sleepy foods

The International Load Line, formerly called the Plimsoll Line, is an internationally adopted system for ensuring ships aren’t overloaded. Safe loading levels vary depending on the salinity—how salty it is—and the temperature of the water.

The Plimsoll line

Thunder clouds are so impressive. Lightning forms due to air currents in the cloud as warm moist air rises up quickly. All the collisions between particles cause different charges to develop between the top and the bottom of the cloud. When that gets large enough, kapow!

Also see: thunderclap or rumble, dirty thunderstorms.

Thunder clouds

Reproduction. Excess. Variation. Selection. Divergence.

Darwin’s 5 principles of Natural Selection

And straighter hair is rounder. You can demonstrate this with a strand of you hair by gripping it between the nails of two fingers and squeezing all the way down. As you make it oval, you’ll also see it curl.

Apologies to those who caught this earlier. I accidentally posted several in a row and removed them to post one at a time. Really sorry if it disappeared from your blog, and thanks for sharing.

Curly hair is oval

Stratus: layers AND Cumulus: heaps + height + Cirrus at the very top and you’re a long way already.

Know your clouds

How soap gets things clean is pretty amazing. What’s really nice is how the chemical properties generate such a simple mechanical solution.

The magic of soap

I shall always remember when I was finally taught that the trick is to dip your finger in the wine first.

Make a wine glass sing

Helpful reminder of how fragile the atmosphere is despite it looking pretty big when you’re standing outside.

Our atmosphere is as thick for the Earth a the skin on an apple

One way mirrors definitely do something, but a lot of what they accomplish is also due to maintaining dark on one side and light on another.

Dark and light are the keys to one-way mirrors

The sun behind you, the rain in front of you, and the angle is due to the refraction of light in the raindrops.

The position of a rainbow is predictable

A large boulder, transported and deposited by a glacier. This is my favourite location for glacial erratics. Bonus points if you can tell where it is.

Glacial erratic

Sure the big city is worse than the country. But the reality is back streets in a big city are significantly better than the busy streets in a big city, and air pollution changes massively even for small children down at the height of exhausts versus adults standing higher.

So if you’re not about to move to the country you could help yourself a lot nonetheless by taking the back streets (I read this premise in Focus magazine, but can’t find an online link to reference).

Pollution is highly localized: take the back streets

Part of the reason why bottles should really have their necks to one side instead of in the centre.

Give air a pathway to avoid glugging

Whichever way you look at it, water is a remarkable substance.

Why ice doesn’t sink

A supermoon is when the Moon appears at its largest. Because most orbits are actually ellipses—an oval shape—rather than circular, the moon changes how close it is to Earth each day. A supermoon occurs when the Moon is at least 90% of perigee, the point at which it is closest to Earth. The point it is furthest from Earth is known as the apogee—for our moon, that's around 50,000km further away than when it's at the perigee.

According to NASA, a supermoon can appear around 17% larger and 20% brighter than the faintest moon of the year.

Super moons are a treat for photographers with big zooms and aspirational-looking cityscapes or yachts on the horizon (or ET on a flying bike). Hat tip to Science Llama.

Supermoon

I love this quote from PW Anderson. More often seems like it should be more of the same, but more is different. It would be good if more people considered this.

More is different

The anatomy of a wave showing the key features of a wave: the crest, amplitude, trough, wavelength and when and how it starts to break on a beach.

Common in experience. Less commonly understood.

Anatomy of a wave

Every time I stop and think about a microwave I am reminded of Arthur C Clarke’s 3rd law of prediction:

“Any sufficiently advanced technology is indistinguishable from magic.”

Right up there with wifi and MRI. All just magic.

Also, I think you can use microwaves that little bit better when you understand what’s really going on.

On microwaves

It shuffles a little, but you’ll notice you can always see the face. The mathematics of it are quite hard to fathom.

Incredibly, we only ever see one side of the moon

the Angle of Incidence equals the Angle of Reflection

Echolocation is a remarkable ability to use reflections of a signal to understand your environment. Dolphins, for example, can scan their environment using echolocation to catch food. And ships use sonar, a form of echolocation, to survey the depth of water around them.

I wish I could echolocate. Then I wouldn’t need the one eye trick.

Science sketches