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

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

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

How far away is the storm? The flash-to-bang method can help.

When lightning is made by a storm the rapid heating and expansion of the air create the thunderclap. But because sound travels slower than light, there's a gap between seeing the lightning and hearing the thunder it produced. Using Distance = speed x time, by counting the seconds from seeing the lightning you can easily estimate how far away it is.

Conveniently, the speed of sound in air is about 330 metres/second. So depending on your unit preference:

every 3s you wait the thunder travels about 1 km

every 5s you wait the thunder travels about 1 mile

Give it a try at a safe distance from your next lightning storm.

Also see: thunderclap or rumble, thunder clouds, dirty thunderstorm

Flash-to-bang method

Banner clouds can form on the side of a high or exposed peak and seem to stick to the mountain face like a banner, even on an otherwise cloudless day. There are several theories for how they form but in general strong winds of cold dry air from one side likely interact with warmer humid air on the other. Look out for them next time you're in the mountains.

Also see lenticular clouds, thunder clouds, and more clouds.

Banner cloud

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

Sonic booms are the noise heard when an object travels at or faster than the speed of sound.

As an object travels through the air it pushes air out of the way creating a shockwave — like the wake of a boat. If you were traveling fast in a plane you can imagine that as the shockwaves move away from you at the speed of sound (around 340 m/s), because you're traveling too, the ones in front of you compressed together a little.

As you reach the speed of sound, you're now traveling as fast as the shockwaves and they all bunch up forming a strong pressure wave.

An object traveling faster than the speed of sound leaves its shockwaves behind it in a cone-shape called a Mach cone after Ernst Mach.

To an observer on the ground the sudden change in pressure as the pressure wave passes is experienced as a loud boom.

There's quite a lot of subtlety to sonic booms and we're still researching technology to reduce them to make faster than sound travel less, well, noisy.

Sonic boom

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

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?

The Doppler effect is the change in frequency of a wave as its source moves relative to the observer. The same effect that causes the change in pitch of a siren 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 approaches I try to imagine the crunching up 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.

The Doppler Effect

For years, I’ve wondered at how as a kid I found the monkey bars in a playground (often a jungle gym in the US) so much easier to swing on than I do as an adult. And I see our kids swinging around easily on them, while now it’s hard for me just to hang off them. The reason why is partly to do with the square-cube law.

The square-cube law is the deceptively simple observation that as you scale up dimensions — say, as you get taller — then area of the object increases proportional to the square of the length, while volume increases proportional to the cube of length. This fundamental relationship has enormous significance in the sizes and shapes of animals and the limits of how big trees can get and how big we can build our bridges and buildings.

Because the strength of our bones, muscles or wooden beams is proportional to their cross-sectional area, this means that while the strength of a larger object, assuming the same proportions as the smaller one, increases according to the square of a length, the weight (from the volume it takes up) increases according to the cube of a length. So, relative strength decreases as size increases.

Some corollaries are therefore that children’s small size relative to the area of their muscles and bones makes them relatively stronger than adults and so they can more easily support their weight as they swing on the monkey bars. In the same way, press ups are harder for bigger people than they are for smaller. And while an ant has tiny spindly legs, those legs could easily support 50 other ants of its size, whereas for an elephant to support its own weight it needs chunky legs — not spindly ones — and there’s no chance it could get close to carrying 50 other elephants on its back.

It’s also part of the reason short trees can be spindly, but big sequoias have relatively chunkier trunks, and we need increasingly strong materials to build bigger and bigger skyscrapers compared to the shed in your garden.

Galileo discussed this back in 1638, and it still requires some getting your head around today.

For this and other fascinating insights of scaling check out Scale, by Geoffrey West.

The Square-Cube law

I’d never really thought this through before, but just a tiny lip makes a massive difference. Should be a standard feature on pretty much every saucepan.

How a lip stops drips.

The effect you may have noticed where things further in the distance lose their intensity and colour until they fade into the sky. Most often noticeable with hills or mountains, but also in a misty forest as mist, dust, fog or things like pollution increase the effect.

If it’s a blue sky day, the distance will take on a bluer tone like the colour of the sky.

This scene painted from our ascent of Mt Rainier in the Pacific Northwest. And here’s a sunset version.

Atmospheric perspective

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

A dirty thunderstorm is caused by ash and rock interacting inside a cloud instead of ice particles.

As you can imagine, you can get this with volcanoes, which can be pretty spectacular.

See more about how lightning forms inside a thunder cloud.

Dirty thunderstorm

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

Koomey's law roughly translates to: The energy efficiency of computers doubles roughly every 18 months.

In a new twist beyond Moore’s Law, which shows signs of reaching it’s limits, there’s Koomey’s Law. In his own words, the idea is:

“…at a fixed computing load, the amount of battery you need will fall by a factor of two every year and a half.”

Why does this matter? It means we can fit more computing power into smaller and smaller devices. This is much of the reason the phone in your pocket is probably more powerful than the EDVAC there in the chart.

Koomey’s Law

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

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

Sink a strawpedo

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

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

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.

Physics sketches