# Physics and mathematics: experiments, motion, geometry and probability

Two oscillations draw Lissajous figures. Change their frequencies and phase, then explore the complete collection of physics and mathematics projects.

https://mariuscomper.uk/en/physics/

- [Cluj under the lid: the winter nights when it is warmer on the mountain than in the city](https://mariuscomper.uk/clujul-sub-capac/en/): On 34.5% of the winter nights measured by the Cluj weather balloon between 1957 and 2012, the air at 1,500 m above sea level was warmer than the air at ground level. Every night, on the real relief, up to 2025. In Romanian and English.
- [Halley’s Comet: where it is now, and its whole 75-year orbit from 1986 to 2061](https://mariuscomper.uk/cometa-halley/en/): Halley’s Comet passed the far point of its orbit on 8 December 2023 and is heading back to the Sun, which it rounds on 28 July 2061. The page follows the whole orbit by scroll, 1986 to 2061, on NASA JPL positions: of 27,563 days, the comet spends 78 closer to the Sun than Earth is and 35 years farther out than Neptune. With a year of birth it shows where the comet was then and how old you will be when it returns.
- [Falling into a black hole: what the sky looks like on the way in](https://mariuscomper.uk/gaura-neagra/en/): A fall into a black hole seen through the faller’s own eyes. Each point of the picture is a ray of light followed through curved space with the equations of general relativity, over NASA’s map of 1.7 billion stars. At the horizon the black disc is 84° across and covers 13% of the sky; the rest is still stars. At Sagittarius A* the fall from the horizon to the centre takes 28 seconds.
- [How a train steers without a steering wheel](https://mariuscomper.uk/trenul-fara-volan/en/): A train wheel is shaped like a cone, and the shape does the steering. Push a wheelset sideways, watch the wave about ten metres long it draws, then test the idea with two cups.
- [How many times can a sheet of paper be folded? The stack from 42 folds reaches the Moon, the paper would span the Milky Way](https://mariuscomper.uk/de-cate-ori-se-poate-impaturi-o-foaie/en/): An A4 sheet folds six times in one direction, the record is 12, and 42 folds would take the stack to the Moon but need a strip 107,052 light-years long. You fold the sheet yourself, then ask for more paper and watch the bill grow fold by fold, by Britney Gallivan's formula.
- [The birthday sky: the Moon, planets and the Sun's constellation](https://mariuscomper.uk/cerul-din-ziua-ta/en/): What was in the sky on the day you were born? Pick a date and a place and get the sky chart: Moon phase, planets above the horizon, sunrise and sunset, plus the constellation the Sun was really in — not the magazine sign, because of precession. All computed in your browser.
- [The solar system at 1:10 billion: Neptune would be 450 m from the Sun](https://mariuscomper.uk/sistemul-solar-pe-strada-ta/en/): If the Sun were 14 cm across, Earth would be a 1.3 mm bead 15 m away, Jupiter at 78 m, Neptune at 450 m. Pin the Sun on your street and walk to each planet, with Voyager 1 on the same map and a printable class sheet. No textbook picture fits to scale.
- [How fast are you moving? Earth's spin, orbit, galaxy and the CMB](https://mariuscomper.uk/cu-ce-viteza-te-misti/en/): You sit still, yet Earth carries you along: spin, orbit, galaxy and cosmic background. Pick a place and see all four speeds on a single ruler.
- [How long does it take to fall through the Earth?](https://mariuscomper.uk/tunelul-prin-pamant/en/): Find your town, see where its tunnel comes out on the other side, and start the race of two fallers: one through the textbook uniform Earth, one through the real Earth. Which wins, and by how much?
- [Skip a stone across a lake. How many bounces can you make?](https://mariuscomper.uk/piatra-pe-apa/en/): A game that follows the laws of physics: skip a stone across a drawn lake and count the bounces. What matters (tilt, spin, speed), what a Latin author wrote about the same game about 1,800 years ago, and the world record: 88 bounces.
- [The Earth rang like a bell for weeks](https://mariuscomper.uk/pamantul-a-sunat-ca-un-clopot/en/): After the earthquake of 26 December 2004, which with the tsunami it set off killed or left missing 227,898 people, the whole planet vibrated like a bell. Hold a button to hear a month of the real record played back 500,000 times faster while a globe takes the shape of each tone; the Earth's breath, 0.05 mm every 20½ minutes, was recorded in Romania too.
- [The 52 Hz whale, ‘the loneliest in the world’, and the blue whales singing ever deeper since 1963](https://mariuscomper.uk/cea-mai-singura-balena/en/): What US Navy hydrophones heard from 1989 to 2004, and what is not known about the 52 Hz whale. From 1963 to 2019 the song of northeast Pacific blue whales dropped by a third; type your birth year and hear a NOAA recording played at that year's note and at the 2019 note. In Romanian and English.
- [Big Ben’s clock is adjusted with old pennies: the Great Clock of Westminster, and what one coin does to its day](https://mariuscomper.uk/big-ben-pennies/): UK Parliament says one old penny on the Great Clock’s pendulum makes it gain 0.4 seconds a day. Slide the coin along the 4.4-metre rod to see where it speeds the clock, where it does nothing and where it slows it; then let the days run, hear the hour strike in a real recording and make a card of your tray.
- [How many molecules are in a glass of water? Brownian motion and Avogadro's number, measured by you](https://mariuscomper.uk/numara-moleculele/en/): Catch real one-micron beads filmed in water under a microscope, one by one, and their tremble gives you the number of molecules in a mole, as in Jean Perrin's 1908 experiment. What Robert Brown actually saw, what Einstein predicted, the path without a tangent, your glass of water. In Romanian and English.
- [How does a hailstone get that big? Ride one through the storm](https://mariuscomper.uk/grindina/en/): Pick the size of the hail you remember and see how fast it fell and how hard it hit. Then grow a stone in an updraft, cut it in half, and learn what is known — and what is not — about anti-hail rockets. In Romanian and English.
- [The 1977 earthquake, over today's red-dot buildings](https://mariuscomper.uk/cutremurul-peste-bulina/en/): Follow the 1977 wave across a 3D map of Bucharest, see the damage recorded for each square kilometre and search today's seismic-risk list. The historic record describes map squares, not what happened to any one building.
- [Drag the sky back 640 million years and watch the Moon change](https://mariuscomper.uk/luna-pleaca/en/): The Moon moves away 38.3 mm a year, almost as fast as your fingernails grow. Drag the sky back through time and see the Sun and Moon at their size then, with a shorter day and different eclipses; every number is marked measured, counted in rock or calculated.
- [Older Than Earth: which stars made you?](https://mariuscomper.uk/older-than-earth/en/): Nearly every atom in your body is older than the Earth: about 63 in 100 are primordial hydrogen, older than the stars. Follow one gold atom from the Big Bang to you, weigh your own stardust, and find where gold comes from. In Romanian and English.
- [Where Light Dies](https://mariuscomper.uk/where-light-dies/en/): From the sunlit surface to 10,935 metres down: five ocean zones, the red light that dies first, the 2004 giant squid, the Titanic at 3,800 metres and the three crews that touched the bottom of the Mariana Trench — a scrolling descent, in Romanian and English.
- [Their last breath is in your next one](https://mariuscomper.uk/ultima-suflare/en/): Breathe out and watch your breath travel around the Earth on the real winds. Then find out how many molecules from the breath of someone you have lost enter you with every breath. In Romanian and English.
- [Bats aren't blind, but they hunt by ear. Find the moth by its echo](https://mariuscomper.uk/liliacul-nu-e-orb/en/): Hear a pipistrelle's call 10 times slower, so you can hear it at all, and find a moth in the dark by its echo. Then a whole attack, slowed down, the moth that hears the bat from 30 metres, and where the 1,000-mosquitoes-an-hour myth comes from. In Romanian and English.
- [What a sound looks like](https://mariuscomper.uk/cum-arata-un-sunet/en/): A brass plate computed from real physics, strewn with sand. Bow it or sing to it, and the sand runs onto the lines that stand still, as it did for Ernst Chladni in 1787. Then find eight of his figures. In Romanian and English.
- [The last colour of a soap bubble](https://mariuscomper.uk/ultima-culoare/en/): A soap bubble painted only with the physics of light: every colour comes from the thickness of the film. Watch it drain until it turns black, then set Newton's words from 1704 beside the colours computed today. In Romanian and English.
- [The church Gaudí hung from the ceiling](https://mariuscomper.uk/biserica-atarnata/en/): Gaudí designed the Colònia Güell church upside down, from string and sacks of shot. Hang the weights, turn the model over and walk into the crypt that gravity drew. In Romanian, English, Spanish and Catalan.
- [It is raining through you right now](https://mariuscomper.uk/ploaia-invizibila/en/): Your screen becomes a detector: see the cosmic-ray muons crossing it, about 17 a second through your body. Then climb 15 km to where one proton becomes a cascade, watch relativity on two clocks, the pyramid of Khufu x-rayed and the neutrinos that arrive through the Earth at night. And how to see them at home. In Romanian and English.
- [Are all 17 in the Alhambra? Count them yourself](https://mariuscomper.uk/alhambra/en/): Researchers found 11, 12, 13, 14 or all 17 ways to repeat a pattern in the Alhambra, by different rules. Choose whose examples you trust and which rules you accept, and count for yourself. In Romanian and English.
- [Can you weigh an element no one has ever seen?](https://mariuscomper.uk/elementul-care-lipsea/en/): In 1871 Mendeleev left gaps in the periodic table and described gallium, scandium and germanium in advance. Work out the element in the “?72” box from its neighbours, then see what Winkler measured in 1886, who was right about gallium, and how many elements were known in the year you were born. In Romanian and English.
- [Measure the Earth with a pencil](https://mariuscomper.uk/masoara-pamantul/en/): At your local noon, a pencil's shadow shows how far you are from the Equator; two shadows in two towns give the size of the Earth, as for Eratosthenes. Your exact noon, a class mode and what the ancient sources say. In Romanian and English.
- [How many ancestors did you have in the year 1000?](https://mariuscomper.uk/cati-stramosi/en/): The places in your family tree double every generation. By the year 1000 they need billions of people, in a Europe of about 36 million. Put your grandparents' towns on the map, follow your ancestors generation by generation and compare them with a classmate's. In Romanian and English.
- [The middle of your eye is made of carbon from the air of the year you were born](https://mariuscomper.uk/anul-din-ochi/en/): Nuclear tests in the 1950s and 60s nearly doubled the carbon-14 in the air, and every human body kept the mark. Put your family's birth years on the curve and see which year each part of you is made of: lens, tendon, heart, blood. In Romanian and English.
- [Three shuffles won’t hide a card](https://mariuscomper.uk/sapte-amestecari/en/): Shuffle a new deck three times, push one card into the middle and find it yourself from the threads the shuffles leave behind. Then see why mathematicians say “seven”. In Romanian and English.
- [The prime meridian: voted in 1884, moved 102.5 metres, and your own noon](https://mariuscomper.uk/greenwich-meridian/en/): Zero longitude at Greenwich as a scroll scene: your own true noon today, worked out for where you are, the 1884 vote, the 102.5 metres between the courtyard line and the zero in use today, crossed by the sun in 0.35 seconds, and the minute to step outside and look at your shadow.
- [Thousands of starlings, no leader: how they turn as one](https://mariuscomper.uk/murmuration/): Each starling keeps track of just six or seven neighbours, near or far. Play the falcon over a live flock of thousands, watch a turn sweep through at 20 to 40 metres a second, and find out where to see a murmuration.
- [Most of your atoms are 13.8 billion years old: where each part of your body was made](https://mariuscomper.uk/made-of-stars/): Six in ten of your atoms are hydrogen from the Big Bang. Your oxygen came from exploding giant stars, much of your carbon from dying stars, half the calcium in your bones from exploding white dwarfs, your iodine from colliding neutron stars. Set your weight and watch your body come apart.
- [Jump into a hole through the Earth](https://mariuscomper.uk/fall-through-the-earth/): A straight tunnel through the centre of the Earth and a fall of 38 minutes 11 seconds, computed from the PREM model: you get heavier on the way down, the trip splits into three equal thirds, and from Bucharest you come out in the South Pacific. With a real-time fall, antipode globes and straight tunnels between cities, in English and Romanian.
- [How Marian Rejewski broke Enigma: a working machine and his mathematical attack](https://mariuscomper.uk/enigma-rejewski/en/): An exact Enigma that decrypts a real German message from 7 July 1941, then Rejewski's attack run on your device: the doubled key, the loops the cables cannot change and the 105,456-row catalogue, built in seconds. Plus the codebreakers' passage through Romania in 1939.
- [Why is the night sky dark? Olbers' paradox and the light that has not reached us yet](https://mariuscomper.uk/paradoxul-lui-olbers/en/): If the stars went on for ever, the sky would blaze like the Sun. A forest where every line of sight hits a tree, a sky filling with suns, three centuries of wrong answers, and the 13.8-billion-year-old light that covers the whole sky, invisibly.
- [When the sun really reaches you: sunrise and sunset behind the mountains for any place in Romania](https://mariuscomper.uk/soarele-de-dupa-munte/en/): Almanac sunrise assumes a flat horizon. Calculated from the terrain for every day of the year: at Băile Herculane on 21 December the sun only clears the mountains at 10:54; 6.7 million people live where the terrain takes at least half an hour of sun on the shortest day.
- [Which mountains you can see from your town: a panorama computed from the terrain for anywhere in Romania](https://mariuscomper.uk/se-vad-muntii/en/): Type a town and see which peaks rise above its horizon and how far away they are. More than half of Romanians live where a peak over 2,000 m would be in view; from the Retezat you can see Bulgaria, from the Apuseni the Tatras.
- [Nine seconds between the flash and the thunder. How far away was it?](https://mariuscomper.uk/cat-de-departe-a-fost-fulgerul/en/): Divide the seconds by three for kilometres, and heard thunder means the storm can strike. With a map of your town.
- [The space station flies over your house. Here is when to look up](https://mariuscomper.uk/statia-spatiala-deasupra-ta/en/): You can see it with the naked eye, like a very bright star. Pick your town for the next passes, to the minute.
- [The northern lights have been seen from Romania. How many times since records began?](https://mariuscomper.uk/aurora-din-romania/en/): Three times in three years: November 2023, May 2024, January 2026. Since 1932, 23 storms have reached Kp 9.
- [The Plough didn't look like this 100,000 years ago](https://mariuscomper.uk/cerul-de-acum-100000-de-ani/en/): 100,000 years ago the Plough's bowl gaped almost twice as wide. Drag time across the sky, watch Polaris lose the pole, and meet the people who looked up then.
- [All the DNA in you would reach the Sun and back. How many times?](https://mariuscomper.uk/cat-adn-ai-in-tine/en/): About 21 times: 6.2 billion kilometres of DNA in 3 trillion nucleated cells. Guess first, then redo the sum with your own numbers and learn why the 600-trips myth no longer stands.
- [The cloud above you weighs as much as 80 elephants](https://mariuscomper.uk/cat-cantareste-un-nor/en/): An ordinary summer cloud gathers about 500 tonnes of water, as much as 80 bull elephants, and still does not fall. Weigh your own cloud, with your own weight on the scales, and learn what holds it up.
- [The farthest thing people have ever made is a day away, even for light](https://mariuscomper.uk/voyager-1/en/): Romanian is one of the 55 languages on Voyager 1's golden record. On 18 November 2026 the craft reaches one light-day from Earth, a moment with three different dates depending on how you measure it. The story, from the tour that was never made to the instruments going out.
- [When will the sky go dark at noon over your town?](https://mariuscomper.uk/eclipsele-tale/en/): Pick the nearest town and see every solar eclipse it gets from 1900 to 2100: which were total, how much Sun was left each time, and when the next shadow comes.
- [How old is sunlight: 8 minutes across space, 170,000 years inside the Sun](https://mariuscomper.uk/lumina-veche-de-100000-de-ani/en/): Light flies eight minutes to reach you, but its energy wandered inside the Sun for 170,000 years. A random-walk simulation, a race with a neutrino, and eight true-or-false sentences.
- [The water bear survived open space. A 37-degree day kills it](https://mariuscomper.uk/ursul-de-apa/en/): Dried out, the water bear spent ten days in the vacuum of space and woke after over 30 years frozen. Awake, it dies at 37 degrees. Measure yourself against it, to scale, and play with its limits.
- [What a raindrop looks like: sphere, bun, mid-air breakup](https://mariuscomper.uk/cum-arata-o-picatura-de-ploaie/en/): No raindrop looks like a teardrop: small it is a sphere, large a flattened bun falling at 31 km/h, and the giants break up in mid-air. Pick a diameter, see the shape and speed, then play eight true-or-false sentences.
- [Pizza Size Comparison — Which Pizza Is Worth More? Calculator](https://mariuscomper.uk/calculator-pizza/en/): A 40 cm pizza is not 25% bigger than a 32 cm one. It is 56.25% more pizza. Unless the price grows by at least that much, the large one is the better deal.
- [What do HB, 2B, 4B and 2H mean on a pencil?](https://mariuscomper.uk/duritate-creioane/en/): H is hard and pale, B is soft and black, and the number says how much. A 20-grade scale, from 9H to 9B, with HB in the middle.
- [Why Phone Batteries Die in the Cold](https://mariuscomper.uk/bateria-la-frig/en/): Phone batteries do not lose electrical charge in the freeze: the electrolyte thickens, internal resistance surges tenfold, and the processor cuts off power to prevent critical voltage collapse.
- [The other side of the Moon: why it looks so different, and who has landed there](https://mariuscomper.uk/cealalta-luna/en/): Turn a globe of the Moon and watch the dark seas almost disappear: they cover 30% of the near side and 2% of the far side. With a map of crust thickness, the South Pole–Aitken basin, the places where Chang’e 4 and Chang’e 6 landed, and what the first samples brought back from there say.
- [Your climate has moved — Marius Comper](https://mariuscomper.uk/clima-ta-s-a-mutat/en/): Compare your Romanian locality’s summers with Europe in 1971–1990. An interactive ERA5 atlas of temperature and rainfall.
- [The Clock Inside Your Inner Ear](https://mariuscomper.uk/douazeci-de-secunde/en/): Spin in a chair and stop dead: you feel a rotation that isn't there. Keep turning instead, and the sensation disappears entirely — an interactive physical model of the inner ear shows why, and how a pilot ends up in a graveyard spiral believing they're flying straight.
- [Where does the rain here go? — The path of rain](https://mariuscomper.uk/drumul-ploii/en/): At Arad, the Mureș flows west: through the Tisza, then into the Danube and the Black Sea. Search for a river or pick a place to follow the water, then discover the land that feeds it.
- [Inside a note — An instrument for curious ears](https://mariuscomper.uk/inside-a-note/en/): Take a sound apart. Shape its harmonics, see the waveform, and listen to the same pitch change character.
- [The North That Moves](https://mariuscomper.uk/nordul-care-nu-sta/en/): A compass for the wandering north magnetic pole: 36 kilometres in one year, a NOAA/BGS model, and two norths that separate over time.
- [We Never See the Planets](https://mariuscomper.uk/nu-vedem-planetele/en/): A planet becomes visible through the light it removes. Move a planet across a star and see the signal, then choose a real world from NASA's archive.
- [Pocket gravity](https://mariuscomper.uk/pocket-gravity/en/): Hold and drag the sky to bend 1,800 orbits. Try to tear the ring apart — then let gravity gather it again.
- [How Small Is the Present?](https://mariuscomper.uk/cat-de-mic-este-prezentul/en/): The only “now” you can be sure of is the point where you stand. At any distance, the present is a window no signal can close, and one step moves it.
- [You pick first. I pick second.](https://mariuscomper.uk/aleg-al-doilea/en/): Choose one of three dice and play against the house. All average 5, yet each beats another more often. Open the table and check every outcome.
- [Would you open the shortcut?](https://mariuscomper.uk/scurtatura/en/): Open a road in an imaginary town and see why 65 minutes can become 80. Then change the traffic until the shortcut starts to help.
- [No Dice: Can You Actually Be Unpredictable?](https://mariuscomper.uk/fara-zar/en/): Press 0 or 1 across 20 rounds. An 8-state automaton tries to guess your every choice before you press.
- [The Falling Ruler: Can you catch it in mid-air?](https://mariuscomper.uk/caderea-riglei/en/): Five drops test how fast the brain converts visual motion into mechanical grip. Each catch leaves a stamped mark on the ruler's body.
- [Can You Find the Center of Gravity?](https://mariuscomper.uk/punctul-de-echilibru/en/): Five asymmetrical silhouettes test human intuition against static rotational moments. Touch the plate to see if it balances or topples.
- [Where Does the Beam Emerge?](https://mariuscomper.uk/unde-iese-raza/en/): Five rounds test subjective vision against Euclidean geometry. Fire a laser through an opaque wall and measure the V1 angular distortion.
- [Can you eyeball a perfect square?](https://mariuscomper.uk/patratul-perfect/en/): The width is fixed at 200 mm. Raise the top edge until the rectangle looks like a perfect square. On each round, the master caliper gauge drops over the slab and measures your error.
- [Through the Tunnel: Can You Catch the Exit?](https://mariuscomper.uk/prin-tunel/en/): Five rounds test how the brain projects the velocity of an invisible mark. The point freezes instantly on trigger, revealing the signed error in milliseconds.
- [Same Tile or Mirror?](https://mariuscomper.uk/acelasi-sau-oglinda/en/): Eight pairs of blue tiles, four matching and four mirrored, in the same order for everyone. Instant verdicts, final score at the end.
- [Can You Find the Center of the Circle?](https://mariuscomper.uk/fara-compas/en/): Five geometric shapes wait on the drafting board. Tap where you think the exact center is, and the compass needle measures your error in millimetres.
- [Sixty-Six Times: Oxygen Held by Haemoglobin](https://mariuscomper.uk/saizeci-si-sase-de-ori/en/): Haemoglobin's binding capacity is about 66 times the dissolved fraction at 100 mmHg. Without haemoglobin, about 82 L/min would be only the theoretical minimum scale of flow required.
- [Can you set the angle to exactly 90 degrees?](https://mariuscomper.uk/fara-echer/en/): Rotate the blade until you believe it forms a perfect right angle. Then drop the steel square and measure your error in tenths of a degree.
- [The Speed of Sound](https://mariuscomper.uk/viteza-sunetului/en/): From Yakutsk to Bangkok, sound gains 6.83% in speed — nearly a full second over every 5 kilometres.
- [No Spirit Level: Can You Level a Beam by Eye?](https://mariuscomper.uk/fara-cumpana/en/): Level the beam and release the ball. Gravity measures your eyes' angular tilt.
- [Ninety Millimetres of Mercury: The Calf's Second Heart and the Pressure Drop in the Ankle](https://mariuscomper.uk/nouazeci-de-milimetri/en/): When you stand motionless, the column of blood raises ankle pressure to 90 millimetres of mercury. Six to seven steps bring it down towards approximately 25 millimetres, while sustained walking maintains a 20–25 millimetre plateau.
- [A Slinky Starts Falling from the Top](https://mariuscomper.uk/cade-de-sus-in-jos/en/): The top falls, the bottom stays almost stationary for about 0.27 seconds, and the centre of mass descends by an ideal 35.8 centimetres.
- [Why Buttered Toast Always Lands Butter-Side Down](https://mariuscomper.uk/jumatate-de-rotatie/en/): 180° at 0.75 metres, ordinary table height; it would take almost 3 metres for 360° and a butter-up landing.
- [How one square metre becomes A4](https://mariuscomper.uk/de-ce-a4/en/): A0 has a nominal area of 1 m², while its published 841 × 1,189 mm dimensions leave a gap of 51 square millimetres. Four halvings yield A4, and the 1:√2 ratio preserves the shape.
- [Twenty Minutes for a Bubble: The Biophysics of Knuckle Cracking and the Cavitation Refractory Period](https://mariuscomper.uk/douazeci-de-minute/en/): Under >60 N tensile force, synovial pressure falls to −2.5 bar and the cavity appears in <310 ms. MRI supports cavity formation, while the 2018 model leaves a role for partial collapse open; the ~20-minute clock is illustrative.
- [Your Ear Has Its Own Amplifier](https://mariuscomper.uk/patruzeci-de-decibeli/en/): The quantitative biophysics of the active cochlear amplifier: how 12,000 outer hair cells leverage a 150 mV transmembrane gradient to oscillate nanomechanically at over 20,000 Hz, generating otoacoustic emissions and the Tartini phantom tone (2f1 - f2).
- [The Body Stands Like an Inverted Pendulum](https://mariuscomper.uk/pendulul-din-glezna/en/): In quiet standing, the ankle keeps correcting an unstable pendulum. In a no-correction model, a 0.5° sway grows to 5° in 0.72 seconds at the default height of 1.75 m.
- [One Volt per Centimetre: The Skin's Epithelial Battery and the Electric Field That Heals Wounds](https://mariuscomper.uk/un-volt-pe-centimetru/en/): Skin maintains a 20–50 mV potential; a wound collapses local resistance and creates a 100–200 V/m field that mechanically steers keratinocytes to the cut long before chemical gradients can diffuse.
- [Fifty Grams in the Skull](https://mariuscomper.uk/cincizeci-de-grame/en/): Submerged in 140 millilitres of fluid, the brain sheds 97% of its effective weight through buoyant force, while deep sleep unleashes a hydraulic tide that purges cellular waste.
- [Tens of Picoamperes in the Dark](https://mariuscomper.uk/patruzeci-de-picoamperi/en/): In darkness, rod ion channels remain open; a 20 pA illustrative model shows why light can reduce energy consumption by more than 75% in mammalian rods.
- [Walking is controlled falling](https://mariuscomper.uk/mersul-ca-un-pendul/en/): In walking, the body passes over the stance foot like an inverted pendulum and recovers about 65% of external mechanical energy. Measure your walk and see where its Froude number lands.
- [Pupil squared](https://mariuscomper.uk/pupila-la-patrat/en/): The pupil can widen from 2 to 8 millimetres: fourfold in diameter, sixteenfold in opening area. The geometry is simple; the retina adapts separately.
- [One Kilogram at Arm's Length](https://mariuscomper.uk/un-kilogram-la-capatul-bratului/en/): At the same mass, distance from the elbow can change torque tenfold. Play with mass, distance, and angle, then see what static force would balance the object at the biceps.
- [Seven Milliseconds Behind the Head: The Biophysics of the Vestibulo-Ocular Reflex and Why Your Eyes Beat Any Gimbal](https://mariuscomper.uk/sapte-milisecunde/en/): While the cortical visual system needs 150 milliseconds to process motion, the inner ear vestibulo-ocular reflex rotates the eyes in the opposite direction in just 7 milliseconds through the fastest neural arc in the human body.
- [Why You Don't Deafen Yourself Talking](https://mariuscomper.uk/douazeci-de-decibeli/en/): The quantitative biophysics of the stapedius reflex: anticipatory activity observed during vocalisation and frequency-dependent filtering in the middle ear. The simulator uses 20 decibels as an explicit model example.
- [Thirteen Nanometres: The Biophysics of Fingerprints and the Nanoscale Limit of Touch](https://mariuscomper.uk/treisprezece-nanometri/en/): A static touch on the skin resolves two separate pins only when spaced at least 1.6 millimetres apart. Yet the moment a fingertip slides laterally, epidermal friction ridges convert microscopic surface relief into a 250 Hz shear wave, allowing the detection of surface grooves just 13 nanometres high.
- [Five Hundred and Eighty Calories per Gram: The Extreme Biophysics of Sweat and the Human Heat Engine](https://mariuscomper.uk/cinci-sute-optzeci-de-calorii/en/): Why humans are Earth's greatest endurance coolers in the heat: the biophysics of water phase transition, 1,343-watt cooling power, and the dripping sweat paradox.
- [Two Millinewtons per Metre: The Surface Tension of Lungs and the 480-Million-Bubble Paradox](https://mariuscomper.uk/doi-milinewtoni/en/): If human lungs were lined with pure water, all 480 million alveoli would collapse immediately. A 2.5-gram lipid film reduces surface tension to 2 mN/m at expiration.
- [One and a Half Watts: The Hydraulic Mechanics of the Human Heart](https://mariuscomper.uk/un-watt-si-jumatate/en/): A pump displacing 7.6 tonnes of fluid daily operates at a mechanical output of just 1.33 watts and a total metabolic power of 7.4 watts.
- [Nine Degrees Under Your Fingertip: Why Metal Feels Colder Than Wood](https://mariuscomper.uk/noua-grade-sub-deget/en/): From the same 20 °C starting point, the skin interface reaches 20.6 °C on aluminium and 29.2 °C on wood; the idealised 8.65 °C gap comes from an effusivity ratio of almost 67 to 1.
- [Ten Oscillations a Second: The Hand's Physiological Tremor](https://mariuscomper.uk/zece-oscilatii/en/): In a human centrifuge experiment, resonant mechanics predicted 99% of postural-tremor peak frequency. The phone used for measurement adds inertia and changes the observed spectrum.
- [Seven Hundred Newtons on the Molar: The Biomechanics of the Bite and Enamel's 100-Atmosphere Strength](https://mariuscomper.uk/sapte-sute-de-newtoni/en/): Although the human jaw operates as a Class III lever with a mechanical disadvantage at the incisors (150–250 N), back at the second molar bite force surges to 700–900 N (70–90 kgf). Concentrated onto just a few square millimetres, contact stress exceeds 150–300 MPa (over 1,500 atmospheres — higher than the Mariana Trench), resisted without fracture by enamel's decussating prism architecture.
- [Ten Microseconds Between the Ears: How the Brain Computes Sound Location](https://mariuscomper.uk/zece-microsecunde/en/): The human brainstem detects sound arrival disparities down to 10 microseconds (3.4 mm in air) using axonal delay lines and coincidence detector neurons in the medial superior olive.
- [Sixty kilograms a day? How much ATP your body really makes](https://mariuscomper.uk/saizeci-de-kilograme/en/): Your body holds only 50–100 grams of ATP, yet remakes 36–47 kg of it a day at 2,000 kcal. Turn the machine that makes it with your finger, and find out where the famous 21,000 rpm comes from.
- [Half a Millimetre per Second: Why Blood Nearly Stops in the Capillaries](https://mariuscomper.uk/jumatate-de-milimetru/en/): At a resting cardiac output of 5.0 L/min, Q = A × v gives about 185 mm/s in the aorta and 0.19–0.24 mm/s across the capillary bed. Systemic oxygen exchange depends on tissue, metabolism, diffusion distance and flow distribution.
- [Forty-Three Dioptres: Why We See Completely Blurred Underwater and Where the Eye's True Lens Really Is](https://mariuscomper.uk/patruzeci-si-trei-de-dioptrii/en/): The eye's true lens is the cornea's curvature in air. That is why a dive mask restores sharp vision with completely flat glass.
- [Nine Photons in the Dark: The Quantum Limit of Human Vision](https://mariuscomper.uk/noua-fotoni/en/): Hecht estimated the visual threshold at 5–14 absorbed photons; 9 is representative. Modern intact-rod experiments estimate about 2,000 cGMP molecules hydrolyzed per R*, while the roughly 1 pA measurement came from toad rods.
- [One Million to One: The Stomach's Impossible Acid Gradient](https://mariuscomper.uk/un-milion-la-unu/en/): At the parietal-cell apical membrane, the H⁺/K⁺-ATPase produces one of the steepest proton gradients known in mammalian tissue: from pH 7.40 in the cytosol to pH 1.40 in the secretory canaliculus, or one million to one. The mucus-bicarbonate barrier is 200 µm thick.
- [Eight Nanometres per Step: Kinesin's Invisible March](https://mariuscomper.uk/opt-nanometri/en/): To haul cargo across one metre of axon, delivery accumulates the kinematic equivalent of 125 million 8-nm steps through coordinating kinesin relays. While free diffusion would exceed 150,000 years, in vivo fast axonal transport completes delivery in 2.5–5 days.
- [Forty Millimetres on the Back, Two on the Fingertip](https://mariuscomper.uk/patruzeci-de-milimetri/en/): On the index fingertip we resolve two points 1.6 millimetres apart, but on the back they must be spread 42 millimetres apart to avoid fusing. The back compresses space by 26 times due to mechanoreceptor density and cortical magnification.
- [Ten Picometres in the Eardrum](https://mariuscomper.uk/zece-picometri/en/): If sound struck inner ear fluid directly, 99.89% of energy would bounce off like a wall. To bridge the impedance mismatch, evolution built a mechanical three-bone lever that amplifies pressure over 22-fold — enabling the eardrum to detect vibrations of just 10 picometres.
- [Ten Million Volts per Metre](https://mariuscomper.uk/zece-milioane-de-volti/en/): A human cell maintains a resting potential of just 70 millivolts. Yet because this voltage drops across a lipid bilayer only 7 nanometres thick, the transverse electric field reaches 10,000,000 V/m — over three times the dielectric breakdown threshold of a lightning strike in air.
- [Thirty-Nine Bits per Second](https://mariuscomper.uk/treizeci-si-noua-de-biti/en/): The 17-language mean is 39.15 bits per second, but languages differ, from 33.8 to 45.9. The rate varies less than syllable speed or information per syllable.
- [The Clay That Never Cools](https://mariuscomper.uk/lutul-londrei/en/): In 1900, the Tube was 14°C. After 125 years of braking, 500 GWh of annual heat have saturated the clay mantle, turning the earth into a 30°C radiator.
- [The Heat per Kilogram](https://mariuscomper.uk/caldura-pe-kilogram/en/): The Sun sheds 0.19 mW/kg; powering a 10 W LED bulb requires 52 tonnes of solar matter.
- [Thermodynamics of the Tongue and Blood: Butter and Margarine](https://mariuscomper.uk/unt-sau-margarina/en/): Butter melts at 34°C on the tongue, while industrial margarine melts at 44°C like wax: 150 years of chemistry, gastronomy, and clinical trials.
- [34 Hours and 17 Minutes: The Floor Under the Pendulum](https://mariuscomper.uk/sub-pendul/en/): If you let a pendulum swing freely in Bucharest, its plane completes a full rotation in 34 hours and 17 minutes.
- [Five Hundred Tonnes in a Clear Sky](https://mariuscomper.uk/cinci-sute-de-tone/en/): A standard 1 km³ cumulus cloud holds 500 tonnes of liquid water. Dispersal into 119 quadrillion droplets caps settling speed at 1.2 cm/s, allowing rising thermal currents to support the entire mass.
- [The Horizon That Lies](https://mariuscomper.uk/orizontul-care-minte/en/): 150 km to the Bucegi Mountains, only 43 km of curvature reserve — the air is the culprit.
- [Two Notes in the Mouth](https://mariuscomper.uk/doua-note/en/): Vocal folds produce only a raw drone: what we hear as speech is a chord of two frequencies. In “i”, the gap spans over 3 octaves; from “u” to “i”, the second frequency triples; and Romanian anchors two central vowels along the midline.
- [The Deep Ocean Highway](https://mariuscomper.uk/sofar/en/): At one thousand metres depth, the ocean forms a natural waveguide carrying sound across global basins. In 1991, a tone emitted near Antarctica was recorded in Bermuda, 18,200 kilometres away.
- [Fifty Beats per Second](https://mariuscomper.uk/cincizeci-de-hertzi/en/): The power socket dictates time for millions of microwave and radio clocks. In 2018, a 113 GWh shortfall stole 346 seconds (5m 46s) from 400 million people without causing a single blackout.
- [The Tree That Closes](https://mariuscomper.uk/arborele-care-se-inchide/en/): By generation 30, a family tree requires 1,073,741,824 ancestors, while Earth held only 320 million people in 1100 AD. Travel through 40 generations on the ancestry spindle.
- [Smell does not fit in one word](https://mariuscomper.uk/mirosul-nu-incape/en/): Choose up to three words from an olfactory catalogue and see how many molecules carry them together.
- [The 23-Cent Comma](https://mariuscomper.uk/coma-pitagoreica/en/): Why every piano lies to your ear.
- [The Dandelion and the Ring in the Air](https://mariuscomper.uk/inelul-din-aer/en/): Turn a solid disk into a dandelion pappus and watch the gaps between its filaments maintain a separated vortex ring. At its measured porosity, the pappus produces more than four times as much drag per unit projected area as the solid reference disk.
- [Nine Drops in a Century](https://mariuscomper.uk/noua-picaturi/en/): At room temperature it shatters like glass under a hammer. Under decadal gravity, it flows as a liquid 230 billion times more viscous than water. In 99 years, only nine drops have fallen from the University of Queensland funnel.
- [The charged drop sharpened before impact](https://mariuscomper.uk/picatura-care-a-alunecat/en/): A saltwater drop slid over an insulator, formed a cone near copper, and left local defects after 3,000 charged impacts. The neutral control stayed smooth.
- [Seven Metres per Second: Why the Pulse at Your Wrist Is Not the Blood Flowing](https://mariuscomper.uk/sapte-metri-pe-secunda/en/): When you take your pulse, you feel an elastic shockwave travelling 35 times faster along the arterial wall than the blood itself.
- [Eleven Joules at the Heel](https://mariuscomper.uk/tendonul-arcului/en/): An in-vivo study measured 11.3 J of propulsive recoil at 3.5 m/s; the historical 35 J figure is 3.1 times larger, but it does not describe the same measurement.
- [The Cat Without a Push](https://mariuscomper.uk/pisica-fara-impingere/en/): A cat can turn its paws down after changing shape in mid-air. Angular-momentum conservation still holds, and the two-segment model shows where the net rotation comes from.
- [Why spaghetti snaps into three](https://mariuscomper.uk/rasuceste-inainte-sa-rupi/en/): Dry spaghetti usually breaks into at least three pieces under simple bending. Twist can quench the cascade because the torsional wave unloads energy faster.
- [A Wet Mouse Shakes 30 Times a Second](https://mariuscomper.uk/treizeci-de-ori/en/): A Labrador shakes at about 4.5 Hz and a brown bear at 4 Hz. The stroboscopic plate links that rhythm to the acceleration needed to release water from fur.
- [Can you cut the ribbon exactly in half?](https://mariuscomper.uk/taie-la-jumatate/en/): Touch the spot where you would cut. The ribbon straightens and shows the difference at once.
- [The Paradox of Romania's Coastline](https://mariuscomper.uk/rigla-ascunde/en/): Drag the ruler and watch the compass measure Romania's real coastline; the length recalculates live.
- [Why Sink Water Ignores the Hemispheres](https://mariuscomper.uk/trei-ore-de-liniste/en/): A sink drains in thirty seconds. Earth's rotation needs nearly three hours of stillness to dominate the water's motion.
- [The Dunning-Kruger chart, explained — how a famous psychology chart draws itself](https://mariuscomper.uk/graficul-dunning-kruger/en/): The chart behind the Dunning-Kruger effect can be reproduced from pure random numbers. An interactive simulator shows the mechanism, and a 2026 paper says the truth runs the other way.
- [Why no piano can be perfectly in tune](https://mariuscomper.uk/coarda/en/): Twelve pure fifths miss the C seven octaves up by 23.46 cents. Tune a fifth by ear, climb twelve like it, and hear where Pythagorean, meantone and equal tuning hid the difference.
- [The Micromort Hall of Fame](https://mariuscomper.uk/micromort-hall-of-fame/en/): A leaderboard of documented survivors, ranked by incident-conditioned paper micromorts.
- [Why the Copier Always Says 141%](https://mariuscomper.uk/o-suta-patruzeci-si-unu/en/): The enlarge button on any photocopier, from A4 to A3, reads 141%. That number is the square root of two, and it is why paper sizes A0 through A10 can keep halving forever without ever changing shape. An interactive explorer of ISO 216 geometry.
- [Eighty Milliseconds: Why Consciousness Lives in the Past](https://mariuscomper.uk/optzeci-de-milisecunde/en/): To synchronize instantaneous light with sluggish sound and asynchronous nerve impulses, the brain delays conscious perception by 80 milliseconds. An interactive exploration of temporal biophysics.
- [Romania's direct public purchases and Benford's law](https://mariuscomper.uk/prima-cifra/en/): Nearly 600,000 direct purchases each quarter follow Benford's law, while the legal cap remains clear in the amounts. SEAP data from 2022–2024 shows what the method can tell us, plus a tool for checking your own numbers.
- [Sixteen Minutes](https://mariuscomper.uk/saisprezece-minute/en/): The sun reaches its true noon up to sixteen minutes before or after twelve o'clock on your clock. Only four days a year do the two match exactly.
- [A Hundred Times Rarer](https://mariuscomper.uk/craterele-sterse/en/): The Moon has 5,185 confirmed impact craters wider than 20 kilometres. Earth, despite taking more hits per square kilometre, has only 52. An explorer with 70 real craters, from 200 years old to 2.229 billion years old.
- [The Ninth Bell Needs Eight Days Without a Pause](https://mariuscomper.uk/al-noualea-clopot/en/): Eight tower bells can ring in 40,320 different orders, with no repeats allowed. One team has ever rung the complete list without a break, in 1963, over almost eighteen hours. One more bell would take over eight straight days.
- [How long in the microwave at a different wattage? 600–1100W converter](https://mariuscomper.uk/calculator-timp-microunde/en/): Enter the label power and time plus your oven power and get the converted time, including why −20% becomes +25%.
- [The bridge that taught a country engineering: Cernavodă 1895](https://mariuscomper.uk/cernavoda-1895/en/): Fetești–Cernavodă 1890–95: Saligny, 4,087.95 metres, the longest bridge complex in Europe. Caissons, Gerber consoles, the silver rivet and the 15-locomotive test.
- [North Is Not a Place](https://mariuscomper.uk/nordul-nu-e-un-loc/en/): An interactive explainer about the gap between north on a map and north in a compass needle.
- [When the Sun Disappears: An eclipse atlas](https://mariuscomper.uk/eclipse-atlas/): A multidisciplinary atlas of what a total solar eclipse reveals about nature, minds, societies, institutions and knowledge.
- [The 1961 eclipse in Bucharest: two minutes under cloud](https://mariuscomper.uk/eclipsa-1961/en/): The eclipse was total in Bucharest on 15 February 1961, but cloud hid totality from the ground. Newspapers, scientific reports and Romanian archives preserve observations made on the ground and from the aircraft.
- [My rainbow: every observer sees different drops](https://mariuscomper.uk/curcubeul-meu/en/): A rainbow appears when sunlight, water drops, and your eyes line up in a precise geometry. Move the observer and see which drops send light towards you.
- [The Same Year. Two Measures.](https://mariuscomper.uk/seismic-year-2026/en/): 17,373 earthquakes in the USGS snapshot. The same year looks crowded by count and concentrated by energy.
- [Urban shadow](https://mariuscomper.uk/umbra-urbana/en/): An interactive view of daylight: choose a city, move the hour, and watch the sun, building, and shadow reshape the same day.
- [The light that left](https://mariuscomper.uk/lumina-care-a-plecat/en/): Choose a year and see the stars whose light set out for Earth then. 8,714 stars from HYG 4.1 form an interactive map of the sky.
- [Twenty-Seven Seconds, Then Silence](https://mariuscomper.uk/secunda-negativa/en/): 27 leap seconds kept the world's clocks aligned with Earth between 1972 and 2016. None since: the planet has entered a decade spinning faster, on average, than any other on direct record, and 5 July 2024 is the shortest day ever measured. In October 2026, in Versailles, delegates will vote on Draft Resolution C, which would make UTC continuous from 20 May 2027 before a negative leap second becomes necessary.
- [Before the S-wave](https://mariuscomper.uk/inainte-de-unda-s/en/): The P–S window matters when the next action was decided beforehand.
- [A Tiny Star, Built by Hand](https://tiny-star-fusion-explainer.mariuscomper.uk/): An interactive guide to fusion energy with a kids mode, field atlas, plant cutaway, plasma-control game, reactor tradeoff game, fuels, materials and caveats.
- [Seizing Iran's Uranium: The Physics of an Impossible Operation](https://mariuscomper.github.io/presentations/): A visual analysis of the impossible operation of locating, suppressing, accessing and evacuating enriched uranium from Iran.
- [Same Ballots, Three Winners](https://mariuscomper.uk/aceleasi-buletine/en/): The same 9 ballots. Three real rules. Three winners.
- [The room sings back](https://mariuscomper.uk/camera-canta/en/): Walls give a room notes of its own. Where you listen changes how loud each mode sounds.
- [Loto 6/49: the draws are close to random, the numbers people play are not](https://mariuscomper.uk/sase-din-49/en/): All 2,376 official draws up to 1 October 2026, put to the test: the balls, overdue numbers and the winning entries.
- [The faintest sound you can hear moves your eardrum less than an atom](https://mariuscomper.uk/pana-la-atom/en/): Go down into your own body, order of magnitude after order of magnitude: from a candle seen kilometres away, through two needles on the skin, a red cell and a 10-nanometre turbine, down to an atom. At every step, a measurement from 43 other pages.
- [How does a hummingbird hover?](https://mariuscomper.uk/zborul-colibriului/en/): Pause one wingbeat to see how a hummingbird holds its position above a flower. Real photographs, an interactive explanation and the research behind it.
- [Romania's time: what time was it in Iași at Bucharest noon](https://mariuscomper.uk/ora-romaniei-meridian/en/): When Bucharest read noon, Iași already read 12:06 and Craiova only 11:51. Pick a city, slide the year across 1891 and watch four local noons become a single railway time.
- [Travelling near the speed of light: fly to Andromeda in one lifetime](https://mariuscomper.uk/how-far-in-one-lifetime/): Accelerate at 1 g, the pull you feel standing on Earth, and in 28 years and 7 months aboard you reach the Andromeda galaxy. Fly there through a sky of 85,611 catalogued stars and watch two clocks for home: the one that runs in Earth’s frame, and the latest light from Earth that has caught up with you.
- [What was the Moon on the night you were born? Find your birth Moon](https://mariuscomper.uk/the-moon-you-were-born-under/): On the night you arrived, the Moon had a shape. Put in your birthday and the sky turns back to it, then find out when it returns.
- [The will to gamble: games of chance through history, from knucklebones to slot machines](https://mariuscomper.uk/vointa-de-pacanele/en/): You get 100 coins and carry them through history: knucklebones, the gambling hall of the Arthaśāstra, the ball machine at Constantinople's Hippodrome, the Chevalier de Méré's bets, Dostoevsky's roulette and a modern slot built from its technical sheet. Plus the brain, young men, Romania and today's 2.3 billion gamblers.
- [The 7 frieze patterns: every repeating border is one of seven, stitch your own](https://mariuscomper.uk/sapte-margini/en/): Stitch a motif in cross-stitch and see it repeated every way a border can repeat. By shape, there are seven, and it has been proved there is no eighth. Try to find one. In Romanian and English.
- [After sunset, the sky is blue for a different reason](https://mariuscomper.uk/albastrul-de-dupa-apus/en/): A sky computed from the physics of air, for your place and evening. Scroll and the Sun sinks to the stars; take out the ozone and the blue hour turns yellow.
- [The evenings the sun sits on Ceaușescu's palace](https://mariuscomper.uk/soarele-in-capatul-strazii/en/): Seen from Alba Iulia Square, the setting sun comes down exactly onto the top of Bucharest's Palace of the Parliament on 29 March and 13 September. Look up your street and see the evenings the sun sets or rises at its end, in a view drawn from the city's real buildings.
- [Rhythmic applause: why an audience claps in unison, and why the beat falls apart](https://mariuscomper.uk/aplauze-in-ritm/en/): A theatre audience claps in time with no conductor. Clap along with a simulated hall of 300 people and find out why the beat appears only when people clap more slowly, and why it breaks.
- [Krakatoa 1883 and Tonga 2022: the air wave, town by town](https://mariuscomper.uk/air-wave-around-the-earth/): A globe of the Krakatoa (1883) and Hunga Tonga (2022) air waves around the Earth, with the hour each passed any town, checked against barograph records.
- [Who measured the universe?](https://mariuscomper.uk/cine-a-masurat-universul/en/): Henrietta Leavitt found the relation between a Cepheid’s period and brightness, but did not measure distances. Plot the 25 stars in Table I and follow how Hertzsprung and Hubble turned the relation into a cosmic distance scale.
- [Sibiu’s three-stage rocket — Conrad Haas’s notebook](https://mariuscomper.uk/racheta-din-sibiu/en/): Explore Conrad Haas’s drawing and a 3D cutaway, then decide which casings to leave behind in an experiment about rocket mass.

## Sources

- [University of New South Wales — Lissajous figures](https://animations.physics.unsw.edu.au/jw/Lissajous.htm)
- [OpenStax — University Physics, 15.1: Simple harmonic motion](https://openstax.org/books/university-physics-volume-1/pages/15-1-simple-harmonic-motion)
- [Dietmar Rabich — Lissajous-Figur, 2020](https://commons.wikimedia.org/wiki/File:Lissajous-Figur_--_2020_--_7742.jpg)