Cope's rule

Dutch family archives hold marriage records going back to 1600. From these records, like entries in an old ledger, you can extract two columns: how many children a person had and how many years they lived. Evolutionary biologists have been arguing for half a century over whether these columns are connected.

In a rubber band stretched in the lab, three different elasticity mechanisms operate simultaneously. At small strains, Hooke's law prevails; at intermediate strains, entropic chain elasticity; at large strains, strain-induced crystallization.

Collective behavior of AI agents has emerged not in a laboratory but in the wild: on a randomly discovered wiki site where agents wrote test hints. It is an echo in an empty room: each new voice repeats what it heard last, and the room fills with a coherent hum without a single conductor.

Two runners start a race on a course with changing incline. One starts earlier, the other later, and the judge measures their speeds without knowing about the staggered starts. So it is with virus variants: data arrive with delays, and if those delays are unequal, estimates of competitive advantage can be badly wrong.

The orchestra starts playing, but each musician has their own tempo. If everyone plays at roughly the same speed, the music flows in a continuous stream. But if one group of instruments plays noticeably slower than the rest, the sound gathers into a dense clump that slowly moves forward.

In the dark room of the scanner, a person watches for rare flashes on a screen. An infrared camera records their pupil a thousand times per second, while an MRI scanner simultaneously logs which brain areas light up. In this way, 89 volunteers aged 19 to 78 helped scientists see how the pupil becomes a display on which the brain outputs two different signals.

Cosmic rays are particles that race across our Galaxy at enormous speeds. Their energies can be millions of times higher than those of particles in the most powerful accelerator on Earth. But the higher the energy, the fewer such particles there are: the plot of their numbers shows a noticeable kink, which is called the knee.

Rare species in a large community are like thin branches on a tree: a random gust can easily snap them. Even if conditions are stable, a small population simply lacks enough individuals to survive a bad season. In a new study, scientists added this factor to an ecosystem model and watched the community clean itself out.

In the heart of an old city stands a clock tower whose hands have never been adjusted since it was built. By how far it runs slow, you can calculate how much time has stretched since then. In space, the role of such towers is played by relic galaxies — dense stellar systems that formed in the first few billion years and have since neither merged with neighbors nor given birth to new stars.

A choir where every singer hits the notes precisely sounds louder than you'd expect from a simple sum of voices. A hundred singers aren't just a hundred times louder than one: they're ten thousand times louder. In the world of atoms, something similar happens. In collective behavior discovered by Robert H.

In 1970, mathematician John Conway invented the Game of Life — a cellular field where just three rules generate surprisingly complex patterns. Forty years later, SmoothLife appeared: a version where space is no longer cellular but smooth, like a blurred patch. The authors of the new study took an even simpler variant of this continuous game: now everything changes smoothly in time as well.

For a long time, biologists argued: if a herd of animals stably maintains a mix of aggressive and peaceful individuals, does each one alternately change behavior, or do some always fight while others always yield? In classical equations, these options are indistinguishable.

In the web of life, predators and prey exchange carbon and water, and each act of eating slightly increases the universe's disorder. But the intrusion of disease turns this system into a giant seesaw. When a mid-level predator gets sick, its hunting abilities decline, and it becomes easy prey.

Quantum chromodynamics is the theory that describes how quarks and gluons assemble into protons and neutrons. In its equations, there is a strange angle, the parameter θ (theta).

Forget the flat sheet: embryonic tissue is a dynamic landscape of hills and folds. On convexities, cells stretch; in concavities, they compress, as if performing a dance governed by laws eerily similar to spacetime curvature.

When the cooling cosmos, in the aftermath of the Big Bang, lost its primordial symmetry, tensions arose in the fields, like microcracks forming in solidifying glass. Global monopoles, predicted by Gerard 't Hooft and Polyakov, became such “scars” on the fabric of the universe. Each monopole is a tiny but incredibly massive knot of field.

The frost pattern on a windowpane doesn't spread uniformly: it sprouts branches, captures new areas, sometimes sealing off voids. This growth is not a smooth expansion but a series of leaps. This image resonates surprisingly with a mathematical model devised by Charles Loewner a century ago.

A person reaches out to a stranger across town. That stranger will never return the favor: they'll never meet. So why help? Biologists call this indirect reciprocity: kindness comes back not from the person you helped, but from someone else, down the line. In a new study, two variants of this idea were pitted against each other.

Cosmology is going through strange times. On one hand, the standard model with dark matter and dark energy beautifully describes the large-scale structure. On the other, it's cracking at the seams.

A vast hall with a thousand doors, and only one leads to the stars. The rest are locked, and the keys aren't just hidden: they're wrapped in other keys and tangled into a knot. That's the Great Filter in a new reading: not a chain of failures but a tangled hierarchy where each step depends on the previous one nonlinearly.

An eight-kilogram rhesus macaque can live up to forty years. A cat of the same weight rarely sees its twentieth birthday. This difference is no accident: across all primates, from tiny marmosets to gorillas, lifespan is markedly longer than in other mammals of similar body mass. Standard models linking lifespan to metabolic rate fall short here.

Every shell is a stone diary of growth. The mollusk doesn't build it from a blueprint like an architect; it simply adds material along the edge, following the same rule over and over. It's as if a snail glued a new strip to its house each day, nudging it slightly sideways and making it a bit bigger. It's this repetition, not complex control, that creates the species' characteristic shape.

The heart doesn't push blood in a steady stream but in pulses. Each beat sends a wave racing through the arteries, like ripples along a taut garden hose. For a long time, it was thought that an animal's metabolic rate depended only on how vessels branch, like pipes in a house. But new work flips that view: what matters isn't the shape of the pipes but the pulse itself.

Before measurement, a quantum object lives in a world of possibilities, where wave amplitudes add up like sound waves in a studio before pressing the “record” button. Crests amplify each other, troughs cancel out.

An epidemic is like a fire in a dry forest: a spark flares up, the flames leap from tree to tree, and within a week the whole area is burning. A hundred years ago, scientists devised a simple mathematical model for such a fire: they divided people into those who had not yet fallen ill, those who were ill, and those who had already recovered.

A snowdrift grows by strict rules: falling snowflakes form bumps, those attract more snow, and the bumps amplify. The same mathematics describes city growth, patterns on bark, ripples on water, and clusters of cosmic dust. Physicists call this uniformity universality.

A stag beetle the size of a fingernail stands on the ground with its legs spread wider than its own height. An elephant as tall as a room, on the other hand, towers above the ground like a tower. Why is that? Both animals walk on the same ground, but they see it differently. For a beetle, each pebble is a boulder, while for an elephant, it's a grain of sand.

In the first moments after the Big Bang, space expanded at an incredible rate. A tiny quantum ripple, embedded in the uncertainty principle itself, pushed matter apart more strongly than any known force. This ripple is the generalized uncertainty principle, or GUP.

The Galaxy is a forest where birds don't start singing right away. First, trees must grow — stars, around which planets eventually appear. The Drake equation counts how many birds might be singing in this forest right now, but it implicitly assumes that their number doesn't change: as many as there are, that's how many there have always been.