Within topology, time can be modeled as restarting after reaching its 'edge'

Explore a visualization of curved spacetime under general relativity

While depictions involving bends in elastic fabrics are common to illustrate gravity, they are circular representations that rely on gravity in the real world to depict gravity in the model. The river model instead shows how bends in spacetime convert speed through time into speed through space, producing acceleration.

What is space-time?

Space-time is a complex subject, but this Livescience article makes an effort to disentangle the topic. Somewhat akin to a sheet of rubber that can be warped and bent in parts, space-time is a bit more involved that that. However, the analogy makes this and other aspects of the concept simpler to grasp.

Time may be an emergent, rather than a fundamental, property of the universe

Some theories of everything—mathematical models that try to explain all aspects of the universe, including quantum phenomena and gravity—do not incorporate time. If a time-neglecting version of such a theory were ever validated, it might suggest that time is a feature that emerges from our limited perception of the universe.

Time crystals are systems of atoms organized into periodic patterns of motion

Unlike traditional crystals—whose atomic structures cause them to look identical no matter how you look at them in space—time crystals exhibit this behavior through time, where the motion of atoms will bring them to the same positions relative to one another regularly.

Time seems to stop for objects at the event horizon of black holes

At that location, the warping of space-time is so severe that the entirety of an object's space-time motion is solely through space, leaving it immobile in the time dimension. Faraway observers looking at the object would see it appear frozen before slowly dimming and reddening.

According to the physics of black holes, our 4D reality may be a hologram—a projection of information coded on a 2D surface on the edge of the universe.

Branching timelines are allowed and resolve grandfather paradoxes in physics

According to quantum physics, traveling back in time to kill one's grandfather would not cause a paradox because time travel would bring one to a new timeline, where the person killed is not one's grandfather. Alternatively, causality would not be violated because the universe would prevent the murder from occurring.

Wormholes, though unstable, would offer a theoretical shortcut through spacetime

These hypothetical distortions in the fabric of spacetime may connect vast distances across or even between universes. While science fiction often portrays them as traversable tunnels, the energy and matter required to keep a wormhole open defy current physical understanding.

Imagining a fourth dimension

Famous astronomer Carl Sagan attempts to describe what it's like to think about the fourth dimension using the famous Flatland example from author Edwin Abbott in this classic video.

What is a singularity?

It's hard to imagine a singularity, which are described as an infinitely tiny point, created by gravity, until it has zero volume. The definition feels impossible, though perhaps not at the center of a black hole or at the beginning of the universe. Even then, singularities may be something else entirely. Singularities are a mathematical quandary that challenge us to better understand physics and the universe.

Within mathematics, some infinities are bigger than others

While the concept of infinity refers to a countless set of items, these infinite sets can be compared to one another by matching an item from one set to an item in another, one by one. This analysis shows that certain sets must be larger than others because some infinite sets have leftover, unmatched items.

The Koch snowflake has an infinite perimeter enclosing a finite area

Counterintuitively, although it would be impossible to build a fence along the edges of the shape because it would require an infinite amount of materials, this perimeter can be contained in a larger shape with a finite perimeter and limited area. This is equivalent to enclosing an infinitely long spiral that never reaches the center within a circle.

Understanding turbulence, which is characterized by growing chaos at multiple scales

As energy is lost in fluids undergoing turbulent, non-linear flow, particles will collectively form eddies, or whirlpools, of various sizes that mix together. The energy cascade of larger eddies becoming smaller ones before dissipating completely varies based on the initial conditions of the fluid, a characteristic feature of chaotic systems.

Why are all maps of the world wrong?

This 5-minute video explains why all maps to date are verifiably wrong. While globes can provide an accurate map and scale of the various continents, flattening that sphere has historically meant something will be distorted, whether land, sea, or...

The internet explained at five levels of difficulty, from protocols to internet flattening

Resembling a roadway with traffic laws that all cars must follow, the internet is the hardware that connects a source to a destination, and these connections must follow specific software rules. Although data had to travel through about 10 networks to reach a destination in the past, data centers increasingly consolidate traffic, just as a highway does for cars, to improve data speeds.

An analysis of the logistic map, which shows how chaos can emerge from simple equations

When modeling systems such as the predator-prey cycle of an organism's population in an ecosystem, the logistic map function shows the population normally settles into an equilibrium value. However, at high reproduction and starvation rates, multiple such values arise, making it difficult to accurately model long-term population growth in some environments.

View a breakdown of the mathematics behind the Standard Model

The Lagrangian version of the theory—related to the system's energy—presents a vast mathematical equation, with different components representing various force interactions and types of particles, including ghost particles to cancel out mathematical redundancies.

Objects can be 3D printed with light by projecting 2D computerized tomography (CT) scans onto rotating cylinders of resin, which solidify upon exposure.

The 'overview effect' heightens one's sense of unity and connectedness

Coined by space philosopher Frank White in 1987, the term refers to the paradigm-shifting experience a person undergoes upon viewing Earth from space. Commercial spaceflights aim to bring this perspective to a broader audience, inspiring changes in behavior and worldview among participants.

Objects can be 3D printed with light by projecting 2D computerized tomography (CT) scans onto rotating cylinders of resin, which solidify upon exposure.

Accurate climate models incorporate calculus to account for complex feedback loops

The simplest models assume uniformity across the Earth, with incoming energy from the sun being offset by the planet's albedo, or reflectiveness, which prevents the radiation from being fully absorbed. Incorporating elements such as atmospheric layers, latitude bands, geographic variability, and emissivity yields coupled differential equations quantifying Earth's interconnected systems.

Figuring out how to get a sofa around a corner has been a math problem since 1966

A sofa with the largest possible area that can make a 90-degree turn is known as Gerver's sofa, named after the mathematician who determined the shape in 1992. In 2025, a 119-page paper provided the proof confirming this shape.

The ideas of Einstein and Freud combined in 'The Persistence of Memory'

The Persistence of Memory was painted on a canvas roughly the size of a sheet of paper, depicting a desolate landscape with melting clocks, ants, and a distorted figure. The piece incorporates Freud and Einstein's ideas, resulting in a haunting composition symbolizing time's fluidity and Dalí's personal anxieties.

Mapping early New York

Want to see how Wall Street (and New York City as a whole) has changed over time? Use this timeline and map to see Manhattan today overlaid with the precise boundaries of early land grants to the Dutch in the 1600s. Scroll through the progress of city building through the first century of European settlement there.

The edge of the Milky Way may be identified by its star-forming disk

Like Earth's atmosphere and its core, galaxies become more diffuse with increasing distance from their centers, making it hard to define where they end. However, one approach focuses on where gas concentrations are no longer dense enough to support measurable star formation.

Visualizing the built world compared to the natural world

In the last century, humans have covered the Earth in 1,300 metric gigatons of built material, known as technomass. That amount is more than the Earth's entire biomass at 1,100 GT, which includes all living organisms. To get a sense of the scale of this comparison, click through this striking, simple visualization showcasing the various organisms comprising biomass as well as the materials making up the technomass.

The simplicity of immersed tube tunnels

Tunnels have traditionally bored holes through the earth below the water. On the other hand, immersed tube tunnels connect hollow, massive sections in trenches along the floor of the body of water. Each section is built on land, floated to the site, submerged, and connected. This method saves money by reducing expensive underground work, and it preserves an area's aesthetic appearance.

Explore our favorite visualization of the immense scale of space, from an astronaut to the size of the observable universe

Hurricanes, which rely on air consistently spinning in the same direction, cannot cross the equator because air curves in opposite directions north and south of it.

Volcanoes 'die' when their supply of magma runs out, if they are shifted away from their underlying magma reservoir, or if they get clogged by collapsing or their magma cooling back into rock.

How Amazon operates a 'flywheel' business model, a self-reinforcing cycle that drives continuous growth

Stars appear to twinkle because turbulence in the motion of molecules in Earth's atmosphere causes light to bend and wiggle rapidly on its way to the surface—a phenomenon called scintillation.

While atoms are normally made of protons, neutrons, and electrons, exotic ones have been built with antimatter—alternate versions of normal matter that live for fractions of a second and are about a billion times as rare.

Apeirophobia is an overwhelming fear of living forever, perhaps stemming from the brain's inability to conceptualize an infinite life.

See how each of the more than two million known species relates to each other—and to common ancestors—in this zoomable tree of life.

The Mona Lisa's celebrity status and repeated restorations have obscured what made the painting so revolutionary for its time

'Grand Canyon of the Yellowstone,' a work by American painter Thomas Moran, inspired Congress to establish Yellowstone National Park.

Existentialist writer Jean-Paul Sartre coined the famous phrase 'Hell is—other people' in his play 'No Exit'

Gerrymandering works through two techniques: cracking opposing voters across districts to dilute their power, and packing them into a few to waste their votes in lopsided majorities.

See a 3D reconstruction of Tenochtitlan, the Aztec capital that was home to an estimated population of 200,000 to 400,000.

Explore chaos in this simulation of two double pendulums, where small differences in the release angles produce wildly different outcomes.

Planarian flatworms are small, aquatic worms with exceptional regenerative capabilities. When cut, the worms can regenerate multiple bodies in a matter of weeks.

As of 2025, the most cited papers in science include a review of graphene, methods to improve image recognition, streamlining electron density calculations, and optimizing protein studies.

Hear 50 years of iconic hip-hop samples, the genre's foundational looped tracks

While the first exchange-traded fund (a 'basket' of different assets that can be bought and sold on a stock exchange) in the US only launched in 1993, the global ETF market has grown to more than $10T in the short time since.

The first robot in literature may have been a 'mechanical man' in 1907's 'Ozma of Oz,' a book in L Frank Baum's 'Wizard of Oz' series.

See photos of Meteora, a mountainous site in central Greece, home to 14th-century monasteries perched atop soaring outcroppings.

The identity of the Tank Man in the iconic photo from the 1989 Tiananmen Square protests remains unknown and was possibly killed.

For centuries, it was common to sleep in two shifts: a few hours at the beginning of the night, and a longer period beginning around midnight

Some coin denominations have ridges etched on their sides, partly to prevent counterfeiting, in a practice called 'reeding.'