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# Abstractions blog

## Latest Articles

### How Complex Is a Knot? New Proof Reveals Ranking System That Works.

“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.

### Puzzling Quantum Scenario Appears Not to Conserve Energy

By resolving a paradox about light in a box, researchers hope to clarify the concept of energy in quantum theory.

### Black Hole Image Reveals the Beast Inside the Milky Way’s Heart

In 2019, the Event Horizon Telescope released a historic image of a supermassive black hole in another galaxy. The follow-up — an image of Sagittarius A* — shows it shimmering at the center of our own.

### Why ‘De-Extinction’ Is Impossible (But Could Work Anyway)

Several projects are aiming to bring back mammoths and other species that have vanished from the planet. Whether that’s technically possible is beside the point.

### Physicists Pin Down How Quantum Uncertainty Sharpens Measurements

Throwing out data seems to make measurements of distances and angles more precise. The reason why has been traced to Heisenberg’s uncertainty principle.

### Mathematicians Coax Fluid Equations Into Nonphysical Solutions

The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations.

### New Proof Illuminates the Hidden Structure of Common Equations

Van der Waerden’s conjecture mystified mathematicians for 85 years. Its solution shows how polynomial roots relate to one another.

### Which Computational Universe Do We Live In?

Cryptographers want to know which of five possible worlds we inhabit, which will reveal whether truly secure cryptography is even possible.

### Researchers Gain New Understanding From Simple AI

Language processing programs are notoriously hard to interpret, but smaller versions can provide important insights into how they work.