Black holes are one of the universe’s most exotic and elusive objects. When nothing, not even light, can escape their powerful gravitational grasp, taking a picture of one seems unimaginable. But an image of a black hole, or more accurately its shadow, could offer insights that theory alone may not provide when testing predictions. So how can it be done?

Harvard astrophysicist Shep Doeleman and a team of 250 researchers achieved this extraordinary feat by linking a group of radio telescopes around the world. This network, called the Event Horizon Telescope, produced the first image of a supermassive black hole in the galaxy M87, around 55 million light-years away, and the first image of the black hole at the heart of our galaxy. In this episode, Doeleman tells co-host Janna Levin how he turned the Earth into a telescope capable of seeing a black hole, the incredible level of science and collaboration that was required to achieve this, how the images have furthered our understanding of these exotic objects, and how movies of black holes may be possible by the early 2030s.

People may think of soil as just dirt, but it is anything but inert. Beneath your feet, a vast network of mycorrhizal fungi is hard at work, trading minerals with plant roots. This trading system helps enrich the soil, and it sequesters 13 billion tons of atmospheric carbon dioxide each year — roughly equivalent to one-third of the world’s fossil-fuel emissions. Scientists know that these fungi form partnerships with 80% of all plant species on Earth, a relationship that evolved some 450 million years ago. What they have not understood is how organisms with no brain or central nervous system can decide whom to trade with, and on what terms.

Toby Kiers, an evolutionary biologist at Vrije Universiteit Amsterdam, has spent much of her career making this hidden world visible. Drawing on economics and game theory, and using tools that range from fluorescent quantum dots to imaging robots, her lab is probing how fungi and plants conduct their trade. The work raises new questions about soil, carbon, and even what counts as an individual organism. In this episode, Kiers tells co-host Steven Strogatz how these brainless, decentralized organisms can behave strategically — discriminating between better and worse partners and shifting resources across the network to wherever a plant will “pay” more for it — and how she has built a worldwide community of researchers

We know all about how things exist in the three dimensions of length, width, and height. Physicists often talk about time as a fourth dimension, but what if there were a fourth spatial dimension — another direction entirely? How on earth would we picture that?

Mathematicians use topology to visualize abstract spaces in higher dimensions. Maggie Miller at the University of Texas at Austin explores what happens when knots encounter an extra dimension. Familiar tangled loops behave in unexpectedly complex and counterintuitive ways in 4D: Knots can always come undone, while ordinary surfaces like spheres can — surprisingly — become knotted in ways that can’t be undone.

In this episode, Miller explains to co-host Janna Levin why 4D is the lowest dimension that mathematicians still don’t fully understand, how she and her collaborators resolved a question about knotted surfaces first posed by mathematician Charles Livingston in 1982, and how her interest in art has helped her develop the visual techniques she uses to picture 4D spaces.