This episode of the Physics World Weekly podcast explores two very different scientific debates: one about the shape of the Earth, and the other about the expansion of the universe.

Scientifically speaking, the “debate” about the Earth’s shape was settled hundreds (perhaps even thousands) of years ago: our planet is round, an “oblate spheroid” squashed at its poles and bulging at its equator. But that hasn’t deterred some people from believing it’s a flat disc, and their numbers seem to be on the rise. According to the science writer Rachel Brazil, whose feature article “Fighting flat-Earth theory” appears in the July issue of Physics World, modern flat-Earthism is driven by a wider tendency towards conspiracy-mindedness, with considerable crossover between flat-Earth beliefs and other, unrelated conspiracy theories such as climate-change denial and the anti-vaccination movement. Because of this, Brazil suggests that “arguing the physics” may not actually be the best way to change minds. “With people who are so untrusting, they will just see everything as a hoax,” she tells Physics World editor-in-chief Matin Durrani.

As for the expansion of the universe, this debate is, mercifully, less heated. It centres on the fact that the Hubble constant, which characterizes the speed of the universe’s expansion, has been measured in two ways. The first, “local” method relies on measuring the intrinsic brightness of certain stellar objects (known as “standard candles”). The second, “global” method is based on measurements of the cosmic microwave background radiation. As the science writer Keith Cooper explains, these methods produce different – and incompatible – values for how fast the universe is expanding. You can find out more about this discrepancy (and how to resolve it) in Cooper’s feature “Finding a consistent constant”, and in a related video.