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This American Life episode 450: "So Crazy It Just Might Work". The whole episode is good, but act one (6:48-42:27) is relevant to LW, about a trained scientist teaming up with an amateur on a cancer cure.
It's downloadable until 19 Nov 2011 or so, and streamable thereafter.
(Technical nit: It sounds to me like the reporter doesn't know the difference between sound and electromagnetism.)
Edit: Here's a quick rot13ed summary: Vg qbrfa'g tb jryy. Nagubal Ubyynaq frrf rkcrevzragny pbagebyf naq ercebqhpvovyvgl nf guvatf gung trg va uvf jnl. Ur frrzf gb unir gnxra [gur Penpxcbg Bssre](uggc://yrffjebat.pbz/yj/w8/gur_penpxcbg_bssre/).
The problem is this. The Pioneer 10 and 11 spacecraft were launched towards Jupiter and Saturn in the early 1970s. After their respective flybys, they continued on escape trajectories out of the Solar System, both decelerating under the force of the Sun's gravity. But careful measuremenrs show that the spacecraft are slowing faster than they ought to, as if being pulled by an extra unseen force towards the Sun.
Spacecraft engineers' first thought was that heat emitted by the spacecraft could cause exactly this kind of deceleration. But when they examined the way heat was produced on the craft, by on board plutonium, and how this must have been emitted, they were unable to make the numbers add up.
Now Frederico Francisco at the Instituto de Plasmas e Fusao Nuclear in Lisbon Portugal, and a few pals, say they've worked out where the thermal calculations went wrong.
The NPR show All Things Considered did a short story on the Singularity, including interviews with Eliezer Yudkowsky and others involved with SIAI: