On a foggy Saturday morning in 1953, a tall, skinny 24-year-old man fiddled with shapes he had cut out of cardboard. They represented fragments of a DNA molecule, and young James Watson was trying to figure how they fit together in a way that let DNA do its job as the stuff of genes.

The human genome is made up of 23 pairs of chromosomes, the biological blueprints that make humans … well, human. But it turns out that some of our DNA — about 8% — are the remnants of ancient viruses that embedded themselves into our genetic code ...