Not everyone on Earth in the 35th century is mind-connected or has the 24th chromosome. A whole group of people turned down the opportunity to receive it. Still others, even with the 24th chromosome, are unable to connect. Sometimes it is a birth defect. Sometimes they are cast out by the Overmind itself. This is called Cesdiud. In any event, these people are referred to as mind-deaf or mandasurte.
When one is referred to as mandasurte, it is usually taken to mean that they lack the 24th chromosome but it is not guaranteed. Rei's people, from our century, called the Essessoni, are all mandasurte genetically. Rome became mandasurte for one year when she was Cesdiud, cast out. She was later reconnected, at least partially, during a procedure on Deucado. Rome is a half-breed, called mosdurece, because her father, Fridone, was mandasurte and her mother, Binoda, was a full-blooded Vuduri. The 24th chromosome was induced in a diploid fashion (genes doubled up) so that each successive generation could still gain its advantages. You only need one pair of the 24th chromosome to connect. So Rome is haploid, her mother diploid. But one set of genes is enough.
The mandasurte are more like us than the Vuduri. They think for themselves. They have to. Their native culture, sometimes thought to trace back to Hawaii, allows them to savor and appreciate beauty, art, music, all the pleasures in life. Most Vuduri secretly envy the mandasurte although this envy usually manifests itself in a disdain, an air of false superiority.