In Sid Meier's Alpha Centauri (SMAC), the Dream Twister is a Secret Project. It may be built at a cost of 400 minerals, on discovery of The Will to Power (E9). The Dream Twister gives a +50% psi attack bonus.

How useful is this? If your military is psi-heavy and you've been itching to give a rival faction a good drubbing, here's your chance. If not, the psi attack bonus also applies to regular units attacking wild or enemy-controlled native units. If there's a possibility you'll be on hostile terms with the Gaia's Stepdaughters (Green) faction, it's excellent defensive thinking to build it just so they can't. I consider native units somewhat pricey for what they do, and this Project moves their cost-effectiveness more in line with non-native forces.

The Dream Twister complements the Neural Amplifier Secret Project, which became available back when your faction discovered Neural Grafting (B3).

Secret Project animation narrative:
   "Mary had a little lamb,
   Little lamb little lamb,
   Mary had a little lamb,
   whose fleece was white as snow."
   -- Assassin's Redoubt*,
   Final Transmission

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*Assassin's Redoubt is one the pregenerated base names for the Spartan Federation (gray, Santiago) faction.