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"Science fiction writers, I am sorry to say, really do not know anything. We can't talk about science, because our knowledge of it is limited and unofficial, and usually our fiction is dreadful."
- Philip K. Dick

SSA Machine  
  A machine that compares two people for compatibility; it sees sub specie aeternitatis, literally 'under the aspect of eternity' or outside of time.  

Joe Fernwright sits next to Mali Yojez, an attractive humanoid, on the way to Plowman's Planet to do some work for a large and powerful being named Glimmung. On the way, she agrees to try the SSA machine with him, to give him the experience.

The stewardess began setting up the SSA machine in a rapid, efficient fashion, meanwhile explaining it. "SSA stands for sub specie aeternitatis; that is, something seen outside of time. Now, many individuals imagine that an SSA machine can see into the future, that it is precognitive. This is not true. The mechanism, basically a computer, is attached via electrodes to both of your brains and it swiftly stores up immense quantities of data about both of you. It then synthesizes these data and, on a probability basis, extrapolates as to what would become of you both if you were, for example, joined in marriage or perhaps living with each other. I will have to shave two small spots of hair on both of your heads, please, in order to attach the electrodes... How far ahead are you interested in? ...A year, or ten years? You are free to choose, but the less time-elapse you pick, the more accurate the extrapolation will be..."

"What form does its extrapolation take?" Joe asked. "Written on a paper ribbon in punch form, or-"

"You will be presented pictorially with a representative moment of your two lives entwined together a year from now," the stewardess said. "Projected in 3D and in color on the far wall."

From Galactic Pot-Healer, by Philip K. Dick.
Published by Berkley Publishing in 1969
Additional resources -

The SSA machine takes external data about the two, obtained from other data banks, and then spends about ten minutes pulling information from their brains for the simulation.

This is essentially a computerized dating service that makes use of detailed information about compatibility.

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