One of the many facets of paranormal research. Many reports of contact with aliens or alien craft are odd, but some alien encounters (usually of the third kind) have an element of the bizarre. Things will happen, or objects will be seen, that defy convention and logic. One report in particular is often mentioned in discussions of high strangeness:
“in France in 1954, a UFO witness was accosted by the humanoid occupant [of the UFO] who asked him what time it was. When the man looked at his watch and replied that it was 2:30, the UFOnaut sternly told him “You lie! It is four o’clock!” [...] However, it really had been 2:30!”*
The more famous UFO case of Betty and Barney Hill also exhibits elements with high strangeness. The aliens that the couple were abducted by apparently had no concept of time or ageing, which they needed Betty to explain. However, as they were leaving the UFO one of the aliens said “Wait a minute”. If the aliens didn't understand the concept of time, how did they know how to talk about it? And if they did know about time, why ask for it to be explained?
The paranormalist Jacques Vallee suggested that high strangeness events can be explained as the product of “metalogic”, a system used by aliens to convey concepts “beyond the semantic level” through paradoxes and absurdity. This supports the extraterrestrial explanation that states that UFO‘s come from other planets.**
Others have likened high strangeness to dream logic - the logic that prevails in dreams. This makes sense in terms of the psychological explanation of UFO's, that the UFO phenomenon is a product of the human mind.
*The Encyclopaedia of Alien Encounters, Alan Baker, pg 100.
**The most common, and probably the most unlikely explanation of the UFO phenomena.