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"Always listen to experts. They'll tell you what can't be done and why. Then do it."
- Robert Heinlein

Time Loop  
  A series of events repeats, the stream crosses over itself.  

First use of this phrase in science fiction, as far as I know.

The voice went on after Dakin had signified assent: “I mentioned last time that instinct is repetition simply because time is a looped repetition. Memory is another abstract quality hard to define, unless one thinks of reliving every instant over and over as often as the time loop curls back on itself. Why do we remember some things in our childhood vividly, and forget other events completely a week after happening? Simply — yet not so simply — because the successive loops of time are overlapping in places, far apart in others.

( ’The Time Entity’ by Eando Binder)

“You must think of time as unwinding from a spool, and retaining, like wire, its tendency to curl into loops. Time reels off steadily from the spool, but, after its looping, it falls into a systematic order of intertwined spirals. Wherever the loops touch or lie partly together, you have memory repetitions and instinct repetitions. The former are conscious, the latter subconscious.

“Now any repeated event — where the time loops touch or overlap — has happened only once, yet many times! If you can think of the time wire as braided with three strands — and call those strands past, present, and future — an event can easily happen in all three periods at the place of overlapping loops. And if you multiply the pasts and presents and futures, because they shift position as the time wire reels out, any single event becomes an endlessly repeated oneness! Do you follow me?”

From The Time Entity, by Eando Binder.
Published by Astounding in 1936
Additional resources -

Another early example of the time loop idea can be found in Forever is Today by Charles F. Ksanda, published in Thrilling Wonder Stories in 1946:

( ’Forever is Today’ by Charles F. Ksanda)

The silver sphere began to move away from the basin. It swung slowly on its cable upward along the metal arc toward the center of the room...

Carsten spoke again, and once more seemed to enjoy his role of lecturer.

“The silver sphere before you is a perfect pendulum, its motion exactly adjusted by magnetic currents in the metal rail beneath it. The length of the time loop varies directly with the rate at which the sphere passes through the basin. The sphere actuates the force which will warp time into a loop coinciding exactly with the span of my life.”

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Additional resources:
  More Ideas and Technology from The Time Entity
  More Ideas and Technology by Eando Binder
  Tech news articles related to The Time Entity
  Tech news articles related to works by Eando Binder

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