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This is a novel I read in the 60s. I thought it was by Nourse but it's not. The story was about a young man who used his mind to turn a corner into another dimension that allowed him to take short cuts, allowing him to go from point A to point B without hitting the points between.

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It was Nourse - it's The Universe Between. From an Amazon review:

Scientists inadvertently open a doorway into a parallel universe - one appearing so strange as to drive observers insane. All except one; a young woman who learns to enter the other world at will - as later does her son. This is story of his gradually dawning understanding of what the "Threshold" really is - and it's potential as mankind's route to the stars - but there is a problem... the inhabitants of the other universe.

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