Reversal of the psychological arrow of time on the contraction of the universe In Brief History of Time, it says that the people living in a contracting phase (although unsuitable for living or even existence itself, but lets assume) would remember the future but not the past. But why is that necessary? Why not just contract the universe and let the psychological arrow flow it's way?
 A: He didn't say that – or rather, he said it and then said it was wrong.
By definition, the thermodynamic arrow of time points in the direction of higher entropy; the psychological arrow points in the direction where we don't remember things; and the cosmological arrow points in the direction where the universe is larger.
He argues that the thermodynamic and psychological arrows always point in the same direction.
Then he says "At first, I believed that disorder would decrease when the
universe recollapsed" – i.e., he believed that the thermodynamic and cosmological arrows also always point in the same direction. That would imply that the psychological arrow also reverses direction when the expansion reverses into contraction.
A page later he says "I realized that I had made a mistake: the no boundary condition implied that disorder would in fact continue to increase during the contraction." In other words, the thermodynamic and psychological arrows don't reverse when the cosmological arrow reverses. They just "flow their way" as you put it.
