I had a random philosophical whim and thought to share it.
Imagine if we remembered the future, but never the past. This kind of existence has all sorts of mind-warping possibilities, the most obvious of which would be a working knowledge of everything that would happen to you until the day you day. We could spend endless amounts of time exploring the viability of free will or predetermination in these circumstances, but those are somewhat obvious compared to other interesting facets of such an existence.
Instead, let us think about how people define themselves. In our current mode, we view people as an extension of everything they've ever done. People evolve and change overtime to become what they are in the present, and their memories are a sometimes clear, sometimes fuzzy map of that. How we shape ourselves is determined by what has happened before, and what is happening now.
Supposing that we instead live in a backwards world where we remember things that are going to happen rather than things that did, defining ourselves would be rather different. As memory remains a fickle thing, we would still likely be unable to clearly remember anything but the reasonably near future, with smattering of random thoughts and moments strewn throughout the greater future, and perhaps a few far flung ones toward the end of life.
However, in stark contrast we would have absolutely no working knowledge of anything we'd ever done. The past would be an fearsome black hole of lost existence. Horoscopes would prognosticate what you had already done, rather than what you would do. Alfred Hitchcock's works would drive their suspense not by surprising events but by fear of the unknown past, a plethora of super-Memento films. It would be a very different world.
I could probably write a science fiction novel in which at some arbitrary date everyone's memory switched between these two modes. Then again, writing such a novel would be excruciatingly difficult. How does someone who only remembers the future think? Can one even have a train of thought under such circumstances?
I have mused enough for now, but it'd be a fun topic to explore further with someone able to stand the constant paradigm destruction.