3. As just indicated, the MaxEnt inference runs equally well in reverse. So given a particular final state, we can ask, what can we "retrodict" to improve our knowledge about earlier states? However the Second Law argument above also runs in reverse: given macroscopic information at time t 2, we should expect it too to become less useful. The two procedures are time-symmetric. But now the information will become less and less useful at earlier and earlier times. (Compare with Loschmidt's paradox.) The MaxEnt inference would predict that the most probable origin of a currently low-entropy state would be as a spontaneous fluctuation from an earlier high entropy state. But this conflicts with what we know to have happened, namely that entropy has been increasing steadily, even back in the past.