Cognitive Instability
I know from experience that not everyone is convinced by this argument. One stumbling block is the crucial assertion that what we start with is knowledge of our present macrostate, including some small-scale details about a photograph or a history book or a memory lurking in our brains. Although it seems like a fairly innocent assumption, we have an intuitive feeling that we don't know something only about the present; we *know* something about the past, because we see it, in a way that we don't see the future. Cosmology is a good example, just because the speed of light plays an important role, and we have a palpable sense of "looking at an event in the past." When we try to reconstruct the history of the universe it's tempting to look at (for example) the cosmic microwave background and say, "I can *see* what the universe was like almost 14 billion years ago; I don't have to appeal to any fancy Past Hypothesis to reason my way into drawing any conclusions."
That's not right. When we look at the cosmic microwave background (or light from any other distant source, or a photograph of any purported past event), we're not looking at the past. We're observing what certain photons are doing right here and now. When we scan our radio telescope across the sky and observe a bath of radiation at about 2.7 Kelvin that is very close to uniform in every direction, we've learned something about the radiation passing through our *present* location, which we then need to extrapolate backward to infer something about the past. It's conceivable that this uniform radiation came from a past that was actually highly non-uniform, but from which a set of finely tuned conspiracies between temperatures and Doppler shifts and gravitational effects produced a very smooth-looking set of photons arriving at us today. You may say that's very unlikely, but the time-reverse of that is exactly what we would expect if we took a typical microstate within our present macrostate and evolved it toward a Big Crunch. The truth is, we don't have any more direct empirical access to the past than we have to the future, unless we allow ourselves to assume a Past Hypothesis.
Indeed, the Past Hypothesis is more than just "allowed"; it's completely necessary, if we hope to tell a sensible story about the universe. Imagine that we simply refused to invoke such an idea and stuck solely with the data given to us by our current macrostate, including the state of our brains and our photographs and our history books. We would then predict with strong probability that the past as well as the future was a high-entropy state, and that all of the low-entropy features of our present condition arose as random fluctuations. That sounds bad enough, but the reality is worse. Under such circumstances, among the things that randomly fluctuated into existence are all of the pieces of information we traditionally use to justify our understanding of the laws of physics, or for that matter all of the mental states (or written-down arguments) we traditionally use to justify mathematics and logic and the scientific method. Such assumptions, in other words, give us absolutely no reason to believe that we have justified anything, including those assumptions themselves.
David Albert has referred to such a conundrum as *cognitive instability* - the condition that we face when a set of assumptions undermines the reasons we might have used to justify those very assumptions. It is a kind of helplessness that can't be escaped without reaching beyond the present moment. Without the Past Hypothesis, we simply can't tell any intelligible story about the world; so we seem to be stuck with it, or stuck with trying to find a theory that actually explains it.