Hindsight And The Arrow Of Time

The following is an excerpt from the Wikipedia article on "The Arrow of Time." The specific excerpt refers to the "causal arrow of time."

cause precedes its effect: the causal event occurs before the event it affects. Birth, for example, follows a successful conception and not vice versa. Thus causality is intimately bound up with time's arrow. 
An epistemological problem with using causality as an arrow of time is that, as David Hume maintained, the causal relation per se cannot be perceived; one only perceives sequences of events. Furthermore it is surprisingly difficult to provide a clear explanation of what the terms "cause" and "effect" really mean, or to define the events to which they refer. However, it does seem evident that dropping a cup of water is a cause while the cup subsequently shattering and spilling the water is the effect. 
Physically speaking, the perception of cause and effect in the dropped cup example is a phenomenon of the thermodynamic arrow of time, a consequence of the Second law of thermodynamics.[6] Controlling the future, or causing something to happen, creates correlations between the doer and the effect,[7] and these can only be created as we move forwards in time, not backwards.
I had accessed this article some months ago, and I find that it has now undergone some revision. At the time, I had copy-pasted the above section of the article and highlighted a particular passage that interested me greatly. I now find that the most interesting part of the article has been removed, so I quote it now as it appears in my own personal notes (emphasis mine). The following used to appear immediately following the above passage, without a paragraph break.

However, it is also partly a phenomenon of the relation of physical form and functionality to the attributes and functional capacities of physical agents. For example, the causes of the resultant pattern of cup fragments and water spill are easily attributable in terms of the loss of manual grip, gravity, trajectory of the cup and contents, irregularities in its structure, angle of its impact on the floor, etc. However, applying the same event in reverse, it is difficult to explain how the various pieces of the cup come to possess exactly the nature and number of a cup before assembling, how they could assemble (as neither floors nor hands can create china cups unaided), why they should assemble precisely into the shape of a cup and fly up into the human hand (as immobile floors cannot throw and, without contact, the human hand lacks the capacity to move objects unaided) and why the water should position itself entirely within the cup.
As I think about this concept today, what strikes me most is the concept that the remains of a theoretical shattered cup can be hypothetically reassembled by playing the events in reverse, according to the known laws of thermodynamics. The important lesson here is that myriad possible events can potentially result in the same pattern of shattered debris. 

This is might be because small variations in initial circumstances do not significantly impact the end results if the process of a shattering cup is sufficiently complex. It might also be due to the fact that knowing the precise set of initial circumstances ex post facto is impossible. Theoretically, I suppose it could also be a combination of those two ideas.

I wonder how this might impact analyses in hindsight.

For example, is it possible to conduct any sort of worthwhile historical analysis? There are as many possible reconstructions of history as there are attempts to reconstruct it. But, importantly, there is no way to determine whether any of those reconstructions reflect events as they actually occurred. The nature of the causal arrow of time is such that many valid explanations exist for the same set of circumstances. What differentiates them is mere probability. Only a firsthand observer would know for sure, and then, too the observer's memory would be subject to human error.

For that matter, the observer's memory is itself a reconstruction of history. Might it also lack the same kind of credibility?

This is not idle philosophical posturing on my part. Consider the real-world problem of psychological therapy. I once heard a story about someone whose therapist had allegedly botched a hypnosis session and implanted a false memory of childhood abuse that could never be reversed. While I cannot actually vouch for the truth of that story, I think it serves to illustrate my point here. One need not be implanted with a false memory to misjudge the true initial set of circumstances that lead to one's current position.

Someone undergoing psycho-therapy, then, may come to believe something false about their past, even when the utmost care is taken to prevent error. This is not because psycho-therapy is bad, but because there is an inherent epistemological problem involved in linking current conditions to past circumstances. That inherent problem is this: one can easily construct a perfectly valid, but nonetheless entirely false, explanation for one's current set of conditions

What do we conclude from this? Is every investigation of the past inconclusive by its very nature? Valid logic, after all, is not necessarily true logic. The devil isn't even in the details. The devil is in the analysis itself.

It is a strange and fascinating concept. I'm not sure I'm capable of giving an answer, but I welcome your comments.