It's both profitable and gratifying to use one's reasoning skills to attempting to figure out answers to complex and murky questions. Even failing the ability to say definitively what happened, we can still make and update our own statistical distributions of what could have possibly happened. 

Unfortunately, it's typically questions like "Who killed JFK?" that draw the brunt of this type of speculative research and reasoning. Which is, I think, not a very good place to study and develop better skills for this type of thinking.

There's many reasons why, but just one will suffice — it's very helpful to be able to discuss and reason through these problems with another person, and almost any item that's emotionally charged in our culture will lead to less productive discussions.

An alternative for you.

I've found it better to train this type of thinking on incidents that are well-sourced and controversial in other cultures, but which are obscure or almost completely unknown in our own.

Things like —

(1) Was the 'Bardiya' that Darius the Great overthrew and killed the natural born son of Cyrus or not?

(2) Did Uesugi Kenshin die of natural causes?

(3) Did Scipio Africanus's brother misappropriate money?

And so on.

While it might be hard at first to get a friend interested in whether Bardiya was the actual Bardiya or a pretender, you can see how it's unlikely someone would have a heated opinion on the matter. It's a fun puzzle to work on with someone.

Many of these questions aren't definitively answerable — we'll probably never know for sure on Bardiya — but every now and then you find a problem that seems like it's unsolvable but for which you eventually find extremely conclusive evidence.

This is great when it happens.

I've come across a couple of these, where I was wracking my brain weighing evidence of whether a certain action during, say, the Russian Civil War was just an accident or coordinated — until I found a translation of an almost-certainly-not-forged-given-the-context set of orders. 

It's like, you've been digging through the evidence and building a spectrum of probability in your mind, and then you get something like a 'wave function collapse' where you 99% know what happened...

It's very satisfying. Though, unfortunately, this class of problem resists documentation if you want it to remain answerable-only-with-digging. If you wrote down a list of such problems in a blog post or forum post, (1) someone would probably just solve it and post the answers even if you requested that no one would do so, but also (2) you're telling people in advance that this is a "solvable with enough digging" problem and thus people are going to search wide and broad for a definitive answer instead of approaching it the normal way.

Too bad, eh?

Nevertheless, even when a problem isn't definitively solvable, it's profitable to explore these to train one's thinking. And there's a rounds-to-infinite set of problems for reasoning here.

Oh, sure, I highlighted "sexy" ones like leadership changes — but this type of reasoning can just as easily be done to try to figure out if two financial magnates had coordinated in some financial speculation in the 1800s or whether some on-the-side gratuity payments had been made in some complex business deal in the 1700s, and so on, and so forth, down to much lesser-impact and less-complex problems like trying to figure out which dairy farmer was the official provider of milk and cheese to the palace in a given year in the distant past.

All of these cases can be great ways to learn about reasoning and probability in general... and a way to productively redirect the desire to dig through evidence and reason about common emotionally-charged-for-my-culture issues and replace them with things that were controversies in another time and place but which are largely obscure and unknown to us.

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