Who shot first in Burr and Hamilton's duel?
We don't know. Not only don't we know, but we can't know. We know what Burr (the survivor) wrote and did afterwards, and what their seconds (who didn't watch the shots) reported. We can guess based on those contradictory accounts, but we don't know what actually happened. This's a gap in history.
There're other gaps like this. I don't just mean points where we don't know what someone was thinking, or points where we don't know whether one event was really caused by another - we hardly ever know that; that's the sort of thing historians debate throughout the story of history. I'm talking about gaps where the actual facts are unknown and can't be known.
A little while ago, I decided to dig a little further into the story of the smallpox vaccine (since I'd left some loose ends in my previous research on the smallpox eradication campaign). As I said in my previous post, the live "cowpox" virus used in smallpox vaccines (technically called Vaccinia) isn't the same as the cowpox that we see in the wild today. They're related, but no more closely than they're both related to smallpox. So, where did the actual Vaccinia virus come from?
So, I bought and read Jenner's Smallpox Vaccine: The Riddle of Vaccinia Virus and Its Origin, by Derrick Baxby, which digs into this question. The question's fascinating, because the historical record has important gaps I hadn't appreciated. Throughout the 1800's, local vaccinators kept passing Vaccinia virus between people and animals, to keep it available to easily vaccinate more people in the future. They didn't keep good records of exactly who they passed it to and from - which didn't hurt what they were doing, but it means we don't know where exactly our current Vaccinia came from. Presumably it was originally from 1790's Europe, around Jenner's time. Though, we know from Jenner's papers it didn't originally come from Jenner himself. Jenner's contemporaries weren't as exacting as we want - nobody was doing genetic analysis of viruses, none of them were sanitary by modern standards, and one of them was actually working in a smallpox hospital. So where did Vaccinia come from?
We can make a supported guess, of course. Baxby, after close reading of historical accounts and genetic study, guesses that Vaccinia was a horsepox virus that's since gone extinct in the wild. I agree that's the best guess. But, we don't - and can't - know for sure. The information just isn't there.
This might be most common in historical epidemiology, because people didn't have the tools to analyze pathogens till recently, most ancient people didn't describe illnesses precisely, and pathogens usually change over time. We still have no idea about a lot of historical plagues, and until recently some people were doubting even that the Black Death was actually bubonic plague. But it goes far beyond epidemiology.
For another recent example, the news has been announcing that archaeologists have discovered a new Roman Emperor: Sponsian. A few coins bearing his name had been found in 1713 Romania and dismissed as forgeries, but a recent analysis shows they were most likely genuine. So, it appears that there was an actual Sponsian reigning in Dacia during the Crisis of the Third Century. How long did he reign? What happened to him? We don't know, and unless someone finds a new reference to him, we can't know.
Things are even less clear with King Arthur: historians are still debating whether he ever actually existed. If he was real, there's very little about him we can know. The earliest written source mentioning him (the Annales Cambriae) says that he defeated the Saxons at Mount Badon, and then died at Camlann along with someone named Medraut - but that's it. Everything else is later stories which may or may not have acreted from some historical basis. Even the Annales Cambriae might be legendary. Personally, I believe it is historical - but that's just a guess. We don't, and can't, know.
There can also be gaps like this even in the middle of a known story. For example, one ancient source totally contradicts the other two sources writing about Alexander the Great's first battle against the Persians, at the Granicus River. Historian Peter Green, in his 1974 Alexander of Macedon, proposes this discrepancy's because Alexander's first assault was defeated, and he tried to cover up this defeat. Most modern historians disagree with him - but it's still possible. We don't know which of the sources is correct (if either - Green would argue neither), and we can't.
This can be frustrating or even shocking. We have this Vaccinia virus; where did it come from? We have all these stories about King Arthur; where did they come from? We're very curious, but we don't know, and we can't know.
But where can we go from here? What does this mean?
I said before that history almost has fractal depth; there're always more details to learn. That's true. But you can't always find more details about some one thing you're interested in. If you're interested in Sponsian, you're out of luck. Or rather, you can look into details in other directions that might peripherally bear on Sponsian and let you guess better - like studying other Roman generals during the Crisis of the Third Century, or the Gallic Empire which broke away in Gaul during that crisis, similar to some guesses of what Sponsian might've done in Dacia.
When you're in those gaps - if you want, you can act like the prototypical scholar and just say "we don't know; it could've been X or Y." Or, you can argue which interpretation is more likely, or even try to build out one likely interpretation. This's similar to what fandoms do in building "fanon" when the canon material is silent. They know no fanon is canonical, but they can still argue which fanon is most likely based on canon, or most in tune with canon. When we do this with history, it isn't scholarly rigor, but I'm convinced that it still can still preserve the spirit of the story of history. After all, there must have been some sequence of events there, and the people there would've known, even if we don't know which events they were.
Fortunately, these gaps are much less common in the modern era thanks to our plethora of records. They're still around - for example, a 1973 fire destroyed a lot of irreplaceable US military records - but less so than in previous eras. But because of the nature of these gaps, unless some lost documents are found again, there can never be fewer gaps than there were. We don't, and can't, know all the story for sure.
You may be interested in this video I stumbled over. It's a bit borderline in terms of speculation but it's not the first time I've heard a plausible sounding case that Earth had civilization(s) more than 10K years ago.
I'm not quite clear what the connection is to the 'two day orbit' he discovered unless you want to imagine some sort of monolith concept ala 2001.
https://www.youtube.com/watch?v=_HytJn6uaRk
So I would suggest an addition between gaps that matter versus ones that don't. Whoever shot first with Hamilton-Burr is interesting but would it change the big narrative much?
But some possible gaps could be quite dramatic. For example, whether there were sophisticated civilizations that pre-dated the earlies ones we know about? Imagine a Rome level civilization 75,000 years ago that lasted 3,000 years and then collapsed into a long dark period until around 4000 BCE or so. If that turns out to be the story that's pretty amazing. If we are able to rule that out entirely, less amazing because it doesn't overturn our current narrative but still helpful.