“Implication Vector” in historical narrative

The job of a historian is not only to uncover and publish facts of the past, but also to assemble them into coherent logical chains. There are at least two reasons for this: first, to make the facts we know understandable, interesting and useful; second, to use the facts that we do know to reasonably fill in the gaps in our understanding of times and places where history is silent. The assembly of these narrative chains is difficult in many ways: we never know as much about the past as we would like, and sometimes the facts that we do know are inconvenient for our currrently-preferred narratives. It takes great discipline and integrity to assemble narratives that are consistent with available evidence and to avoid narratives (especially currently-fashionable narratives) for which the evidence is weak (or even conflicting or refuting – see here for an apparently still-controversial example of this in the physical sciences).

The particular poor reasoning present in much of the oikiphobia-inducing Bad History is a type of logical error in narrative construction that I’ve not seen discussed in precisely these terms – I make no claim of originality for this observation, but if I’ve seen it, I don’t remember doing so. Perhaps this is a case where poor note-taking is indistinguishable from originality (and maybe the current sentence is another one!).

To discuss it, I need a bit of background from relativity – don’t worry, I don’t really plan to get technical at all (and many details will be omitted – it’s an analogy, after all). One of the tools used in relativity is the notion of spacetime, that is, of a united field of space and time together, in which there are (normally) 3 spatial directions and 1 time direction. Rather than thinking of a 3-dimensional x,y,z-coordinate space with an independent time coordinate t, we think of a 4-dimensional x,y,z,t-coordinate spacetime. There are important mathematical and physical reasons for doing this (that don’t matter so much in this analogy) but the important idea is that all four directions and combinations thereof are part of the same coordinate system. However, it is still important to be able to distinguish between what’s called the “spacelike” directions (vectors) and “timelike” vectors. One does this by considering the sign of the inner product of a given vector with itself – it doesn’t matter what this is exactly, only that it can be done: there is a fundamental, readily discernible difference between the directions that, say, a particle with mass can move along locally (timelike directions) and the directions that might represent locally “simultaneous” points in an inertial frame of reference (spacelike directions). That is, directions that locally represent moving into the past or future as opposed to directions that locally represent moving in space at the “same” time.

Now, consider a point in history – say, a fact about late 18th century America – which direction(s) are the directions in which that point has its “implications?” Said differently, given a fact about America in 1790, does it tell you more about other places at roughly 1790, or about America in 1820? Is the “implication vector” spacelike or timelike?

It’s important to note that both answers are possible – some facts about late 18th century America tell you more about the late 18th century globally, while others tell you more about America, even possibly contemporary America. Evidence is needed either way, though!

As an example, consider this pair of historical points in spacetime: a group of men in Philadelphia in July of 1776 wrote a document that would be the foundational document for American government and society, including the famous line that “all men are created equal;” that same group of men included slaveholders. Are the implication vectors from those two points spacelike or timelike?

I would claim that the evidence shows that the first point has a timelike implication vector: the sentiments expressed in the document, while not completely unprecedented, were novel enough that it would be inaccurate to say that this tells us about what was happening in 1776 around the world – it does, though, have implications that reverberate forward in time to the present day.

What about the second? The evidence shows that it has a spacelike implication vector: slavery, unfortunately, was widespread at the time and, while many of those same writers wrote vehemently about their desire to end it, they didn’t make it happen for nearly a century in what was to become the USA; it ended somewhat sooner in other places for a variety of reasons, but the existence of slavery was nearly uniform at that time (and, indeed, nearly all times throughout human history).

Now, imagine that I took the same two points and made the opposite claims about their implication vector directions: that the real forward-looking implication was that they were slaveholders, and that their fine words about the equality of man were just what everyone else was saying at the time – nothing special or unique in that: just a bunch of white slaveholders setting up a country where they could own slaves while mouthing the same platitudes everyone else was saying about “equality.” Reads a bit differently, doesn’t it? To be clear, no evidence I’m aware of supports this viewpoint, but it’s a choice of narrative that can be superimposed onto the same “points” in historical spacetime.