Thursday, May 22, 2014

Thinking probabilistically about historical facts

EDIT on 5/23/14 - I've changed the language a little to clarify that I don't want to talk about the whole field of history, but rather just the part that makes factual claims about the past. In particular, I don't mean to say anything about the theories of history that - by inference from historical fact - make larger claims about why things happened or how things work in general. Thanks to a few of you for pointing this out.

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Different academic fields have different criteria for what makes a theory "good".

In science, we usually evaluate theories on their ability to predict future evidence. Since scientific theories are usually at least locally time-invariant (they work the same at different times, all else equal), we can have them predict what will happen, and then see if they're correct.

In other fields - like evolutionary biology, archaeology, and the fact-finding part of history - we're trying to say what happened at a some particular time in the past, a past which no longer exists, so we need different criteria for differentiating between theories. However, none of the remaining criteria seem quite as straightforward as predictive ability.

My impression - and this is also a question - is that these fields don't have a fixed standard of what constitutes a "good" theory. Desirable qualities include consistency with documents and the current state of the world; as well as properties of the story implied by the facts, such as its simplicity, beauty, ability to explain the past, or generalizability to other historical or present situations. But is there a consensus on which claims about the past are the "best"?

A way to evaluate claims about the past

I'd like to propose a different way to think about historical facts. This might not end up being practical, but we can play with it as a thought experiment.

Let's take as an axiom that the past really did occur, and there is a right answer to the question of what happened. And let's also acknowledge since there is no way to go back and witness the past, we have at least some degree of uncertainty about all statements about it.

Then let's evaluate claims about the past by finding the likelihood that they occurred, given our current state. For some claim p = "at time t, the state of the world was such that X", we are interested in P(p | the current state of the world). We can think of story about the past as a set of such such claims, and then we are interested in the chance that the whole story is correct, or P(p, for all p in S | the current state of the world).

We could start by estimating P(p | the current state of the world) using rough, macro-level theories. For instance, we could use data about how often historical sources have been wrong in the past in order to infer how likely a claim is to be true when it's supported by some type of record. If p is something like "Napolean was alive in 1800", we could look at how many letters, decrees, etc. from 1800 confirm p and how many deny it; then we can assign rough probabilities to how likely each document is to be accurate; and then appropriately combine these to give some sort of estimate of how likely we think the claim is to be true.

There might be some benefits to this way of thinking. First, this kind of thinking might help to split disagreements about history into two categories. On one hand, we could disagree about the technical question of how likely different past states are. On the other hand, we could disagree about what the "best" way to think about these states are. In my experience, this kind of division is useful when you're having an argument.

Second this way of thinking just seems more honest - we often don't have a good idea of what happened in the past, so it seems silly to focus on the most likely story when there are other comparably likely stories to explore. Finally, on a more existential level, it's just really cool to start thinking about the past as uncertain and, in this way, comparable to the future - try it! It's much more stimulating!

Thinking in terms of quantum mechanics

It's illustrative to think about how we would obtain P(p | the current state of the world) using quantum physics, if we had enough computational power. Our current observations give us a probability distribution over all the possible quantum states of the world, weighted by how likely they would be to give our observations. We could evolve all the wavefunctions backwards in time to get a corresponding distribution over the possible states of the world at some time in the past. Finally, we just have to see which fraction of these states satisfy our claim p about the world at that time.

This way of thinking has two interesting consequences. First - since there's only a sign difference in the evolution of a wavefunction when we change the direction of time - our ability to predict the future should be about as good as our ability to know what happened in the past. This is counterintuitive, since it generally seems like we are better at knowing what went on during the past than we are at predicting the future; maybe that's only true for more macro-level theories than quantum mechanics, or maybe we have a cognitive bias towards thinking we know what happened in the past. (Another possibility is that this is counterintuitive because I'm wrong about it - does anyone think I messed up here?)

Second, we can establish bounds on our ability to infer what the past was - that is, what details of history we will really never be able to know. Quantum uncertainty tells us that we cannot know the exact state of the world now, so we can't perfectly infer the past or predict the future. In the case of predicting the future, quantum uncertainty might actually give a pretty strong bound, since there are chaotic systems - think butterfly effect - in which tiny differences of state cause drastically different futures (e.g. a hurricane occurring or not, and everything that follows). I haven't been able to figure out whether or not there is a similarly strong bound our ability to infer the past - does anyone else have ideas here? I'd really like to hear them!

Summary (mostly questions - please answer them if you can!)

  1. Unfortunately, we can't evaluate claims about the past on how well they predict data. How are claims about the past evaluated?
  2. I like the idea of assigning likelihoods-of-truth values to historical claims, based on what we know about the world now. It seems like this could be done in a semi-rigorous way.
  3. We can consider the extreme computational limit where we can do this quantum mechanically. In this case:
    1. Should we be able to predict the future equally as well as we can infer the past?
    2. How strong of a lower bound can we establish on our uncertainty about the past?

Thanks

  1. To Mike Casson, for the first conversation about this
  2. To you, For answering the questions I have!

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