Comments on “The Spanish Inquisition”

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Unknown unknowns

Peter Corbett's picture

How does Good-Turing frequency estimation - and all of the smoothing techniques that follow - fit into all of this? It’s all about leaving some room for previously unseen stuff in your probability distribution, estimating how much by looking at how many things you’ve seen only rarely.

Possibly it’s analogous to having a feeling for how “crud-prone” some particular endeavour is; some things are generally pretty reliable, with some things you know you can pretty much rely on unexpected trouble and delays. “If I think of all the work I know needs to be done, this looks like a day-and-a-half job. If I think of how long similar jobs have taken in the past, two weeks”, and it ends up taking three weeks.

In thinking about epistemics

Romeo Stevens's picture

In thinking about epistemics I’ve found it helpful to think about modularity. I think this is closer to what we’re actually doing: https://imgur.com/a/n0LscP2
Find the way to decompose the messy territory into easy to represent and propagate simpler distributions that are side effect free wrt one another so that we can build plans out of stacks of them and not need to track tons of corner cases.

Probabilistic models

I’ve now posted a page that treats the same issues as this one, but in a probabilistic framework. It might be relevant to both comments above.

having a feeling for how “crud-prone” some particular endeavour is

Yes, this is a characteristically meta-rational form of cognition! “Having a feeling for…” is often the way people talk about meta-rationality in practice. (I hope we can learn to do better than that, to be more specific, but the available vocabulary is currently poor.)

Good-Turing frequency estimation

As with all statistical methods, this depends on a priori assumptions about the domain. Specifically, in this case, that the frequency of outcomes has a binomial distribution.

leaving some room for previously unseen stuff in your probability distribution

Yes, this is a good thing to do, but it depends on your (necessarily meta-rational) prior for crud-proneness. See “The probability of green cheese.”

I think this is closer to what we’re actually doing

I’m not totally sure where you are going with this… The model in the image you linked may often be a good one, but it can also be badly wrong, depending on what the territory itself looks like. It’s a statistical independence assumption, right? Which is a commonly-used approach because it often works, and one is also taught that it commonly fails. So you have to do some work to figure out whether it’s adequate in a specific case.

Hiding the problem of induction in your closet and locking it

Alexander's picture

First, your website has helped me a lot in general, so thank you.
Second, just another example of the sort of thing beyond the limits of reason: the problem of induction. It seems to me that people often either think it’s just a bad joke or that there’s a good counter argument to it. There isn’t: causality is superstition. Normal unknown unknowns either cannot possibly be enumerated through or cannot be assigned a non-arbitrary probability. However, what’s unique about the PoI is that although it’s a known unknown whether or not the sun will rise tomorrow, it would be just inconceivable to assign a probability to this event. The “good” news is that causality breaking down would probably invalidate most of our other probabilities (or destroy us), so we wouldn’t have to worry about it anyway, as there’d be nothing we could do. So in some sense, it is reasonable to not care about the PoI because no action would have any knowable utility in that case: you might as well do anything. So perhaps we cannot resolve the PoI, but instead walk around it.

Rather, it is trying to

Romeo Stevens's picture

Rather, it is trying to discover statistical independence by finding the right representation/rotation of the given data.

Or another frame: sample

Romeo Stevens's picture

Or another frame: sample complexity reduction is a large part of what we need to do in order to do anything else at all.

Priors

Peter Corbett's picture

it depends on your (necessarily meta-rational) prior for crud-proneness.

I have some thoughts about “Objective Bayesian” methods, starting with Laplace’s study of the probability of the sun coming up tomorrow. Basically, you pick priors based on equiprobability assumptions and things like that.

Everyone - including Laplace, in the work where he presents it - feels the “probabilty” he calculated of the sun coming up was tomorrow was absurdly low. There’s so much we know about the solar system that his little calculation doesn’t take account of.

There’s something about these methods which appeals to the part of my mind that has overstrong metaphysical intuitions about what the world “should” be like and what some over- and yet under-idealised system of knowledge could do, but which always results in crashing disappointment when they’re actually applied to anything in particular.

I’m wondering whether the problem isn’t truly unknown unknowns, but what I might call “murkily known unknowns”, things we don’t know how to formalise, or don’t know how to formalise well, or don’t have time to formalise, but whenever we try to sweep them into a nice formalised “other” pile they feel known enough that you can be blamed - quite possibly by yourself - for not including them in your model. And so the model can create answers that make you say - rightly - “but this is absurd”, like the green cheese example.

Hang on. “Murkily”? That’s like “nebulously” isn’t it?

Induction & complexity reduction

Alexander, glad you’ve found it useful. And, yes, there’s no general method for induction, as philosophers of science finally concluded in the mid-20th-century. The Eggplant will summarize the explanation for that. On the other hand, the Popperian claim that we don’t do induction at all is obviously false (we do it all the time, both in science and in everyday life). There are many specific methods that work well enough in practice. (That’s what one does in the lab.)

Romeo, re sample complexity reduction. Yes. I think about this in terms of “finding an adequate ontology,” which is a large part of what The Eggplant is about. (That part is still just notes and drafts, so it’s not up on the web yet.)

Peter, re “murkily known unknowns”—I like that! And, yeah, nebulosity.

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