Unifying stuff is hard

Grognor draws the following picture, and says that we are much more likely to err by treating two things as one than by treating one things as two, because our limited mental faculties make one thing much easier to deal with than two. He praises making distinctions as harder and more important.

mistakseandrectitudes

The point I want to press upon you is that the situations in the top row are easier or more likely than the situations in the bottom row, due to working memory constraints. An ontology with fewer objects in it is easier to understand, so it’s relatively easy for humans to correctly identify that what they thought was two things is actually one thing, and correspondingly, to mistakenly conflate two things into one. Mutatis mutandis, it’s hard for people to notice subtle distinctions. And likewise people have low propensity to mistakenly think that one thing is two things.

I’m not convinced.

For one thing, seeing two superficially dissimilar things as the same in a useful way requires dealing with large spaces of things and characteristics. So I don’t think the difference between one and two items in the question should be a deciding factor in how computationally hard the problem is for a brain. Figuring out how a raven is like a writing desk is way harder than imagining a raven and also a writing desk.

Also, this argument doesn’t distinguish between the upfront costs of seeing one thing as two or two things as one, and the long term costs. I think there are a very large class of things where there is a substantial upfront mental effort to see two things as the same, so we don’t. You can’t just go around mistaking a field of emus for a corporate office. However if you put careful thought into it, you might find that both represent a similar game theoretic situation. And once that has been noticed, it is relatively cheap to notice again in future. If it is true that seeing two things as one is less mentally taxing than seeing them as two, then those who originally make it easy to see two disparate things as one should get credit for making this easier for others later.

Also, I think it is often much more valuable to see two things as analogous that were not than it is to distinguish two things. Distinguishing things usually means deciding that the way you were treating both of them is not quite applicable to both, and you should treat at least one differently. But if you are only noticing this now, it probably wasn’t *that* inapplicable, and now you have to come up with a new way to deal with the thing. (I don’t have examples here, and I’m probably missing other useful effects of distinguishing things, e.g. relating to understanding them.)  But treating what were previously two things as the same things means you get to port a whole bunch of things that you learned from one context into another context for free.

Grognor says that science means division. Maybe i’m biased, but I like the bits of science more that are about unifying. Physics over taxonomies. Which is perhaps just because our brains are small. But they really are.

6 responses to “Unifying stuff is hard

  1. Alfred Korzybski already claimed in *Science and Sanity* that the root cause of many human problems is treating two different things as one, if they only have one point in the map representing two different points in the territory.

    The process goes like this: X and Y happen to be represented by the same point on the map. We notice that X has a property P. From now on, we take it as proven that Y has a property P.

    What you say, Katja, is that there may be good reasons for doing this. X and Y may be two instances of something where P applies equally, so proving P about the whole set makes it simultaneously proven for both X and Y. — X is a square made of wood; Y is a square made of metal; P is a claim that there is a right angle at the corner; you notice P of X, and you automatically assume P of Y, because both of them are squares, and P is relevant to the squareness itself.

    But the problem happens when P is *not* relevant to what X and Y have in common. Or rather when people automatically (without even noticing that they are doing that, so they cannot reflect upon that) assume that because X and Y have *something* in common, then surely they must be the same with regards to P. Or even worse, when people don’t even notice that X and Y are two different things.

    So the analogical example could be that X is a wooden square, Y is a wooden triangle, people notice that X has right angles, and automatically assume that Y has right angles, too. But even “automatically assume” is not the precise word here; it’s more like they *observe* that X has right angles, and their brain automatically stores this as an “observation” that Y has right angles. Instead of separate points for X and Y on their map, they only have one XY point, so when they see that X has right angles, they put a note on their map saying “XY has right angles; it has been experimentally proven”.

    Specific examples of this process are known as “fallacy of equivocation”, “false equivalence”, “motte and bailey fallacy”, “noncentral fallacy”.

    The observation that there are sometimes good reasons for doing what others consider a bad thing… well, that’s a repeating theme in the whole “heuristics and biases” area. Yes, in many situations heuristics are useful. Sometimes the limited capacity of human brain requires that we use some heuristic. But they still sometimes provide bad answers, often predictably.

  2. Pingback: Want like want want | Meteuphoric

  3. Hm I tried to post a comment here but it seems to have vanished?

  4. OK, I’m going to just try reposting my comment and hoping it works this time?

    Original comment follows:

    I’m going to claim that yes, mistaken unifications are much more common than mistaken divisions. But the details matter here; it’s not just about “unification” vs. “division”. There are multiple ways we can “unify” things.

    One way is to put them into a verbal cluster together. The thing is that this is often pretty useless for inference. Clusters aren’t interfaces, and trying to make serious inferences from such similarities doesn’t really work very well. The fundamental mistake people make here really of course is not thinking that clusters are interfaces but thinking that they’re essences — which goes along with thinking, ah, these are different manifestations of the same underlying phenomenon. Of course, the latter inference is sometimes true, but people make it too often; and, of course, there are no essences. Basically, 37 ways that words can be wrong, etc.

    Another way is to say that two things are different manifestations of the same underlying phenomenon, even if they don’t resemble each other (e.g. grasshoppers and locusts or water and ice). This of course is a useful thing. I don’t think people make this mistake on its own too often; generally they seem to make this mistake as a result of clustering above. It only really becomes a problem of course when you apply one word to the whole thing and start conflating things. Note that this sort of unification while important still doesn’t let you make straightforward inferences about one thing from the other.

    A third way is to notice (or claim) that two things are isomorphic, that they “implement the same interface”. This is useful for inference (within the domain that the isomorphism is valid, of course). But it would be a mistake to, seeing such an isomorphism, then fall back on naïve verbal categories and conclude that the isomorphs share an essence. Because, of course, there are no essences. But this is (roughly) a mistake I see people actually make. Isomorphisms aren’t essences or identities, they’re isomorphisms. Thoughtless “unification” is still a mistake.

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