Sloppy Interior Vs. Careful Border Travel

Imagine that you are floating weightless in space, and holding on to one corner of a large cube-shaped structure. This cube has only corners and struts between adjacent corners; the interior and faces are empty. Now imagine that you want to travel to the opposite corner of this cube. The safe thing to do would be to pull yourself along a strut to an adjacent corner, always keeping at least one hand on a strut, and then repeat that process two more times. If you are in a hurry you might be tempted to just launch yourself through the middle of the cube. But if you don’t get the direction right, you risk sailing past the opposite corner on into open space.

Now let’s make the problem harder. You are still weightless holding on to a cube of struts, but now you live in 1000 dimensional space, in a fog, and subject to random winds. Each corner connects to 1000 struts. Now it would take 1000 single-strut moves to reach the opposite corner, while the direct distance across is only 32 times the length of one strut. You have only a limited ability to tell if you are near a corner or a strut, and now there are over 10300 corners, which look a lot alike. In this case you should be a lot more reluctant to leave sight of your nearest strut, or to risk forgetting your current orientation. Slow and steady wins this race.

If you were part of a group of dozens of people tethered together, it might make more sense to jump across the middle, at least in the case of the ordinary three dimensional cube. If any one of you grabs a corner or strut, they could pull the rest of you in to there. However, this strategy looks a lot more risky in a thousand dimensions with fog and wind, where there are so many more ways to go wrong. Even more so in a million dimensions.

Let me offer these problems as metaphors for the choice between careful and sloppy thinking. In general, you start with what you know now, and seek to learn more, in part to help you make key decisions. You have some degree of confidence in every relevant claim, and these can combine to specify a vector in a high dimensional cube of possible beliefs. Your key choice: how to move within this belief cube.

In a “sloppy interior” approach, you throw together weak tentative beliefs on everything relevant, using any basis available, and then try to crudely adjust them via considerations of consistency, evidence, elegance, rhetoric, and social conformity. You think intuitively, on your feet, and respond to social pressures. That is, a big group of you throw yourselves toward the middle of the cube, and pull on the tethers when you think that could help others get to a strut or corner you see. Sometimes a big group splits into two main groups who have a tug-o-war contest along one main tether axis, because that’s what humans do.

In a “careful border” approach, you try to move methodically along, or at least within sight of, struts. You make sure to carefully identify enough struts at your current corner to check your orientation and learn which strut to take next. Sometimes you “cut a corner”, jumping more than one corner at a time, but only via carefully chosen and controlled moves. It is great when you can move with a large group who work together, as individuals can specialize in particular strut directions, etc. But as there are more different paths to reach the same destination on the border, groups there more naturally split up. If your group seems inclined toward overly risk jumps, you can split off and move more methodically along the struts. Conversely, you might try to cut a corner to jump ahead when others nearby seem excessively careful.

Today public conversations tend more to take a sloppy interior approach, while expert conversations tend more to take a careful border approach. Academics often claim to believe nothing unless it has been demonstrated to the rigorous standards of their discipline, and they are fine with splitting into differing non-interacting groups that take different paths. Outsiders often see academics as moving excessively slowly; surely more corners could be cut with little risk. Public conversations, in contrast, are centered in much larger groups of socially-focused discussants who use more emotional, elegant, and less precise and expert language and reasoning tools.

Yes, this metaphor isn’t exactly right; for example, there is a sense in which we start more naturally from the middle a belief space. But I think it gets some important things right. It can feel more emotionally “relevant” to jump to where everyone else is talking, pick a position like others do there, use the kind of arguments and language they use, and then pull on your side of the nearest tug-o-war rope. That way you are “making a difference.” People who instead step slowly and carefully, making foundations they have sufficient confidence to build on, may seem to others as “lost” and “out of touch”, too “chicken” to engage the important issues.

And yes, in the short term sloppy interior fights have the most influence on politics, culture, and mob rule enforcement. But if you want to play the long game, careful border work is where most of the action is. In the long run, most of what we know results from many small careful moves of relatively high confidence. Yes, academics are often overly careful, as most are more eager to seem impressive than useful. And there are many kinds of non-academic experts. Even so, real progress is mostly in collecting relevant things one can say with high enough confidence, and slowly connecting them together into reliable structures that can reach high, not only into political relevance, but eventually into the stars of significance.

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