Brokenness is inaccurate emergence

One of the weirder tech issues I’ve had is that my laptop refuses to connect to wifi while its backup hard-drive is plugged in — it took me a while to figure out that’s what was even going on! I want my things to “just work,” and it’s so frustrating when they don’t. But it got me thinking about what “just working” means, and what it means for something to be broken — my conclusion is there aren’t really broken things, just places where our abstracted descriptions of reality are inaccurate.

I prefer drinking out of a water bottle made of glass instead of metal or plastic, but I’ve had it happen that a glass water bottle in my bag can break when I set the bag down too quickly on a stone bench or other hard surface. There are at least a couple of true senses in which the water bottle is now “broken”:

  • The bottle started out in one piece; now it’s in multiple pieces.
  • The bottle no longer fulfills its purpose of being able to store water; the water is getting my bag and the rest of its contents wet.

When I’m disappointed by these events, it’s because I had in mind a couple of rules for how things work that are now being violated:

  • *A solid object stays one solid object (with certain exceptions like ice).
  • *Water in a bottle stays there until I take it out.

The fact that these rules are reliable even most of the time is an example of emergence, which I think of roughly as follows: if we have a model A of reality consisting of a space S of states and rules for how those states change over time (with a subspace T of S consisting of states we call “typical,” such that typical states stay typical for at least short amounts of time), another more abstract model B, with its own state space U and evolution rules, and some kind of “interpretation” function T -> U, such that for each state t of T, evolving t according to the rules of model A and then applying the interpretation map gives approximately the same results as interpreting t as a state in model B and then evolving it there.

In the water bottle example, model A could have as its state space the set of all possible configurations of matter in my bag (or really, the whole universe) and how they would evolve according to the laws of physics, where the “typical” states are those in which the matter of my bag is organized into recognizable pieces of glass, water, paper, etc. The more abstract model B could have states consisting of descriptions of what objects are in my bag and in what arrangement — this is the model where states evolve according to rules like “Water in a bottle stays there until I take it out.” This higher-level description is emergent from the laws of physics, because I can mostly ignore the precise details of the configuration of the matter in my bag, as long as I’m content to make only predictions about similarly high-level descriptions of the future.

The water bottle breaking is an example of the emergent description not being completely accurate. If you start with the physical state of my bag and its contents, make a high-level description of it as “My bag, containing a water bottle and some papers, in my hand” then when I put down the bag on the bench the abstract model leaves the contents intact: “My bag, containing a water bottle and some papers, on a stone bench.” However, when you evolve the original physical state, the stone breaks the glass and the water spills, and the high-level description of the evolved physical state (“My bag, containing pieces of glass and wet papers, on a stone bench”) doesn’t match the evolved high-level description. The brokenness of the water bottle is the inaccuracy in the emergence.

So let’s say I’m trying to learn my lesson about accidentally breaking glass water bottles. I broadly see two kinds of actions to take:

  1. Stay where the emergence is accurate. This might mean learning to be gentle with glass objects so they don’t break.
  2. Reduce the amount of emergence you require. This might mean updating the high-level description state space and evolution rules so that an “intact water bottle” can evolve into a “shattered water bottle” under certain conditions; making the model a little closer to the underlying reality.

Most of my life, I’ve tried to stick to option #1. It’s part of why I chose to study math instead of physics: in my physics lab things would sometimes mysteriously not work, whereas in math, things “just work” because if they don’t we change the definitions until they do (and then they keep working forever).

But lately I’ve been trying to be more okay with, and even appreciative of, option #2. If I ever found myself in a situation where I needed sharp pieces of glass, it’s helpful to have a model of my water bottle that allows it to be shattered. And digging around on the internet for what causes my external hard drive to interfere with my wifi, it sounds like the cable connecting the computer to the drive acts inadvertently as a second antenna that the wifi doesn’t have a protocol to handle, and wrapping the cable in aluminum foil to keep it from picking up the signal seems to do the trick. So a more accurate model of reality, relying on less error-prone emergence, can open up new options for solving problems.

But even beyond that, I find it comforting and compelling to think that nothing is really broken — everything from shattered glassware to a glitchy computer is correctly following the laws of physics, and the only reason it seems broken is because I’m expecting reality to conform to models that are only approximately true at best. Even the times that I’m frustrated with myself for not meeting my own expectations, I’m not broken; all my parts are doing their thing, maybe serving essential functions that I don’t have the mental vocabulary to describe. I can learn that vocabulary and make my expectations more realistic, maybe ending up able to do more than I realized.

How about you? Is there a time you’ve been frustrated that things don’t work the way you want them to, and ended up with a more nuanced view of reality? I’d love to hear about it in the comments!

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