The Limits of Problem Analysis

The bot watches one point

Watch the color of one point on the HP bar. When it turns from red to gray, health has fallen below a threshold: press heal. When it changes the other way, do nothing.

The game’s internal logic is a black box. But to be playable, it must give a human ways to provide input and read output. The bot connects those interfaces: take a small piece of output, apply one simple rule, and take over a tiny loop from a person’s eyes, brain and hands.

The bot has no ambition to decode the whole system. It grasps just a little of the output. That is enough to free a person from this simple loop and leave their energy for more complex, more interesting things. It is a textbook case of modular thinking.

Try “Poison the hero.” The health bar turns green, but the bot only knows red and gray. It can no longer detect that red-to-gray transition. Its tiny piece of understanding works only within its boundaries. (The poison scenario was added for this interactive edition.)

From description to mechanism

In data science, analysis can be classified by its purpose, with increasing levels of difficulty. The simplest is descriptive: clearly describe the data you see. The deepest is mechanistic: understand which variables changed in each individual within the system that produced the data, and which other changes they caused.

Take a pear. Work down the levels to see how the questions deepen and how much more you need to answer them.

The original essay described only the two ends. Description asks me to record a pear’s shape, color and size. Mechanism asks why it has that shape, color and size, and how the three relate. Then comes another question: if we try a different pear, does our model still hold?

The six types come from Jeff Leek’s Types of Questions lecture in The Data Scientist’s Toolbox on Coursera. The four middle pear examples and the variables in the mechanism diagram were added for this edition. They are illustrations, not botanical findings.

There is never enough information

Ideally, we want mechanistic answers: to pick out, clearly and precisely, the flap of a butterfly’s wings within a hurricane. In practice, the information we can get hold of is always far too little.

Below are two identical worlds, with one difference: in one of them, a butterfly flaps its wings once.

Even in an age of enormous data production, what changes? We have more data, but extracting information becomes harder too. Here, raising the number of observation points from 12 to 9,000 cuts error by more than twentyfold, yet reveals the difference only a little over a day earlier. By then, the hurricanes are about to part ways. At times like this, we have to rein in our greed and advance one step at a time.

Come back when it is enough

Sometimes, after weighing cost against return, we find that studying a problem to a certain depth and breadth already meets our needs, as with the bot. The resources left over are better spent where they count.

The three problems below share one budget of time and effort. Each column runs down the same six levels of analysis. Choose a cell to decide how far to go.

To analyze a problem well, we need the focus and persistence to get to the bottom of it. But we must keep reminding ourselves: in the rough real world, a problem needs a boundary, one that keeps us from losing the way back as we dig our tunnel.