Eigenquestions: The Art of Framing Problems

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Technique 1: Eigenquestions

Framing often starts with asking the right question. In many cases, a decision can look like it has ten related questions, and if asked in the wrong order, they can seem intractable. Often the best path through a decision is to pick the right question to start with.

What's an eigenquestion?

"Eigenquestion" is a made-up-word that borrows from the linear algebra concept of

eigenvectors⁠

. Essentially, eigenvectors describe the "most discriminating vector in a multidimensional space". In other words, if you have 10 dimensions of points, the eigenvector points out a single dimension that will capture the majority of the points. Here's a visualization:

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Similarly, great framing starts by searching for the Eigenquestion, the most discriminating question in a set.

For a simplistic definition, the eigenquestion is the question where, if answered, it likely answers the subsequent questions as well.

As an example, let’s consider the YouTube story at the

start of this doc⁠

ー what was the Eigenquestion. We initially started with the question "link out vs don't link out." We also had a latent set of questions that seemed unrelated: for example, should we build our own iOS app for YouTube?In our discussion, we reframed this to be focused on "consistent vs comprehensive." In finding the "consistent vs comprehensive" eigenquestion, the YouTube team was able to turn one decision into a principle to be used in many future decisions.

An exercise: Teleportation device

Here's a variant of an interview question I sometimes use to measure this skill. Over the years, I've found it to also be a useful tool in teaching the same skill. The question starts as follows:

A group of scientists have invented a teleportation device. They have come to you and asked for your assistance in bringing it to market. What do you do?

At this point, most candidates will go into question asking mode. They will generally start rattling off questions one after the other, often dozens of them. This is considered good ー being inquisitive and creative is a key skill that I look for. They'll ask how big the device is, does it need a sender and a receiver, how fast is it to operate, what does it cost, etc. I'll generally humor this for some time, and then at some point, I'll add a twist:

It turns out these scientists are introverts and they are not enjoying all your questions. They have decided that they will only answer two questions, and from that, they expect you to give a clear go-to-market plan. What two questions would you like to ask?

Now we're in eigenquestion mode. There are many good ways to handle this twist. At this point, the candidate generally has a list of 10+ questions that they have asked and the job is to prioritize among them to find the two most discerning questions. Of course there's no "right answer", but I find this to be a useful exercise in exploring eigenquestions. Here is one example of an answer, in our standard

diagraming colors⁠

⁠

This candidate focused on two questions: How safe is the device (safe enough for humans vs not), and where the primary cost is (is it in operating the device or purchasing them). With only this info, they were able to describe four very different go-to-market paths:

If the device is safe enough for humans, but is more expensive to deploy than operate, then it should probably be stationed at a fixed set of locations and run much like an airport system.

If it's similarly safe, and is cheap to deploy but expensive to operate, then we should enable everyone to have a device like this in their homes, workplaces, etc and then just use them when they find the use case valuable enough. In this way, it might be more similar to "fax machines."

On the other hand, if the device is not safe enough for humans, but is still cheap to deploy, then we probably shift this plan and think of it a bit more like an upgrade to fax machines to be able to transmit 3D objects.

And finally, if it's not safe for humans, and expensive to deploy, then perhaps we are building a freight network.

This is just one example question, but an illustrative one for the concept of eigenquestions.

Training yourself to find eigenquestions

If you're trying to learn this technique, I would encourage practicing with questions as you encounter them. Here's a few thought starters:

You run a grocery store and you'd like to increase the frequency of customer visits, what do you do?

You are designing a game to teach kids math in a fun way, where do you start?

You'd like to shift your company's communication patterns from being primarily "synchronous" to primarily "asynchronous," what do you do?

In each case, start by making a list of questions and considerations. Then consider ranking them ー which ones, if answered first, would provide answers for most of the other questions?

A note on the name: Eigenquestion

I have a mathematical background, so the term eigenquestion was natural to me. I found eigenvectors and eigenvalues to be one of the most beautiful and powerful concepts in linear algebra, and it turns out to be the basis of machine learning systems as well.

That said, beyond the history, the math definition is mostly irrelevant to the technique. Just remember eigenquestion as “the most important question”.

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👉 Next up:
`Great Diagrams`⁠
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