I'm starting a new Sequence on Agency and Maps. Each post will introduce some new small concept or focus on a specific aspect that I need.

Follow-up to: Skill: The Map is Not the Territory

You walk into the office with your laptop ready to present to your colleagues. The screen shows "HDMI-1 no input". The beamer in front of you has three inputs: HDMI-1, HDMI-2, HDMI-3. Cables are going everywhere.

Three ways this can go:

• A. Someone put tiny labels with "Laptop", "Camera", "Apple TV" on the cables.
• B. Someone says: “Use the left/middle/right cable.”
• C. Nothing. Someone helpfully repeats the screen: "Use HDMI-1."

People are watching. Which one is going to work best?

What you do (not what you think)

A. Names by device

Laptop.
You plug-in your laptop into the correspondingly named cable. The screen mirrors your laptop screen.

No translation step. No guessing. The label matches the intent. The Useful Idea of Truth. Let's hope nobody messes with them.

B. Numbers by physical order

“Left / Middle / Right.” Neat. Until you wonder: Do they mean from the their side or from my side?

You half-smile, half-gamble, and pick the wrong one first. That tidy compression just betrayed you, oh these Fallacies of Compression. “Left/right” are 2-Place instead of 1-Place Words.

C. Bare numbers

You find the port on the beamer and track the cable... Except you miss one twist...

This is extra work for you. Maybe you will remember next time. But every now and then somebody moves the cables around. Next week, you may be wrong with confidence. 

Each method of (helping) building a map - labels, positions, IDs - has different trade-offs. It compresses different aspects of reality. We can call that Task-Conditioned Compression. A representation M is better for a task T if it yields cheaper correct actions for the most likely situation for T^[1]. 

We can ask: What action does this map make cheap for the next person? See also By Which It May Be Judged

One-minute exercise

Picture the above room. Which methods would still work...

• if the projector were upside down?
• if the cables were removed?
• if the HDMI-1 port is broken?

When we look into the economics of modeling, we will see that some models win more often. When we review The Lens That Sees Its Flaws (or rather the flaws of other lenses) we will see that this becomes a problem.

Next up: Intentional Stance vs. Gears.

1. ^{^}

   We may be interested in terms like this:

   $TCC(M;T)=\underset{\text{predict what the task needs}}{\underset{}{E_{x\sim T}[{\ell }_{\text{pred}}(M;x)]}}+\lambda \underset{\text{make the action cheap}}{\underset{}{E[policy/complexity]}}+\mu \underset{\text{stay right after we act}}{\underset{}{E[update\_drag(M;T)]}}$