The Math of Being on the Same Wavelength

An explainer by Gemini 4 Argon

Written from the formula Dan and Mike worked out.

When you train an AI on your taste, most of your effort goes into reading raw outputs and answering questions the AI could have already guessed. A great interviewer never does that. They do the homework first, lead with a sharp observation ("I notice you like when X happens"), and only ask you the close calls where your answer actually changes their mental model of you. The formula below measures the value of any question an AI might ask you by multiplying two things: the odds you will actually want to answer it, and how much your answer will update the system. It turns "this feels like a chore" into a specific engineering target: bits of taste learned per minute of your attention.

The Problem: Why Labeling Felt Like a Chore

Recently, you spent time teaching an AI skill your taste by comparing candidate "next beat" answers and picking the best one. And it felt like work.

The reason it felt like work is that you were carrying all the cognitive load. You had to read multiple raw candidates, hold them in working memory, figure out why one was better, and register a verdict. Worse, many of those comparisons were probably obvious. If one candidate is clearly flat and another is alive, clicking "B is better" barely teaches the system anything it couldn't have inferred on its own.

Contrast that with sitting across from a great podcast interviewer. They don't hand you five transcripts and ask which one you like. They read everything beforehand, notice a pattern, and say: "It seems like whenever a draft gets abstract, you want the very next beat to drop into a concrete scene. Except here, you didn't. Why?"

That feels great to answer. It takes almost no effort, you learn something about yourself just by hearing the question, and your two-sentence reply gives the interviewer a massive update.

The formula below is a blueprint for building an AI that learns your taste the second way instead of the first. Here is the whole thing up front, so you can see where we are headed:

The formula

value(q) = P(engage | q) × I(θ; A | q)

Worth of asking question q = chance you answer × how much the AI learns.

P(engage) ∝ G + E + C − (c(q) − h)

Chance you answer rises with insight first + end result you want + curiosity − (effort, minus help).

Let's build it from scratch, piece by piece.

Idea 1: Not All Questions Are Equal

Start with the right half of the first line: I(θ; A | q).

First, the symbols:

• q is the question the AI is considering asking you right now.
• θ (the Greek letter) is the AI's current mental model of your taste. Think of it as all the sliders and rules inside the system that represent "what Dan likes."
• A is your answer to the question.

The whole expression I(θ; A | q) is called mutual information (the I stands for information, and the vertical bar | just means "given"). In plain English, it means: "Given that the AI asks question q, how much will your answer A actually change its model of your taste θ?"

Information theory measures this in bits. A bit is not a metaphor here; it is the exact unit of a 50/50 coin flip.

AI is 95% sure of your pick
0.29 bits
You did the reading; the model barely moved.

AI is 80% sure
0.72 bits
Still useful. You could easily surprise it.

A true 50/50 coin flip
1.00 bit
Your answer resolves real uncertainty. The full update.

In statistics and machine learning, choosing questions to maximize I(θ; A | q) is called Bayesian experimental design or active learning. For your product, the takeaway is simple: the AI should read and rank the raw candidates itself, throw out the 95/5 blowouts, and only bring you the 50/50 close calls.

Idea 2: A Great Question Nobody Answers Is Worth Zero

If information were the only thing that mattered, the AI would hand you ten-page essays that split its model 50/50 and demand a verdict. You would close the tab.

That brings us to the left half of the first line: P(engage | q).

• P(...) means probability, a number between 0 (never happens) and 1 (guaranteed).
• P(engage | q) is the probability that you actually engage and answer, given that the AI puts question q in front of you.

Notice the multiplication sign in the main formula:

value(q) = P(engage | q) × I(θ; A | q)

Because they are multiplied, if either side hits zero, the whole thing hits zero. A question with 1.00 bit of theoretical value that you skip (P = 0) produces zero learning.

So what makes P(engage | q) go up or down? That is the second line of the formula:

P(engage) rises with: G + E + C − (c(q) − h)

Think of this as a simple balance scale: three things that pull you in (G + E + C), minus the net effort required (c(q) − h).

What pulls you in: G + E + C

• G is the Gift (or insight) the AI gives you up front. Formally, we can write G = I(you; X), which uses the same I (information) as before: how much you learn from an observation X that the AI shares before asking its question. When the AI says, "I noticed you always cut throat-clearing sentences, except when the piece is personal," that is X. You get a small epiphany about your own taste (G) before you do any work. Paying you first makes the interaction feel generous rather than extractive. Better yet, reacting to a sharp hypothesis makes your answer more informative while lowering your effort.
• E is the Expected payoff of the finished skill. It breaks down into p(works) × V: how clearly you can picture the thing actually working (p(works)) times how much you value that result (V). If the end state feels fuzzy or uncertain, people discount the payoff and stop answering.
• C is intrinsic Curiosity. How fun or interesting do you find this process for its own sake?

Crucially, different people weight G, E, and C differently. You have unusually high E and C: you can clearly see what a trained skill will do for Every, and you are intrinsically fascinated by how AI learns taste. That is why you pushed through the manual labeling chore. Most users will not. They need a high G (an immediate insight) on question one, or they bounce. A smart system learns each user's weights on G, E, and C just like it learns their taste.

What pushes you away: c(q) − h

• c(q) is the cognitive cost of answering question q. Reading four paragraphs and ranking them has a high c(q). Saying "yes, that's right, except when..." to a one-sentence observation has a tiny c(q).
• h is hands-on human help. This is when a person, like Mike Taylor or an early builder on the team, sits with the user and carries part of the load. Notice the minus sign: c(q) − h. When h goes up, the net effort the user feels goes down.

A Quick Worked Example

Suppose you have five minutes between meetings. The AI has two ways to ask about the same underlying taste rule:

The raw chore

"Read these three candidate next beats and pick the best."

The AI already has an 80% hunch on your pick. No insight up front, lots of reading. You only engage about a quarter of the time.

25% chance you answer × 0.72 bits = 0.18 bits

The interviewer question

"I see you like punchy transitions, but here A is punchy while B keeps the emotional thread. Which wins?"

The AI ranked the candidates itself and found a real 50/50. It leads with an observation and takes ten seconds. You answer about 90% of the time.

90% chance you answer × 1.00 bit = 0.90 bits

Same user, same model, 5x more learning, just by moving the work onto the AI before asking.

The Flywheel: How h Builds the Product

That little h (hands-on help) does double duty.

In the moment, having Mike or a builder sit with someone lowers c(q) so the person actually finishes the session. But the second effect is bigger: the human helper sees where the user hesitates, which questions make their eyes light up, and what they skip. Those observations get baked into the software, which lowers c(q) and raises G for every future user without a human in the room.

This gives you a natural rollout order:

1. Builders first (You and Mike): High E and high C. You tolerate high c(q) and zero G, revealing which questions actually carry bits of taste.
2. Enthusiasts next: Once the AI does the reading and ranking itself and only surfaces 50/50 close calls (high I, lower c(q)).
3. Busy experts (with h): Sit with them at first; lead every question with a sharp insight G.
4. Everyone: Once G is reliably high and c(q) is low, training the AI feels like a great conversation that happens to make the software smarter.

What to Measure: The "Same Wavelength" Metric

If you want one number on a dashboard, track bits of preference learned per minute of the user's time, flowing in both directions.

When I(θ; A | q) (what the AI learns about you) and G = I(you; X) (what you learn about yourself) are both high, and c(q) (effort) is low, we have a phrase for that in everyday life. We call it being on the same wavelength.

Cheat Sheet: The Formula in Plain English

• value(q): The true worth of asking question q...
• = P(engage | q): ...equals the odds you won't ignore it...
• × I(θ; A | q): ...times how much your answer updates the AI's model of your taste.
• P(engage) rises with: You are much more likely to answer when...
• G: ...the AI teaches you something about yourself first,
• + E: ...you can clearly see and want the end result,
• + C: ...and you're naturally curious,
• − (c(q) − h): ...minus the mental effort required, softened by any human help in the room.