Module 1 · Foundations of Agentic AI · scripted

Framing: The Description Chooses the Solution

25 minoutcomes: prompt-engineering, context-engineering

The description chooses the model

We have seen how much of the world we can cast onto the wall. This one is about something subtler: which language we cast it in. The way we describe a situation carries a mental model with it — and the model carried by the words influences how the problem gets solved. Different descriptions of the same problem can lead to very different solutions, and sometimes to much easier, faster ones.

Same circle, two languages

The classic example is coordinate systems. Here is one circle, described in two languages:

One circle, two descriptions

Cartesian:all points (x, y) such that x² + y² = 2500

Polar:all points at distance r = 50 from the center

Both are exactly right. But now try to work in each language:

Example 1 · The circle, framed in x and y

user

A boat holds position exactly 50 m from a buoy at the origin, circling it once every 2 minutes. Using x and y coordinates, give me its position over time and check it stays 50 m away.

assistant

x(t) = 50·cos(πt/60), y(t) = 50·sin(πt/60), with t in seconds. To verify the distance: compute √(x(t)² + y(t)²) = √(2500·cos²(πt/60) + 2500·sin²(πt/60)) = √2500 = 50 — using the identity cos² + sin² = 1, the distance is constant.

NoteCorrect — but notice the work: two coupled functions and a trigonometric identity, just to establish something the problem said in plain words: the distance never changes.

Example 2 · The same circle, framed in r and θ

user

Same boat, same buoy. Using polar coordinates centered on the buoy, give me its position over time.

assistant

r(t) = 50, θ(t) = πt/60. Done — the distance is the coordinate: r is constant at 50 by construction, and one lap per 2 minutes is just θ advancing by 2π every 120 seconds.

Note"Stays 50 m away" stopped being a theorem to prove and became a constant to write down. The problem didn't change. The language did — and the reasoning it required collapsed.

The frame that unlocks a proof

Sometimes the right description doesn't just shorten the work — it makes an impossible-looking problem transparent:

Example 3 · The chessboard, framed as tiling

user

Take a chessboard and remove two opposite corner squares, leaving 62 squares. Can you cover it exactly with 31 dominoes, each covering two adjacent squares? Try to work it out.

assistant

Let me try constructions. Starting along the top row, dominoes lay cleanly until the missing corner forces a vertical placement, which displaces the next row… let me try a different arrangement — a brick pattern… that fails near the opposite corner as well. After several attempts I believe the answer is no, but I haven't shown why — an exhaustive search of placements would be enormous.

NoteThe model is dutifully working inside the frame we gave it: dominoes, placements, arrangements. In that language, the problem is a haystack.

Example 4 · The chessboard, framed as colors

user

Same problem — but describe the board in terms of the colors of the squares before you reason.

assistant

The two opposite corners of a chessboard are the same color — say both white. Removing them leaves 32 black and 30 white squares. Every domino, wherever it lies, covers exactly one black and one white square. So 31 dominoes cover 31 black and 31 white — but we need 32 and 30. Impossible. No arrangement exists.

NoteFour sentences, and it's a proof, not a search. Nothing about chessboards changed. The description put color into the model's working vocabulary — and the entire solution lives in that word.

Numbers that think for you

The effect isn't limited to puzzles. Here is one your research will meet constantly — the same statistical question in two languages:

One question, two framings

As probabilities:Prevalence 1%. Sensitivity 90%. False-positive rate 9%. A person tests positive. How likely do they have the condition?

As counts of people:Out of 1,000 people, 10 have the condition; 9 of them test positive. Of the 990 without it, about 89 also test positive. A person tests positive. How likely do they have the condition?

In the first language, most humans — including doctors in published studies — answer "about 90%." In the second, the answer is sitting on the surface: 9 true positives out of 98 total positives — roughly 9%. Same information, different representation; one language invites a famous error, the other makes the correct reasoning almost automatic. LLMs, trained on our text, inherit our framings' strengths and traps — and your description decides which ones are in play.

The frame is a boundary

Why does this matter so much for agents? Because of alignment. The model is trying to honor your request — and it will not readily go outside the boundaries of what you state. Describe the chessboard problem as arranging dominoes, and it arranges dominoes. Frame the analysis in probabilities, and it computes in probabilities. The words, and the associations attached to the words, constrain the reasoning — they summon one mental model and quietly leave the others asleep.

So when you hand an agent a task, you are choosing more than content. You are choosing the language of the domain the problem solving will happen in: the representation, the vocabulary, the model of the situation. It is the same act as before — casting shadows on the wall — but at its most profound: the shape of the shadows selects the reasoning.

The frames you already use

Your discipline has a house language — its own coordinates, its own "colors of the squares." What is it?
Name a problem in your research that is hard in that language. What would the polar-coordinates version of your problem be?
When would you want to tell an agent "feel free to change the representation before solving"?

Your turn

Take one real problem from your research and write the task description twice, in two genuinely different domain languages — different vocabulary, different representation, same problem. Give both to an LLM and compare not the answers but the kind of reasoning each one triggered. Which frame made the model smarter?