st+1 = st + λt̂
Each step in solution space equals the previous state plus an amplified move toward the target.
The Amplification Thesis
In the equation, the human provides v — the direction.
But direction isn't monolithic. It's a vector with two components:
The crucial insight: they're partially substitutable.
You don't need to be an expert to begin.
Willpower can compensate for knowledge gaps.
The feedback loop
Real collaboration is closed-loop. You set direction, observe results, adjust. Each iteration sharpens your aim — but it also sharpens you. The loop isn't just for course-correction; it's for learning. Use it to build knowledge and gain more amplification in the future.
The loop is forgiving. You can iterate your way there.
Alone, you pick a path and commit. Together, you scout them all.
Three possible paths. Pick one. Commit. Hope. All paths. Scout. Compare. Choose.
Complementary coverage
The gain isn't just speed — it's complementary coverage. AI can go wide while you go deep, or deep while you go wide. The more you understand your own strengths, the better you steer.
Self-knowledge becomes part of the multiplier.
Amplification isn't magic. It's mathematics.
Each step in solution space equals the previous state plus an amplified move toward the target.
The amplification factor is observable. Count the steps:
100 steps alone, 10 steps with AI → λ = 10
The AI (Λ) is a multiplier. But λ is the multiplier toward your goal. Even the most powerful AI can't help if you can't control the direction. Your leverage comes from three things:
Direction
What you know shapes where you aim. Domain expertise, pattern recognition, understanding of the problem space — these determine whether v points toward t or away from it.
Magnitude
The strength of your velocity vector. How many steps you take, how much effort you sustain, how persistently you iterate. Willpower is ‖v‖.
Calibration
Knowing what you're good at and what the AI handles better. You cover its blind spots, it covers yours. Effective collaboration requires understanding yourself as much as the AI you are talking to.
The AI amplifies. But what gets amplified — that's on you.
Our logo is a lambda (Λ, λ) with a dot encircled at its heart.
Together: directed amplification.
The human drives the initial conditions; the AI amplifies the trajectory; the world is our shared phase space.
Read the full paper →