Marr, Tinbergen & representations
The two frameworks the course uses to ask any brain question properly — and the demos from Lecture 4 showing that how you represent a problem decides how you solve it.
1. Why we need frameworks at all
Something as complex as the brain can't be understood from a single perspective. You could know every feather on a bird and still not know that flight is about generating lift. You could know aerodynamics and still not know what a feather is made of. Both are true, at different levels. The frameworks in this chapter are checklists that stop you answering at only one level.
2. Marr's three levels
| Level | Question | Who asks it | Bird-flight analogy |
|---|---|---|---|
| Computational | Why? What problem is being solved, and why? | — | Get off the ground |
| Algorithmic | What rules? What representations and processes solve it? ("software") | Cognitive psychologist | Aerodynamics — lift |
| Implementation | How physically? What hardware — or wetware — runs it? | Neuroscientist | Feathers, muscles |
The lecture's flight table
The same computational goal can have several algorithms, and the same algorithm several implementations. That's the key insight — the levels are loosely coupled:
| Computational | Algorithm (software) | Implementation (hardware / wetware) |
|---|---|---|
| Flight gives access to food and mates, and escape from predators | Flapping wings | Bird |
| Thrust | Rocket engine | |
| Rotation to generate lift | Helicopter blades | |
| Temperature differential | Hot-air balloon |
Worked through: edge detection
- Computational: Why detect edges? To recognize objects, detect motion, navigate.
- Algorithmic: If you were to write an algorithm, how? The Sobel operator — an image-processing method that detects where visual intensity changes sharply.
- Implementation: Neurons that respond to different areas in space, to different intensities of light, and to the orientation of an edge (receptive fields — Ch. 10).
The study guide's version of the algorithm: "higher numbers = more white → edge detected if there's a big difference in numbers." Here's what that means concretely. Paint on the grid; each cell is a pixel's brightness.
Three rows of pixels, each row identical: 10 10 10 200 200. The
horizontal Sobel kernel is
$$G_x=\begin{bmatrix}-1&0&1\\-2&0&2\\-1&0&1\end{bmatrix}$$
Centre the kernel on the middle row at columns 2, 3 and 4 (counting from 1). Multiply each pixel by the kernel entry on top of it and add. Where is the edge?
Step 1 — What's the kernel doing?
Left column gets negative weights, right column positive: it computes (right side − left side), with the middle row counted twice. It's a "difference detector".
Step 2 — Column 2 (neighbours: 10, 10, 10)
Each row contributes $(10 - 10)$ times its weight, so the total is $0$. Uniform region → no edge.
Step 3 — Column 3 (neighbours: 10 left, 200 right)
Each row gives $200 - 10 = 190$; weights $1 + 2 + 1 = 4$; total $4 \times 190 = 760$. Column 4 has left = 10 (column 3), right = 200 (column 5), so it's also $760$.
Answer & the takeaway
$0, 760, 760$: the response is large on both sides of the 10→200 boundary and zero inside the flat region. That's the algorithmic level. The implementation level is a neuron whose receptive field has an excitatory side and an inhibitory side — the simple cells of Chapter 10 compute something very like this.
3. Tinbergen's four questions
Marr's levels are about a system as it is right now. Tinbergen (1963) — an ethologist — added time: how did this behavior come about in the individual, and in the species?
| Question | Core question | Closest Marr level | Example: movement |
|---|---|---|---|
| Function (adaptation) | Why does this behavior exist? What is it good for? | Computational | Find food, avoid danger, build shelter, interact with the world |
| Mechanism (causation) | What produces the behavior right now? | Algorithmic + Implementation | Algorithm: maximize utility — rewards (food) minus costs (effort, error). Implementation: neural circuits represent costs and rewards, select actions, issue motor commands, activate muscles |
| Development (ontogeny) | How does it emerge over the lifespan? | Cuts across all 3 | Reactive → predictive: early movements rely on slow sensory feedback; with experience, control becomes predictive and efficient |
| Evolution (phylogeny) | How did it arise across generations / species? | Cuts across all 3 | Brains may have evolved, in part, for movement — the sea-squirt story |
Apply Marr's 3 levels and Tinbergen's 4 questions to face recognition. (Everything you need is in Chapter 8, but try it cold first.)
Marr's three levels
Computational: recognize individuals for communication, social interaction and emotion perception. Algorithmic: store many orientation-specific face templates; process faces holistically (the inversion effect). Implementation: the fusiform face area, responding ~150–170 ms after a face appears.
Tinbergen's four questions
Function: social living. Mechanism: the Marr algorithm + implementation answers above. Development: face recognition improves with experience — familiar faces are recognized across angles far better (the Dutch-politician demo). Evolution: social primates that could tell group members apart would have had an advantage.
The takeaway
Function ≈ computational; mechanism ≈ algorithmic + implementation; development and evolution are the extra questions Tinbergen adds, and they apply at every Marr level.
4. Representations: how you encode it decides how you solve it
Problem 1 — fold a sheet of paper 50 times
Estimate the thickness before you look. If you imagine it visually — a stack of paper getting a bit taller — you'll guess a few centimetres or metres. Represent it symbolically — thickness × $2^{50}$ — and the answer is suddenly obvious: it's astronomical.
Problem 2 — the mountain climber
A climber leaves the base of Mt. Washington at 8 am and reaches the summit at 8 pm. Next morning she leaves the summit at 8 am and reaches the base at 8 pm, same path. Must there be a spot she passes at exactly the same time of day on both trips?
Symbolically this is hard. Visually it's trivial: draw both days on the same clock.
The mental imagery debate
5. Processes — and how they shape representations
The influence runs both ways:
1 4 9 2 1 7 7 6 2 0 0 1 in memory — hard. Now hold
1492 · 1776 · 2001 — easy. Same digits; the chunked representation leverages long-term memory,
so short-term memory has 3 items to maintain instead of 12.The "12 and 5" demo
Answer 2+2, 4+4, 8+8, 16+16 quickly, then "pick a number between 12 and 5." Most people say 7. Two hypotheses from lecture:
- Arithmetic priming: you were primed to do arithmetic — $12 - 5 = 7$ (or $12 + 5 = 17$).
- Trying to be random: people disproportionately choose 7, avoiding even numbers (6, 8, 10) and "obvious" ones (9 = 3×3; 11).
Design an experiment that tells hypothesis 1 from hypothesis 2.
Step 1 — What does each predict differently?
Priming says the preceding arithmetic causes 7. "Random-seeming" says people pick 7 regardless of what came before.
Step 2 — Manipulate the thing hypothesis 1 cares about
Two groups: one does the addition warm-up, one does an unrelated warm-up (e.g. naming colours). Then both pick a number between 12 and 5. Bonus: a third group primed with subtraction, and a range where the difference isn't 7 (e.g. between 13 and 5 → difference 8).
Answer & the takeaway
If the addition group says 7 much more than the control group, priming matters. If both groups say 7 equally, it's the "random-looking" preference. With 13 and 5: priming predicts 8, randomness-preference still predicts 7. The skill: turn each hypothesis into a behavioral prediction that the other hypothesis doesn't make.
Count the F's
FINISHED FILES ARE THE RESULT OF YEARS OF SCIENTIFIC STUDY COMBINED WITH THE EXPERIENCE OF YEARS
Answer: 6 (FINISHED, FILES, SCIENTIFIC, and three OFs). Many people count 3. Why? We read for meaning, not letter by letter, so function words like "of" are skimmed — and in "of" the F sounds like a V, so a sound-based check misses it too. The process (reading for meaning) determines the representation (the words that "count").