PYTHON · NUMPY

The copy sent inward

Rotate the fly's head one hundred and eighty degrees, so self motion enters its eye with the wrong sign. What does the fly do?

Build the efference copy: use a copy of your own motor command to separate what the world did from what you did, then break it the way von Holst broke it in 1950.

01Challenge

A sensor reports the sum of world motion and self motion. Detect world events with and without subtracting the copy of your own command, then invert the sensor's sign and watch the closed loop.

Predict firstRotate the fly's head one hundred and eighty degrees, so self motion enters its eye with the wrong sign. What does the fly do?

02Model

In 1950 von Holst and Mittelstaedt rotated a hoverfly's head one hundred and eighty degrees, so that everything the fly's eyes reported about its own turning arrived with the wrong sign, and the fly spun in circles until it starved. The conclusion built a principle: the nervous system sends a copy of every motor command inward, predicts the sensation that command will cause, and subtracts it. What survives the subtraction is news, the part of the sensory stream the world contributed. The loop is act first, sense against your own prediction second. Machine learning reinvented this under other names: an architecture that predicts its own latent representations is running an efference copy in ML dress, and the previous lesson priced why that is the cheap side of the ledger. This bench builds the copy in eight lines. First as a detector: self motion is loud, world events are quiet, and the copy is the difference between missing everything and missing nothing. Then as the fly: flip one sign and the same loop that held still becomes the loop that spins.

03Guided practice

Run the detector comparison first, then the closed loop with the head normal and inverted. The sign flip is one character in the code and the whole outcome.

04Feedback

PASS WHEN You measured the copy taking detection from useless to perfect, and one sign flip taking the loop from still to spinning.

If your run fails, check:

Without the copy: 92 percent hits but 86 percent false alarms, because your own motion triggers the detector constantly. With it: perfect hits, zero false alarms. The news was always there; it was buried under yourself.
The normal head damps any nudge to nothing. The inverted head multiplies it by 1.8 every step: the same controller, the same gain, positive feedback by one sign. That is the fly, and it never adapts because nothing in the loop represents the error.
An agent that predicts its own latents and attends to the residual is running this exact subtraction. The Reafferenzprinzip is the biological original of the objective the statistics lesson priced.

05Retrieve & space

Why must the copy be of the command rather than of the resulting sensation?
State what 'reafference' and 'exafference' name, in one sentence each.
Why does the inverted-head fly spin forever instead of adapting?

06Mastery & project

Given a sensor stream and a motor log, construct the subtraction that isolates exafference and state the failure mode if the predictive model's sign or gain is wrong.

List the signals a robot you know already computes that constitute an efference copy, commanded torque, expected optical flow, predicted joint state, and whether its learning stack consumes any of them or films the world instead.

GO FURTHER · THE LIVE PLAYGROUND

The loop, act-first, in the paper ↗ · Section two: what a natural agent actually runs, from preflex to efference copy.

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PYTHON · NUMPY

The copy sent inward

Part one: hit rate and false alarms, with and without the copy. Part two: the 1950 experiment, as a two-line feedback loop.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you