The A-not-B Error: Object Permanence and Infant Working Memory

Search Setup

Infant age 8 months

Search delay 4.0 s

Prior reaches to A 3

Live Readouts

Memory trace for B0%

Habit strength for A0%

P(correct reach → B)

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Elapsed delay

0.0 s

Trials run

A-not-B errors

0 (0%)

How it works

Piaget's A-not-B error: an infant who has repeatedly found a toy hidden at location A will, even after watching it hidden at a new location B, often reach back to A. The classic account (Diamond, 1985; Munakata, 1998) treats this as a race between a decaying working-memory trace for B and a learned prepotent reaching habit toward A:

τ(age)   = 1.0 + 0.55 · age_months            (memory time-constant, seconds)
mem(B)   = exp( -delay / τ(age) )              (trace strength at search time)
hab(A)   = 1 − exp( -0.5 · priorReachesToA )   (learned motor bias, saturating)
P(reach B correct) = mem(B) / ( mem(B) + hab(A) + ε )

Age — older infants have longer working-memory persistence (larger τ), so the trace for B survives longer delays.
Search delay — the longer the wait between hiding and searching, the more the B-trace decays exponentially.
Prior reaches to A — more training trials at A build a stronger prepotent motor habit that competes with the (correct) memory-guided response.
The purple field over box B visualises the live decaying trace; the reach indicator moves to whichever location wins the race, sampled stochastically from the probability above — exactly the mix of correct search and perseverative "A-not-B" error seen in real 8–12-month-olds.

This is a simplified, order-of-magnitude model for teaching the mechanism, not a fit to a specific published dataset.

Ready

Box A (trained location) Box B (new hiding location) Hidden object

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