Retrieval check (from lesson 2, new setting). Working memory holds about seven items,
plus-or-minus two — but a chunk (lesson 2’s term: a group of raw items recoded as one familiar
unit, with the pattern itself stored in long-term memory) lets you fit far more content into that same
small number of slots. An engineer glances at the IPv4 address 192.168.1.100 and holds it easily.
Read as twelve individual digits, that’s over budget for working memory. Chunked the way every network
engineer actually reads it — by octet, the dot-separated groups — how many chunks is it? Work it out;
the solution confirms it.
Back to activation
Lesson 9 introduced activation — a number capturing how easily a declarative chunk (a fact, in ACT-R’s terms) can be retrieved right now. Lesson 10 gave the single-use formula:
B = −d · ln(t)
where t is time since the chunk was last used, and d is a decay rate, ACT-R’s default
d = 0.5. That formula is exact for a chunk used exactly once. It is not the general formula, and
reading d as something that “happens once per use” — a counter that ticks up with each retrieval —
is a natural but wrong generalization. d is an exponent applied to elapsed time for a single use; it
does not accumulate or count uses at all.
The real formula sums a power-law term across every past use of the chunk:
B = ln( Σᵢ tᵢ^(−d) )
where the sum runs over every time the chunk was retrieved, tᵢ is how long ago that particular use happened, and each use contributes its own term tᵢ^(−d) to the sum inside the log. One use is just this formula with a single term — which is exactly why lesson 10’s simplified version worked for that case and no other.
Two chunks, two retrieval histories:
- Chunk A — the name of a colleague you spoke with exactly once, 1 day ago.
- Chunk B — the name of a colleague you’ve spoken with on three separate occasions: 2, 4, and 8 days ago.
Using d = 0.5, compute chunk B’s base-level activation, summing its power-law term across all three uses. (Compute chunk A’s too, informally, before you check the solution — comparing them is the point.)