The case
The owner, 2026-07-02, captured verbatim in Mathematics of Meaning
(homelab/own-words.md, “The Lego parable — retrieval, detection, and the
time–space trade”, at MOM commit d987e2a):
the problem is retrieval. you’re building something and you want to find a specific brick. you have a bin that contains a bunch of different similar bricks. the noise is the other bricks.
If there’s a particular brick that you have very few of but use often, you can put those bricks in their own tiny bin to make sure you can find them and they don’t get subsumed and lost in a big pile.
if I need a particular lego brick that I only have 1 of and I put it in a bin with hundreds of other similar legos, I may as well not have the brick. I can’t access it when I need it.
if it’s a single black brick in a box of white bricks: ok, it’s buried but its’ still detectable. no problem. it can be a unique member of the family that goes in that bin. if it’s too similar to the other bricks though, the difficulty to locate it manifests an imperative to set it aside as a new kind in a designated box.
ultimately, every brick in my collection is detectable if I have the time to go through my entire collection, one at a time, checking every single brick. but life is short and my time is limited, so if I can’t find it quickly enough, it may as well not be there.
In the same passage the owner tells the EMT story this record holds as CASE-085, and ends it on the same line: “if you can’t find it, it isn’t there”.
What it can show
- The cause of a retrieval failure can be similarity, not size. The black brick and the similar brick are equally buried. Only the second is lost. Holding the bin fixed and changing only how much the wanted item resembles its binmates is the contrast this case is for.
- What decides a new bin is copy count and use, not evidence. “Very few of but use often” names the cell where a bin pays. CLAIM-307 works this out: it is the cell where evidence that a distinction exists is weakest.
- Presence is never in doubt; time is. Exhaustive search always succeeds. So “may as well not have the brick” is a claim about retrieval before a deadline, as in CLAIM-296 and TERM-055, and not about inventory.
- A bin is made when the item is found. The practice described is setting a hard-to-find brick aside once it has been found, so the extra cost of the new bin is small. That bears on QUESTION-095: sorting spends search once against later retrievals (QUESTION-114). Sleator and Tarjan (LIT-1093, read) give the practice a bound. For one pile searched from the top, moving each found item to the top costs at most twice what any rule costs on the same requests, even one that knows them in advance. Paying to rearrange ahead of need never beats it. Bins are outside their model.
What it cannot show
- How long any search took, how often the brick was wanted, or how the owner’s bins are in fact arranged. None of it was measured.
- Why a similar brick is hard to find. Treisman and Gelade (LIT-1082, read) put serial search down to conjunctions of features, not similarity. A lone brick of a unique colour is their easiest case, found almost regardless of numbers. A difference on one dimension only, like size, made search slow but not item by item. The similarity account the owner’s words fit, Duncan and Humphreys (LIT-1081), could not be obtained.
- That the owner’s bins are a good arrangement. CLAIM-310 argues that which arrangement is good depends on what a builder searches for.
Standing
Stipulated, as CASE-085 is. The collection and the practice are real; the record has them only on the owner’s account.