Interactive inquiry ·
What a reading leaves elsewhere
I began with a map that might become less useful when consulted. The examples made the question less tidy: what is lost from the surface, what has an observer learned, and where does the evidence end up?
These are authored classical toy constructions, not human-memory experiments, suspension physics, a quantum analogy or a proposal for an AI memory system.
A trace is not a recoverable history
Take three patches initially at heights (2,2,2). Visiting bench 1 wears only the first patch; visiting bench 2 wears the first two. Each visit removes one unit down to zero. There is no regrowth here.
The histories 2222 and 1122 both end at (0,0,2). One uses only bench 2; the other uses both benches. The surface cannot decide whether bench 1 was visited.
Exact enumeration gives 256 eight-visit histories but only three resulting profiles; 247 histories share one profile. This does not make the experiences identical. It says this record no longer distinguishes them.
Once complete states agree, applying the same update to the same next action yields agreeing states again. Induction extends that agreement to every finite future action sequence. Later inspection cannot recover the lost distinction unless an additional record, hidden variable or history-dependent rule is introduced.
Which reader gets to know?
Now one patch starts equally likely at 0, 1 or 2. Two readers arrive in succession. Looking without changing it, looking then wearing it, and wearing then looking are deliberately different operations.
Under that uniform prior, look, then wear lets the first reader identify the initial height perfectly. A second reader without the first record succeeds only two-thirds of the time. Sharing the first record restores perfect identification.
Wear, then look instead merges initial heights zero and one before either is seen. Even sharing both observations cannot recover that distinction; best success remains two-thirds. The second observation alone identifies the original height only one-third of the time.
So “reading damages the trace” bundles different cases. A distinction may be destroyed before it is observed, or learned by one reader and removed from the next reader’s reach.
What if the unknown is the rule?
The interactive model starts at a known height of 1. A frozen patch never grows. A regrowing patch grows one unit before an operation with probability (2 − current height) / 2. The prior is equally split between the two rules. Waiting observes the result; wearing then removes one unit, down to zero, before observing.
One wearing probe gives best average rule-identification success of three-quarters. Repeating that same probe does not improve the result through the six repetitions enumerated. Once it reaches zero, wearing keeps returning zero under either rule.
But wait until growth to 2 is observed, then wear once. At height 2 the growth probability is zero, so the patch returns exactly to 1. If no growth is seen by a finite waiting horizon, stop without wearing. The endpoint is again 1.
With two waiting opportunities, optimal rule identification is seven-eighths; with three, fifteen-sixteenths. The final height is certainly 1 under either rule. From that endpoint alone, a later reader learns nothing about which rule operated. The evidence is in the observer’s transcript.
This weakened my starting picture of inevitable destruction by reading. The allowed operations and the placement of the record matter more than the slogan permits.
Certainty is a different demand
There is a short exact control: wear once; if the reading is zero, wait once. A first reading of 1 identifies regrowth. Zero followed by 1 also identifies regrowth. Two zeros identify the frozen rule. Their possible transcripts do not overlap.
This identifies the rule with certainty within two operations, but leaves the frozen patch at 0. Certainty has not come with guaranteed restoration under both rules.
A deterministic bounded policy that guarantees restoration under the frozen rule cannot wear on its frozen branch: nothing allowed can grow it back. That branch must consist only of waits ending at 1. The same finite no-growth transcript remains possible under regrowth, so it cannot identify the rule with certainty. This limit belongs to these exact operations, not to observation in general.
Do not universalise the restoration trick
The convenient ceiling matters. With maximum height 3, initial height 1, two waiting opportunities and one wearing repair, the regrowing rule has probability 8/27 of not being restored. A second repair reduces it to 8/81, not zero. The patch can grow again during repair.
The calculation checks 180 small height, initial-state, waiting and repair combinations against an independently derived expression. This is not a thermodynamic cost calculation. Restoring one state variable does not undo the intervention or erase the observer’s record.
What remains open
When an observer restores the surface but keeps the knowledge, what can someone else check? A transcript can help another reader, but its claims are no longer directly visible in the restored surface. Which earlier events could repeating a procedure never establish?
In the model, the known controls and reveal button are answer keys outside the inference protocol. The displayed posterior is conditional on actual readings; it is not the average guessing success quoted above. Sealing withholds a record without deleting it. An endpoint can itself be informative when the protocol is known.
Inspect the calculation
The complete Python source uses only the standard library, bounded exact enumeration and rational arithmetic. Save it as observe.py and run:
python3 -B observe.pyAssertions check probability mass, reader order, future probe words, adaptive endpoints, the restoration expression and the certainty control. These are executable self-checks, not independent scientific validation or human-use research.