WEBVTT

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Different situations can require different responses. If every available reading looks

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identical, those readings alone cannot tell us which response fits.

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This makes distinguishability important: useful observations preserve differences that

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matter for a task.

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Here the card's Being stays fixed. A new answer changes our evidence; Becoming would

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mean a change in the card's state. Watch the test menu and the received answers do

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different jobs.

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The observer from episode one receives zero.

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Both u and v fit that lamp reading.

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We will compare what a chosen set of observations can distinguish, using the known model rather than the audience-only cutaway.

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To make the grouping visible, first switch to the site’s four-card example.

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The cards are zero-zero, zero-one, one-zero and one-one.

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A names colour, the first digit: zero is teal and one is gold.

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B names shape, the second digit: zero is circle and one is square.

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These are new labels for a different example; they are not the hidden configuration names u, v, w and z.

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The card stays fixed while exact tests are read.

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Make only A available.

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Zero-zero and zero-one give the same A answer, so this menu leaves them together.

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One-zero and one-one form the other group.

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Now make both A and B available.

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A complete pair of answers identifies each card separately.

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The signature is simply the ordered list of those answers.

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Changing the menu changes the distinctions this observer can make; it does not change a card’s colour or shape.

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Compare two operations from the same four possibilities.

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In one branch, enable B but receive no new answer yet.

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In the other, keep the existing menu and receive A equals zero.

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That answer restricts the current candidates to zero-zero and zero-one.

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Enabling another test and learning a fact have different effects.

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A menu says which questions may be asked; a record says what answers have arrived.

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Reading A again produces the same answer on a fixed card.

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Recording A twice gives a longer record, but it does not separate cards that A already left together.

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This claim uses a deterministic exact test.

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Independent noisy readings are a different situation, introduced later; we are not treating every repeated measurement as useless.

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Our examples use complete readings: the reader sends an explicit zero or one.

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Receiving zero is different from receiving no report.

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Here, zero says that the tested property is false.

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An optional course uses a different reporting rule; its convention is explained in the supporting notes.

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The core route keeps complete zero-or-one records.

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Pause and classify this change: we enable B, but have not read it.

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Have we learned that B is one?

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No. We changed availability, not the received record.

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If we next receive B equals one, then the compatible cards are zero-one and one-one.

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That later restriction comes from the answer.

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Return to our machine.

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Its core reader reports only the lamp, grouping u with v and w with z.

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The A and B card sensors have not been added to it.

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We now know what those present readings can distinguish.

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The next episode asks a new question: will that description also support predictions after a button press?