T-shirt magic

This is the worked-example companion to the main intro. It picks up where the intro's Step 4 leaves off and adds two things the intro skipped:

a second observer's account of the same scene - a layered variant where the observer saw Patrick wearing black over white, with no take-on of the white t-shirt at all;
open-world probe events - single sightings that decide which observer's account is the one that actually happened.

Note: every ipm graph is an observer's account - somebody else watching Patrick, not Patrick's own account. The first model below is told from one chosen viewpoint; further down, we'll see a different observer's account of the same wearBW event.

Recap - the intro's Step 4 graph#↑

So the file stands on its own, here is the three-level model the intro's Step 4 ends with - its events, participants and two concepts; the color concepts come back in scenario 2 below. The top-level wearBW event names only the observable outcome - Patrick wore black, then he wore white - and stays silent on how the change happened. That mechanism is hidden inside the wrapper event; the sub-events reveal it. This observer saw a take-off and take-on (an exchange), so call this scenario 1: the exchange. Its discriminating shape is that the two t-shirts are never simultaneously on Patrick.

The ipmt source for this graph lives in a sibling file (tshirt-magic-recap.ipmt) and is included here via ipm-include:

Step 1 - event chain with evidence and hypothesis#↑

The intro's Step 1 keeps only the two states the observer directly saw: Patrick wore a black t-shirt at one moment, then later Patrick wore a white t-shirt. Those two wears are the evidence. There is an obvious gap between them - the observer didn't actually witness the moment of change.

A modeler can fill that gap with a hypothesis: an event drawn from a shared library of common stories and processes. "When someone goes from wearing X to wearing Y, something like a swap usually happened in between." The hypothesized event isn't observed; it's an inference shaped by familiarity with similar past scenes. A future observation can confirm it, contradict it, or replace it with something entirely different (a layered wearing, a costume change, a sleight-of-hand). Patrick himself might tell us what happened, providing direct testimony rather than the observer's inference.

# Parent event - the whole observable story matches a library pattern
wearBW::a Patrick wears black then wears white ::e
wearBW --> common t-shirt swap pattern ::c

# Sub-events: two observed wears + one hypothesized swap, each part-of the parent
wearB::a Patrick wears black t-shirt ::e
  --> swapT::a Patrick swaps t-shirt ::e
  --> wearW::a Patrick wears white t-shirt ::e

wearB --::P--> wearBW
swapT --::P--> wearBW
wearW --::P--> wearBW

# Evidence - directly observed wears
wearB --> evidence ::c
wearW --> evidence ::c

# Hypothesis - the swap is inferred from the library pattern on the parent
swapT --> hypothesis ::c

This is the same three-event chain the intro uses from Step 2 onward, but each event now carries the observer's epistemic stance: the wears are facts; the swap is a guess that fits a familiar process template. From here on, the rest of this file builds on the swap hypothesis the way the intro's Step 2+ does - treating it as the model the observer has settled on - while remembering it could be wrong.

Observation is open-world - positive evidence#↑

Before we draw the alternative scenario, a methodological note. An ipmt observation records what was seen, not what was absent - two honest observers can differ without contradicting each other. To decide which scenario actually happened, the observer needs positive evidence for one of the discriminating shapes. A single sighting is enough.

Here are two such probe events. The first confirms the exchange scenario (the recap above) by catching the white t-shirt being put on - a positive transition that only the exchange contains:

# Confirms scenario 1 (exchange): the white t-shirt observed being taken on
probeTakeOnW::a white t-shirt seen being taken on ::e
Patrick       --> probeTakeOnW
white t-shirt --> probeTakeOnW

# What this observation expresses
probeTakeOnW --> taking on ::c
probeTakeOnW --> positive evidence ::c

The second confirms the layered scenario by catching both t-shirts on Patrick at the same instant - a configuration that only the layered observation contains:

# Confirms scenario 2 (layered): black observed on top of white
probeBOverW::a black over white seen on Patrick ::e
Patrick       --> probeBOverW
black t-shirt --> probeBOverW
white t-shirt --> probeBOverW

# What this observation expresses
probeBOverW --> wearing two t-shirts ::c
probeBOverW --> positive evidence ::c

Without either probe succeeding, the scenario stays undecided - the honest open-world answer. Note also what we did not record: the absence of a take-on does not by itself confirm the layered scenario; we still need the positive black over white seen on Patrick sighting.

Alternative scenario - layered, in detail#↑

This second observer captured a different sub-event structure under the same top-level wearBW. At some moment during it, Patrick was wearing both t-shirts at once - black layered over white. The observer never saw a take-on of white; they saw only a take-off of black at the end.

First, the event structure alone - no participants attached yet, so the difference from scenario 1 is plain:

wearBW::a Patrick wears black then wears white ::e

# Mid-level sub-events - wear-layered -> take off black -> wear white
wearLayered::a Patrick wears black over white ::e
  --> takeOffB::a Take off black ::e
  --> wearW::a Patrick wears white t-shirt ::e

wearLayered --::P--> wearBW
takeOffB --::P--> wearBW
wearW --::P--> wearBW

Same parent wearBW as scenario 1; what differs is the mid-level sub-event the observer recorded - wearLayered instead of wearB, and no swapT/takeOn pair.

Alternative scenario - layered, full#↑

Now layer everything in: participants and concepts.

# Top event (same name and alias as scenario 1)
wearBW::a Patrick wears black then wears white ::e

# Mid-level sub-events
wearLayered::a Patrick wears black over white ::e
  --> takeOffB::a Take off black ::e
  --> wearW::a Patrick wears white t-shirt ::e

wearLayered --::P--> wearBW
takeOffB --::P--> wearBW
wearW --::P--> wearBW

# Patrick is present throughout
Patrick --> wearBW
Patrick --> human ::c

# White t-shirt is worn throughout - even underneath the black one in wearLayered
white t-shirt --> wearLayered, wearW

# Black t-shirt is on during the layered wearing and removed in takeOffB
black t-shirt --> wearLayered, takeOffB

# Concepts each event expresses
wearLayered --> wearing two t-shirts ::c
takeOffB    --> taking off ::c
wearW       --> wearing t-shirt ::c

# T-shirt color (thing --> concept)
black t-shirt --> t-shirt ::c, black ::c
white t-shirt --> t-shirt ::c, white ::c

# "Wearing two t-shirts" is a kind of "wearing t-shirt" (concept --> concept)
wearing two t-shirts ::c --> wearing t-shirt ::c

# Color taxonomy
black ::c --> color ::c
white ::c --> color ::c

Call this scenario 2: the layered observation. Both scenarios share the top-level wearBW event; they differ only in which sub-events the observer recorded, and therefore in which concepts the events express.

Color taxonomy#↑

White and Black are kinds of Color - a concept-to-concept EXPRESSES relation:

white ::c --> color ::c
black ::c --> color ::c

Thing taxonomies#↑

t-shirt T1 --> t-shirt ::c --> clothes ::c --> human thing ::c
human thing ::c --> thing ::c
human thing ::c --- human ::c

stone S1 --> stone ::c --> natural thing ::c --> thing ::c
natural thing ::c --- nature ::c