MPE StudioMath of Planet Earth
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Interactive Story · 6–8 min

One Planet,
No Controlled Rerun

How can we learn cause and effect from a planet we cannot experimentally rerun?

ObservationWhat happened?CounterfactualWhat would have happened otherwise?Causal inferenceWhat evidence constrains the difference?
Enter the Story↓
Scene 01

The storm stalls over Aster Bay

A persistent storm brings intense rainfall. Rivers rise, the saturated ground sheds water quickly, and Aster Bay floods.

What made this event so severe?

The event is the evidence, not yet the explanation.

Aster Bayfictional storm · three days
Aster BaySTALLED STORMINTENSE RAINRISING RIVERSSATURATED GROUNDDISRUPTED TRANSPORT
The event is visible.Its causal explanation is not contained in the image.
Scene 02

Several things changed together

Warm water, unusual circulation, abundant moisture, wet soil, and local land conditions were all present. Their co-occurrence describes the event, but does not isolate what difference any one factor made.

Several things changed togetherAster Bay event
ASTER BAYstalled storm
01Warm ocean
02Unusual circulation
03Abundant moisture
04Wet soil
05Local terrain + land
OBSERVATIONX and Y change together
≠
CAUSAL QUESTIONChange X → does Y change?
Scene 03

Imagine the experiment we wish we could run

Keep the storm setup, circulation, season, and land state comparable. Change the ocean condition, then compare rainfall.

Ideal causal comparisonchange one condition
KEEP COMPARABLECHANGE ONE FACTOR
✓ same season✓ same storm setup✓ similar circulation✓ same land state
OBSERVED CONDITIONWarm ocean
HOLD→
ALTERNATIVE CONDITIONWarm ocean
THEN COMPARE THE OUTCOME
Observed rainfallAlternative rainfall
Rainfall difference = effect of this intervention
Scene 04

But Earth follows only one history

We observe rainfall under the ocean condition that occurred. We do not simultaneously observe rainfall under the alternative condition.

The comparison that defines the effectonly one outcome exists in the record
OBSERVED WORLD
286mm rainfall
Actual Aster Bay event✓ observed
CAUSAL
EFFECT
COUNTERFACTUAL WORLD
?
Rainfall under the alternative? not observed
Observed evidence+Physics+Assumptions→Constructed counterfactual
The comparison is partly missing.
Scene 05

Where can causal information come from?

We cannot observe the missing Earth directly. But variation, timing, causal structure, and physical knowledge can constrain what the alternative would have implied.

Model experiments are one possible source of evidence. They are not causal inference by themselves.

Sources of causal informationmodels are one tool, not the definition
Δ
OBSERVATIONSRepeated variation
t
SEQUENCETime ordering
→
PATHWAYSCausal structure
∂
CONSTRAINTSPhysical knowledge
M
ONE POSSIBLE TOOLModel experiments
Δ
OBSERVATIONS

Repeated variation

Conditions vary across times, places, and events. Those natural differences can create informative comparisons.

Scene 06

Relationships can play different causal roles

Ocean state, circulation, moisture, rainfall, soil, and flooding form pathways, not a flat list of correlated variables.

Does ocean state influence rainfall through moisture, or do both mainly reflect circulation?

Correlation alone does not reveal the pathway. Causal reasoning requires structure.
Aster Bay causal structureselect a variable to trace pathways
OceanconditionAtmosphericcirculationAtmosphericmoistureRainfallSoilmoistureFlooding
Ocean condition

Ocean conditions may affect rainfall indirectly by changing atmospheric moisture.

Scene 07

Not every causal question can be answered from the available data

Different causal structures can produce similar observed correlations. More measurements help only when they distinguish the competing explanations.

Can the observations distinguish them?

Sometimes yes, sometimes only with additional assumptions, and sometimes not. Then the causal effect is not identifiable from the available information.

Competing causal explanationssame patterns · different pathways
EXPLANATION AOcean-led pathway
OceanconditionMoistureRainfallCirculation

Ocean conditions affect rainfall through moisture; circulation adds another influence.

EXPLANATION BCirculation-led pathway
CirculationMoistureRainOcean-relatedconditions

Circulation drives moisture and rainfall while also shaping ocean-related conditions.

Both explanations may be consistent with similar observed patterns.

Can observations distinguish them?
01Sometimes yes02Sometimes only with additional assumptions03Sometimes not
Scene 08

One history can still support causal knowledge

We cannot rerun the planet. But variation, timing, structure, physics, and explicit assumptions can still constrain how one part of the system influences another.

From one history to causal knowledgeAster Bay synthesis
01
Observed eventWhat happened?
↓
02
Variation and timingWhat differences did the system naturally reveal?
↓
03
Causal structureWhich pathways are plausible?
↓
04
Physical knowledgeWhich explanations fit the system dynamics?
↓
05
Assumptions and inferenceWhich effects can be identified or bounded?
↓
06
Causal knowledgeWhat difference did this factor make?
01

Causation requires comparison

Knowing what happened is not enough. Causal questions ask what would change under an intervention.

02

The alternative is not observed

Counterfactual reasoning requires evidence, structure, mechanisms, and assumptions.

03

Causal knowledge has limits

Some effects can be estimated, some only bounded, and some cannot be identified.

We cannot rerun the planet, but we can still infer how one part of the system influences another.

Causal knowledge is constructed from evidence, structure, physics, and explicit assumptions.

Continue exploring
Foundation

Covariance and Correlation

Why variables that change together do not necessarily reveal what happens under intervention.

Coming Soon →
Concept Exploration

From Pattern to Trust

Explore models, mechanisms, evidence, causal reasoning, and bounded trust.

Open the Exploration →
Previous Story

When Rare Events Stop Being Rare

How probability, feedbacks, and thresholds reshape extreme-event risk.

Return to the story →
Next Story

When Models Disagree

What disagreement between plausible models reveals about assumptions and uncertainty.

Coming Soon