A New Way to See: Concepts

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Bayes’ Theorem

Summary

Bayes’ Theorem is a mathematical compass for updating beliefs in light of new evidence. It formalizes how prior expectations and fresh data combine to refine our understanding, turning uncertainty into a dynamic process rather than a static state.

1. Background Context

Bayes’ Theorem originated in the 18th century from Reverend Thomas Bayes’ posthumous work on probability. Its rise to prominence came much later, especially in statistics, AI, epidemiology, and decision theory.
Before Bayes, probability often felt static—fixed odds from dice, cards, or coins. Bayes introduced a way to handle learning over time, where new information shifts the landscape of likelihood.
In the 20th century, Bayesian thinking evolved into a philosophical approach to reasoning under uncertainty, shaping modern AI, medical diagnostics, and even intelligence analysis.

2. Core Concept

At its heart, Bayes’ Theorem says:

$P(H|E) = \frac{P(E|H) \times P(H)}{P(E)}$

Where:

H = Hypothesis
E = Evidence
P(H) = Prior probability (belief before evidence)
P(E|H) = Likelihood (how probable evidence is if hypothesis is true)
P(H|E) = Posterior probability (updated belief after evidence)
P(E) = Normalizing constant (overall probability of the evidence)

It’s a formal rule for rational belief-updating: start with what you think, weigh the new clue, adjust proportionally.

3. Examples / Variations

Medical diagnosis: Updating the probability of a disease after a positive test, accounting for false positives.
Spam filtering: Adjusting whether an email is spam given certain words appear.
Forensic analysis: Revising likelihood of guilt given DNA evidence.
Search-and-rescue: Improving location estimates of a lost hiker with each sighting report.
Variations:

Naïve Bayes classifier (assumes features are independent)
Bayesian networks (graphical models of interdependent variables)
Bayesian inference in scientific modeling

4. Latest Relevance

Today, Bayes is everywhere—from machine learning algorithms to pandemic modeling.

AI: Large language models use Bayesian-like updates in probabilistic reasoning layers.
Climate science: Updating forecasts as new temperature and ice-melt data arrive.
Cybersecurity: Adaptive intrusion detection.
Philosophy: Framework for epistemic humility—beliefs are never final, always provisional.

5. Visual or Metaphoric Form

A map being redrawn in pencil as new landmarks are discovered.
A set of scales that shifts with each new pebble of evidence.
Fog lifting in patches, revealing a clearer view piece by piece.
A detective’s corkboard, where strings between clues are rearranged with each new lead.

6. Resonance from Great Thinkers / Writings

Richard Cox: Probability as the logic of plausible reasoning.
E.T. Jaynes: Bayesian inference as “the logic of science.”
Laplace: Extended Bayes into a general inferential method.
David Hume (precursor spirit): Understanding belief as proportional to evidence.
Thomas Bayes: The man who gave uncertainty a method.

7. Infographic / Timeline Notes

Timeline:

1763: Bayes’ essay published posthumously
1812: Laplace generalizes and popularizes method
20th century: Bayesian vs. frequentist statistics debate
1990s+: Computational advances fuel Bayesian AI & modeling
2020s: Bayesian reasoning embedded in global risk analysis

Process Diagram:

Start with prior (belief before data)
Gather evidence
Calculate likelihood
Normalize (P(E))
Arrive at posterior
Repeat as new evidence comes in

Classic vs Behavioral Macroeconomic Models

🟦 THOUGHT CARD: CLASSIC vs. BEHAVIORAL MACROECONOMIC MODELS

1. Background Context

Classic macroeconomics emerged from the quest to explain economic cycles, growth, and policy impacts using abstract, mathematical models—rooted in assumptions of rational, self-interested agents operating in efficient markets.
Behavioral macroeconomics responds to the growing realization (from Kahneman, Tversky, Akerlof, Shiller, and others) that real human behavior—shaped by psychology, norms, and collective narratives—often departs from these tidy rational assumptions, especially at the macro level where whole economies can behave “irrationally.”

2. Core Concepts

Classic Macroeconomics

Homo economicus: Individuals maximize utility; firms maximize profit.
Decisions are “rational,” forward-looking, and based on available information.
Markets tend toward equilibrium; prices adjust to clear markets.
Macro outcomes are the sum of micro-level optimizing behavior.
Key drivers: Interest rates, inflation, government spending, monetary and fiscal policy.

Behavioral Macroeconomics

Humans are social, emotional, and boundedly rational.
Decisions shaped by norms, trust, fairness, identity, and narratives—not just prices.
Systematic biases, sticky expectations, and “animal spirits” can drive persistent deviations from equilibrium.
Macro phenomena (unemployment, bubbles, crises) can arise from cascades of belief, not just shocks or policy missteps.
Policies must be designed with attention to actual psychological and social dynamics.

3. Examples / Variations

Classic:

Unemployment: Seen as voluntary (choice between work/leisure) or due to wage inflexibility.
Savings: Determined by interest rates and time preferences.
Booms & Busts: Result from shocks (technology, policy, external forces).

Behavioral:

Unemployment: May persist due to fairness norms (“sticky” wages), morale, or social stigma.
Savings: Influenced by peer behavior, self-control issues, and framing.
Booms & Busts: Can be amplified by collective euphoria or panic—contagion of beliefs, not just fundamentals.

4. Latest Relevance

Policy: Classic models inform interest rate setting, tax policy, stimulus packages.
Behavioral: “Nudge” interventions, credibility-building, attention to trust and social context in crisis response.
Financial Stability: Classic theory missed causes of 2008 crisis; behavioral models better captured “herd behavior” and loss of trust.
Climate & Inequality: Behavioral models address why rational incentives often fail to drive big changes (social tipping points, identity threats, norm shifts).

5. Visual or Metaphoric Form

Classic Model: Economy as a well-oiled machine—predictable, with clear levers and gears.
Behavioral Model: Economy as a network of minds—shaped by stories, feedback loops, emotional contagion; like a flock that suddenly changes direction.
Chess vs. Poker: Classic macro like chess (full information, clear rules); behavioral macro like poker (bluffing, uncertainty, social cues).

6. Resonance from Great Thinkers / Writings

Adam Smith: Saw both rational self-interest and the “moral sentiments” underlying economic life.
Keynes: “Animal spirits”—economies are moved by hopes, fears, and group dynamics.
Akerlof & Shiller: “Phishing for Phools”—markets can systematically exploit biases.
Milton Friedman: Advocated classic models, but also recognized the limits of prediction.
Kahneman & Tversky: Proved systematic departures from rational choice.
Robert Shiller: “Narrative Economics”—stories drive macro cycles.

7. Infographic or Timeline Notes

Timeline:

1930s: Keynes introduces psychological elements into macro (animal spirits).
1950s–70s: Classic models dominate (rational expectations, DSGE).
1970s–90s: Behavioral evidence mounts; experiments and anomalies multiply.
2000s: Behavioral macro gains traction after repeated crises and empirical failures of classic models.

Model Comparison Table:

Feature	Classic Macro	Behavioral Macro
Agent Model	Rational, optimizing	Bounded, social, emotional
Info Assumptions	Full/rational expectations	Sticky, biased, narrative
Market Outcomes	Efficient, stable	Often unstable, path-dependent
Key Tools	Monetary/fiscal policy	Nudge, communication, trust
Example Failures	Bubbles, panics	Accounted for as social contagion

8. Other Tangents from this Idea

Network effects: How beliefs and behaviors spread through economies like epidemics.
Digital economies: How social media accelerates narrative cycles.
Resilience: Behavioral insights for designing robust policies in uncertain times.
Ethics: What does fairness mean in macro policy if people are not always rational?

Reflective Prompt:
When have you witnessed “the economy” behaving less like a machine, and more like a story or social drama? How might policies shift if we accept that people are not always rational, but always human?

🎴 Metaphor Card: The Veil and the Dice

🎴 Metaphor Card: The Veil and the Dice

A meditation on living with uncertainty, updating belief, and seeing through partial light

🎭 The Veil

We do not see the world directly.
We see it through a veil—
of past experiences,
partial data,
patterned expectations,
invisible priors.

Every decision, every belief, is made under this veil.
We rarely know everything—but we must still choose.

Some try to tear the veil.
Some pretend it isn’t there.
But the wise learn to ask:

“Given what I now know… what should I believe?”

🎲 The Dice

Life rolls dice behind that veil.

Sometimes they’re fair.
Sometimes they’re loaded.
Sometimes the table’s tilted.
Sometimes the game isn’t what you thought it was.

Probability is not a trick. It’s a candle.
It doesn’t banish the dark. But it shows where to step next.

And when a new clue arrives—
a test result, a shift in tone, a crack in the logic—
the wise do not cling.

They adjust.

They re-roll their map, not the dice.

🧠 The Bayesian Mind

To live with the veil and the dice is not to live in fear.
It is to live with:

Curiosity (What else might be true?)
Humility (What did I not know before?)
Responsiveness (What does this new light change?)
Coherence (How do I hold meaning that flexes, but does not fracture?)

The Bayesian mind is not about being right—it is about getting less wrong over time.

📜 Parable Fragment

A traveler was asked:
“Do you believe the sun will rise tomorrow?”

He answered:
“I believed it more before the sky turned red. But now, I believe it still—but a little less.

Let us prepare for rain.”

✨ Reflective Prompts

What veil have I mistaken for truth?
Where am I using old priors despite new evidence?
Can I let go of the need for certainty—and instead commit to responsive clarity?

🔗 Thematic Echoes

🔄 Bayes’ Theorem – Updating beliefs with evidence
🎲 Probability – Making decisions under uncertainty
🧠 Cognitive Biases – The refusal to lift the veil
🔮 Wisdom – Choosing with care, not with guarantees

📚 Suggested Pairings

Poem: “The Guest House” by Rumi
Essay: “What Is It Like to Be Certain?” by Oliver Sacks
Paradox: The Monty Hall problem—how the veil misleads the un-updated
Practice: Journaling belief updates over time, no matter how small

🔄Conditional Probability & Bayes’ Theorem

🔄 Foundational Thought Card: Conditional Probability & Bayes’ Theorem

How new information reshapes likelihood—and the logic of learning itself

1. Background Context

Probability gives us a framework for uncertainty.
Conditional probability takes it a step further:

How does the probability of something change when we know something else has already happened?

This is not just about numbers.
It’s the foundation of intelligent updating, medical diagnostics, weather forecasts, legal reasoning—and even trust.

2. Core Concept

Conditional probability is the probability of an event A, given that another event B has occurred.
Written as:

P(A|B) = \frac{P(A \cap B)}{P(B)}
]

Bayes’ Theorem allows us to reverse conditional probabilities—to update belief in light of evidence:

P(A∣B)=P(B∣A)⋅P(A)P(B)P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}P(A∣B)=P(B)P(B∣A)⋅P(A)

3. Foreground Examples

Scenario	What It Means
🩺 Medical Test	Probability of disease given a positive result
🧠 AI Decision	Updating model prediction when new data arrives
⚖️ Legal	Likelihood of guilt given evidence—not just likelihood of evidence
🌧️ Weather	Chance of rain given dark clouds—not unconditional chance

Conditional probability is how the mind learns: What does this new piece of evidence tell me about what I already suspect?

4. Bayes in Action

Let’s say:

1% of people have a rare disease
A test is 99% accurate
You test positive

What’s the probability you actually have the disease?

Not 99%! Using Bayes:

Out of 10,000 people:

~100 will test positive (1% actually sick, 99% false positives)
Only 1 in 100 is actually sick

So, P(Disease | Positive Test) ≈ 1%

Bayesian reasoning corrects for base rates, which our brains often ignore.

5. Current Relevance

AI & Machine Learning: Bayesian models continuously update predictions
Healthcare: Diagnoses must adjust for prior likelihoods
Climate forecasting: Incorporates prior trends with new signals
Ethics: Assumptions must be revisable when new facts emerge

6. Visual / Metaphoric Forms

Bayes is like updating your map when you find a new trail
Conditional probability is the light that shines through one filter onto another
Think of nested circles: the overlap becomes the new focus

Visual cues:

Venn diagrams of A and B
Probability trees branching with new evidence
A scale tipping as new weights (information) are added

7. Great Thinkers & Expanding Paths

Thinker	Insight
Thomas Bayes (1701–1761)	Developed the formula posthumously published in 1763
Pierre-Simon Laplace	Extended Bayes into formal scientific reasoning
Richard Thaler / Daniel Kahneman	Human decision-making often ignores base rates
Judea Pearl (Causal Inference)	Bayes is central to reasoning under uncertainty

🧠 Suggested reading:

“The Signal and the Noise” by Nate Silver
“Bayes’ Rule” by James Stone
2011 Nobel Lectures on Behavioral Economics

8. Reflective Prompts

Where in my thinking do I assume something without updating?
Do I treat new information as confirming, or as recalibrating?
What beliefs have I revised meaningfully with evidence?

9. Fractal & Thematic Links

🎯 Probability – Conditionality is the bridge between chance and belief
📊 Data & Inference – Updating beliefs responsibly is the soul of statistics
🧠 Biases – Base rate neglect is a common cognitive error
🔍 Decision Science – Bayesian thinking frames smarter choices

Use This Card To:

Model reasoning that is adaptive, not rigid
Clarify how evidence changes what we know
Learn to challenge assumptions with structure—not just intuition
Avoid common fallacies (e.g., assuming test accuracy = truth)

🎲 Probability

🎲 Foundational Thought Card: Probability

The mathematics of uncertainty, expectation, and the possible

1. Background Context

Probability is the language we use to describe uncertainty and likelihood.
It began as a way to study gambling and risk—but now underpins science, AI, finance, medicine, and everyday decisions.

Probability doesn’t tell us what will happen—only how likely something is to happen.
It gives us clarity without certainty.

2. Core Concept

Probability is a number between 0 and 1 that expresses how likely an event is.

0 = Impossible
1 = Certain
0.5 = Equally likely / unlikely

Often expressed as:

Fractions (1/2), decimals (0.5), or percentages (50%)

3. Foreground Ideas

Concept	Meaning	Example
🎯 Experiment	An action with uncertain outcome	Flipping a coin
🎲 Sample Space (S)	All possible outcomes	{Heads, Tails}
✅ Event	A subset of outcomes we care about	Getting a head
📊 Probability of Event A	# of favorable outcomes ÷ total outcomes	1 out of 2 = 0.5

4. Rules of Probability

Rule	Description	Example
➕ Addition Rule	For A or B (mutually exclusive): P(A ∪ B) = P(A) + P(B)	Rolling 1 or 6 on die: 1/6 + 1/6 = 1/3
✖️ Multiplication Rule	For A and B (independent): P(A ∩ B) = P(A) × P(B)	Coin: Head and die: 3 → 1/2 × 1/6 = 1/12
🔄 Complement Rule	P(Not A) = 1 − P(A)	If P(rain) = 0.2, then P(no rain) = 0.8

5. Current Relevance

Medicine: Probability of treatment success or disease risk
AI & ML: Probabilistic inference drives decision-making algorithms
Climate science: Forecasting based on likelihood, not certainty
Ethics and law: Risk assessment, forensic probabilities, prediction markets

Our world is too complex for certainty—but not for informed belief.

6. Visual / Metaphoric Forms

Probability is the shadow cast by uncertainty when held up to light
Sample space is a sky of stars; probability is how many light your path
A deck of cards: chance made visible and countable

Visuals to imagine:

Pie charts showing portions of a whole
Trees of outcomes branching with each decision
A dartboard—some areas larger, some smaller, all part of the space

7. Key Thinkers & Expanding Paths

Thinker / Work	Contribution
Pierre de Fermat & Blaise Pascal	Early foundations of probability theory through gambling problems
Thomas Bayes	Bayesian probability: updating belief with new evidence
Richard Thaler (Nobel Lecture, 2017)	How humans misunderstand probability in economic behavior
Nassim Nicholas Taleb (The Black Swan)	On rare events and probability blindness
Amos Tversky & Daniel Kahneman (Prospect Theory)	Cognitive biases in probability judgment (Nobel Prize, 2002)

🧠 Suggested reading:

“The Drunkard’s Walk” by Leonard Mlodinow
“The Art of Statistics” by David Spiegelhalter
Pascal’s original correspondence with Fermat (on dice and fairness)

8. Reflective Prompts

Do I treat probability as uncertainty with structure—or just guesswork?
How do I confuse chance with choice?
In my life, where do I need to act based on likelihood, not guarantees?

9. Fractal & Thematic Links

🧮 Distributions – probability determines shape
🔁 Conditional Probability – how new information reshapes likelihood
🧠 Cognitive Biases – misjudging chance is a deeply human trait
🔮 Risk vs Uncertainty – probability quantifies the known unknowns

Use This Card To:

Build a clear foundation for more advanced statistics
Clarify assumptions behind everyday decisions
Move from anecdote to pattern, from fear to informed chance

📊 Common Statistical Distributions

📊 Foundational Thought Card: Common Statistical Distributions

The distinct shapes data takes—each with its own meaning, use, and personality

1. Background Context

Not all data behaves the same. Some events:

Are binary (yes/no)
Cluster around a center
Spread evenly
Happen rarely but with outsized effects

To work with data wisely, we must know what shape it follows—this is the role of distributions.

A distribution is a map of how often values occur.
It tells us what’s likely, what’s rare, and what’s normal—for this kind of data.

2. Core Concept

A probability distribution describes how values in a dataset are expected to be distributed.
Each type of distribution has its own rules, applications, and implications.

3. Common Distributions & Their Traits

Distribution	Shape & Behavior	Common Uses
🧭 Normal (Gaussian)	Bell-shaped, symmetric, most data near mean	Human height, test scores, measurement errors
⚖️ Uniform	All values equally likely (flat)	Dice rolls, random number generators
✅ Binomial	Discrete outcomes of repeated yes/no trials	Coin tosses, success/failure counts
📉 Exponential	High values rare, time until event	Time between radioactive decays, failure of devices
🧨 Poisson	Counts of rare events in fixed space/time	Number of emails per hour, mutation counts
💥 Power Law	Many small events, few very large	Earthquakes, city sizes, wealth distributions
📊 Skewed	Long tail on one side	Income, wait times, biological processes

4. Current Relevance

Finance: Risk often misunderstood by assuming normality (when returns may follow fat-tailed distributions)
Epidemiology: Disease outbreaks modeled with exponential or Poisson distributions
Machine Learning: Models assume data follows certain distributions; wrong assumption = bad predictions
Inequality Analysis: Wealth often follows power-law distribution—not symmetric or fair

5. Metaphoric Forms (Short Preview)

Normal = a hill
Uniform = a plateau
Binomial = a stepwise staircase
Poisson = a bumpy sidewalk
Power law = a steep cliff with a long flat plain
Exponential = a sudden drop
(See full Metaphor Card next: "The Landscape of Distributions")

6. Reflective Prompts

What kind of distribution does my data assume?
Am I modeling using normal assumptions when the data is not normal?
Where do the rare but impactful events live in this curve?

7. Fractal & Thematic Links

🎯 Probability – every distribution reflects an underlying event logic
📈 Spread & Shape – distributions are the "personality" of variation
⚠️ Outliers – tail behavior differs dramatically by distribution
🔄 Simulation & Inference – most models simulate or fit to distributions

Use This Card To:

Identify the right distribution for your data
Understand risk, rarity, and regularity
Improve modeling, forecasting, and interpretation
See the story your data’s shape is telling you

🧭 Skewness & Kurtosis

🧭 Foundational Thought Card: Skewness & Kurtosis

Understanding the shape and character of a data distribution

1. Background Context

Central tendency tells us the “average.”
Spread tells us how much data varies.
But to really understand a dataset, we need to ask:

What is the shape of this data? Is it lopsided? Is it peaked or flat? Are outliers lurking?

This is where skewness and kurtosis come in.

2. Core Concept

Skewness measures asymmetry.
Kurtosis measures tailedness (how thick or thin the extremes are).

Together, they reveal:

Whether the average tells the truth
How likely extreme values are
What kind of real-world behavior the data reflects

3. Foreground Measures

Measure	Description	Visual Insight
🔀 Skewness	Degree of asymmetry in the data	Lopsidedness
🧨 Kurtosis	Heaviness of tails compared to a normal curve	Peakedness / tail thickness

4. Types of Skewness

Type	Description	Example
↘️ Negative Skew	Tail on the left (low values stretch out)	Retirement age (most retire ~65, some much earlier)
➖ Symmetric	Data balanced around the center	Heights of adults
↗️ Positive Skew	Tail on the right (high values stretch out)	Income (most people earn modestly; a few earn extremely high)

5. Types of Kurtosis

Type	Description	Behavior
🔺 Leptokurtic	High peak, fat tails	More outliers than normal; risk of extremes
🔵 Mesokurtic	Normal distribution (bell curve)	Moderate tails
🟰 Platykurtic	Flat peak, thin tails	Less extreme variation; more middle values

6. Current Relevance

Finance: Investment returns often show high kurtosis → extreme risk events
Social science: Skewness affects fairness of grading, policy design
AI / ML: Algorithms must be tested on real-world distributions, not idealized curves
Medicine: Response to treatment may be skewed → personalized care needed

In real life, very few distributions are perfectly symmetrical or “normal.”

7. Visual / Metaphoric Forms

Skewness is a leaning tree—weighted to one side
Kurtosis is a mountain vs. a mesa—steepness and edge behavior
Skewed data feels like a crowded elevator with one person carrying all the bags
High kurtosis is like a calm day with surprise lightning

8. Blind Spot Warnings

Many people use the mean even in skewed distributions—can be misleading
High kurtosis may not be visible unless graphed
Skewness and kurtosis can distort confidence intervals, p-values, and predictions

9. Reflective Prompts

Am I assuming my data is symmetric—when it might not be?
Is the "average" being distorted by a long tail?
Are there outliers hiding in plain sight?
What does the shape of this distribution tell me about risk, fairness, or expectation?

10. Fractal & Thematic Links

📊 Central Tendency – may mislead without shape awareness
📈 Measures of Spread – interact with tails and skew
🔍 Outliers – often visible in skew or kurtosis
⚠️ Real-World Risk – depends more on tail behavior than center

Use This Card To:

Analyze datasets for bias, asymmetry, and surprises
Communicate the risk and realism in data-based claims
Choose appropriate statistical tests and models
Build a mindset of shape-aware thinking in uncertainty

📈 Measures of Spread

📈 Foundational Thought Card: Measures of Spread

How we understand variation, dispersion, and the shape of difference in data

1. Background Context

After identifying the center of a dataset (via mean, median, or mode), we must ask:

How far do values stray from that center?

Measures of spread (also called dispersion) tell us how consistent, volatile, or unequal the data is.

A center alone is misleading without knowing how far things vary around it.

2. Core Concept

Measures of spread describe the extent to which data points differ from each other or from a central value.
They tell us whether a dataset is tight or wide, predictable or scattered.

3. Foreground Measures

Measure	Description	Best Use
📏 Range	Max – Min	Simple sense of span (but sensitive to outliers)
🧮 Variance (σ²)	Average squared distance from the mean	Theoretical foundation for many models
📉 Standard Deviation (σ)	Square root of variance; in same units as data	Most common measure of spread
🟰 Interquartile Range (IQR)	Difference between 75th and 25th percentiles	Robust to outliers; shows middle spread
🧮 MAD (Mean Absolute Deviation)	Average of absolute deviations from the mean	Simpler and more intuitive than variance in some contexts

4. Current Relevance

Finance: Standard deviation measures investment volatility
Education: Test scores with same mean but different spread = different learning outcomes
Social Science: Income spread tells more about inequality than averages alone
Healthcare: Variation in patient response crucial for treatment evaluation

Spread often reveals what averages hide.

5. Visual / Metaphoric Forms

Range is the “stretch” of the data rubber band
Standard deviation is the “typical wobble” around the center
IQR is the “heart of the hive”—where the central 50% lives

6. Real-World Example: Income Inequality

Dataset A	Dataset B
Mean: $50,000	Mean: $50,000
Std Dev: $5,000	Std Dev: $50,000

Both have the same average—but in Dataset B, wealth is concentrated in a few hands.
Spread tells the truth behind the average.

7. Blind Spot Warnings

Outliers skew range and variance
Standard deviation assumes normality—not always valid for skewed data
IQR omits extreme values—great for robustness, but hides tails
No one measure tells the whole story

8. Reflective Prompts

What does the spread of my data suggest about reliability or fairness?
Am I too focused on the center—missing important variation?
How do different kinds of spread change my interpretation?

9. Fractal & Thematic Links

📊 Central Tendency – center is meaningless without understanding variation
📏 Skewness & Kurtosis – describe shape of spread
🔍 Uncertainty & Risk – all modeled using spread
🧠 Cognitive Bias – humans often ignore variance and assume averages

Use This Card To:

Evaluate consistency, inequality, or volatility in a dataset
Add nuance to interpretation beyond central tendency
Communicate why one average is not like another
Design fairer systems or policies informed by range, not just center