The Mathematics of Social Change: A Look at Misogyny's Progression
When I first encountered the problem of systemic misogyny, the scale of it felt overwhelming. It's a persistent, ambient force in society, seemingly immune to simple fixes. I realized that to combat something so deeply embedded, I needed a way to model its dynamics—to see how it spreads and, more importantly, how targeted effort might break its hold. This is what led me to develop the mathematical tool I'm sharing with you.
The Challenge of Modeling Belief Systems
Most models we use in science deal with predictable physical systems. Social issues, however, are non-linear. They don't react to effort in a straight line. Often, a massive effort yields only minor results, yet sometimes, a small, sustained push can create a tipping point.1 I needed a framework that captured this complexity.
My solution was to borrow concepts from epidemiology, specifically discrete-time difference equations, which are typically used to track infectious diseases. Here, the "disease" is Misogyny Prevalence ($M_t$), the proportion of misogynistic attitudes in a society at a given time $t$. The cure is the Anti-Misogyny Intervention ($A$), representing our collective societal effort (education, policy, activism).
The Mathematical Theory of Misogyny Progression
Run the simulation by adjusting the Anti-Misogyny Intervention level. The model shows the non-linear relationship between intervention effort and long-term societal outcomes.
Long-Term Misogyny ($M_{t=100}$):
Societal Health Score ($S_{t=100}$):
Progression Dynamics Over 100 Time Steps
Understanding the Progression Equation
The core of the model lies in its ability to simulate the push and pull between the system's intrinsic desire to perpetuate itself and our efforts to stop it.
The equation that calculates the prevalence in the next time step ($M_{t+1}$) is:
$$M_{t+1} = M_t + \underbrace{(k_1 \cdot M_t \cdot (1 - M_t))}_{\text{Intrinsic Spread}} - \underbrace{(k_2 \cdot A \cdot M_t)}_{\text{Intervention Reduction}}$$
1. The Force of Intrinsic Spread (Self-Perpetuation)
The first term, Intrinsic Spread, uses a component similar to the Logistic Growth model. It's defined as $k_1 \cdot M_t \cdot (1 - M_t)$.
- $M_t$: The current level of misogyny.
- $(1 - M_t)$: The remaining "non-saturated" portion of society.
This means that misogyny spreads fastest when its prevalence is moderate, and it slows down as it approaches 1 (saturation). This captures how systemic beliefs become self-sustaining because they are already normalized—they require less effort to spread through casual social interaction. I set the Intrinsic Spread Factor ($k_1$) to $0.1$ in the tool.
2. The Force of Intervention Reduction (Mitigation)
The second term, Intervention Reduction, is where our effort comes in: $k_2 \cdot A \cdot M_t$.
- $A$: The Anti-Misogyny Intervention level (controlled by you, ranging from 0 to 1).
- $M_t$: The reduction is proportional to the current problem size; you can't reduce what isn't there.
- $k_2$: The inherent effectiveness of our interventions. I set the Intervention Efficacy Factor ($k_2$) to $0.15$.
This shows that the success of an intervention is directly proportional to how much effort we apply ($A$).
The Non-Linear Impact on Societal Health
The most critical insight this tool reveals is found in the output: the Societal Health Score ($S_t$).
I define the Negative Societal Impact ($I_t$) as a non-linear function of misogyny:
$$I_t = 100 \cdot M_t^2$$
Why $M_t^2$? Because the harm caused by social prejudice—violence, economic disenfranchisement, mental health crises—often compounds disproportionately to the initial cause.2 A small increase in normalized misogyny can lead to an exponential increase in actual harm.
The desired Societal Health Score ($S_t$) is simply the inverse of this impact, normalized to 100:
$$S_t = 100 - I_t$$
If $M_t$ is low (e.g., 0.1), $S_t$ is high (99.0). But if $M_t$ reaches 0.5, $S_t$ plummets to 75.0.
My Core Analytical Insight
I invite you to use the tool above and run a few scenarios. You'll quickly see the model's core argument: The effect of intervention is non-linear and amplified.
- Try setting the intervention (A) very low (e.g., 0.1). You will observe that misogyny stabilizes at a high, persistent level because the intrinsic spread is stronger than the reduction. The societal cost remains high.
- Now, increase A just a little bit more (e.g., to 0.6). You will often find a tipping point where the entire system flips. The intervention reduction term now permanently dominates the spread term, and $M_t$ collapses towards zero, pushing $S_t$ rapidly towards 100.
This mathematical realization is, to me, incredibly hopeful. It suggests that sustained, strategic effort, even if it feels small initially, can fundamentally change the long-term trajectory of society, yielding an amplified positive effect. It transforms the overwhelming problem of misogyny into a clear challenge: find and sustain the necessary intervention threshold (A) to tip the scales.