E Pluribus Unum

The Dancing Opposites:

A Statistical Perspective

Understanding complex societal dynamics can be challenging. Complex ideas are often best understood through metaphors, and this is where the world of statistics can lend us a helping hand.

In statistics, we encounter different types of data distributions. Some, like the bimodal distribution, have two distinct peaks, symbolizing two separate groups or opinions. Others, like the standard normal distribution, have a single peak (unimodal distribution), representing unity or consensus within the diversity of the extremes.

Imagine a dance floor where two groups, each moving to their own distinct rhythm, are trying to find a common beat. This scene mirrors a mathematical concept known as a ‘bimodal distribution’ – the graph with two peaks representing two different groups or opinions. Now imagine these groups gradually finding a shared rhythm, moving together around a center until the dance floor pulses with a unified beat. This is akin to a ‘standard normal distribution’ – a graph with one peak indicating a consensus. This dance is similar to the statistical concept of merging two curves into one.

However, transforming a divided society (bimodal curve) into a united one (unimodal curve) isn’t straightforward. Reframing this problem, let’s consider two dancers – labeled Sensitivity and Specificity. Sensitivity would represent the ability to correctly identify truth, while Specificity would signify the capacity to spot falsehood. But they are just labels. Neither really knows what’s really true or false.

In our dance metaphor, these two dancers start on opposite sides of the dance floor (two different peaks). Their dance involves slowly moving towards each other until they share the same spot on the floor, dancing at the same rhythm (one common peak).

This movement signifies societal compromise and dialogue leading to unity. This doesn’t mean that truth and error should be averaged, thus compromising truth. It means that our understanding of truth and error — of good and evil — is always relative to our frame of reference. It is this frame of reference that must find a common ground of ever evolving factual truths, as earlier apparently all-inclusive facts are realized to be but minor aspects of still greater facts.

In real-world terms, Sensitivity and Specificity represent two opposing viewpoints in society. As they move towards a common ground — from what appears to be true and from what appears to be false — they symbolize societal integration. But getting there requires each side to make concessions, to change their steps to meet in the middle, dispassionate detachment from the outer disguises of good and evil, through dialogue, compromise, and the finding of common ground of factual truths.

The key to a successful dance, then, is to move from emotionally-driven positions towards a rational consensus. This shift is like turning down the volume on our emotional reactions to focus on the music’s beat – objective facts and mutually beneficial solutions. It’s about finding that common rhythm that allows the actors to reset to a new frame of reference and share the dance floor harmoniously.

However, it’s essential to remember that our dance metaphor, like all metaphors, is a simplification. Real-world societal dynamics are far more complex, influenced by factors such as power imbalances, systemic biases, and deeply ingrained beliefs. These can throw off the rhythm of our dance, making the path to unity more challenging.

The idea of transforming a bimodal curve into a standard normal curve offers a compelling visualization of societal reconciliation. It reminds us of the importance of dialogue, compromise, and above all, the need for “right human relations based on goodwill.” Right means just.

While statistics can’t capture every nuance of societal dynamics, it provides us with a conceptual framework to better understand our complex world. The transformation from a bimodal curve to a bell-shaped normal curve offers a compelling visualization of societal reconciliation. This dance metaphor may not be perfect, but it gives us a starting point to talk about, and work towards, societal unity.

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Post Script

A consensus, unimodal curve does not necessarily imply “regression to the mean.” Progression to new means is not only possible but necessary for a democracy to thrive. However, this new rhythm can be achieved by rational consensus of a common vision (new centers) rather than by divisive emotions of competing selfish interests (old extremes).

We may transform our current bimodal political spectrum into a normal (bell-shaped) curve progressively centered around a positive trend of unbiased means aiming at more inclusive expressions of the common good. The extremes may serve the good purpose of pulling the center without breaking cohesion. Unity does not mean uniformity. However, the center must speak up to better balance the usually more vocal extremes.

The best of the past must be preserved as we embrace the future. Only a healthy, resilient center can accomplish such balance between conservative and progressive values, as we progress and realize that earlier apparently all-inclusive facts are but minor aspects of still greater facts. The greater does not nullify the minor, but enhances it, as is always the case in a hierarchical democracy.

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Original 2023.11.28 version. This essay will be under constant revision as the metaphor is revised to make it consistent with the statistical theory of binary classifiers.

2023.11.29: A simpler, and probably more elegant solution, amenable to more flexible interpretations, without compromising statistical principles, would be mixing harmonics so that a normal curve would result, such as:

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