# Metastability

My latest Epsilon Theory note is about the metastability of social systems.

A social system remains metastable as long as there is a reasonably broad consensus regarding its core values and mythology. Without this consensus, metastability weakens. Put another way: first-order threats to social stability, such as isolated riots and street crime, are risks that lie in the body of the distribution of outcomes, both for individuals and society. Metainstability is a higher-order threat. The risks associated with metainstability lie in the tails of the distribution. They fall under the broad category heading of Really Bad Stuff and include things like:

• violent revolution
• war
• property expropriation

Back to the Ants and the Grasshopper. Would it behoove the Ants to share a bit of food with the other insects to shore up the metastability of the forest’s social system?

Metastability is a rich concept to explore. I didn’t spend a lot of time defining metastability in my ET piece, but I find it worthwhile to look at the concept through the lens of elementary calculus.

If you’re reading this blog, you’re probably familiar with the differentiation of the simple quadratic function f(x) = x^2. The first derivative (a.k.a “instantaneous rate of change”) of f(x) = X^2 is 2x. The second derivative of f(x) = x^2 is just the derivative of 2x, the constant, 2. This, in turn, can be interpreted as the “instantaneous rate of change” for the function f(x) = 2x.

So you can see there’s some mathematical intuition behind that old saw, “change is the only constant.” It’s rates of change all the way down.

These concepts show up in finance all the time. In fixed income, there’s an inverse relationship between bond prices and yields. The first derivative of this function is a bond’s duration. The second derivative is its convexity.

With an option, the payoff depends on the price of the underlying relative to the strike price at expiration. The sensitivity of the option’s price to changes in the price of the underlying is the first derivative of this relationship. This is the option’s delta. The second derivative of this relationship, the sensitivity of the option’s delta to changes in the price of the underlying, is the option’s gamma.

(homework: consider the CAPM or any other linear factor model of financial asset returns in this context)

Anyway, on to metastability.

Take a society at any given point in time.

Social stability is its first derivative. Social stability is the instantaneous rate of change for society’s consensus values and norms.

Metastability is the second derivative. Metastability is the rate of acceleration (or deceleration) of changes in social stability.

In the language of options traders, social stability is society’s delta. Metastability is society’s gamma. Unfortunately for society, it’s generally short gamma. Which is just a fancy way of saying change is dangerous. Change stresses human social systems. The greater the magnitude of social change, and the faster the rate of change accelerates, the greater the stress on the existing social order.

Want to destroy social order in a hurry?

Lose a big war. That typically gets the job done.

Of course, this also invites the question, how would you strengthen social metastability?

By cultivating shared values and mythology.

The most common negative responses to my ET piece were comments along the lines of “the ants shouldn’t have to ‘share’/the Grasshopper should have to ‘earn’.” That’s a fine point of view. But it’s only a first-order look at the issue. Heck, from a first-order perspective, I completely agree. But that says nothing about metastability. I wish I’d made this a bit more explicit in the original post, but I did elaborate in the comments.

Actually, as far as metastability is concerned, in the fable’s base case involving the ants and a single grasshopper, it’s perfectly fine to just let the grasshopper starve. A moral philosopher might challenge that view, but the moral philosophy of this is a whole other issue.

In fact, you can easily imagine the Ayn Rand version of my “extended edition,” where all the insects are strict utilitarians. Here there’d be no need for any “metastability insurance” because of a strong consensus around libertarian utilitarian values as the organizing principles for society.

Likewise, you can imagine a Scandinavian “extended edition” where all the insects are social democrats or whatever. That society may have a very different set of consensus values and an entirely different level of metastability.

This is what I’m driving at when writing about metastability as a reflexive process, and why the social contract is necessarily something that’s negotiated. The obnoxious, twenty-five cent word for this process would be “dialectic.” Outside of relatively small, culturally homogenous communities, it becomes increasingly difficult to establish a strong consensus around values. The example of Prussia used in the post is a prime example. The Prussian “solution” to the problem of forging consensus around shared values at scale was to bind cultural identity to the state. It worked pretty well. Too well, in fact.

Anyway, for the purposes of this post I’m not concerned at all with whether libertarian or social democratic values are inherently superior. I’m more concerned with the idea that at the scale of a large, technologically advanced nation-state, maintaining social metastability is a balancing act across different constituencies.

I think I will likely have more to say on this subject in future posts.