Concave and Convex

The best and worst of both worlds

Hello 👋 and welcome to another issue of this newsletter. To the new subscribers, it’s nice to have you here.

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Some situations or worlds are concave. Others are convex.

A situation where both extremes are better than a lukewarm or mid-ground is a convex disposition.

The opposite, where either extreme is worse than a mid-ground, is a concave disposition.

Horseshoe Theory

This is where both extremes tend to be the same.

Convex

Using the COVID-19 virus, a 100% lockdown and a 0% lockdown were better than a 50% lockdown.

In a 100% lockdown, you had the transmission of the virus in check, but the downside was businesses were closed.

In a 0% lockdown, you had businesses open. However, the spread of the virus was very high.

In a 50% lockdown, businesses were closed, and the virus still spread. This is the worst of both worlds.1

In the tweet below, assuming it is true, we have a convex situation.

Concave

Imagine if you had to choose between full-blown socialism (eat the rich) or full-blown capitalism (total free market). Both situations result in worse outcomes than, say, a mix of both.

A capitalist society with social benefit structures such as health care schemes and food banks etc.

Would you rather take a bath with any extreme temperatures of water(freezing water or boiling water)??

None, I am sure. Lukewarm water would do.

Look at immigration too.

Would allowing everybody in do any better than allowing nobody in? It is best only to allow some.

A heuristic for distinguishing between both is :

  1. If it is the worst of both worlds, it is a convex disposition.

  2. If it is the best of both worlds, it is a concave disposition.

To read more on this, Vitalik Buterin explains it with more concrete examples here: Convex and Concave Dispositions (vitalik.ca)

That wraps it up for this week. See you next Sunday.

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1

This scenario was true during the early part of the pandemic. Now, it doesn’t seem so. So you all stay safe.