Dark Patterns: "the power law distribution that generally defines the longevity of Roman emperors"

A repost from October 2021.

About ten years ago the popularization of a rather arcane area of study, power laws seemed to capture the imagination of the public. All of a sudden people were seeing power law distributions everywhere they looked. But as I and many others have pointed out: humans are so good at seeing patterns that we sometimes see them when they aren't even there.

So I now take all power law discussions with a grain or two of sāl.*

Some links after the jump.

From ScienceAlert, October 18:

Dark Pattern Explains Why So Few Roman Emperors Died of Natural Causes 

A staggering amount of Roman emperors did not die of natural causes. That's not breaking news; it's literally ancient history.

But in those untimely and often violent deaths, scientists have now identified a new mathematical pattern: a power law that describes the fate of so many who died with an entire empire at their feet.

"Although they appear to be random, power-law distributions of probabilities are found in many other phenomena associated with complex systems," says data scientist Francisco Rodrigues from the University of São Paulo in Brazil, noting that the reigns of the Caesars themselves are one such context.

According to Rodrigues, the power law distribution that generally defines the longevity of Roman emperors is what's called the Pareto principle.

Also known as the 80/20 rule, the Pareto principle is usually concerned with economic inputs and outcomes, but in terms of probability distribution, it can be simplified to mean that common occurrences have about 80 percent probability, while rare events have about 20 percent.

In this case, with regards to the fates of Roman emperors, violent ends are the more common events, with death from natural causes being significantly rarer – especially in the early days of the Western Roman Empire.

During that period – from the first emperor Augustus (who died in 14 CE) through to Theodosius (who died in 395 CE) – the rulers only had about a one-in-four (24.8 percent) chance of living long enough to die from natural causes, the researchers found in their new study....

....MUCH MORE

Some of our posts on power laws:

Power Laws: “The greatest shortcoming of the human race is our inability to understand the exponential function.”
Scale: "The Hidden Power Laws of Ecosystems"
"The Key to Everything" Freeman Dyson on Geoffrey West's "Scale..."
Financial Physics: "Power laws in finance"
Scientific American: "Can Math Beat Financial Markets?"
Economists and Econophysics
"The Philosophy of Complexity: Are Complex Systems Inherently Tyrannical?"

Yes.
In the end the universe itself is inherently tyrannical.
You are not the boss....

But then:
Power Laws: Raise Those Eyebrows

And then, from Quanta:
Scale: "Scant Evidence of Power Laws in Real-World Networks"
Wait, what?

 *As regards Latin, the wictionary reminds us: 

Sāl is occasionally found as a neuter noun in the singular. The gender is observable only from agreement in the nominative case, and from agreement and the use of sāl (neuter) vs. salem (masculine) in the accusative case. The neuter nominative and accusative singular form can alternatively be sale, e.g. in Ennius Ann. 385 and Varro d. Non. 223, 17. In the nominative and accusative plural, the word is found only in the masculine gender, with the form salēs.

Got that, pronoun police?