MIN-LESSON 8b: (Power Laws) Q& A

Summary

In this insightful lecture, the speaker addresses the prevalence of power laws in various aspects of life, such as wars and pandemics, which exhibit an alpha close to one-half, indicating heavy tails. The speaker criticizes the use of small sample sizes to make general claims, emphasizing the importance of avoiding sampling errors in scientific analysis. They also explore the concept of infinity in the context of power laws, explaining how it differs from finite observations and how it contributes to the unpredictability of large-scale events. The talk concludes with a discussion on the origins of power laws, including the Matthew effect and social contagion, and how constraints can alter their distribution.

Takeaways

• 📚 The speaker discusses the concept of power laws and their relation to events like wars and pandemics, emphasizing the importance of understanding their statistical properties.
• 🕊️ Stephen Pinker's view on the decline of violence is critiqued, with the speaker pointing out the limitations of drawing conclusions from a small sample size and the potential for sampling errors.
• ⏱️ Wars and pandemics are highlighted as having power law distributions with an alpha close to one half, indicating heavy tails and the possibility of extreme events.
• 🔍 The speaker emphasizes the need for caution when making statistical claims based on historical data, especially given the unreliability of historical records and the potential for exaggeration over time.
• 📉 The concept of 'infinite' in the context of power laws is explained, describing it as a situation where the mean or upper bound is not well-defined due to the nature of the data.
• 📈 Power laws are contrasted with Gaussian distributions, with the former being characterized by heavy tails and the latter by a more balanced distribution around the mean.
• 🌐 The speaker introduces the idea of maximum entropy distributions as a way to understand why power laws occur and under what conditions they might not.
• 💡 The 'Matthew effect' and 'preferential attachment' are mentioned as mechanisms that can lead to power law distributions, where successful entities become more successful over time.
• 🏪 An example of how power laws can emerge is given through the scenario of storefront allocations, where success leads to greater opportunities and further success.
• 📊 The speaker discusses the transformation of data to fit power law distributions, such as converting the maximum possible deaths in a conflict to an equivalent 'infinity' for statistical analysis.
• 🚫 The existence of constraints, like energy or biological limits, is presented as a reason why not all phenomena follow power law distributions, with human height being an example of a constrained variable.

Q & A

What is the main topic discussed in the transcript?

The main topic discussed in the transcript is the concept of power laws, particularly in the context of wars, pandemics, and their statistical properties.

Who is Stephen Pinker and what is his claim regarding violence?

Stephen Pinker is a journalist and author who wrote a book claiming that violence has declined over history, based on his analysis of 100 observations.

What is the issue with using a small sample size to derive general properties, according to the speaker?

The issue with using a small sample size is that it introduces sampling errors and the risk of being misled by randomness, which goes against the scientific method of avoiding noise and not being fooled by randomness.

What is the significance of the 'alpha' value in the context of power laws?

The 'alpha' value in power laws represents the steepness of the tail of the distribution. Wars and pandemics have an alpha close to one half, indicating a thick tail, which means rare but extreme events are more likely than what a normal distribution would predict.

What is the average inter-arrival time for a conflict causing more than 50 million deaths, according to the speaker?

The average inter-arrival time for a conflict causing more than 50 million deaths is approximately 80 years.

Why does the speaker argue that it is not scientifically valid to claim the world is a 'better place' without wars based on a short period of observation?

The speaker argues that to make a statistically significant claim about the absence of large-scale wars, one must wait for a period at least three times the average inter-arrival time to account for the variability in such rare events.

What is the issue with historical data when it comes to statistical inference?

The issue with historical data is that historians are not rigorous scientists; they often cite other people and provide numbers without a clear methodology, leading to potential inaccuracies in statistical inference.

How does the speaker address the problem of variability in historical death tolls due to conflicts?

The speaker addresses this by building over 500 events with high and low estimates of death tolls, creating 100,000 different histories to test hypotheses and account for variability.

What is the concept of 'infinite' in the context of power laws and statistical analysis?

In the context of power laws, 'infinite' means that the mean or other metrics do not converge to a specific value but rather fluctuate widely, indicating that the upper bound is not defined.

What are the two types of distributions mentioned by the speaker, and how do they relate to power laws?

The two types of distributions mentioned are one-tailed distributions, which are skewed to the left or right, and two-tailed distributions, which have both positive and negative tails. Power laws are typically one-tailed, with a heavy emphasis on the right side (positive values).

How does the speaker explain the formation of power laws in real-world phenomena?

The speaker explains the formation of power laws through mechanisms like the Matthew effect (rich get richer), preferential attachment, and social contagion effects, which can lead to a snowball effect and the creation of power-law distributions.

Why does the speaker believe that the world is naturally power law distributed, except under certain constraints?

The speaker believes that the world is naturally power law distributed because many phenomena follow this pattern unless there are specific constraints like growth limitations, energy constraints, or biological constraints that prevent a power law distribution.