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Mind Matters Reporting on Natural and Artificial Intelligence

TagProbability

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The Settlers of Catan

In Science, We Can’t Just “Settle” for Data Clusters

The board game, Settlers of Catan, offers a clear illustration of what can go wrong when we are duped by data clusters

Settlers of Catan is an incredible board game created by Klaus Teuber, a German game designer. It has been translated into dozens of languages and tens of millions of sets have been sold. The basic four-player board consists of 19 hexagons (hexes) representing resources: 3 brick, 4 lumber, 4 wool, 4 grain, 3 ore, and 1 desert. Players acquire and use resources based on dice rolls, card draws, trading, and the location of their settlements and cities. Part of the game’s seductive appeal is that there are many, many ways to arrange the 19 hexagons and successful strategies depend on how the hexagons are arranged. The rules are simple but winning strategies are complex and elusive. The official rules of…

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Business Finance Marketing and Budget Report

What Happened When 1950s China Dreamed of “Total Information”?

When China rejected random sampling in favor of exhaustive enumeration of individuals, masses of “data” flooded in, but what did it mean?

A historian of modern China recounts the outcome of a momentous decision that China’s new Communist rulers made in the 1950s. They decided to abandon conventional methods of gathering statistics that use probability and adopted the method of exhaustive counting of everybody and everything. Why did their dream of total information became a nightmare? Harvard historian Arunabh Ghosh (right), author of Making It Count: Statistics and Statecraft in the Early People’s Republic of China (2020), explains that in the 1950s, newly communist China faced a choice about how to survey the population accurately while making “a clean break with the past.” For philosophical reasons, debates about how to gather statistics came to the fore: In a speech in 1951, Li…

Missing piece

Machine Learning: Decision Trees Can Solve Murders

Decision trees increase our chance at a right answer. We can see how that works in a mystery board game like Clue

Entropy is a concept in information theory that characterizes the number of choices available when a probability distribution is involved. Understanding how it works helps us make better guesses.

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Machine Learning: Using Occam’s Razor to Generalize

A simple thought experiment shows us how

This approach is contrary to Fisher's method where we formulate all theories before encountering the data. We came up with the model after we saw the cards we drew.

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Occam’s Razor Can Shave Away Data Snooping

The greater an object's information content, the lower its probability.

One technique to avoid data snooping is based on the intersection of information theory and probability: An object’s probability is related to its information content. The greater an object’s information content, the lower its probability. We measure a model’s information content as the logarithmic difference between the probability that the data occurred by chance and the number of bits required to store the model. The negative exponential of the difference is the model’s probability of occurring by chance. If the data cannot be compressed, then these two values are equal. Then the model has zero information and we cannot know if the data was generated by chance or not. For a dataset that is incompressible and uninformative, swirl some tea…

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How Do We Know What Superintelligent AI Will Do?

If superintelligent systems existed, logic demonstrates that they would be unpredictable

A lower intelligence can’t accurately predict all decisions of a higher intelligence, a concept known as Vinge’s Principle.

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The World Series: What the Luck?

Who will win the World Series? I don’t know, but I do know that baseball is the quintessential game of luck

Think about it. Line drives hit right at fielders, mis-hit balls dying in the infield. Fly balls barely caught and barely missed. Balls called strikes and strikes called balls. Even the best batters make twice as many outs as hits. Even the best teams lose more than a third of their games. This season, the Houston Astros had the highest win percentage (66.0%) in baseball, yet they lost two out of six games to Baltimore, which only won a third of their games—not because Baltimore was the better team, but because Baltimore was the luckier team in those two games. The Astros are one of the 10 best teams this season (along with the Yankees, Tampa Bay, Minnesota, Cleveland, Oakland,…

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The Paradox of Luck and Skill

Why did Shane Lowry win the British Open golf championship? Because someone had to

In any competition including academic tests, athletic events, and company management where there is an element of luck that causes performances to be an imperfect measure of ability, there is an important difference between competitions among people with high ability and competitions among people of lesser ability.

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