Mind Matters Natural and Artificial Intelligence News and Analysis

TagProbability

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close up view of silver coin in hand of gambler scratching lottery card

The Two-Sided Lottery Card Paradox and Infinity

Assuming the infinite often leads to ridiculous conclusions.
Here’s the takeaway. Infinity does not exist in reality. There are not an infinite number of parallel universes. It's thought candy. Read More ›
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This is exactly what heaven looks like - looking over the top of a blanket of gorgeous pastel coloured fluffy clouds depicting heavenly lansdcape background ideal for a spiritual theme

Could Our Minds Be Bigger Than Even a Multiverse?

The relationship between information, entropy, and probability suggests startling possibilities. If you find the math hard, a face-in-the-clouds illustration works too
This article has equal entropy to gibberish letters of the same length, yet it contains information and gibberish does not. Much follows from that fact. Read More ›
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3d render gold metallic pie chart icon on dark background concept for analyze data information

Let’s Dispose of Exploding Pie Charts

Pie charts are seldom a good idea. Here's why.

A picture can be worth a thousand words. A graph can be worth a thousand numbers. Unfortunately, pictures and words can be deceptive — either intentionally or unintentionally. One common type of deception involves the use of two- or three-dimensional figures to represent single numbers. For example, the Washington Post once used the figure below to illustrate how inflation had eroded the purchasing power of the U.S. dollar between 1958 and 1978. To make the figure memorable, each of the dollar bills contained a photo of the U.S. President that year in place of the George Washington image that actually appears on the $1 bill. Washington Post, October 25, 1978 Prices more than doubled between 1958 (when Dwight Eisenhower was Read More ›

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Baseball

The MLB Coin-Flipping Contest

What are the chances that wild-card teams will make it to the World Series and win?
One anomaly this year is that Seattle didn’t qualify for the playoffs even though it had a better record than the Central Division winner, Minnesota. Read More ›
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Scoring the winning points at a basketball game

Sabrina Ionescu’s Hot Hand

When basketball players hit a "streak," does that elevate the probability of success?
Athletes do sometimes get hot—not that their chance of success is 100% but that it is temporarily elevated above their normal probability. Read More ›
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Multi Casino Games Concept

Gambling: WHY the House Always Wins in the Long Run…

The casinos are not cheating. They rely on the Law of Large Numbers, part of the mathematical structure underlying our universe

In this week’s podcast, “The house always wins in the long run” (June 2, 2022), Walter Bradley Center director Robert J. Marks interviews mathematician, computer scientist, and engineer Salvador Cordova on a subject on which he has strong views: gambling. Marks tells us, “I teach a graduate course on probability and stochastic processes. There I teach the stupidity of casino gambling. In statistics, there’s a theorem called the Law of Large Numbers. It teaches that you can’t win in the long run at casino games. Period. The law of large numbers is a mathematical truth. It’s a law as serious as the law of gravity. It’s why casinos always get rich and the gambler always gets poor. There is a Read More ›

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Father And Son Competing In Video Games At Home

Why Did Video Gamers Uncover Fraud More Easily Than Scientists?

Video gamers are subject, a psychologist tells us, to much more rigorous constraints than scientists

In a recent article at The Atlantic, King’s College psychologist Stuart Ritchie, author of Science Fictions: How Fraud, Bias, Negligence and Hype Undermine the Search for Truth (2020), has noted a curious fact: Video gamers are much quicker to spot fraud than scientists. The video game fraud he focuses on involved a gamer’s claim that he had finished a round of Minecraft in a little over 19 minutes, a feat he attributed, Ritchie tells us, to “an incredible stretch of good luck.” “Incredible” is the right choice of word here. “Dream,” as the player was known, later admitted — in the face of skepticism — that he had “inadvertently” left some software running that improved his game — thus disqualifying Read More ›

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Futuristic heads up display blue green abstract interface

How the Explanatory Filter Can Help Quash Conspiracy Theories

I found Dembski’s explanatory filter quite helpful in investigating voter fraud claims

William Dembski’s explanatory filter is a decision strategy for identifying events that are unlikely to have happened purely by chance. The filter proceeds in three main steps, which can be illustrated via the plot device in Contact, a novel (1985) by Carl Sagan, followed by a film (1997): Eliminate events of large probability (necessity): A radio telescope receives a pattern of beeps and pauses. Perhaps the pattern seems strange to us but we could just be overinterpreting inevitable space noise. Eliminate events of medium probability (chance): The pattern turns out to be a sequence of prime numbers. However, large randomly generated numbers sometimes feature apparent patterns (five 5s in a row, for example) that don’t signify anything. Specify the event Read More ›

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Basketball scoring basket at a sports arena

Steph Curry Got Red Hot and Torched the “Hot Hand Fallacy”

Many statisticians dismiss remarkable streaks like his as the Hot Hand Fallacy. Are they right?
Is “Hot Hands” really a fallacy, as some claim? Steph Curry is arguably the greatest shooter in National Basketball Association (NBA) history. In 2020, during practice the day after Christmas, Curry demolished that record by making 105 consecutive 3-point shots. Read More ›
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high risk cholesterol test results

Can an 18th Century Statistician Help Us Think More Clearly?

Distinguishing between types of probability can help us worry less and do more

Thomas Bayes (1702–1761) (pictured), a statistician and clergyman, developed a theory of decision-making which was only discussed after his death and only became important in the 20th century. It is now a significant topic in philosophy, in the form of Bayesian epistemology. Understanding Bayes’ Rule may be essential to making good decisions. Let’s say that you are a generally healthy person and have no symptoms of any illness and no specific risk factors for any illness. Acting on a friend’s suggestion, you get screened for a variety of diseases, just to be sure. Of the diseases you test for, the HIV test comes back positive. You read on the package that the test is 99.6% accurate. Are you more likely Read More ›

Quantum particle, quantum mechanics

How Scientists Have Learned To Work With the Quantum World

It’s still pretty weird, though

In last week’s podcast, “Enrique Blair on quantum computing,” Walter Bradley Center director Robert J. Marks talks with fellow computer engineer Enrique Blair about why quantum mechanics is so strange. But scientists have learned to work with QM, despite many questions, like how to work with particles that can be in two different places (quantum superposition): https://episodes.castos.com/mindmatters/Mind-Matters-110-Enrique-Blair.mp3 [Starts at approximately 13:16.] The Show Notes and transcript follow. Excerpts from the transcript: Robert J. Marks: What’s superposition? What’s going on there? Enrique Blair: Quantum superposition is really a mathematical description. We use wave functions to describe these particles. There’s a wave function for the photon going through Slit One and a wave function for the photon going through Slit Two. To Read More ›

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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 Read More ›

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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 Read More ›

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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Playing cards for poker and gambling, isolated on white background with clipping path

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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Brush and razor for shaving beard. Concept background of hair salon men, barber shop

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 Read More ›

3D Rendering of abstract highway path through digital binary towers in city. Concept of big data, machine learning, artificial intelligence, hyper loop, virtual reality, high speed network.

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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Baseball fans and crowd cheering in stadium and watching the game in ballpark. Happy people enjoying a match and sport event in arena. Friends watching ballgame live.

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, Read More ›

4er Golf flight

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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