Category: Mathematics | Page 8

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Jonathan Bartlett
Date
November 23, 2020

Categorized
Education, Mathematics

Tagged
Featured, Mathematics education reform}

How Can We Really Fix the Way Math Is Taught?

_{First, we must understand why we teach math in the first place} _{Jonathan Bartlett
November 23, 2020

4

Education, Mathematics}

Many people recognize that there are problems with modern mathematics curricula. However, the solutions proposed by current would-be math reformers are, I fear, worse than the cure. Some reformers want to stop having kids memorize their arithmetic facts, some want kids to just use computers to solve their problems, others think that the way we teach mathematics is racist, and still others seem to want to just greatly reduce the quantity of math education altogether. In this first part of a four-part series of short posts, I want to look at the most basic question: Why do we teach math? Earlier this month, an article by Yoree Koh in the Wall Street Journal took a look at the “Movement to Read More ›

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Robert J. Marks
Date
October 5, 2020

Categorized
Mathematics, Natural Intelligence

Tagged
Featured, Marilyn vos Savant, Monty Hall Problem, Paul Erdős}

Pigeons Can Solve the Monty Hall Problem. But Can You?

_{The dilemma pits human folk intuition against actual probability theory, with surprising results} _{Robert J. Marks
October 5, 2020

6

Mathematics, Natural Intelligence}

Animals often outperform humans. My son’s dog is more friendly than I could ever be. Cheetahs run faster, baby horses walk earlier, and elephants can lift more. Birds fly and humans can’t. Is there anything else birds can do better than humans? Yes. Apparently, pigeons learn to solve the Monty Hall problem more quickly. Let’s Make a Deal was a television game show first hosted by Monty Hall (1921–2017) in 1963. There have been various remakes since then. The basic idea is that there are three doors and a contestant’s job is to barter with Monty for the most valuable prize behind the doors. The Monty Hall problem, loosely based on the quiz show, was popularized by Marilyn vos Savant Read More ›

Girl business woman sitting at a wooden table with a laptop and discussing a new project with her mentor boss teacher. The man is fooling around. New business development concept

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Gary Smith
Date
September 24, 2020

Categorized
Mathematics

Tagged
Featured, Intelligence quotient (IQ), IQ, marriage, Regression toward the mean, Statistics}

Why Intelligent Women Marry Less Intelligent Men

_{Are they trying to avoid competition at home as well as at work? Or is there a statistical reason we are overlooking?} _{Gary Smith
September 24, 2020

7

Mathematics}

When I read that Ruth Bader Ginsburg’s late husband was a wonderful man but less accomplished than his wife, I was reminded of “Ivy,” one of the most impressive students I ever had the privilege to teach. Ivy excelled in her coursework, won a prestigious scholarship for postgraduate study in England, went to a top-five law school, clerked for a Supreme Court Justice, and is now a law professor at a great university. Like Ruth Ginsberg (1933–2020, pictured), Ivy married a man who is very nice but less intelligent than she. This is not an unusual situation. I made a list of the dozen most intelligent female students with whom I’ve kept in touch over the years. These women are Read More ›

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post

Gary Smith and Jay Cordes
Date
August 17, 2020

Categorized
Artificial Intelligence, Mathematics

Tagged
Electromagnetic fields (EMFs), Featured, Power lines, Probability, Statistics}

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} _{Gary Smith and Jay Cordes
August 17, 2020

7

Artificial Intelligence, Mathematics}

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 ›

tropical hurricane approaching the USA.Elements of this image are furnished by NASA.

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Gary Smith
Date
August 10, 2020

Categorized
Mathematics

Tagged
Featured}

Female Hurricanes: How A Mass of Hot Air Became a Zombie Study

_{When a reporter first asked me about a study claiming that “Female Hurricanes are Deadlier than Male Hurricanes,” I was skeptical} _{Gary Smith
August 10, 2020

7

Mathematics}

It is once again hurricane season on the East Coast and social media are reliably abuzz with reports of a debunked study that claimed that hurricanes given feminine-sounding names are deadlier than those given masculine-sounding names. (Full disclosure: I was one of the debunkers.) When a reporter initially asked me about this study, titled “Female Hurricanes are Deadlier than Male Hurricanes,” I was skeptical. Hurricane names alternate between female and male on a schedule set before the hurricane season begins so any relationship between name and death toll was surely coincidental. I looked at the study and discovered that the authors were not arguing that female hurricanes are inherently deadlier but that sexist humans die because they don’t take female Read More ›

man riding on self balancing board graffiti

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Gary Smith
Date
July 13, 2020

Categorized
Mathematics

Tagged
Alan Lichtman, Data Mining, Donald Trump, Elections, Featured, Helmut Norpoth, Hillary Clinton, Joe Biden, John von Neumann, predictions}

Election Models: Predicting the Past is Easy — and Useless

_{You can seldom see where you are going by looking in a rear-view mirror} _{Gary Smith
July 13, 2020

8

Mathematics}

I told my students that I had a model that predicted the popular vote for the the last ten presidential elections (1980–2016) perfectly. Read More ›

Groupe de Bonobos autour d'un hôtel à insectes

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post

Michael Egnor
Date
July 12, 2020

Categorized
Mathematics, Natural Intelligence, Philosophy of Mind

Tagged
___longform, Abstractions, Animal Intelligence, Bonobos, Designators, Featured, Language, Mathematics, Sue Savage-Rumbaugh, symbols}

Can Animal Minds Rival Humans Under the Right Circumstances?

_{Are we just not being fair to animals, as some researchers think?} _{Michael Egnor
July 12, 2020

8

Mathematics, Natural Intelligence, Philosophy of Mind}

In 2007, Sue Savage-Rumbaugh, a psychologist and primatologist , published a paper in the Journal of Applied Animal Welfare Science with a remarkable citation: Sue Savage-Rumbaugh, Kanzi Wamba, Panbanisha Wamba, and Nyota Wamba, “Welfare of Apes in Captive Environments: Comments on, and by, a Specific Group of Apes,” Journal of Applied Animal Welfare Science 10:1 (2007): 7–19. What is remarkable about the paper is not the text but the authorship statement. Kanzi, Panbanisha, and Nyota Wamba are not co-author colleagues—they’re apes, bonobos to be specific. Dr. Savage-Rumbaugh (right) is a controversial scientist who believes that animals have intellectual powers that can, under the right circumstances, rival the human intellect. She included her ape subjects as co-authors on the paper because Read More ›

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post

Eric Holloway
Date
June 29, 2020

Categorized
Information Theory, Mathematics

Tagged
Conservation of Information (COI), Featured, John Bell, Robert J. Marks, William Dembski}

Why is Bell’s Theorem Important for Conservation of Information?

_{Proving a negative is difficult. Demonstrating that there are no leafy green crows is hard to do without examining every crow. But there's another way.} _{Eric Holloway
June 29, 2020

4

Information Theory, Mathematics}

Proving a negative is difficult. Think about it. For example, demonstrating that there are no leafy green crows is hard to do without exhaustively examining every crow in existence. On the other hand, proving there are no crows naturally emblazoned with the text of the King James Bible is a bit easier to do. Proving a negative is possible if the extremes are large enough. Such as result is known as a no-go theorem. One of the most profound no-go theorems can be found in quantum physics. Physicist John Bell (1928–1990) proved — entirely from first principles — that there is a fundamental difference between how particles interact classically compared with how they interact within quantum physics. In classical physics, Read More ›

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post

Robert J. Marks
Date
June 4, 2020

Categorized
Arts & Culture, Mathematics

Tagged
Featured, Max Tegmark, Multiverse}

Is Big Bang Theory’s Sheldon Right re the Multiverse?

_{Sheldon Cooper insists that in no universe would he dance with Penny} _{Robert J. Marks
June 4, 2020

6

Arts & Culture, Mathematics}

A collection of universes is called a multiverse. If there are enough universes in a multiverse, can almost anything happen? No. Common models of the universe aren’t big enough. The argument that anything can happen in a multiverse is nicely presented in a 2011 scene in the sitcom The Big Bang Theory (2007–2019) involving consummate nerd Sheldon Cooper and Penny, the girl next door (here). Penny: Morning, Sheldon! Come dance with me! Sheldon: No. Penny: Why not? Sheldon: While I subscribe to the Many Worlds theory, which posits the existence of an infinite number of Sheldons in an infinite number of universes, I assure you that in none of them I am dancing. Penny: Are you fun in any of Read More ›

medical statistics and graphic charts with stethoscope

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post

Heather Zeiger
Date
May 26, 2020

Categorized
Mathematics, Medicine and Health, Social Media

Tagged
___longform, COVID-19, Featured, Statistics}

Making Sense of the Numbers Behind COVID-19

_{Media and politicians put statistics before us to sway our opinions. But what do they really mean?} _{Heather Zeiger
May 26, 2020

9

Mathematics, Medicine and Health, Social Media}

Numbers can frighten or enlighten. The secret is making them explain themselves. Here’s a quick primer.

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post

News
Date
May 19, 2020

Categorized
Artificial Intelligence, Mathematics, Programming

Tagged
___longform, Ada Lovelace, Alan Turing, Charles Babbage, Featured, Gary Smith, Lovelace test, Selmer Bringsjord, Turing Test}

Lovelace: The Programmer Who Spooked Alan Turing

_{Ada Lovelace understood her mentor Charles Babbage’s plans for his new Analytical Engine and was better than he at explaining what it could do} _{News
May 19, 2020

9

Artificial Intelligence, Mathematics, Programming}

Turing thought that computers could be got to think. Thus he had to address Lovelace’s objection from a century earlier, that they could not be creative.

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post

Michael Egnor
Date
May 13, 2020

Categorized
Mathematics, Philosophy of Mind

Tagged
Featured, free will, Jerry Coyne, Logic, Physics, Sean Carroll}

Physicist Rejects Free Will — and Thus Fails Logic

_{If we accepted his argument for materialism, we would have to stop believing in it—a curious, self-refuting result} _{Michael Egnor
May 13, 2020

7

Mathematics, Philosophy of Mind}

Carroll’s argument that man is wholly governed by physics is self-refuting. Because physics and logic share no commonality, materialists like Carroll implicitly assert that their own arguments lack logic. One might say that the only thing materialists get right is that their ideas are nonsense. If man is all physics, he can have no logic.

If Then logic statement written in white chalk on a black chalkboard isolated on white

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News
Date
May 10, 2020

Categorized
Artificial Intelligence, Mathematics, Religion

Tagged
___longform, Featured, Gottfried Wilhelm Leibniz, Kurt Gödel, Mathematics, Rene Descartes, Robert J. Marks, Saint Anselm, Selmer Bringsjord}

Gödel and God: A Surprising History

_{A thought-provoking account of master logician Gödel’s largely unknown proof of the existence of God} _{News
May 10, 2020

11

Artificial Intelligence, Mathematics, Religion}

In an unsanitized, politically incorrect (but factual) history, Selmer Bringsjord talks about how the tormented genius Kurt Gödel took up a quest that dated back a thousand years to prove the existence of God by formal logic. His original version didn’t quite work but his editor’s version passed an important logic test.

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post

Eric Holloway
Date
March 29, 2020

Categorized
Mathematics, Philosophy of Mind

Tagged
Kurt Gödel, Leonid Levin}

Math Shows Why the Mind Is Not Just a Formula

_{The Liar’s Paradox shows that even mathematics cannot be reduced to a fixed set of axioms} _{Eric Holloway
March 29, 2020

4

Mathematics, Philosophy of Mind}

Gödel’s discovery brought back a sense of wonder to mathematics and to the rest of human knowledge. His incompleteness theorem underlies the fact that human investigation can never exhaust all that can be known. Every discovery builds a path to a new discovery.

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post

News
Date
March 28, 2020

Categorized
Education, Mathematics

Tagged
calculus, Featured, Jonathan Bartlett}

Bartlett’s Calculus Paper Reviewed in Mathematics Magazine

_{The paper offers fixes for long-standing flaws in the teaching of elementary calculus} _{News
March 28, 2020

2

Education, Mathematics}

Jonathan Bartlett tells us, “The review was mixed, but most importantly the reviewer didn’t disagree with the results, only their potential usefulness."

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post

Michael Egnor
Date
March 6, 2020

Categorized
Mathematics, Natural Intelligence

Tagged
Abstraction, Animals, Birds, Parrots, Statistics}

Polly Want a … Statistician?

_{Ethology, the science of animal behavior, offers interesting data but the interpretations are too often witless} _{Michael Egnor
March 6, 2020

6

Mathematics, Natural Intelligence}

Can birds really do statistics? A reporter writing up the results of a study for a popular science magazine seems to think so. The researchers are (appropriately) more cautious. But what are the issues here?

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post

Jonathan Bartlett
Date
February 10, 2020

Categorized
Mathematics

Tagged
Eugene Wigner}

Why Does Mathematics Interpret Reality?

_{In the latest issue of Communications of the Blyth Institute, Gordon Mullings presents his account of why mathematics and physics are connected} _{Jonathan Bartlett
February 10, 2020

4

Mathematics}

The amazing applicability of mathematics to the real world has caused many mathematicians, philosophers, and physicists to pause throughout history. How can something as abstract and ideal as mathematics apply to the real world?

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post

Jonathan Bartlett
Date
February 8, 2020

Categorized
Education, Mathematics

Tagged
Featured, Georg Cantor, Hyperreal numbers, Srinivasa Ramanujan}

Are Divergent Series Really an “Invention of the Devil”?

_{The real villain in the piece is horrendously non-specific concepts of infinity. But that can be fixed} _{Jonathan Bartlett
February 8, 2020

6

Education, Mathematics}

It turns out that hyperreal numbers (i.e., infinities that obey algebraic rules) resolve many of the paradoxes that previously plagued conceptions of divergent series. It is now possible to assign specific values to divergent series.

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News
Date
January 24, 2020

Categorized
Mathematics, Philosophy of Mind

Tagged
Dark Matter, Information Theory, Melvin Vopson, William Dembski}

Could Information Be — at Long Last — the Missing Dark Matter?

_{Materialist thinkers may need to see information as material, whether that approach fits information or not} _{News
January 24, 2020

5

Mathematics, Philosophy of Mind}

There is no evidence that information is dark matter or that consciousness is physical but materialists understandably long for evidence that would make their theory more viable.

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post

Gary Smith
Date
January 20, 2020

Categorized
Arts & Culture, Mathematics

Tagged
Randomness}

Bridge: Why Shuffle the Deck Seven Times?

_{For years, competitive bridge players complained that computer shuffling of cards produced goofy results. Statisticians sided with the computers} _{Gary Smith
January 20, 2020

6

Arts & Culture, Mathematics}

Bridge is one of the few games where computer algorithms have not yet demolished the best human players but, despite claims to the contrary, algorithms do a much better job of random shuffling of the deck.