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CategoryMathematics

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man riding on self balancing board graffiti

Election Models: Predicting the Past is Easy — and Useless

You can seldom see where you are going by looking in a rear-view mirror
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 ›
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Groupe de Bonobos autour d'un hôtel à insectes

Can Animal Minds Rival Humans Under the Right Circumstances?

Are we just not being fair to animals, as some researchers think?

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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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.

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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Blue glowing multiverse in space

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

Sheldon Cooper insists that in no universe would he dance with Penny

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 ›

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medical statistics and graphic charts with stethoscope

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?

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

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Close-up view of the Difference Engine

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

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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American Earth Venn Diagram

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

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.

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

Gödel and God: A Surprising History

A thought-provoking account of master logician Gödel’s largely unknown proof of the existence of God

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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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

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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Blackboard inscribed with scientific formulas and calculations in physics and mathematics.

Bartlett’s Calculus Paper Reviewed in Mathematics Magazine

The paper offers fixes for long-standing flaws in the teaching of elementary calculus

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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Polly Want a … Statistician?

Ethology, the science of animal behavior, offers interesting data but the interpretations are too often witless

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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Photo by Gayatri Malhotra

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

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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An abstract computer generated fractal design. A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales.

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

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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Dark matter black and white abstract background

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

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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Photo by Amanda Jones

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

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.

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black mathematics board with formulas

Faith Is the Most Fundamental of the Mathematical Tools

An early twentieth century clash of giants showed that even mathematics depends on some unprovable assumptions

David Hilbert wanted all mathematics to be proved by logical steps. Kurt Gödel showed that no axiomatic system could be complete and consistent at the same time.

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child girl playing with counter toy at nursery

Babies Have a Number Sense Before They Can Count

The study showed that counting with babies makes a difference, even though their understanding is not very exact

The question was not whether the infants understood the exact numbers (they didn’t) but whether they understood that the researchers were, in fact, counting things.

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Yes, You Can Manipulate Infinity—in Math

The hyperreals are bigger (and smaller) than your average number — and better!

Hyperreal numbers are a new type of number that was developed to simplify and rethink the way that we deal with very large and very small numbers.

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Mathematics Gives Us Life Skills and Mental Tools

Unfortunately, some professors, like the one who attacked my recent article, seem to prefer pedantry

What makes you an expert today is not your clarity of thought but rather your ability to conform your thoughts entirely to the constraints of your profession’s vocabulary.

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A pen on top of several math equations

Walter Bradley Center Fellow Discovers Longstanding Flaw in an Aspect of Elementary Calculus

The flaw doesn't lead directly to wrong answers but it does create confusion

The lead author, Jonathan Bartlett, noted that the likely source of the bad notation was a philosophical issue. Because no one wanted to give differentials that same ontological status as other numbers, everyone presumed that the notational problems were simply the result of this fact, and no one pursued it further.

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