Get the FREE DIGITAL BOOK: The Case for Killer Robots
Mind Matters Reporting on Natural and Artificial Intelligence

CategoryMathematics

medical-statistics-and-graphic-charts-with-stethoscope-stockpack-adobe-stock.jpg
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.

Read More ›
close-up-view-of-the-difference-engine-stockpack-adobe-stock.jpg
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.

Read More ›
american-earth-venn-diagram-stockpack-adobe-stock.jpg
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.

Read More ›
if-then-logic-statement-written-in-white-chalk-on-a-black-chalkboard-isolated-on-white-stockpack-adobe-stock.jpg
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.

Read More ›
ft9104_7833

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.

Read More ›
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."

Read More ›
Head shot close up portrait of red-and-green macaw in zoo

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?

Read More ›
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?

Read More ›
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.

Read More ›
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.

Read More ›
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.

Read More ›
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.

Read More ›
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.

Read More ›
Infinity sign black and white texture

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.

Read More ›
Mathematics in everyday life Reuben Teo Unsplash Hba7In7vnoM

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.

Read More ›
antoine-dautry-428780-unsplash
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.

Read More ›