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CategoryMathematics

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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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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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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