Mind Matters Natural and Artificial Intelligence News and Analysis

CategoryMathematics

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Prehistoric hand paintings at the Cave of the Hands (Spanish: Cueva de Las Manos ) in Santa Cruz Province, Patagonia, Argentina. The art in the cave dates from 13,000 to 9,000 years ago.

Do We Need Language To Think? Some Researchers Say No

At one time, it was strictly a philosophical issue but then neuroscientists got involved

A controversy about whether we need language to think pits two MIT scholars against each other: Noam Chomsky (yes) vs. Evelina Fedorenko (no). For a long time, it was only a philosophical issue: Plato saw thinking as a conversation with oneself. If you don’t form concepts into words are you really thinking? Chomsky agreed. But later, neuroscientists like Fedorenko got involved, offering some research findings. Last summer at the New York Times, science writer Carl Zimmer reported, When Dr. Fedorenko began this work in 2009, studies had found that the same brain regions required for language were also active when people reasoned or carried out arithmetic. But Dr. Fedorenko and other researchers discovered that this overlap was a mirage. Part Read More ›

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A group of monkeys dressed in business attire, sitting at desks in a brightly lit office, each wearing a headset and typing on a computer keyboard. Copy space: above the image

Math prof: Monkeys can’t type out Shakespeare in our universe

University of Technology Sydney mathematicians Associate Professor Stephen Woodcock and Jay Falletta decided to test the oft-heard Infinite Monkey Theorem
If we want to play around with infinity concepts, we can have fun. But we can’t use them to decide what might or might not happen in our finite universe. Read More ›
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Four-leaf clover stands out against green leaves

Bad Luck Seldom Persists — But it Never Guarantees Good Luck

Many people embrace the fallacious law of averages in their daily lives when "regression toward the mean" is a more realistic picture
For example, the baseball player with the highest batting average in any season generally does not do as well the season before or the season after. Read More ›
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Microscopic view inside a human cell, science, biology, anatomy, microscopic, cellular, organelles, nucleus, cytoplasm

Will a Machine Ever Behave Like a Life Form?

A theoretical biologist developed a mathematical theory in 1991— so far not disproven — that a machine could not replicate life via calculations
The “strange loop” of life — a loop with no apparent beginning in non-life — was, Robert Rosen concluded, beyond the reach of computing. Read More ›
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Beautiful mystical forest in blue fog in autumn. Colorful landscape with enchanted trees with orange and red leaves. Scenery with path in dreamy foggy forest. Fall colors in october. Nature background

Can Mathematics Describe Our Innermost Life When Words Fail?

What if the researchers end up with a number that means nothing while the experience itself remains a barely describable personal event?
“Evolution” theories about the human mind play a key role in the manufacture of non-knowledge posing as knowledge, and we are urged to treat them as knowledge. Read More ›
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3D rendering of abstract blocks of mathematical formulas located in the virtual space

Will Artificial Intelligence Revolutionize Math?

In an article in Nature, mathematician Thomas Fink makes the case that AI can rapidly falsify wrong conjectures. But what about its built-in limitations?
The limitations created by the nature of computing mean that a mathematician’s true job of discovering novel theorems is quite safe at present. Read More ›
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: A journey through a kaleidoscopic, mathematical dreamscape, punctuated with intricate details, entwined and layered to create a mesmerizing wonder.

Arts major cracks hard math through practice, practice, practice

She became an engineering prof that way. The war on math is certainly not over but the warriors may be starting to find themselves on the back foot
Mathematics underlies our entire universe at its most basic level. Correct answers conform to reality. The war on 2 + 2 = 4 is just plain doomed. Read More ›
technology-chemistry-and-science-banner-design-template-molecule-and-communication-pattern-connected-lines-with-dots-stockpack-adobe-stock
Technology, chemistry and science banner design template. Molecule and communication pattern. Connected lines with dots.

Kurt Gödel’s “Incompleteness Theorem”

For Kurt Gödel, mathematics pointed to a remarkable world of transcendent order and meaning
Gödel saw the beauty of numbers and associated them with a transcendent order. Read More ›
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An amazing fibonacci pattern in a nautilus shell Generative AI

Gregory Chaitin’s New Books About Math Make It Actual Fun

He is a favorite podcast guest of ours and, it turns out, a fan of Mind Matters
Chaitin is best known in the math world discovering the remarkable Omega number, which demonstrated the fundamental unknowability of math. Read More ›
physics-or-mathematical-equations-on-a-universe-decorative-led-background-give-the-impression-of-interstellar-space-travel-stockpack-adobe-stock
Physics or mathematical equations on a universe decorative LED background give the impression of interstellar space travel.

Does Mathematics Belong to an Eternal Realm?

Whether Platonism is the only possible approach or not, positions like anti-realism seem like an effort to evade the reality of immaterial things. 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.
Points can be made without sensationalized graphs that undermine the credibility of the argument. Let’s dispose of exploding pie charts. Read More ›
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Van, Turkey Ancient Urartu cuneiform from Van fortress. IX-VI century BC e.

Can AI Open Doors to Ancient Human History?

It’s not a time machine, to be sure, but it may help bring the past to life by motoring through dull, time-consuming translation tasks
There’s a lot to discover. Recently, scholars learned that the Babylonians were using trigonometry 3700 years ago, centuries before the Greeks. Read More ›
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Science and research of the universe, spiral galaxy and physical formulas, concept of knowledge and education

From Physics to Faith?

A podcast episode looking at how physics points to more than meets the eye

Do you recognize the number 1/137.035999206? It might seem arbitrary, but if the fine-structure constant were any higher or lower than it is, you might not exist! On this episode of ID the Future, host Brian Miller kicks off an engaging conversation with Rabbi Elie Feder and Rabbi Aaron Zimmer, hosts of the Physics to God podcast. Feder has a PhD in mathematics and has published articles on graph theory. Zimmer has training in physics, and has studied mathematics, philosophy, and psychology. Both men also have extensive rabbinical training. Through their podcast, Feder and Zimmer invite both secular and religious listeners on a journey through modern physics as they offer rational arguments for an intelligent cause of the universe. In Part 1 of Read More ›

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aerial perspective of a crop circle with mathematical symbols

Does Deep Social Change Underlie the War on Math?

Why is the universal language of science sinking under the weight of claims about trauma and privilege?
Ours is an age of private truth but math and science both took hold in ages of public truth. Neither of them can survive private truth for long. 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.

The War on Math Becomes a Fight Over Textbooks

Florida, for example, rejected 54 math textbooks of 132 submitted by publishers on account of political content
Social justice messaging, right or wrong, is hardly going to help address the fact that American students lag behind most wealthy nations in math. Read More ›
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fire infinity

Of Infinity and Beyond

What are the problems and solutions with infinity in mathematics?

The concept of infinity has plagued a great many proofs, both formal and informal. I think that there are two foundational problems at play in most people’s thinking about infinity that causes issues. The first problem people have with infinity is that they treat it as if it were a single value. Because infinity is bigger than all possible natural numbers, people assume that it is bigger than any number, and therefore there is nothing beyond infinity. Therefore, people have the concept that if I have two infinities, then I still have the same number.  They believe that 2 * infinity = infinity. However, using that logic can quickly lead to contradictions. This problem is exacerbated by much mathematical notation. People often will Read More ›

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Silhouette of a man, with thoughts in the form of physico-mathematical formulas. The concept of scientific and education topics.

Is Mathematics Discovered or Invented?

Some think math is invented. Evidence, though, points towards discovery.

Some think math is invented. (See the article by Peter Biles.) Evidence, though, points towards discovery. Simultaneous mathematical discovery supports this viewpoint. Many mathematical breakthroughs are sometimes independently reported by two or more mathematicians at roughly the same time. The most famous is the simultaneous discovery of calculus by Isaac Newton and Gottfried Wilhelm Leibniz. Newton was secretive about his discovery and shared his results with only a few members of the Royal Society. When Leibnitz published his discovery of the calculus, Newton charged him with plagiarism. Today, historians agree that the discoveries were independent of each other. Here are some other lesser-known examples of simultaneous discovery. The Papoulis-Gerchberg Algorithm (PGA).  The PGA is an ingenious method for recovering lost Read More ›

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Milky Way over Cordillera Huayhuash

Is Mathematics an Illusion? Lawrence Krauss and Cormac McCarthy Discuss

McCarthy asked, "Would mathematics be here if we weren't?"

In December, physicist and author Lawrence Krauss interviewed the late American novelist Cormac McCarthy, who died on June 13th at the age of 89 in Santa Fe, N.M. McCarthy is famous for his remarkable fictional works like The Road and Blood Meridian, but he was also deeply fascinated with mathematics and science. Apparently, he enjoyed reading science more than he did fiction! He moved to Santa Fe from El Paso to be closer to the Santa Fe Institute, a science think tank where McCarthy would spend time speaking with various physicists, scientists, and mathematicians. His latest two novels, The Passenger and Stella Maris, are about a brother and sister who are both brilliant mathematicians. Towards the beginning of the interview, Read More ›

3d-rendering-of-abstract-blocks-of-mathematical-formulas-located-in-the-virtual-space-stockpack-adobe-stock
3D rendering of abstract blocks of mathematical formulas located in the virtual space

Math, Mind, and Matter

The surprising similarities between mathematics and literature

Last October, legendary American author Cormac McCarthy, who wrote Blood Meridian and The Road, released a pair of interconnected novels called The Passenger and Stella Maris. The books arrived after a sixteen-year silence from the desk of McCarthy. The books deal, per usual, with themes of mortality, fate, and the “God question,” and are predictably lyrical, vivid, and dark. But McCarthy plows new ground in these sibling novels. The books are about mathematicians. It’s fiction about math.  The story revolves around the complex relationship between a brother and sister: Bobby and Alicia Western. Bobby is a deep-sea diver with some history in the field of mathematics, while Alicia is a once-in-a-generation math prodigy.  Not Estranged, but Akin After reading these books myself, I marveled at McCarthy’s ability to Read More ›