Mind Matters Natural and Artificial Intelligence News and Analysis

CategoryMathematics

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Three fabric gift bags in gray, beige, and red, sitting on a marble surface against a bokeh background of Christmas lights.

Monday Micro Softy 17: Mixed-up Bags of Marbles

The bags-of-marbles puzzle is comparatively simple: How many marbles must you pull from the mislabeled bags in order to relabel them correctly?
There’s a rough solution to the “leaky bucket” problem but an exact solution requires some use of fluid dynamics. And the Moon, surprisingly, changes nothing. Read More ›
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Sandcastle at St Aubin's Beach

How Mathematician Kurt Gödel Proved the Unprovable Proposition

He kicked over the mathematical sandcastles of those who proposed a mathematical Theory of Everything
While Gödel’s technique was unheard of in his day, we are very familiar with it today. It is the same technique that computers use to store information. Read More ›
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stained-glass window

Monday Micro Softy 13: Garbage Trucks, String Theory…

… and Stained-Glass Windows. What connects them?
These puzzles, associated with the great mathematician Leonard Euler (1707‒1783), have a practical use, for example, in laying water pipes. Read More ›
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Training of dog. Close up of pet keeper holding treats over blurred background of adorable golden retriever. Excited fluffy dog waiting for favorite snack while executing sit command

Science Writing: Dog Intelligence Compared With Baby Intelligence

It’s an odd question because what we should be asking is, “Are kittens and puppies smarter than babies?”
The comparison doesn’t really work but it underlines the *doctrine* that human intelligence is just another type of animal intelligence. Read More ›
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group of musicians after the performance of his work

Monday Micro Softy 11: What Happened to That Other Dollar?

Shirley, Goodness, and Mercy get the discount for their cheap hotel rooms but the figures don’t really add up
To solve this Micro Softy, you need to pinpoint the flaw in the logic that hinges on the Law of Conservation of Money. Read More ›
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A vintage, rustic barber shop sign hangs prominently outside an establishment on a quaint street, evoking a nostalgic atmosphere from a bygone era

Monday Micro Softy 8: Who’s the Better Barber?

There are only two barbers to choose from and the choice may not be as easy as it looks. Also, here's the answer to Who's the Champ?
Micro Softy 7 is an illustration of Simpson’s Paradox, which says that averaging averages doesn’t always work. Read More ›
baseball-player-hitting-ball-with-bat-in-close-up-stockpack-289408349-stockpack-adobe_stock
Baseball player hitting ball with bat in close up

Monday Micro Softy 7:  Who’s the Champ?

A single number does not always determine which player is better
And here’s the answer to why young Clay’s arithmetic didn’t make sense at first to Claude — but then Claude realized that the boy was right. Read More ›
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Universität Hörsaal mit schwebenden transparenten Blasen

Michael Shermer: Wokeness Poisons Science and I Am No Longer Woke

A number of well-known one-way skeptics and atheists are beginning to feel the consequences of prescribed insufferable virtue
Maybe we need to believe that there is a Mind behind the universe in order to provide guardrails against deeply crazy stuff claiming to be science. Read More ›
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Mathematic or education concept

Monday Micro Softy 6: Bad Adding?

It looked to Claude like young Clay’s numbers didn’t add up but he seemed confident. What did he know that his father at first didn’t?
And here’s the answer to the probability question: What are the chances that Claude and Chloe’s younger child is also a boy? Read More ›
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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 ›

a-group-of-monkeys-dressed-in-business-attire-sitting-at-des-1057631580-stockpack-adobe_stock
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 ›
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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 ›