Mind Matters Natural and Artificial Intelligence News and Analysis

CategoryMathematics

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A mesmerizing illustration of mathematics featuring a vibrant swirling vortex of numbers symbols and geometric shapes in shades of electric blue crimson and gold set against a rich dark gray backgroun

Is AI Truly Creative? Here Is the Ultimate Test

People use the term “creative” in different ways. We need to define it rigorously and use a test based on that agreed definition

AI does not, at present, originate the kind of deep insight required to solve a open mathematical problem.

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Closeup of Baseball Glove and Baseball on turf

Monday Micro Softy 37: A Unique Baseball Game

Something was missing from the game played on June 30, 1997, that occured in every MLB game for decades before

The answer to Micro Softy 36 lies in considering the problem from a number of angles…

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Desert Locust on Sand Dune with Green Vegetation in Arid Environment

Monday Micro Softy 36: A Glass Half Empty? Half Full? Too Big?

The professors on a research expedition must make sure that each glass of rationed water is exactly half full

Here’s our thirst-quenching Micro Softy for this week. Three professors were on a trip through the Sahara Desert. They had an NSF grant to study the sleep patterns of the Saharan Grasshopper (Heteracris littoralis).  They brought exactly enough drinking water with them to last for four days. To stay hydrated, each was allowed a half glass of water every hour during each sixteen-hour workday. The professors shared the water glass shown in the picture. To make sure the water lasted the entire four days, the professors made sure each portion of water filled the glass exactly halfway. There were no markings on the glass. How can they do this? We’ll give an answer next Monday right here on MindMatters.ai.    Solution Read More ›

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Montana

Monday Micro Softy 35: A House With a View

A billionaire, used to getting what he wants, demands a house where all the walls' windows offer a view in the same direction

The solution to Monday Micro Softy 34 is quite simple if we pay attention to the exact measurements of the poles and the wires.

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Mathematics lesson differential and integral calculus Chalkboard.

Monday Micro Softy 32: Elementary Calculus is Inconsistent!

This is a fascinating puzzle — one that usually stumps even my best graduate students

The solution to Micro Softy 31 is to work back from the end of the alphabet. You will soon notice a term you can easily solve.

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operaciones-matematicas-escritas-a-mano-con-una-tiza-en-la-p-478224078-stockpack-adobestock
Operaciones matemáticas escritas a mano con una tiza en la pizarra

Monday Micro Softy 31: Elementary Algebra

How much can an equation be simplified?

In last week’s puzzle, the car was handling like a cement mixer because something was wrong with the tires. The solution lies in finding out what that is.

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Abstract numbers background - big data concept.

Human Mind: Logic Shows Abstract Thought Is an Immaterial Power

Neuroscience evidence helps us see the spiritual nature of our minds but we can use the power of our reason to demonstrate that too

A question for materialists: How can infinite states of my intellect be generated by finite states of my brain?

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the-image-contains-various-celestial-objects-and-mathematica-887102858-stockpack-adobestock
The image contains various celestial objects and mathematical calculations subtly illustrated on a dark starry background, ideal for space and science enthusiasts.

Michael Egnor on Faith, Reason, and the Architecture of Reality

In this week’s podcast, discussion with Robert J. Marks, he talks about the relationship between arguments from philosophical reasoning and faith

Egnor describes faith as a deep relationship that may not always yield happiness about life circumstances but fosters lasting joy, independent of circumstances.

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a-hyper-realistic-depiction-of-a-small-explosion-caused-by-f-1136351196-stockpack-adobestock
A hyper-realistic depiction of a small explosion caused by fireworks, capturing every spark and color detail in slow motion

How the Physicalist Theory of Mind Blows Itself Up

If we examine its basic premise that the brain is a computer and the mind is software we come across a startling contradiction

Mathematics is not material, yet artificial intelligence proponents believe that the mathematics of their neural networks is the seat of consciousness.

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Interlocking triangles in primary colors layered with precision

Monday Micro Softy 26: Arguing with Pythagoras

Will the diagonal of a triangle with sides of 3 and 4 feet be 5 feet or, as a visiting mathematician suggests, 7 feet?

The answer to last week’s puzzle lies in remembering what happens when you put a rod on a diagonal inside a square box.

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hand-made-wood-burn-tic-tac-toe-game-with-painted-rock-game-531760391-stockpack-adobestock
Hand made wood burn tic tac toe game with painted rock game pieces; yellow and red beetles and a wooden x and o game, sunset light

Micro Softy Monday 24: Have You Ever Tried 3D Tic Tac Toe?

To liven up a predictable game, try doing it in three — or even four — dimensions! You won't be bored

To solve the Barnum’s Circus ticket receipts puzzle, recall that X, Y and Z must all be whole numbers. Algebra then enables us to work out the solution.

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African American teacher writing codes on blackboard, she teaching IT lesson at school

Why the Human Mind Cannot Be Reduced to A Mathematical System

Philosophers Roger Penrose and J.R. Lucas walk us through an argument based on Gödel’s incompleteness theorem

Gödel’s theorem started by upending mathematics nearly a century ago by showing that it is impossible to create a mathematical Theory of Everything.

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Circus lion. Ai art

Monday Micro Softy 23: Barnum’s Circus Receipts

Circus master Barnum's ticket seller had not kept proper track of the tickets sold. Can the limited information — and some algebra — help Barnum figure it out?

The solution to Micro Softy 22, given here, depends on the assumptions we make about Timmy’s surgeon.

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Microscopic Flatworm in Low Light, Detailed Platyhelminthes Anatomy

Mind Rules, Not Matter, Biologists Say — in Journal Article

They argue that simple natural processes cannot explain embryological development. Instead, biology is directed by cognition

A revolution in biology? Too soon to tell but the fact that they are permitted to make their case signals greater openness to considering the evidence.

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Ai copywriting bot using chatgpt for content creation artificial intelligence concept 3d illustration. Artificial Intelligence. Illustration

Analysts: AIs Are Often Wrong But Never Uncertain

Gary Marcus and Ernest Davis note that getting AIs to admit uncertainty is "one of the most important *unsolved* challenges" in the field

We will be dealing with problems around non-conscious AI that some people suppose is conscious long before we deal with conscious AI — if we ever do.

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