Micro Softy 34: Two Poles and a Wire
Given the measurements, how far apart must the poles be to make sure the power line does not touch the ground?For a solution to last week’s Micro Softy, look at the last week of the previous year.
Read More ›CategoryMathematics
Monday Micro Softy 33: How Fast Can a Person Age?
Can a person go from being five this year to being seven next year?The solution to Micro Softy 32 is to remember what types of functions derivatives apply to.
Read More ›
Monday Micro Softy 32: Elementary Calculus is Inconsistent!
This is a fascinating puzzle — one that usually stumps even my best graduate studentsThe 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.
Read More ›
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.
Read More ›
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 tooA question for materialists: How can infinite states of my intellect be generated by finite states of my brain?
Read More ›
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 faithEgnor describes faith as a deep relationship that may not always yield happiness about life circumstances but fosters lasting joy, independent of circumstances.
Read More ›
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 contradictionMathematics is not material, yet artificial intelligence proponents believe that the mathematics of their neural networks is the seat of consciousness.
Read More ›
Micro Softy 27: Diamond in the Rough
Why did the mathematician want all the diamond rings — hundreds of fake ones, plus a real one — divided into two bags?The solution to Micro Softy 26 lies in recognizing that there are different ways of measuring distance.
Read More ›
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.
Read More ›
Monday Micro Softy 25: The Fishing Rod Blues
The Memphis bus driver was sympathetic but he couldn't let Johnny ride with his overlong fishing pole. Johnny solved the problem—but how?About last week’s Micro Softy: You CAN have a tie in 3D Tic Tac Toe. We illustrate it. And we show what the 4D game is like.
Read More ›
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 boredTo 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.
Read More ›
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 theoremGödel’s theorem started by upending mathematics nearly a century ago by showing that it is impossible to create a mathematical Theory of Everything.
Read More ›
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.
Read More ›
Mind Rules, Not Matter, Biologists Say — in Journal Article
They argue that simple natural processes cannot explain embryological development. Instead, biology is directed by cognitionA 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.
Read More ›
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 fieldWe 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.
Read More ›
Micro Softy 20: Which Bottle Holds the Deadly Fentanyl?
You can find out the answer, using advanced technology — but there is a priceAbout the “Bermuda Triangle” puzzle: Look closely. Are they both really triangles?
Read More ›
Monday Micro Softy 19: The “Bermuda Triangle”
Why does the strange triangle, rearranged, appear to have a bit of extra area?The solution to the Twins Paradox lies in considering the possibility that Curt and Rod were not alone in the womb.
Read More ›
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 ›
How Mathematician Kurt Gödel Proved the Unprovable Proposition
He kicked over the mathematical sandcastles of those who proposed a mathematical Theory of EverythingWhile 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 ›
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 ›