Watch Mind-Bending Math: Riddles and Paradoxes

Name: Mind-Bending Math: Riddles and Paradoxes
Released: 2015-07-24
Cast: David Kung

2015
1 Season

Mind-Bending Math: Riddles and Paradoxes is an educational show hosted by David Kung that is part of The Great Courses Signature Collection. Kung, who is a professor of mathematics at St. Maryâs College of Maryland, serves as a guide for viewers as they explore various riddles and paradoxes in the field of math.

Throughout the show, Kung uses everyday objects such as playing cards, ropes, and coins to illustrate a variety of mathematical concepts. He also leads viewers through a series of interactive exercises and thought experiments designed to challenge their understanding of mathematics.

One of the highlights of the show is Kungâs ability to explain complex mathematical concepts in a way that is both approachable and engaging. Whether heâs discussing the paradox of Achilles and the Tortoise or explaining the mathematical logic behind the game of tic-tac-toe, Kung presents concepts in a clear and concise manner that viewers of all levels of math proficiency can appreciate.

In addition to exploring riddles and paradoxes, Mind-Bending Math also covers topics such as infinity, probability, and game theory. These topics are explored through a series of real-world examples that make the often abstract world of mathematics feel more relevant and tangible.

Throughout the show, Kung emphasizes the beauty and creativity that exists within the world of mathematics. By demonstrating how math can be used to solve problems, Kung encourages viewers to develop their own problem-solving skills and embrace the joy of discovery that comes with understanding complex concepts.

Overall, Mind-Bending Math: Riddles and Paradoxes is a thought-provoking and engaging show that provides viewers with a deeper appreciation for the often-overlooked world of mathematics. Whether youâre a math enthusiast or just looking to expand your understanding of this fascinating field, this show is sure to leave you with a newfound appreciation for the power of math.

Mind-Bending Math: Riddles and Paradoxes is a series that ran for 1 seasons (24 episodes) between July 24, 2015 and on The Great Courses Signature Collection

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Seasons

24. The Paradox of Paradoxes

July 24, 2015

Close the course by asking the big questions about puzzles and paradoxes: Why are we so obsessed with them? Why do we relish the mental dismay that comes from contemplating a paradox? Why do we expend so much effort trying to solve conundrums and riddles? Professor Kung shows that there's method to this madness!

23. Banach-Tarski's 1 = 1 + 1

July 24, 2015

The Banach-Tarski paradox shows that you can take a solid ball, split it into five pieces, reassemble three of them into a complete ball the same size as the original, and reassemble the other two into another complete ball, also the same size as the original. Professor Kung explains the mathematics behind this astonishing result.

22. When Measurement Is Impossible

July 24, 2015

Prove that some sets can't be measured - a result that is crucial to understanding the Banach-Tarski paradox, the strangest theorem in all of mathematics, which is presented in Lecture 23. Start by asking why mathematicians want to measure sets. Then learn how to construct a non-measurable set.

21. More with Less, Something for Nothing

July 24, 2015

Many puzzles are optimization problems in disguise. Discover that nature often reveals shortcuts to the solutions. See how light, bubbles, balloons, and other phenomena provide powerful hints to these conundrums. Close with the surprising answer to the Kakeya needle problem to determine the space required to turn a needle completely around.

20. Twisted Topological Universes

July 24, 2015

Consider the complexities of topological surfaces. For example, a Möbius strip is non-orientable, which means that left and right switch as you move around it. Go deeper into this and other paradoxes, and learn how to determine the shape of the planet on which you live; after all, it could be a cube or a torus!

19. Crazy Kinds of Connectedness

July 24, 2015

Visit the land of topology, where one shape morphs into another by stretching, pushing, pulling, and deforming - no cutting allowed. Start simply, with figures such as the Möbius strip and torus. Then get truly strange with the Alexander horned sphere and Klein bottle. Study the minimum number of colors needed to distinguish their different regions.

18. Filling the Gap between Dimensions

July 24, 2015

Enter another dimension - a fractional dimension! First, hone your understanding of dimensionality by solving the riddle of Gabriel's horn, which has finite volume but infinite surface area. Then venture into the fractal world of Sierpinski's triangle, which has 1.58 dimensions, and the Menger sponge, which has 2.73 dimensions.

17. Bending Space and Time

July 24, 2015

Search for the solutions to classic geometric puzzles, including the vanishing leprechaun, in which 15 leprechauns become 14 before your eyes. Next, scratch your head over a missing square, try to connect an array of dots with the fewest lines, and test yourself with map challenges. Also learn how to ride a bicycle with square wheels.

16. Surprises of the Small and Speedy

July 24, 2015

Investigate the paradoxes of near-light-speed travel according to Einstein's special theory of relativity. Separated twins age at different rates, dimensions contract, and other weirdness unfolds. Then venture into the quantum realm to explore the curious nature of light and the true meaning of the Heisenberg uncertainty principle.

15. Enigmas of Everyday Objects

July 24, 2015

Classical mechanics is full of paradoxical phenomena, which Professor Kung demonstrates using springs, a slinky, a spool, and oobleck (a non-Newtonian fluid). Learn some of the physical principles that make everyday objects do strange things. Also discussed (but not demonstrated) is how to float a cruise ship in a gallon of water.

14. Losing to Win, Strategizing to Survive

July 24, 2015

Continue your exploration of game theory by spotting the hidden strange loop in the unexpected exam paradox. Next, contemplate Parrando's paradox that two losing strategies can combine to make a winning strategy. Finally, try increasingly more challenging hat games, using the axiom of choice from set theory to perform a miracle.

13. Games with Strange Loops

July 24, 2015

Leap into puzzles and mind-benders that teach you the rudiments of game theory. Divide loot with bloodthirsty pirates, ponder the two-envelope problem, learn about Newcomb's paradox, visit the island where everyone has blue eyes, and try your luck at prisoner's dilemma.

12. Why No Distribution Is Fully Fair

July 24, 2015

See how the founders of the U.S. struggled with a mathematical problem rife with paradoxes: how to apportion representatives to Congress based on population. Consider the strange results possible with different methods and the origin of the approach used now. As with voting, discover that no perfect system exists.

11. Voting Paradoxes

July 24, 2015

Learn that determining the will of the voters can require a mathematician. Delve into paradoxical outcomes of elections at national, state, and even club levels. Study Kenneth Arrow's Nobel prize-winning impossibility theorem, and assess the U.S. Electoral College system, which is especially prone to counterintuitive results.

10. Gödel Proves the Unprovable

July 24, 2015

Study the discovery that destroyed the dream of an axiomatic system that could prove all mathematical truths - Kurt Gödel's demonstration that mathematical consistency is a mirage and that the price for avoiding paradoxes is incompleteness. Outline Gödel's proof, seeing how it relates to the liar's paradox from Lecture 1.

9. Impossible Sets

July 24, 2015

Delve into Bertrand Russell's profoundly simple paradox that undermined Cantor's theory of sets. Then follow the scramble to fix set theory and all of mathematics with a new set of axioms, designed to avoid all paradoxes and keep mathematics consistent - a goal that was partly met by the Zermelo-Fraenkel set theory.

8. Cantor's Infinity of Infinities

July 24, 2015

Randomly pick a real number between 0 and 1. What is the probability that the number is a fraction, such as ¼? Would you believe that the probability is zero? Probe this and other mind-bending facts about infinite sets, including the discovery that made Cantor exclaim, "I see it, but I don't believe it!"

7. More Than One Infinity

July 24, 2015

Learn how Georg Cantor tamed infinity and astonished the mathematical world by showing that some infinite sets are larger than others. Then use a matching game inspired by dodge ball to prove that the set of real numbers is infinitely larger than the set of natural numbers, which is also infinite.

6. Infinity Is Not a Number

July 24, 2015

The paradoxes associated with infinity are... infinite! Begin with strategies for fitting ever more visitors into a hotel that has an infinite number of rooms, but where every room is already occupied. Also sample a selection of supertasks, which are exercises with an infinite number of steps that are completed in finite time.

5. Zeno's Paradoxes of Motion

July 24, 2015

Tour a series of philosophical problems from 2,400 years ago: Zeno's paradoxes of motion, space, and time. Explore solutions using calculus and other techniques. Then look at the deeper philosophical implications, which have gained new relevance through the discoveries of modern physics.

4. Strangeness in Statistics

July 24, 2015

While some statistics are deliberately misleading, others are the product of confused thinking due to Simpson's paradox and similar errors of statistical reasoning. See how this problem arises in sports, social science, and especially medicine, where it can lead to inappropriate treatments.

3. Probability Paradoxes

July 24, 2015

Investigate a puzzle that defied some of the most brilliant minds in mathematics: the Monty Hall problem, named after the host of Let's Make a Deal! Hall would let contestants change their guess about the location of a hidden prize after revealing new information about where it was not.

2. Elementary Math Isn't Elementary

July 24, 2015

Discover why all numbers are interesting and why 0.99999... is nothing less than the number 1. Learn that your intuition about breaking spaghetti noodles is probably wrong. Finally, see how averages - from mileage to the Dow Jones Industrial Average - can be deceptive.

1. Everything in This Lecture Is False

July 24, 2015

Plunge into the world of paradoxes and puzzles with a "strange loop," a self-contradictory problem from which there is no escape. Two examples: the liar's paradox and the barber's paradox. Then "prove" that 1+1=1, and visit the Island of Knights and Knaves, where only the logically minded survive!

Description

Where to Watch Mind-Bending Math: Riddles and Paradoxes

Mind-Bending Math: Riddles and Paradoxes is available for streaming on the The Great Courses Signature Collection website, both individual episodes and full seasons. You can also watch Mind-Bending Math: Riddles and Paradoxes on demand at Amazon Prime, Amazon, Kanopy and Hoopla.