# David Kung

### David Kung >

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Everything in This Lecture Is False

Episode 1 of Mind-Bending Math: Riddles and Paradoxes

Episode 1 of Mind-Bending Math: Riddles and Paradoxes

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…

Elementary Math Isn't Elementary

Episode 2 of Mind-Bending Math: Riddles and Paradoxes

Episode 2 of Mind-Bending Math: Riddles and Paradoxes

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…

Strangeness in Statistics

Episode 4 of Mind-Bending Math: Riddles and Paradoxes

Episode 4 of Mind-Bending Math: Riddles and Paradoxes

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…

Games with Strange Loops

Episode 13 of Mind-Bending Math: Riddles and Paradoxes

Episode 13 of Mind-Bending Math: Riddles and Paradoxes

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…

Probability Paradoxes

Episode 3 of Mind-Bending Math: Riddles and Paradoxes

Episode 3 of Mind-Bending Math: Riddles and Paradoxes

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…

Zeno's Paradoxes of Motion

Episode 5 of Mind-Bending Math: Riddles and Paradoxes

Episode 5 of Mind-Bending Math: Riddles and Paradoxes

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…

Infinity Is Not a Number

Episode 6 of Mind-Bending Math: Riddles and Paradoxes

Episode 6 of Mind-Bending Math: Riddles and Paradoxes

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…

Impossible Sets

Episode 9 of Mind-Bending Math: Riddles and Paradoxes

Episode 9 of Mind-Bending Math: Riddles and Paradoxes

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…

Enigmas of Everyday Objects

Episode 15 of Mind-Bending Math: Riddles and Paradoxes

Episode 15 of Mind-Bending Math: Riddles and Paradoxes

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)…

Voting Paradoxes

Episode 11 of Mind-Bending Math: Riddles and Paradoxes

Episode 11 of Mind-Bending Math: Riddles and Paradoxes

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…

Gödel Proves the Unprovable

Episode 10 of Mind-Bending Math: Riddles and Paradoxes

Episode 10 of Mind-Bending Math: Riddles and Paradoxes

Study the discovery that destroyed the dream of an axiomatic system that could prove all mathematical truths - Kurt Godel's demonstration that mathematical consistency is a mirage and that the price for avoiding paradoxes is incompleteness. Outline Godel's proof, seeing…

Cantor's Infinity of Infinities

Episode 8 of Mind-Bending Math: Riddles and Paradoxes

Episode 8 of Mind-Bending Math: Riddles and Paradoxes

Randomly pick a real number between 0 and 1. What is the probability that the number is a fraction, such as 1/4? Would you believe that the probability is zero? Probe this and other mind-bending facts about infinite sets, including…

More Than One Infinity

Episode 7 of Mind-Bending Math: Riddles and Paradoxes

Episode 7 of Mind-Bending Math: Riddles and Paradoxes

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…

Surprises of the Small and Speedy

Episode 16 of Mind-Bending Math: Riddles and Paradoxes

Episode 16 of Mind-Bending Math: Riddles and Paradoxes

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…

Bending Space and Time

Episode 17 of Mind-Bending Math: Riddles and Paradoxes

Episode 17 of Mind-Bending Math: Riddles and Paradoxes

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,…

Filling the Gap between Dimensions

Episode 18 of Mind-Bending Math: Riddles and Paradoxes

Episode 18 of Mind-Bending Math: Riddles and Paradoxes

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…

Banach-Tarski's 1 = 1 + 1

Episode 23 of Mind-Bending Math: Riddles and Paradoxes

Episode 23 of Mind-Bending Math: Riddles and Paradoxes

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…

Twisted Topological Universes

Episode 20 of Mind-Bending Math: Riddles and Paradoxes

Episode 20 of Mind-Bending Math: Riddles and Paradoxes

Consider the complexities of topological surfaces. For example, a Mobius 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…

More with Less, Something for Nothing

Episode 21 of Mind-Bending Math: Riddles and Paradoxes

Episode 21 of Mind-Bending Math: Riddles and Paradoxes

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…

Losing to Win, Strategizing to Survive

Episode 14 of Mind-Bending Math: Riddles and Paradoxes

Episode 14 of Mind-Bending Math: Riddles and Paradoxes

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…