# The last banana: A thought experiment in probability • TED-Ed

Imagine a game of dice: if the biggest number rolled is one, two, three, or four, player 1 wins. If the biggest number rolled is five or six, player 2 wins. Who has the best probability of winning the game? Leonardo Barichello explains how probability holds the answer to this seemingly counterintuitive puzzle.

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## TED-Ed • 2013 - 2023 • 44 episodes •

How do we measure distance in space?

When we look at the sky, we have a flat, two-dimensional view. So how do astronomers figure the distances of stars and galaxies from Earth? Yuan-Sen Ting shows us how trigonometric parallaxes, standard candles and more help us determine the distance of objects several billion light years away from Earth.

2014 • Physics

How many ways can you arrange a deck of cards?

One deck. Fifty-two cards. How many arrangements? Let's put it this way: Any time you pick up a well shuffled deck, you are almost certainly holding an arrangement of cards that has never before existed and might not exist again. Yannay Khaikin explains how factorials allow us to pinpoint the exact (very large) number of permutations in a standard deck of cards.

2014 • Math

Is math discovered or invented?

Would mathematics exist if people didn't? Did we create mathematical concepts to help us understand the world around us, or is math the native language of the universe itself? Jeff Dekofsky traces some famous arguments in this ancient and hotly debated question.

2014 • Math

The History of Keeping Time

Where did time-telling come from? What are time zones and why are there so many of them? Get the answers to these questions and more in this journey through the history of time -- from sundials to hourglasses to modern clocks.

How playing an instrument benefits your brain

When you listen to music, multiple areas of your brain become engaged and active. But when you actually play an instrument, that activity becomes more like a full-body brain workout. What's going on? Anita Collins explains the fireworks that go off in musicians' brains when they play, and examines some of the long-term positive effects of this mental workout.

How to understand power

Every day, we move and operate within systems of power that other people have constructed. But we’re often uncomfortable talking about power. Why? Eric Liu describes the six sources of power and explains how understanding them is key to being an effective citizen.

How big is infinity?

Using the fundamentals of set theory, explore the mind-bending concept of the "infinity of infinities" -- and how it led mathematicians to conclude that math itself contains unanswerable questions.

The death of the universe

The shape, contents and future of the universe are all intricately related. We know that it's mostly flat; we know that it's made up of baryonic matter (like stars and planets), but mostly dark matter and dark energy; and we know that it's expanding constantly, so that all stars will eventually burn out into a cold nothingness. Renée Hlozek expands on the beauty of this dark ending.

What's an algorithm?

An algorithm is a method of solving problems both big and small. Though computers run algorithms constantly, humans can also solve problems with algorithms. David J. Malan explains how algorithms can be used in seemingly simple situations and also complex ones.

The physics of sperm vs. the physics of sperm whales

Traveling is extremely arduous for microscopic sperm -- think of a human trying to swim in a pool made of...other humans.

The loathsome, lethal mosquito

Everyone hates mosquitos. So shouldn't we just get rid of them?

The mighty mathematics of the lever

Archimedes once said “Give me a place to stand, and I shall move the Earth.”

The language of lying

We hear anywhere from 10 to 200 lies a day. And although we’ve spent much of our history coming up with ways to detect these lies by tracking physiological changes in their tellers, these methods have proved unreliable. Is there a more direct approach?

How do the lungs work?

When you breathe, you transport oxygen to the body’s cells to keep them working, while also clearing your system of the carbon dioxide that this work generates. How do we accomplish this crucial and complex task without even thinking about it? Emma Bryce takes us into the lungs to investigate how they help keep us alive.

What does the liver do?

There’s a factory inside you that weighs about 1.4 kilograms and runs for 24 hours a day. It’s your liver: the heaviest organ in your body, which simultaneously acts as a storehouse, a manufacturing hub, and a processing plant.

How a wound heals itself

Our skin is the largest organ in our bodies, with a surface area of about 20 square feet in adults. When we are cut or wounded, our skin begins to repair itself through a complex, well-coordinated process. Sarthak Sinha takes us past the epidermis and into the dermis to investigate this regenerative response.

The Higgs Field, explained

One of the most significant scientific discoveries of the early 21st century is surely the Higgs boson, but the boson and the Higgs Field that allows for that magic particle are extremely difficult to grasp. Don Lincoln outlines an analogy (originally conceived by David Miller) that all of us can appreciate, starring a large dinner party, a raucous group of physicists, and Peter Higgs himself.

Schrödinger's cat: A thought experiment in quantum mechanics

Austrian physicist Erwin Schrödinger, one of the founders of quantum mechanics, posed this famous question: If you put a cat in a sealed box with a device that has a 50% chance of killing the cat in the next hour, what will be the state of the cat when that time is up?

Particles and waves: The central mystery of quantum mechanics

One of the most amazing facts in physics is that everything in the universe, from light to electrons to atoms, behaves like both a particle and a wave at the same time. But how did physicists arrive at this mind-boggling conclusion?

Einstein's brilliant mistake: Entangled states

When you think about Einstein and physics, E=mc^2 is probably the first thing that comes to mind. But one of his greatest contributions to the field actually came in the form of an odd philosophical footnote in a 1935 paper he co-wrote -- which ended up being wrong.

What is the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle states that you can never simultaneously know the exact position and the exact speed of an object.

What can Schrödinger's cat teach us about quantum mechanics?

The classical physics that we encounter in our everyday, macroscopic world is very different from the quantum physics that governs systems on a much smaller scale (like atoms).

Music and Math: The genius of Beethoven

How is it that Beethoven, who is celebrated as one of the most significant composers of all time, wrote many of his most beloved songs while going deaf?

The 2,400-year search for the atom

How do we know what matter is made of? The quest for the atom has been a long one, beginning 2,400 years ago with the work of a Greek philosopher and later continued by a Quaker and a few Nobel Prize-winning scientists. Theresa Doud details the history of atomic theory.?

What is Fat?

As the narrative goes, fat is bad. Well, it's actually more nuanced than that. The type of fat you eat is more impactful on your health than the quantity. George Zaidan examines triglycerides, the varied molecules that make up fat, and how to identify which types of fat you are consuming.

Why we love repetition in music

How many times does the chorus repeat in your favorite song? How many times have you listened to that chorus? Repetition in music isn’t just a feature of Western pop songs, either; it’s a global phenomenon. Why? Elizabeth Hellmuth Margulis walks us through the basic principles of the ‘exposure effect,’ detailing how repetition invites us into music as active participants, rather than passive listeners.

A different way to visualize rhythm

In standard notation, rhythm is indicated on a musical bar line. But there are other ways to visualize rhythm that can be more intuitive. John Varney describes the ‘wheel method’ of tracing rhythm and uses it to take us on a musical journey around the world.

Dead stuff: The secret ingredient in our food chain

When you picture the lowest levels of the food chain, you might imagine herbivores happily munching on lush, living green plants. But this idyllic image leaves out a huge (and slightly less appetizing) source of nourishment: dead stuff. John C. Moore details the "brown food chain," explaining how such unlikely delicacies as pond scum and animal poop contribute enormous amounts of energy to our ecosystems.

How do you know you exist?

How do you know you’re real? Is existence all just a big dream? Has some mad scientist duped us into simply believing that we exist? James Zucker investigates all of these questions (and more) in this mind-boggling tribute to René Descartes’s "Meditations on First Philosophy."

Population pyramids: Powerful predictors of the future

Population statistics are like crystal balls -- when examined closely, they can help predict a country's future (and give important clues about the past). Kim Preshoff explains how using a visual tool called a population pyramid helps policymakers and social scientists make sense of the statistics, using three different countries' pyramids as examples.

From the top of the food chain down: Rewilding our world

Our planet was once populated by megafauna, big top-of-the-food-chain predators that played their part in balancing our ecosystems. When those megafauna disappear, the result is a "trophic cascade," where every part of the ecosystem reacts to the loss. How can we stay in balance? George Monbiot suggests rewilding: putting wolves, lions and other predators back on top -- with surprising results.

The fundamentals of space-time (Part 2)

Light always travels at a speed of 299,792,458 meters per second. But if you're in motion too, you're going to perceive it as traveling even faster -- which isn't possible! In this second installment of a three-part series on space-time, CERN scientists Andrew Pontzen and Tom Whyntie use a space-time diagram to analyze the sometimes confounding motion of light.

The evolution of the human eye

The human eye is an amazing mechanism, able to detect anywhere from a few photons to a few quadrillion, or switch focus from the screen in front of you to the distant horizon in a third of a second. How did these complex structures evolve? Joshua Harvey details the 500 million year story of the human eye.

The Benefits of a Good Night's Sleep

It’s 4am, and the big test is in 8 hours. You’ve been studying for days, but you still don’t feel ready. Should you drink another cup of coffee and spend the next few hours cramming? Or should you go to sleep? Shai Marcu defends the latter option, showing how sleep restructures your brain in a way that’s crucial for how our memory works.

8 traits of successful people

Ten years of research and 500 face-to-face-interviews led Richard St. John to a collection of eight common traits in successful leaders around the world.

How spontaneous Brain Activity Keeps You Alive

The wheels in your brain are constantly turning, even when you're asleep or not paying attention. In fact, most of your brain’s activities are ones you’d never be aware of … unless they suddenly stopped. Nathan S. Jacobs takes us inside the always active, surprisingly spontaneous brain.

GPS location apps on a smartphone can be very handy when mapping a travel route or finding nearby events. But how does your smartphone know where you are?

The Distracted Mind

Everyone knows we're not supposed to multitask while driving, but do you know why? It turns out your brain literally can't focus on too much at once.

Why do buildings fall in earthquakes?

Earthquakes have always been a terrifying phenomenon, and they’ve become more deadly as our cities have grown — with collapsing buildings posing one of the largest risks. But why do buildings collapse in an earthquake? And how can it be prevented? Vicki V. May explains the physics of why it is not the sturdiest buildings, but the smartest, that will remain standing.

The Five Major World Religions

It's perfectly human to grapple with questions, like 'Where do we come from?' and 'How do I live a life of meaning?' These existential questions are central to the five major world religions -- and that's not all that connects these faiths. John Bellaimey explains the intertwined histories and cultures of Hinduism, Judaism, Buddhism, Christianity and Islam.

After drinking a few glasses of water on a hot day, you might be struck with a sudden ... urge. Behind that feeling are two bean-shaped organs that work as fine-tuned internal sensors.

Should you trust your first impression?

You can't help it; sometimes, you just get a bad feeling about someone that's hard to shake. So, what's happening in your brain when you make that critical (and often lasting) first judgment? Peter Mende-Siedlecki shares the social psychology of first impressions -- and why they may indicate that, deep down, people are basically good.

The last banana: A thought experiment in probability

Imagine a game of dice: if the biggest number rolled is one, two, three, or four, player 1 wins. If the biggest number rolled is five or six, player 2 wins. Who has the best probability of winning the game? Leonardo Barichello explains how probability holds the answer to this seemingly counterintuitive puzzle.

Why do cats act so weird?

They're cute, they're lovable, and judging by the 26 billion views on over 2 million YouTube videos of them, one thing is certain: cats are very entertaining. But their strange feline behaviors, both amusing and baffling, leave many of us asking: Why do cats do that? Tony Buffington explains the science behind some of your cat's strangest behaviors.

2016 • Science

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Our Mathematical Universe

Renowned cosmologist Max Tegmark will take us on a journey through some of the greatest mysteries of our existence, and through the physics, astronomy and mathematics that are the foundation of his work.

S1E4Curiosity Retreats: 2016 Lectures • 2016 • Math

How many ways can you arrange a deck of cards?

One deck. Fifty-two cards. How many arrangements? Let's put it this way: Any time you pick up a well shuffled deck, you are almost certainly holding an arrangement of cards that has never before existed and might not exist again. Yannay Khaikin explains how factorials allow us to pinpoint the exact (very large) number of permutations in a standard deck of cards.

TED-Ed • 2014 • Math

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Wherever we find patterns and symmetry in nature, we also find that nature conforms to certain rules. Rules that combine elegance with efficiency. Rules that shape trees and river estuaries alike, and that continue to baffle scientists by their often unfathomable ubiquity.

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PBS Nova - Zero to Infinity

Zero and infinity. These seemingly opposite, obvious, and indispensable concepts are relatively recent human inventions. Discover the surprising story of how these key concepts that revolutionized mathematics came to be – not just once, but over and over again as different cultures invented and re-invented them across thousands of years.

2022 • Math

How to Get Lucky

Kicking off the lectures with a mind-boggling stunt to prove how counterintuitive our gut instincts can be, Hannah launches into a lecture full of daring live experiments and surprising discoveries. From predicting the chance of snow at Christmas to dodging erupting volcanoes with Prof Chris Jackson, Hannah explores whether we really can predict the future. She meets the maths gurus behind Liverpool Football Club's winning streak to spill the beans on how analysing the numbers can give a team an edge in the Premier League, and reveals the tricks to perfecting your Christmas cracker pull to win the prize every time. Hannah also gathers tips from mind-performance coach Dr Michael Gervais, the 'secret weapon' crafting Olympic athletes' lucky mindsets, and the man responsible for Felix Baumgartner's jump from space, when 'first time lucky' meant life or death. Enrolling the help of maths comedian Matt Parker for the pinnacles of the lecture, the duo find order in unruly crowds, and whittle the audience down to the luckiest person in a series of challenges, before finally putting them to the test to prove whether they truly are one in a million. Using a host of maths tricks - from probability to game theory - Hannah discovers if we can in fact make our own luck, and ultimately shares the secrets to help us all lead luckier lives.

History of Everest

Where earth meets sky: how the most thrilling and dangerous point at the top of the world continues to fascinate, and what it takes to conquer the Big One.

S1E1History By The Numbers • 2021 • Math