Vsauce2

Welcome to the official Vsauce2 YouTube channel! Hosted by Kevin Lieber, Vsauce2
explores recreational mathematics including, paradoxes, math games, riddles and more to uncover the surprising complexity beneath seemingly simple concepts.
Vsauce2 launched in December 2010 and is run by Kevin Lieber.
Vsauce is...
Michael Stevens: Producer/Host of Vsauce1
Kevin Lieber: Producer/Host of Vsauce2
Jake Roper: Producer/Host of Vsauce3
Matthew Tabor: Writer for Vsauce2

280 videos

2 years ago

Find out which companies have your data and reclaim it by visiting: https://bit.ly/saymine-vsauce2
Thanks to Mine for supporting Vsauce2.
When tragedy struck Madrid on March 11, 2004, the international community including the FBI rushed to help Spanish police identify the perpetrators. Some of them were too eager.
A partial fingerprint match to Oregon lawyer Brandon Mayfield thrust him directly into the sights of law enforcement -- and eventually into a jail cell. Despite being 5,000 miles away and not even having a valid passport at the time, the FBI started collecting all sorts of evidence to suggest Mayfield’s guilt. And the problem was having *too much* data to sort through.
The FBI committed a series of errors from having far too much confidence in fingerprint forensics to employing one of the most common and easily avoidable logical fallacies. They also failed to acknowledge confirmation bias throughout their investigation, and the result was a case against Mayfield that rested on carefully selecting

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2 years ago

What IS 1? It seems like a really stupid, obvious question, but the truth is that 1 is seriously complex. Is it even a number? Number theory pushes and pulls on 1, showing that it's everything all at once -- yet sometimes it's powerless. Cube it, multiply, divide it... whatever you do, it's the unity. And there's not another number like it. #shorts
#vsauce #education

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2 years ago

There are infinite ways to write the number 1 without even using a 1. But what's the simplest way to write 1 using all 10 digits 0 to 9?
You can do it with exponents, square roots, multiplication and division... really, anything goes. But the easiest, least-complicated way to get all 10 digits into a mathematical expression totaling 1 is to add two fractions that each equal one half.
#vsauce #education #math

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2 years ago

Of all the numbers, why is THIS one so weird? Multiply it and you'll get the same re-arranged digits, or leave it on its own -- which happens to coincide with the repeating value of 1/7...
It shouldn't be like this. Why is this happening? WHY IS 142,857 SO SPECIAL?
#vsauce #education #math

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2 years ago

Was "alogon" unsayable because it was a mathematical Voldemort, or because the concept of irrationality was so difficult to express? Probably a little bit of both. Hippasus's fate is a mix of legends, with some saying he was drowned at sea by the will of the Gods after discovering irrationality, and others suggesting he angered the Pythagoreans to the point of murder. What's true? Who knows! Greek mathematics makes the Wild West look tame.
#shorts

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2 years ago

Think about how people discovered fractions and what problem they were meant to solve. How do we take a thing and express its division into smaller equal parts? A lot of little somethings add up to 1... until 2/3 came along. Using a numerator that isn't 1 doesn't sound like much, but it was a massive conceptual leap for humanity. #shorts

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3 years ago

The Egyptians didn't know the Pythagorean Theorem, but they figured out a way to make perfect 3-4-5 right triangles using segments of rope. It's so common sense, unsophisticated, and elegant that it's an example of a proof without words AND mathematical beauty. #shorts

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3 years ago

Just think of all the questions that arise when a seemingly-healthy baby dies. Was there an illness that went undetected? Was there a rare genetic defect that couldn’t possibly have been known? Are any signs of physical trauma related to the resuscitation efforts of a fragile infant, or something more sinister? Every time a baby dies, police investigate with a host of complex questions to determine whether the death is natural and accidental, or… not. And the odds are anything but clear.
So what do we do when it happens twice to the same person? What are the odds of THAT?
A British mother named Sally Clark suffered two separate tragedies with the deaths of her infant sons. Her resulting trial for murder included expert testimony from Sir Roy Meadow, a noted expert on child abuse cases. And Meadow’s misuse of conditional probability painted Sally Clark as perpetrator rather than a victim.
Math is often theoretical, but sometimes doing it right is the difference between life and death.
*** PARTIAL LIST OF S

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3 years ago

Nicomachus wrote "Introduction to Arithmetic" nearly 2,000 years ago, but he also seems to have come up with the first mathematically-based mind blows in Syria. Given the average person's understanding of mathematics at that time, who WOULDN'T think Nicomachus was a wizard?
#shorts

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3 years ago

Get the Vsauce Curiosity Box: https://www.curiositybox.com/vsauce2
Probability is one of the clearest, more straightforward disciplines within mathematics. Unfortunately, almost nothing in mathematics is murkier and more misleading than… probability. WHAT?!
Belgian mathematician Maurice Kraitchik posed a simple question about wagering wallets, and in doing so he revealed a paradoxical mismatch between a raw, indisputable math conclusion and common sense logic. Why does the math say one thing and reality says another? What do we do when the numbers don’t lie, but we know they aren’t telling the whole truth?
Probability density functions. Bayesian subjectivist analysis. You can put it all together and still not be able to square the math with the simple nagging logic that tells you something different.
Maybe there are some antinomical paradoxes we just have to live with. And maybe that’s okay.
*** SOURCES ***
Merryfield, K., Viet, N., & Watson, S. (1997). The Wallet Paradox. The American Mathematical Mont

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3 years ago

What happens when you take a number, reverse it and add them together? Over and over and over? Something quite SYMMETRICAL emerges. Except for 196... and no one knows why. #shorts

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3 years ago

Borrow $10, but only take $5. Then your friend will owe you $5, and you'll owe your friend $5, and it'll cancel out... except for the original $5 he's already given you. RIGHT?! And that's the $5 logic trap. #shorts

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3 years ago

Get the Vsauce Curiosity Box: https://www.curiositybox.com/
The transitive property is ingrained in our thinking. It gives our brains a simple, straightforward way to process the world -- especially with numbers. If one thing is better or more valuable than another, and that second thing is better than a third, you KNOW that the first one is better than the third.
But it doesn’t always work that way. And if you fail to recognize when real life violates the pattern of transitivity, you’re going to run head first into a veridical paradox.
Efron’s non-transitive dice demonstrate that hard and fast rules about value don’t always exist. By toying with relative probabilities, Efron discovered that a die’s superiority or weakness can be relative -- and as the dice values get more complex, it becomes nearly impossible to reason out which die is stronger against the others.
In math, our first impressions are often deceptive. Occasionally they’re just plain wrong. And sometimes a game is designed to deceive you in

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3 years ago

It seems impossible that you can turn your back on a roll of three dice, then ask some math questions to determine the exact roll and exact order of the dice. But you can do this perfectly EVERY TIME and look like a super-genius when you pull it off.
#shorts

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3 years ago

If Pinocchio's nose when he lies, what happens if he says, "My nose grows now?" If he's telling the truth, his nose won't grow. But if it doesn't grow, and he's just said it will, then he's lying.
Pinocchio's nose only grows when it doesn't grow? WHAT?
#shorts

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3 years ago

This series goes on forever. Sometimes it's 1. Sometimes it's 0. Can it ever be 1/2? Can we even know? WHAT IS THE ANSWER? #shorts

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3 years ago

Jeffrey Lagarias said the Collatz Conjecture is "completely out of reach of present day mathematics." Can YOU find a number that doesn't eventually reach 1? #shorts

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3 years ago

Get the Vsauce Curiosity Box: https://www.curiositybox.com/
Your mind is a massive collection of information, patterns, trivia, algorithms, and more -- and you have absolutely no idea how or when any of it is going to be useful. If you’ve got 50 stacks of 50 pennies, and you know one of those stacks is fake, do you have all the knowledge you need to find the most efficient measurement to find it?
Yes, you probably do. You just don’t know it. Part of the series is in the problem, but part of the series is inside you.
If you’ve ever thought about adding or subtracting consecutive numbers, mathematical patterns, or more advanced material like convergent and divergent series, you have all the ingredients you need for a solution to the penny brick problem that breaks your brain. The question is whether the two systems of thought in your brain are able to work together to find the answer.
From Euler to an 8-year old Carl Gauss to Ramanujan, the informational and mental tools to solve a simple penny problem like

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3 years ago

Join Our Brains: https://www.curiositybox.com/
How is it possible to roll dice to randomly choose 12 squares out of a grid of 144 and reveal a hidden message in the correct order? It’s not only possible, it’s actually guaranteed.
But why stop at 12 x 12? Why can’t you hide an entire book in an array of colored squares, and have a friend randomly select them until he’s re-written the entire book perfectly, start to finish? If you had enough time and space, that’s guaranteed to work, too.
First we have to have that grid of colored squares and write down all 144 (x, y) coordinates. Then roll our dice -- or you can have a friend just choose a square -- and mark that with an X. Remove all the squares above, below, and to the left and right of the choice. Then keep choosing and removing until there’s only one square left, which is your final selection.
Flip them over and you’ve got whatever message you secretly hid within the grid, and it’ll work every single time. They call it magic, but it’s really not.
M

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3 years ago

IT'S MAGIC SQUARE TIME #shorts
Get the new Vsauce Curiosity Box: https://www.curiositybox.com/

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3 years ago

Get The Curiosity Box: https://bit.ly/2OU3Iik
Save $15 on a platinum subscription with code: WRINKLEBRAIN
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In my video about whether your heart is too hot to hold, I started to wonder whether your body itself could actually cook food inside it. Maybe in your mouth, maybe in your stomach, maybe in your… anyway, what can you cook with the body heat nature gave you? Believe it or not, there are options for identifying the food you can cook inside your body. Yeah, you took the question to r/askreddit, so I'm taking it seriously, because no science question is THAT stupid.
Cooking matters, and even the Italian Ice-Man Otzi was well-equipped to start and maintain fires for cooking and heating. From making food last longer and improving its taste to ensuring you don’t fill your body with bacteria and worms, heating food matters to survivability. But if pregnant moms aren’t slow-cooking their babies, how can you possibly transform food without digesting it?
Maybe y

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3 years ago

The first 1000 people to use this link will get a free trial of Skillshare Premium Membership: https://skl.sh/vsauce202211
Thanks to Skillshare for sponsoring this video.
Every time you squirt minty toothpaste onto the synthetic bristles of a toothbrush and scrub them back and forth across your teeth, a question burns in your brain: Could a toothpaste sandwich brush your teeth just as well instead? You’re doing virtually the same thing ancestors thousands of years ago did with sticks and tooth powders. Yours just tastes better, so why not turn it into a food?
This question has come up on r/askreddit more than once, so people actually want to know. And the honest answer is... well, yes, you probably can brush your teeth with a toothpaste sandwich, with a few conditions.
Dental health has made tremendous progress over centuries, but at the same time, it’s been variations on virtually the same themes. It’s good that we don’t whiten our teeth with urine or sulfuric acid anymore, though. We've come a long way

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3 years ago

Thanks to Stereo for sponsoring this episode, and you can join in on my next live show!
Just download Stereo and follow me here: https://stereo.com/vsauce2
Check out the conversations with YouTubers and the live Stereo audience:
William Osman: https://stereo.com/u/r21buULq4aXcZ21
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To settle a bet with your best friend, you jam your hand deep into his thoracic cavity to grip his heart. You want to see whether it’s actually as searing-hot as he claims it is. Will it burn your hand? Are your internal organs too hot to hold onto? Well… no. But there’s more to it than you think.
Confusion over temperature scales misleads people worldwide, but the biological reality is that homeostasis keeps your insides at a fairly stable core temperature because it has to. Humans just aren’t like lizards, fish, and ostriches. The human hypothalamus acts as a thermostat to keep everything running smoothly -- except when you have a fever. But even that has a purpose.
Thermoregula

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3 years ago

PUT WRINKLES ON YOUR BRAIN
Get The Curiosity Box by Vsauce: https://www.curiositybox.com/
Please don’t use a toaster in the bathtub. The combination of electricity and water will be too much for your heart. But why don’t fish have the same problem when lightning strikes the ocean? It’s basically the same thing.
It turns out that a combination of the properties of both electricity and bodies of water protect *most* fish from being cooked alive when lightning hits the ocean. Between electricity’s skin effect and the vast majority of fish not being near the surface, fish have to be in exactly the wrong place at the wrong time to suffer the effects of an electrical force or a major injection of heat.
It only takes about 100 milliamps of electricity to stop your heart, but even if you’re struck by lightning, chances are you’ll be fine -- just like 99.9999% of fish. And if fish are caught with their metaphorical pants down? Well, there’s just no one around to give them CPR or apply defibrillation to get their

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3 years ago

You probably think you know a circle. Maybe you’ve even thought a little bit about what a circle is and what a circle isn’t. But do you know how many sides a circle has? Australia didn’t, and the answer is more complicated than it seems.
You can do it the easy way with simple geometry. You can do it the common sense way, which is a little more realistic. And you can think in terms of degenerate polygons to really complicate the math.
But there’s more to it than that, and it depends on what we consider a side. Not just a mathematical side, either -- a side in real life, a side of a shape, a body, an animal, or a thing. Humanity has been thinking about sides for a long time, whether it’s inside/outside or left and right. And the one thing we know is that sides are relative to something greater.
So, what’s the side of a circle relative to? Its center? The world around it? Is it an exception to the rule in that there are no sides at all? By looking at language, math, and old-fashioned ingenuity, we employ ever

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3 years ago

Get an intro to the math of Russian Roulette with "Surviving the Deadliest Game": https://www.youtube.com/watch?v=Xtl9orvkDVo
We know from “Surviving the Deadliest Game” that there’s no more dangerous game than Russian Roulette. And is there any game stupider than a duel in which two people stand there and shoot at each other? No -- so what happens when you combine them?!
Legendary scientific thinkers Nikola Tesla and Thomas Edison are about to find out as their balloon avatars battle it out for electrical supremacy.
In this scenario, there’s only one single gun that Edison and Tesla pass back and forth for each shot. Can that game actually be fair if someone can go first and win on the first shot? If the first player has a probabilistic advantage, how much is it?
Is it possible for us to adjust the game in such a way that the first player’s advantage is a lot more fair? Can you EVER have a perfectly fair turn-based game when it’s possible for a player to win on the first turn?
Oh, and there’s actually

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3 years ago

Thanks to LastPass for sponsoring a portion of this video!
Click here to start using LastPass and get 40% off through December 8: https://lastpass.com/Vsauce40
Watch my newest video, "Surviving the Deadliest Two-Player Game": https://youtu.be/ACtsYN1TWLg
A money game exists in which the potential payoff from being robbed makes perfect mathematical sense… but I won’t play it. Will you?
“Pascal’s Mugging” is derived from the classic philosophical scenario of Pascal’s Wager, which posits that it’s rational for humans to behave as though God exists. If they’re wrong, they don’t lose much; if they’re right, they have an infinite payoff in the afterlife.
The scenario of Pascal’s Mugging stems from Eliezer Yudkowsky’s unique twist on the original wager: what if a thief promised you a tremendous payoff tomorrow for stealing your wallet today? At what point would the near-infinitesimal odds of a criminal rewarding you tomorrow actually warrant you giving them a small amount of money right now?
If we process the

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3 years ago

Get Surfshark VPN at https://Surfshark.deals/vsauce2 and enter promo code VSAUCE2 for 84% off and 4 extra months for free.
Thanks to Surfshark VPN for sponsoring this video and supporting Vsauce2.
Watch my newest video, "Surviving the Deadliest Two-Player Game": https://youtu.be/ACtsYN1TWLg
The next time you buy a retro game or old t-shirt in an online auction, thank William Vickrey’s 1961 paper, “Counterspeculation, Auctions, and Competitive Sealed Tenders” -- because the simple auction style we take for granted today is actually filled with nuance and complexity.
Auctions have been around as long as one person has had an item to get rid of and at least two people wanted it. From Herodotus’ writing, we know that the ancient Babylonians held auctions over 4,000 years ago. But auctions haven’t changed very much over time, and the general bidding structures have remained intact. It seems like aside from differences like submitting a single private bid vs. open bidding back and forth, there isn’t a lot to ad

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3 years ago

Thanks to Ridge Wallet for sponsoring this video: https://www.ridge.com/VSAUCE2
Use Code “VSAUCE2 ” for 10% off your order!
Watch my newest video, "Surviving the Deadliest Two-Player Game": https://youtu.be/ACtsYN1TWLg
Your mind is efficient and amazing. It also conspires to ruin your life almost every time you encounter new information. You’re lying to yourself, and you can’t help it.
All the cognitive habits, capabilities, and shortcuts your brain brings to the table also come with serious liabilities… like leading you down the wrong path on simple math depending on which numbers you see first.
Anchoring bias is the perfect example. Work done by cognitive science researchers like Amos Tversky, Daniel Kahneman, Dan Ariely, and Massimo Piatelli-Palmarini show us that you get a little bit of information and then your brain goes to work. Unfortunately, it almost always locks you into a mode of thought that’s just… not quite right. You’ll get the wrong estimates and numbers. You’ll be barricaded into thinki

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3 years ago

Thanks to Ridge Wallet for sponsoring this video: https://www.ridge.com/VSAUCE2
Use Code “VSAUCE2 ” for 10% off your order!
Watch my newest video, "Surviving the Deadliest Two-Player Game": https://youtu.be/ACtsYN1TWLg
You can read Hawking’s “A Brief History of Time.” You can study classical literature. You can read religious texts that detail how we got here and what we’re supposed to do now.
… or you can gather up a bunch of junk from your bedroom and use it to unpack the majesty of the human experience.
The observable universe is unfathomably large, but we can use a piece of paper to understand how it got that way. Humans come in all types and vary tremendously, but really, we’d all fit inside a sugar cube.
And despite nearly 8 billion of us running around the planet, it’s pretty easy for us to stand out and do something unique.
We’re capable of great things because we’re equipped with a supercomputer that can process even the most complex problems in math, science, and ourselves. It’s not that hard

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3 years ago

Watch my newest video, "Surviving the Deadliest Two-Player Game": https://youtu.be/ACtsYN1TWLg
VOTE FOR YOUR PRESIDENT: https://twitter.com/VsauceTwo/status/1310990323670224899
Thanks to Whang! and psychicpebbles for their selfless commitment to public service as we all endeavor to improve our great YouTube Nation:
Whang!: https://www.youtube.com/WhangWhangWhang
Pebbles: https://www.youtube.com/psychicpebbles
Nothing seems easier, clearer, and more obvious than choosing who to vote for. We’ve done it for thousands of years across cultures ranging from Ancient Greek city-states to tribal democracies in the Americas. And now that we’re about to elect a President of YouTube, it’s time to look at how complex seemingly-simple decision theory can really be.
When you decide whether to dive head first into the Whang! Gang or sign your life over to the The Cult of Pebbles, you’re going through a process that involves multiple behavioral paradoxes, quirks of game theory, and… even the same sort of problem when yo

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4 years ago

LG Velvet: https://www.lg.com/us/mobile-phones/velvet-5g
Thanks to LG for sponsoring this video and supporting Vsauce2.
Watch my newest video, "Surviving the Deadliest Two-Player Game": https://youtu.be/ACtsYN1TWLg
No, you CAN'T name one thing in this photo. And neither can I. That level of visual chaos is deliberate, because it reveals what our brain goes through countless times each day as it tries to find meaning in the audio and visual information it processes.
Decades ago we were on our own with processing the noise and confusion around us, and that’s why we were so susceptible to forces like the Mandelbaum Effect. But as technology gets cheaper, more accessible, and more democratic, we have more tools to help us see and hear what we want.
LG sent me the new LG Velvet phone as we talked about technology’s role in improving information processing. From blasting through the limitations of lenses and sensors by utilizing pixel binning and multi-image fusion to isolating the important parts of sound with

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4 years ago

Watch my newest video, "Surviving the Deadliest Two-Player Game": https://youtu.be/ACtsYN1TWLg
Subscribe to Neil deGrasse Tyson's StarTalk: https://youtu.be/A0jI44rXJjc
Get The Curiosity Box: https://www.curiositybox.com/
Huge thanks to Neil deGrasse Tyson and everyone at StarTalk!
It seems easy to know things. The basics of epistemology haven’t changed much since Plato’s time, and we navigate every minute of our lives using a system of justified true belief. If we’re justified in thinking something, that thing is true, and we believe it, then it’s knowledge.
But as Gettier Problems show us, sometimes that justified true belief model just doesn’t work. We can satisfy every condition of JTB and still not know something.
So if that system isn’t reliable, then how can we really know anything at all? It’s a philosophical problem so big that we need Neil deGrasse Tyson to sort it out.
Neil deGrasse Tyson of StarTalk sets the record straight on what knowledge really is. Science, he says, is filled with things

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4 years ago

Go to https://buyraycon.com/vsauce2 for 15% off your order!
Brought to you by Raycon.
Isaac Newton was right about everything from gravity to the calculus, but he didn’t quite get it right on dice and probability.
The Newton-Pepys Problem represents Isaac Newton’s only documented foray into probability. Samuel Pepys sent him a letter asking whether it would be more likely to roll one six in 6 dice, two sixes in 12 dice, or three sixes in 18 dice. In terms of computing the answer, we’ve got it pretty easy in the 21st century, whether we do it the long way, whether we apply binomial distribution, or just run a Monte Carlo simulation. To us, it’s a relatively basic problem in probability.
But Newton had to work it all out himself, and as he did that, he missed a few things. He just… didn’t get it totally right even though his numbers were accurate. The *real* Newton-Pepys Problem is deciding how much that even matters, and the answer gives us insight into the complex relationship between math, numbers, and th

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4 years ago

To get MSCHF’s drops early and access secret drops, download their app here https://mschf.com/vsauce2
Thanks to MSCHF for supporting Vsauce2!
Conway Checkers (proof), Numberphile2 | Zvezdelina Stankova: https://youtu.be/Or0uWM9bT5w
Conway’s Soldiers Interactive Game (Clever Learning): https://www.cleverlearning.co.uk/blogs/blogConwayInteractive.php
John Conway’s work stretched from nearly-inaccessible math theory to fun children’s games, and it defined how we thought about recreational mathematics in the 20th century. Conway’s Soldiers is the perfect example of a Conway-esque math game: the rules are simple, the gameplay is easy, and it becomes very hard very quickly… and in this case of a basic checkers game, it packs a surprising punch of becoming literally impossible for a reason that isn’t even close to obvious.
But the mathematical importance doesn’t end with an unexpected reveal of impossibility. Conway found that the secret to *why* it’s impossible depends on the Golden Ratio of 1.618, which has f

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4 years ago

Get Your Curiosity Box: https://www.curiositybox.com/
NOW YOU'RE THINKING!
I’m an idiot -- and you should be, too. Sometimes.
Thinking is hard, and thinking with a free, open mind might be the hardest thing of all. The Einstellung Effect can create cognitive illusions that blind us to different points of view. It prevents us from seeing simpler solutions or alternative ways to solve a problem. And the more we know about a given topic, the stronger the Einstellung Effect can be.
Psychology, math, and every other field is subject to Einstellung, and it’s why heroes often appear from completely different disciplines. Because a fresh set of eyes isn’t bound by a given set of knowledge, they see something in a brand new light. What’s impossible to trained professionals can be obvious to someone who’s inexperienced.
The Einstellung Effect might be the ultimate psychological paradox: the more we know, the stupider we can be. And the stupider we are, the more we can know.
Get Vsauce2’s Woven Math t-shirts/hoodi

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4 years ago

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We know how difficult the Monty Hall Problem is for so many people even after they’re shown all the math behind the best possible strategy. It’s basic probability, but it’s deceptive -- and it all started with the Bertrand’s Box Paradox.
In this video, I go back to the origins of a probability problem that continues to plague humanity. And it all started in 1889 when French mathematician Joseph Bertrand published his “Calcul des probabilités,” which included a simple scenario involving gold and silver coins.
70 years later, recreational math columnist Martin Gardner unveiled The Three Prisoners Problem involving the pardoning of one of three prisoners scheduled to be executed. The mathematical concept was the

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4 years ago

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Sometimes math is so beautifully tricky, and presented in such a subtle way, that it’s virtually indistinguishable from magic. Welcome to The Kruskal Count.
David Copperfield is probably the most famous living magician/illusionist, and he’s made use of the Kruskal Count to convince millions of people worldwide that he harbors amazing predictive powers. Does he? Well… yes and no.
At the core of his mathematical mind reading is physicist Martin Kruskal’s discovery that certain counting games are really a sequence of chains that can intersect and eventually become one single chain. Using that knowledge of well-concealed probability, it’s easy to perform a mind-blowing demonstration that appears to be pure magic.
But it doesn’t *always* work, because that’s the way probability goes. Sometimes it’s perfect, sometimes it isn’t. By examinin

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4 years ago

Learn more about Lithium-ion Cell Safety: https://www.StaySafeBattery.com
Watch my video on Li-ion Cells: https://youtu.be/gdqtPNangDs
Huge thanks to LG Chem for sponsoring this video and supporting Vsauce2.
And thanks to Allen Pan of Sufficiently Advanced for not burning my house down: https://www.youtube.com/channel/UCVS89U86PwqzNkK2qYNbk5A
Snakes and Ladders -- also called Chutes and Ladders in the US -- might look like a simple board game for kids, but it actually goes back thousands of years with deep, meaningful origins. And along the path of creating a morality-based game to help kids navigate the world around them, humans stumbled onto some pretty interesting math.
From reaching nirvana to exploring Markov chains, Snakes and Ladders weaves a surprisingly complex tale of virtue, vice, and dumb luck. So, I decided to electrify it. Literally.
Imaginative engineering YouTuber Allen Pan of Sufficiently Advanced helped me customize an old Snakes and Ladders board by hooking up batteries to the board it

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There’s no more dangerous game than Russian Roulette. One wrong move and the consequences are fatal… and Balloon Kevin knows it.
The real difficulty is that in the sort of game you see played in a movie, there’s no skill involved when a player makes that move. It’s right or it’s wrong, and it’s a combination of the highest possible stakes with the lowest possible element of human control.
According to Nick Berry of DataGenetics, a common job interview question tests the mathematical reasoning and probability skills of interviewees by asking them to consider an alternative, slightly more complex arrangement: with *two* potentially fatal chambers loaded, and after having successfully survived the first round of a game, does the player request to spin the cylinder, or do they just let it go? Does it even matter?
The answer is surprising, and the exercise is a lesson in

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*** Not a real offer, for educational purposes only. I don't have two envelopes filled with money. I don't have any envelopes OR any money. ***
In The Two Envelopes Paradox -- also called the Exchange Paradox -- you know what the right answer is almost immediately. Until you don’t. And then you do. And then you’re not sure.
The problem isn’t so much the problem itself; it’s figuring out why the setup is wrong. Like several of Zeno’s Paradoxes, we’re lured into thinking about the scenario in a way that leads us down the wrong path… and by the time we realize it, we’re so deep in convincing (or troubling) math that we’ve lost sight of the real issue.
Just like with the Monty Hall Problem, even top academics have trouble elucidating clear, meaningful reasoning for why switching in the Two Envelopes Paradox is or isn’t valuable. That’s why Martin Gardner and

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Edward de Bono is a lot of things -- an author, an economic theorist, a physician -- but he’s also a thinker about… thinking. His 1967 book “The Five-Day Course in Thinking” included a game that’s one of the hardest in the world, yet also one of the simplest.
The idea behind creating the perfectly simple, perfectly impossible exercise that turned into The L-Game was to distill a 2-player experience down to a constant churn of critical strategic decisions. By limiting the board to just 16 spaces with 2 L-shaped tetrominoes and 2 neutral pieces, the board can’t distract from the core task. And with so few rules -- really, just that you need to move your L piece to an open space and then optionally move one of the neutrals -- t

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WOVEN MATH!!!
The easiest fair games depend on equal, binary outcomes like flipping a coin or drawing a playing card that can only be either red or black. If a game depends on both players choosing an equally-probable outcome, how can one player have a massive advantage over the other?
Welcome to the Humble-Nishiyama Randomness Game, a variant of Walter Penney’s classic demonstration of the power of non-transitivity in simple games. In a straightforward transitive situation, A beats B and B beats C -- which means A beats C, too. But if A beats B, B beats C, and C beats A… we’ve gone non-transitive just like Rock, Paper, Scissors. By jumping into the non-transitive game loop at the most advantageous point, Player 2 can become an overwhelming favorite every time. It looks like dumb luck, but it’s really just smart math.
And now introducing… WOVEN MATH.
Woven Math bridges recreational mathematics and art by infusing beautiful designs with cerebellum-bustin

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Every boy grows up chasing the same dream... to fly to a beautiful villa in Rome, Italy to build a pasta chair out of noodles utilizing a team of international spaghetti-building superstars.
Well, every boy doesn’t, but *I* did. And that dream came true.
Our goal was clear: we needed to build a pasta chair that would hold my weight, and we had to do it in just a few days. We studied every possibility, from designs that made use of classic bridge-style trusses to complex arches of thin spaghetti. We balanced functionality with aesthetics, because after all, we wanted it to look like an actual chair. And then we figured out what we could pull off with just the supplies that fit in a backpack and wouldn’t be confiscated on an international flight.
Johnny and Norbi, accomplished spaghetti builders from Óbuda University in Budapest, Hungary, suggested a base of tube-shape

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On Tuesday, February 21, 1967, in the math department common room of Sidney Sussex College, Cambridge, the world of pencil and paper math games changed. John Conway and Michael Paterson were trying to invent a brand new simple-to-play, hard-to-analyze game, and the result came to be known as Sprouts.
The basic setup of Sprouts is easy: start with any number of dots, then connect them with lines. When a dot has 3 lines coming to or from it, that dot can no longer be played. Lines are not allowed to cross, and the player to draw the last line wins. But the most important rule came from Paterson: every time a player draws a line, he or she gets to add a new dot anywhere on that line. As Conway put it, at that point “sprouts sprouted.”
Despite its simplicity, Sprouts is actually a game teeming with mathematical complexity and depth once it’s played with more than a

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I worked with the United States Navy on the USS Pasadena to show that the game of Battleship isn’t just a series of alpha-numeric volleys that result in either a hit or a miss until one player’s entire fleet has been sunk. Whether we realize it or not, Battleship generates a sophisticated probability density algorithm in your brain that’s constantly re-evaluating and updating strategy with every single move.
Nick Berry of DataGenetics founded a software company, received the Queen’s Award for Technology (UK), and spent a decade working for Microsoft’s Casual Game team... and cracking the code for optimal Battleship play is just the tip of the recreational mathematics iceberg he’s mapped out at DG. Berry’s simulations of Battleship strategies showed a massive disparity between the “hunt and target” strategy that m

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Deciding whether to play a game is usually very easy… you crunch the numbers and if they work in your favor, you play. If they don’t, you shouldn’t. Mathematical case closed.
But what happens when the math of a game tells you that you have access to infinite wealth and unlimited expected value and real life tells you not to play? Enter: The St. Petersburg Paradox.
The Bernoulli family first started corresponding about the paradox in the early 1700s with a series of letters examining the puzzling math behind the simple game. But it wasn’t until 1738 when Daniel Bernoulli realized that he could factor real life utility -- how much something actually means to you -- into the calculations.
The St. Petersburg Paradox opens up doors to how we think about what math really mean

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The Frobenius Number -- also called the McNugget Number -- is the highest number you *can’t* make out of two integers that have a greatest common divisor of 1. This late 19th-century math quirk was examined by Ferdinand Frobenius and expanded on by JJ Sylvester, but it came to public consciousness by examining the impossible orders of McDonald’s McNuggets in the United Kingdom.
Poring over the possibilities of ordering chicken nuggets might seem like a trivial affair, but the concept of the Frobenius Number appears in important aspects of real life. It’s the beginning of thinking about optimization in certain areas, like the coin-based currencies we use worldwide. What denominations of coins are best mathematically? Which combinations fit best with how humans actually think and live?
And that’s how we started thinking about whether the United States could need an 18-cent coin.
By looking how we can com

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